- FindStat

Identifier

Mp00061: Permutations —to increasing tree⟶ Binary trees
Mp00020: Binary trees —to Tamari-corresponding Dyck path⟶ Dyck paths
Mp00120: Dyck paths —Lalanne-Kreweras involution⟶ Dyck paths
St000678: Dyck paths ⟶ ℤ

Values

[1,2] => [.,[.,.]] => [1,1,0,0] => [1,0,1,0] => 2

[2,1] => [[.,.],.] => [1,0,1,0] => [1,1,0,0] => 1

[1,2,3] => [.,[.,[.,.]]] => [1,1,1,0,0,0] => [1,0,1,0,1,0] => 3

[1,3,2] => [.,[[.,.],.]] => [1,1,0,1,0,0] => [1,1,0,1,0,0] => 2

[2,1,3] => [[.,.],[.,.]] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 2

[2,3,1] => [[.,[.,.]],.] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1

[3,1,2] => [[.,.],[.,.]] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 2

[3,2,1] => [[[.,.],.],.] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 1

[1,2,3,4] => [.,[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0] => 4

[1,2,4,3] => [.,[.,[[.,.],.]]] => [1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,0] => 3

[1,3,2,4] => [.,[[.,.],[.,.]]] => [1,1,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0] => 3

[1,3,4,2] => [.,[[.,[.,.]],.]] => [1,1,1,0,0,1,0,0] => [1,0,1,1,0,1,0,0] => 2

[1,4,2,3] => [.,[[.,.],[.,.]]] => [1,1,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0] => 3

[1,4,3,2] => [.,[[[.,.],.],.]] => [1,1,0,1,0,1,0,0] => [1,1,1,0,1,0,0,0] => 2

[2,1,3,4] => [[.,.],[.,[.,.]]] => [1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0] => 3

[2,1,4,3] => [[.,.],[[.,.],.]] => [1,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,0] => 2

[2,3,1,4] => [[.,[.,.]],[.,.]] => [1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0] => 2

[2,3,4,1] => [[.,[.,[.,.]]],.] => [1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0] => 1

[2,4,1,3] => [[.,[.,.]],[.,.]] => [1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0] => 2

[2,4,3,1] => [[.,[[.,.],.]],.] => [1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => 1

[3,1,2,4] => [[.,.],[.,[.,.]]] => [1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0] => 3

[3,1,4,2] => [[.,.],[[.,.],.]] => [1,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,0] => 2

[3,2,1,4] => [[[.,.],.],[.,.]] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 2

[3,2,4,1] => [[[.,.],[.,.]],.] => [1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => 1

[3,4,1,2] => [[.,[.,.]],[.,.]] => [1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0] => 2

[3,4,2,1] => [[[.,[.,.]],.],.] => [1,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0] => 1

[4,1,2,3] => [[.,.],[.,[.,.]]] => [1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0] => 3

[4,1,3,2] => [[.,.],[[.,.],.]] => [1,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,0] => 2

[4,2,1,3] => [[[.,.],.],[.,.]] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 2

[4,2,3,1] => [[[.,.],[.,.]],.] => [1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => 1

[4,3,1,2] => [[[.,.],.],[.,.]] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 2

[4,3,2,1] => [[[[.,.],.],.],.] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 1

[1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => [1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => 5

[1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]] => [1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0] => 4

[1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]] => [1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0] => 4

[1,2,4,5,3] => [.,[.,[[.,[.,.]],.]]] => [1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,0,1,0,0] => 3

[1,2,5,3,4] => [.,[.,[[.,.],[.,.]]]] => [1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0] => 4

[1,2,5,4,3] => [.,[.,[[[.,.],.],.]]] => [1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 3

[1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]] => [1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0] => 4

[1,3,2,5,4] => [.,[[.,.],[[.,.],.]]] => [1,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0] => 3

[1,3,4,2,5] => [.,[[.,[.,.]],[.,.]]] => [1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0] => 3

[1,3,4,5,2] => [.,[[.,[.,[.,.]]],.]] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0] => 2

[1,3,5,2,4] => [.,[[.,[.,.]],[.,.]]] => [1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0] => 3

[1,3,5,4,2] => [.,[[.,[[.,.],.]],.]] => [1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 2

[1,4,2,3,5] => [.,[[.,.],[.,[.,.]]]] => [1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0] => 4

[1,4,2,5,3] => [.,[[.,.],[[.,.],.]]] => [1,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0] => 3

[1,4,3,2,5] => [.,[[[.,.],.],[.,.]]] => [1,1,0,1,0,1,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0] => 3

[1,4,3,5,2] => [.,[[[.,.],[.,.]],.]] => [1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0] => 2

[1,4,5,2,3] => [.,[[.,[.,.]],[.,.]]] => [1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0] => 3

[1,4,5,3,2] => [.,[[[.,[.,.]],.],.]] => [1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0] => 2

[1,5,2,3,4] => [.,[[.,.],[.,[.,.]]]] => [1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0] => 4

[1,5,2,4,3] => [.,[[.,.],[[.,.],.]]] => [1,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0] => 3

[1,5,3,2,4] => [.,[[[.,.],.],[.,.]]] => [1,1,0,1,0,1,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0] => 3

[1,5,3,4,2] => [.,[[[.,.],[.,.]],.]] => [1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0] => 2

[1,5,4,2,3] => [.,[[[.,.],.],[.,.]]] => [1,1,0,1,0,1,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0] => 3

[1,5,4,3,2] => [.,[[[[.,.],.],.],.]] => [1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,1,0,0,0,0] => 2

[2,1,3,4,5] => [[.,.],[.,[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0] => 4

[2,1,3,5,4] => [[.,.],[.,[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,0,1,0,1,0,0] => 3

[2,1,4,3,5] => [[.,.],[[.,.],[.,.]]] => [1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0] => 3

[2,1,4,5,3] => [[.,.],[[.,[.,.]],.]] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0] => 2

[2,1,5,3,4] => [[.,.],[[.,.],[.,.]]] => [1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0] => 3

[2,1,5,4,3] => [[.,.],[[[.,.],.],.]] => [1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0] => 2

[2,3,1,4,5] => [[.,[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0] => 3

[2,3,1,5,4] => [[.,[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0] => 2

[2,3,4,1,5] => [[.,[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0] => 2

[2,3,4,5,1] => [[.,[.,[.,[.,.]]]],.] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => 1

[2,3,5,1,4] => [[.,[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0] => 2

[2,3,5,4,1] => [[.,[.,[[.,.],.]]],.] => [1,1,1,0,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,0] => 1

[2,4,1,3,5] => [[.,[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0] => 3

[2,4,1,5,3] => [[.,[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0] => 2

[2,4,3,1,5] => [[.,[[.,.],.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 2

[2,4,3,5,1] => [[.,[[.,.],[.,.]]],.] => [1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => 1

[2,4,5,1,3] => [[.,[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0] => 2

[2,4,5,3,1] => [[.,[[.,[.,.]],.]],.] => [1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0] => 1

[2,5,1,3,4] => [[.,[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0] => 3

[2,5,1,4,3] => [[.,[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0] => 2

[2,5,3,1,4] => [[.,[[.,.],.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 2

[2,5,3,4,1] => [[.,[[.,.],[.,.]]],.] => [1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => 1

[2,5,4,1,3] => [[.,[[.,.],.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 2

[2,5,4,3,1] => [[.,[[[.,.],.],.]],.] => [1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 1

[3,1,2,4,5] => [[.,.],[.,[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0] => 4

[3,1,2,5,4] => [[.,.],[.,[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,0,1,0,1,0,0] => 3

[3,1,4,2,5] => [[.,.],[[.,.],[.,.]]] => [1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0] => 3

[3,1,4,5,2] => [[.,.],[[.,[.,.]],.]] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0] => 2

[3,1,5,2,4] => [[.,.],[[.,.],[.,.]]] => [1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0] => 3

[3,1,5,4,2] => [[.,.],[[[.,.],.],.]] => [1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0] => 2

[3,2,1,4,5] => [[[.,.],.],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0] => 3

[3,2,1,5,4] => [[[.,.],.],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2

[3,2,4,1,5] => [[[.,.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 2

[3,2,4,5,1] => [[[.,.],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0] => 1

[3,2,5,1,4] => [[[.,.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 2

[3,2,5,4,1] => [[[.,.],[[.,.],.]],.] => [1,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0] => 1

[3,4,1,2,5] => [[.,[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0] => 3

[3,4,1,5,2] => [[.,[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0] => 2

[3,4,2,1,5] => [[[.,[.,.]],.],[.,.]] => [1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 2

[3,4,2,5,1] => [[[.,[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0] => 1

[3,4,5,1,2] => [[.,[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0] => 2

[3,4,5,2,1] => [[[.,[.,[.,.]]],.],.] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0] => 1

[3,5,1,2,4] => [[.,[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0] => 3

[3,5,1,4,2] => [[.,[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0] => 2

[3,5,2,1,4] => [[[.,[.,.]],.],[.,.]] => [1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 2

>>> Load all 17237 entries. <<<

[3,5,2,4,1] => [[[.,[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0] => 1

[3,5,4,1,2] => [[.,[[.,.],.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 2

[3,5,4,2,1] => [[[.,[[.,.],.]],.],.] => [1,1,0,1,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => 1

[4,1,2,3,5] => [[.,.],[.,[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0] => 4

[4,1,2,5,3] => [[.,.],[.,[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,0,1,0,1,0,0] => 3

[4,1,3,2,5] => [[.,.],[[.,.],[.,.]]] => [1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0] => 3

[4,1,3,5,2] => [[.,.],[[.,[.,.]],.]] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0] => 2

[4,1,5,2,3] => [[.,.],[[.,.],[.,.]]] => [1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0] => 3

[4,1,5,3,2] => [[.,.],[[[.,.],.],.]] => [1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0] => 2

[4,2,1,3,5] => [[[.,.],.],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0] => 3

[4,2,1,5,3] => [[[.,.],.],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2

[4,2,3,1,5] => [[[.,.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 2

[4,2,3,5,1] => [[[.,.],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0] => 1

[4,2,5,1,3] => [[[.,.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 2

[4,2,5,3,1] => [[[.,.],[[.,.],.]],.] => [1,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0] => 1

[4,3,1,2,5] => [[[.,.],.],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0] => 3

[4,3,1,5,2] => [[[.,.],.],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2

[4,3,2,1,5] => [[[[.,.],.],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 2

[4,3,2,5,1] => [[[[.,.],.],[.,.]],.] => [1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0] => 1

[4,3,5,1,2] => [[[.,.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 2

[4,3,5,2,1] => [[[[.,.],[.,.]],.],.] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0] => 1

[4,5,1,2,3] => [[.,[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0] => 3

[4,5,1,3,2] => [[.,[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0] => 2

[4,5,2,1,3] => [[[.,[.,.]],.],[.,.]] => [1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 2

[4,5,2,3,1] => [[[.,[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0] => 1

[4,5,3,1,2] => [[[.,[.,.]],.],[.,.]] => [1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 2

[4,5,3,2,1] => [[[[.,[.,.]],.],.],.] => [1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,0] => 1

[5,1,2,3,4] => [[.,.],[.,[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0] => 4

[5,1,2,4,3] => [[.,.],[.,[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,0,1,0,1,0,0] => 3

[5,1,3,2,4] => [[.,.],[[.,.],[.,.]]] => [1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0] => 3

[5,1,3,4,2] => [[.,.],[[.,[.,.]],.]] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0] => 2

[5,1,4,2,3] => [[.,.],[[.,.],[.,.]]] => [1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0] => 3

[5,1,4,3,2] => [[.,.],[[[.,.],.],.]] => [1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0] => 2

[5,2,1,3,4] => [[[.,.],.],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0] => 3

[5,2,1,4,3] => [[[.,.],.],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2

[5,2,3,1,4] => [[[.,.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 2

[5,2,3,4,1] => [[[.,.],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0] => 1

[5,2,4,1,3] => [[[.,.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 2

[5,2,4,3,1] => [[[.,.],[[.,.],.]],.] => [1,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0] => 1

[5,3,1,2,4] => [[[.,.],.],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0] => 3

[5,3,1,4,2] => [[[.,.],.],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2

[5,3,2,1,4] => [[[[.,.],.],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 2

[5,3,2,4,1] => [[[[.,.],.],[.,.]],.] => [1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0] => 1

[5,3,4,1,2] => [[[.,.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 2

[5,3,4,2,1] => [[[[.,.],[.,.]],.],.] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0] => 1

[5,4,1,2,3] => [[[.,.],.],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0] => 3

[5,4,1,3,2] => [[[.,.],.],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2

[5,4,2,1,3] => [[[[.,.],.],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 2

[5,4,2,3,1] => [[[[.,.],.],[.,.]],.] => [1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0] => 1

[5,4,3,1,2] => [[[[.,.],.],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 2

[5,4,3,2,1] => [[[[[.,.],.],.],.],.] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 1

[1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 6

[1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 5

[1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 5

[1,2,3,5,6,4] => [.,[.,[.,[[.,[.,.]],.]]]] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 4

[1,2,3,6,4,5] => [.,[.,[.,[[.,.],[.,.]]]]] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 5

[1,2,3,6,5,4] => [.,[.,[.,[[[.,.],.],.]]]] => [1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 4

[1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 5

[1,2,4,3,6,5] => [.,[.,[[.,.],[[.,.],.]]]] => [1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 4

[1,2,4,5,3,6] => [.,[.,[[.,[.,.]],[.,.]]]] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => 4

[1,2,4,5,6,3] => [.,[.,[[.,[.,[.,.]]],.]]] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3

[1,2,4,6,3,5] => [.,[.,[[.,[.,.]],[.,.]]]] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => 4

[1,2,4,6,5,3] => [.,[.,[[.,[[.,.],.]],.]]] => [1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 3

[1,2,5,3,4,6] => [.,[.,[[.,.],[.,[.,.]]]]] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 5

[1,2,5,3,6,4] => [.,[.,[[.,.],[[.,.],.]]]] => [1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 4

[1,2,5,4,3,6] => [.,[.,[[[.,.],.],[.,.]]]] => [1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => 4

[1,2,5,4,6,3] => [.,[.,[[[.,.],[.,.]],.]]] => [1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => 3

[1,2,5,6,3,4] => [.,[.,[[.,[.,.]],[.,.]]]] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => 4

[1,2,5,6,4,3] => [.,[.,[[[.,[.,.]],.],.]]] => [1,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0] => 3

[1,2,6,3,4,5] => [.,[.,[[.,.],[.,[.,.]]]]] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 5

[1,2,6,3,5,4] => [.,[.,[[.,.],[[.,.],.]]]] => [1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 4

[1,2,6,4,3,5] => [.,[.,[[[.,.],.],[.,.]]]] => [1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => 4

[1,2,6,4,5,3] => [.,[.,[[[.,.],[.,.]],.]]] => [1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => 3

[1,2,6,5,3,4] => [.,[.,[[[.,.],.],[.,.]]]] => [1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => 4

[1,2,6,5,4,3] => [.,[.,[[[[.,.],.],.],.]]] => [1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 3

[1,3,2,4,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 5

[1,3,2,4,6,5] => [.,[[.,.],[.,[[.,.],.]]]] => [1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => 4

[1,3,2,5,4,6] => [.,[[.,.],[[.,.],[.,.]]]] => [1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 4

[1,3,2,5,6,4] => [.,[[.,.],[[.,[.,.]],.]]] => [1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => 3

[1,3,2,6,4,5] => [.,[[.,.],[[.,.],[.,.]]]] => [1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 4

[1,3,2,6,5,4] => [.,[[.,.],[[[.,.],.],.]]] => [1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => 3

[1,3,4,2,5,6] => [.,[[.,[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => 4

[1,3,4,2,6,5] => [.,[[.,[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3

[1,3,4,5,2,6] => [.,[[.,[.,[.,.]]],[.,.]]] => [1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => 3

[1,3,4,5,6,2] => [.,[[.,[.,[.,[.,.]]]],.]] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 2

[1,3,4,6,2,5] => [.,[[.,[.,[.,.]]],[.,.]]] => [1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => 3

[1,3,4,6,5,2] => [.,[[.,[.,[[.,.],.]]],.]] => [1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 2

[1,3,5,2,4,6] => [.,[[.,[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => 4

[1,3,5,2,6,4] => [.,[[.,[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3

[1,3,5,4,2,6] => [.,[[.,[[.,.],.]],[.,.]]] => [1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0] => 3

[1,3,5,4,6,2] => [.,[[.,[[.,.],[.,.]]],.]] => [1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => 2

[1,3,5,6,2,4] => [.,[[.,[.,[.,.]]],[.,.]]] => [1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => 3

[1,3,5,6,4,2] => [.,[[.,[[.,[.,.]],.]],.]] => [1,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0] => 2

[1,3,6,2,4,5] => [.,[[.,[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => 4

[1,3,6,2,5,4] => [.,[[.,[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3

[1,3,6,4,2,5] => [.,[[.,[[.,.],.]],[.,.]]] => [1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0] => 3

[1,3,6,4,5,2] => [.,[[.,[[.,.],[.,.]]],.]] => [1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => 2

[1,3,6,5,2,4] => [.,[[.,[[.,.],.]],[.,.]]] => [1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0] => 3

[1,3,6,5,4,2] => [.,[[.,[[[.,.],.],.]],.]] => [1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => 2

[1,4,2,3,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 5

[1,4,2,3,6,5] => [.,[[.,.],[.,[[.,.],.]]]] => [1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => 4

[1,4,2,5,3,6] => [.,[[.,.],[[.,.],[.,.]]]] => [1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 4

[1,4,2,5,6,3] => [.,[[.,.],[[.,[.,.]],.]]] => [1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => 3

[1,4,2,6,3,5] => [.,[[.,.],[[.,.],[.,.]]]] => [1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 4

[1,4,2,6,5,3] => [.,[[.,.],[[[.,.],.],.]]] => [1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => 3

[1,4,3,2,5,6] => [.,[[[.,.],.],[.,[.,.]]]] => [1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 4

[1,4,3,2,6,5] => [.,[[[.,.],.],[[.,.],.]]] => [1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => 3

[1,4,3,5,2,6] => [.,[[[.,.],[.,.]],[.,.]]] => [1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0] => 3

[1,4,3,5,6,2] => [.,[[[.,.],[.,[.,.]]],.]] => [1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => 2

[1,4,3,6,2,5] => [.,[[[.,.],[.,.]],[.,.]]] => [1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0] => 3

[1,4,3,6,5,2] => [.,[[[.,.],[[.,.],.]],.]] => [1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0] => 2

[1,4,5,2,3,6] => [.,[[.,[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => 4

[1,4,5,2,6,3] => [.,[[.,[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3

[1,4,5,3,2,6] => [.,[[[.,[.,.]],.],[.,.]]] => [1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0] => 3

[1,4,5,3,6,2] => [.,[[[.,[.,.]],[.,.]],.]] => [1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0] => 2

[1,4,5,6,2,3] => [.,[[.,[.,[.,.]]],[.,.]]] => [1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => 3

[1,4,5,6,3,2] => [.,[[[.,[.,[.,.]]],.],.]] => [1,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => 2

[1,4,6,2,3,5] => [.,[[.,[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => 4

[1,4,6,2,5,3] => [.,[[.,[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3

[1,4,6,3,2,5] => [.,[[[.,[.,.]],.],[.,.]]] => [1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0] => 3

[1,4,6,3,5,2] => [.,[[[.,[.,.]],[.,.]],.]] => [1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0] => 2

[1,4,6,5,2,3] => [.,[[.,[[.,.],.]],[.,.]]] => [1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0] => 3

[1,4,6,5,3,2] => [.,[[[.,[[.,.],.]],.],.]] => [1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => 2

[1,5,2,3,4,6] => [.,[[.,.],[.,[.,[.,.]]]]] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 5

[1,5,2,3,6,4] => [.,[[.,.],[.,[[.,.],.]]]] => [1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => 4

[1,5,2,4,3,6] => [.,[[.,.],[[.,.],[.,.]]]] => [1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 4

[1,5,2,4,6,3] => [.,[[.,.],[[.,[.,.]],.]]] => [1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => 3

[1,5,2,6,3,4] => [.,[[.,.],[[.,.],[.,.]]]] => [1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 4

[1,5,2,6,4,3] => [.,[[.,.],[[[.,.],.],.]]] => [1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => 3

[1,5,3,2,4,6] => [.,[[[.,.],.],[.,[.,.]]]] => [1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 4

[1,5,3,2,6,4] => [.,[[[.,.],.],[[.,.],.]]] => [1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => 3

[1,5,3,4,2,6] => [.,[[[.,.],[.,.]],[.,.]]] => [1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0] => 3

[1,5,3,4,6,2] => [.,[[[.,.],[.,[.,.]]],.]] => [1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => 2

[1,5,3,6,2,4] => [.,[[[.,.],[.,.]],[.,.]]] => [1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0] => 3

[1,5,3,6,4,2] => [.,[[[.,.],[[.,.],.]],.]] => [1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0] => 2

[1,5,4,2,3,6] => [.,[[[.,.],.],[.,[.,.]]]] => [1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 4

[1,5,4,2,6,3] => [.,[[[.,.],.],[[.,.],.]]] => [1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => 3

[1,5,4,3,2,6] => [.,[[[[.,.],.],.],[.,.]]] => [1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 3

[1,5,4,3,6,2] => [.,[[[[.,.],.],[.,.]],.]] => [1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0] => 2

[1,5,4,6,2,3] => [.,[[[.,.],[.,.]],[.,.]]] => [1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0] => 3

[1,5,4,6,3,2] => [.,[[[[.,.],[.,.]],.],.]] => [1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => 2

[1,5,6,2,3,4] => [.,[[.,[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => 4

[1,5,6,2,4,3] => [.,[[.,[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3

[1,5,6,3,2,4] => [.,[[[.,[.,.]],.],[.,.]]] => [1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0] => 3

[1,5,6,3,4,2] => [.,[[[.,[.,.]],[.,.]],.]] => [1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0] => 2

[1,5,6,4,2,3] => [.,[[[.,[.,.]],.],[.,.]]] => [1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0] => 3

[1,5,6,4,3,2] => [.,[[[[.,[.,.]],.],.],.]] => [1,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => 2

[1,6,2,3,4,5] => [.,[[.,.],[.,[.,[.,.]]]]] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 5

[1,6,2,3,5,4] => [.,[[.,.],[.,[[.,.],.]]]] => [1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => 4

[1,6,2,4,3,5] => [.,[[.,.],[[.,.],[.,.]]]] => [1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 4

[1,6,2,4,5,3] => [.,[[.,.],[[.,[.,.]],.]]] => [1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => 3

[1,6,2,5,3,4] => [.,[[.,.],[[.,.],[.,.]]]] => [1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 4

[1,6,2,5,4,3] => [.,[[.,.],[[[.,.],.],.]]] => [1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => 3

[1,6,3,2,4,5] => [.,[[[.,.],.],[.,[.,.]]]] => [1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 4

[1,6,3,2,5,4] => [.,[[[.,.],.],[[.,.],.]]] => [1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => 3

[1,6,3,4,2,5] => [.,[[[.,.],[.,.]],[.,.]]] => [1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0] => 3

[1,6,3,4,5,2] => [.,[[[.,.],[.,[.,.]]],.]] => [1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => 2

[1,6,3,5,2,4] => [.,[[[.,.],[.,.]],[.,.]]] => [1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0] => 3

[1,6,3,5,4,2] => [.,[[[.,.],[[.,.],.]],.]] => [1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0] => 2

[1,6,4,2,3,5] => [.,[[[.,.],.],[.,[.,.]]]] => [1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 4

[1,6,4,2,5,3] => [.,[[[.,.],.],[[.,.],.]]] => [1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => 3

[1,6,4,3,2,5] => [.,[[[[.,.],.],.],[.,.]]] => [1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 3

[1,6,4,3,5,2] => [.,[[[[.,.],.],[.,.]],.]] => [1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0] => 2

[1,6,4,5,2,3] => [.,[[[.,.],[.,.]],[.,.]]] => [1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0] => 3

[1,6,4,5,3,2] => [.,[[[[.,.],[.,.]],.],.]] => [1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => 2

[1,6,5,2,3,4] => [.,[[[.,.],.],[.,[.,.]]]] => [1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 4

[1,6,5,2,4,3] => [.,[[[.,.],.],[[.,.],.]]] => [1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => 3

[1,6,5,3,2,4] => [.,[[[[.,.],.],.],[.,.]]] => [1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 3

[1,6,5,3,4,2] => [.,[[[[.,.],.],[.,.]],.]] => [1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0] => 2

[1,6,5,4,2,3] => [.,[[[[.,.],.],.],[.,.]]] => [1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 3

[1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]] => [1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 2

[2,1,3,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 5

[2,1,3,4,6,5] => [[.,.],[.,[.,[[.,.],.]]]] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 4

[2,1,3,5,4,6] => [[.,.],[.,[[.,.],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 4

[2,1,3,5,6,4] => [[.,.],[.,[[.,[.,.]],.]]] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => 3

[2,1,3,6,4,5] => [[.,.],[.,[[.,.],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 4

[2,1,3,6,5,4] => [[.,.],[.,[[[.,.],.],.]]] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 3

[2,1,4,3,5,6] => [[.,.],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 4

[2,1,4,3,6,5] => [[.,.],[[.,.],[[.,.],.]]] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 3

[2,1,4,5,3,6] => [[.,.],[[.,[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => 3

[2,1,4,5,6,3] => [[.,.],[[.,[.,[.,.]]],.]] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => 2

[2,1,4,6,3,5] => [[.,.],[[.,[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => 3

[2,1,4,6,5,3] => [[.,.],[[.,[[.,.],.]],.]] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => 2

[2,1,5,3,4,6] => [[.,.],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 4

[2,1,5,3,6,4] => [[.,.],[[.,.],[[.,.],.]]] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 3

[2,1,5,4,3,6] => [[.,.],[[[.,.],.],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 3

[2,1,5,4,6,3] => [[.,.],[[[.,.],[.,.]],.]] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => 2

[2,1,5,6,3,4] => [[.,.],[[.,[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => 3

[2,1,5,6,4,3] => [[.,.],[[[.,[.,.]],.],.]] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0] => 2

[2,1,6,3,4,5] => [[.,.],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 4

[2,1,6,3,5,4] => [[.,.],[[.,.],[[.,.],.]]] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 3

[2,1,6,4,3,5] => [[.,.],[[[.,.],.],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 3

[2,1,6,4,5,3] => [[.,.],[[[.,.],[.,.]],.]] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => 2

[2,1,6,5,3,4] => [[.,.],[[[.,.],.],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 3

[2,1,6,5,4,3] => [[.,.],[[[[.,.],.],.],.]] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 2

[2,3,1,4,5,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => 4

[2,3,1,4,6,5] => [[.,[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3

[2,3,1,5,4,6] => [[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,3,1,5,6,4] => [[.,[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => 2

[2,3,1,6,4,5] => [[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,3,1,6,5,4] => [[.,[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => 2

[2,3,4,1,5,6] => [[.,[.,[.,.]]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => 3

[2,3,4,1,6,5] => [[.,[.,[.,.]]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2

[2,3,4,5,1,6] => [[.,[.,[.,[.,.]]]],[.,.]] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => 2

[2,3,4,5,6,1] => [[.,[.,[.,[.,[.,.]]]]],.] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1

[2,3,4,6,1,5] => [[.,[.,[.,[.,.]]]],[.,.]] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => 2

[2,3,4,6,5,1] => [[.,[.,[.,[[.,.],.]]]],.] => [1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 1

[2,3,5,1,4,6] => [[.,[.,[.,.]]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => 3

[2,3,5,1,6,4] => [[.,[.,[.,.]]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2

[2,3,5,4,1,6] => [[.,[.,[[.,.],.]]],[.,.]] => [1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => 2

[2,3,5,4,6,1] => [[.,[.,[[.,.],[.,.]]]],.] => [1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => 1

[2,3,5,6,1,4] => [[.,[.,[.,[.,.]]]],[.,.]] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => 2

[2,3,5,6,4,1] => [[.,[.,[[.,[.,.]],.]]],.] => [1,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,0,0] => 1

[2,3,6,1,4,5] => [[.,[.,[.,.]]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => 3

[2,3,6,1,5,4] => [[.,[.,[.,.]]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2

[2,3,6,4,1,5] => [[.,[.,[[.,.],.]]],[.,.]] => [1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => 2

[2,3,6,4,5,1] => [[.,[.,[[.,.],[.,.]]]],.] => [1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => 1

[2,3,6,5,1,4] => [[.,[.,[[.,.],.]]],[.,.]] => [1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => 2

[2,3,6,5,4,1] => [[.,[.,[[[.,.],.],.]]],.] => [1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1

[2,4,1,3,5,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => 4

[2,4,1,3,6,5] => [[.,[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3

[2,4,1,5,3,6] => [[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,4,1,5,6,3] => [[.,[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => 2

[2,4,1,6,3,5] => [[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,4,1,6,5,3] => [[.,[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => 2

[2,4,3,1,5,6] => [[.,[[.,.],.]],[.,[.,.]]] => [1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => 3

[2,4,3,1,6,5] => [[.,[[.,.],.]],[[.,.],.]] => [1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 2

[2,4,3,5,1,6] => [[.,[[.,.],[.,.]]],[.,.]] => [1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => 2

[2,4,3,5,6,1] => [[.,[[.,.],[.,[.,.]]]],.] => [1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => 1

[2,4,3,6,1,5] => [[.,[[.,.],[.,.]]],[.,.]] => [1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => 2

[2,4,3,6,5,1] => [[.,[[.,.],[[.,.],.]]],.] => [1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => 1

[2,4,5,1,3,6] => [[.,[.,[.,.]]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => 3

[2,4,5,1,6,3] => [[.,[.,[.,.]]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2

[2,4,5,3,1,6] => [[.,[[.,[.,.]],.]],[.,.]] => [1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0] => 2

[2,4,5,3,6,1] => [[.,[[.,[.,.]],[.,.]]],.] => [1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => 1

[2,4,5,6,1,3] => [[.,[.,[.,[.,.]]]],[.,.]] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => 2

[2,4,5,6,3,1] => [[.,[[.,[.,[.,.]]],.]],.] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,0] => 1

[2,4,6,1,3,5] => [[.,[.,[.,.]]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => 3

[2,4,6,1,5,3] => [[.,[.,[.,.]]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2

[2,4,6,3,1,5] => [[.,[[.,[.,.]],.]],[.,.]] => [1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0] => 2

[2,4,6,3,5,1] => [[.,[[.,[.,.]],[.,.]]],.] => [1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => 1

[2,4,6,5,1,3] => [[.,[.,[[.,.],.]]],[.,.]] => [1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => 2

[2,4,6,5,3,1] => [[.,[[.,[[.,.],.]],.]],.] => [1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => 1

[2,5,1,3,4,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => 4

[2,5,1,3,6,4] => [[.,[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3

[2,5,1,4,3,6] => [[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,5,1,4,6,3] => [[.,[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => 2

[2,5,1,6,3,4] => [[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,5,1,6,4,3] => [[.,[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => 2

[2,5,3,1,4,6] => [[.,[[.,.],.]],[.,[.,.]]] => [1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => 3

[2,5,3,1,6,4] => [[.,[[.,.],.]],[[.,.],.]] => [1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 2

[2,5,3,4,1,6] => [[.,[[.,.],[.,.]]],[.,.]] => [1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => 2

[2,5,3,4,6,1] => [[.,[[.,.],[.,[.,.]]]],.] => [1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => 1

[2,5,3,6,1,4] => [[.,[[.,.],[.,.]]],[.,.]] => [1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => 2

[2,5,3,6,4,1] => [[.,[[.,.],[[.,.],.]]],.] => [1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => 1

[2,5,4,1,3,6] => [[.,[[.,.],.]],[.,[.,.]]] => [1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => 3

[2,5,4,1,6,3] => [[.,[[.,.],.]],[[.,.],.]] => [1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 2

[2,5,4,3,1,6] => [[.,[[[.,.],.],.]],[.,.]] => [1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => 2

[2,5,4,3,6,1] => [[.,[[[.,.],.],[.,.]]],.] => [1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => 1

[2,5,4,6,1,3] => [[.,[[.,.],[.,.]]],[.,.]] => [1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => 2

[2,5,4,6,3,1] => [[.,[[[.,.],[.,.]],.]],.] => [1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => 1

[2,5,6,1,3,4] => [[.,[.,[.,.]]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => 3

[2,5,6,1,4,3] => [[.,[.,[.,.]]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2

[2,5,6,3,1,4] => [[.,[[.,[.,.]],.]],[.,.]] => [1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0] => 2

[2,5,6,3,4,1] => [[.,[[.,[.,.]],[.,.]]],.] => [1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => 1

[2,5,6,4,1,3] => [[.,[[.,[.,.]],.]],[.,.]] => [1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0] => 2

[2,5,6,4,3,1] => [[.,[[[.,[.,.]],.],.]],.] => [1,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => 1

[2,6,1,3,4,5] => [[.,[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => 4

[2,6,1,3,5,4] => [[.,[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3

[2,6,1,4,3,5] => [[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,6,1,4,5,3] => [[.,[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => 2

[2,6,1,5,3,4] => [[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,6,1,5,4,3] => [[.,[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => 2

[2,6,3,1,4,5] => [[.,[[.,.],.]],[.,[.,.]]] => [1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => 3

[2,6,3,1,5,4] => [[.,[[.,.],.]],[[.,.],.]] => [1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 2

[2,6,3,4,1,5] => [[.,[[.,.],[.,.]]],[.,.]] => [1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => 2

[2,6,3,4,5,1] => [[.,[[.,.],[.,[.,.]]]],.] => [1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => 1

[2,6,3,5,1,4] => [[.,[[.,.],[.,.]]],[.,.]] => [1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => 2

[2,6,3,5,4,1] => [[.,[[.,.],[[.,.],.]]],.] => [1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => 1

[2,6,4,1,3,5] => [[.,[[.,.],.]],[.,[.,.]]] => [1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => 3

[2,6,4,1,5,3] => [[.,[[.,.],.]],[[.,.],.]] => [1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 2

[2,6,4,3,1,5] => [[.,[[[.,.],.],.]],[.,.]] => [1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => 2

[2,6,4,3,5,1] => [[.,[[[.,.],.],[.,.]]],.] => [1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => 1

[2,6,4,5,1,3] => [[.,[[.,.],[.,.]]],[.,.]] => [1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => 2

[2,6,4,5,3,1] => [[.,[[[.,.],[.,.]],.]],.] => [1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => 1

[2,6,5,1,3,4] => [[.,[[.,.],.]],[.,[.,.]]] => [1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => 3

[2,6,5,1,4,3] => [[.,[[.,.],.]],[[.,.],.]] => [1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 2

[2,6,5,3,1,4] => [[.,[[[.,.],.],.]],[.,.]] => [1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => 2

[2,6,5,3,4,1] => [[.,[[[.,.],.],[.,.]]],.] => [1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => 1

[2,6,5,4,1,3] => [[.,[[[.,.],.],.]],[.,.]] => [1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => 2

[2,6,5,4,3,1] => [[.,[[[[.,.],.],.],.]],.] => [1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1

[3,1,2,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 5

[3,1,2,4,6,5] => [[.,.],[.,[.,[[.,.],.]]]] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 4

[3,1,2,5,4,6] => [[.,.],[.,[[.,.],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 4

[3,1,2,5,6,4] => [[.,.],[.,[[.,[.,.]],.]]] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => 3

[3,1,2,6,4,5] => [[.,.],[.,[[.,.],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 4

[3,1,2,6,5,4] => [[.,.],[.,[[[.,.],.],.]]] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 3

[3,1,4,2,5,6] => [[.,.],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 4

[3,1,4,2,6,5] => [[.,.],[[.,.],[[.,.],.]]] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 3

[3,1,4,5,2,6] => [[.,.],[[.,[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => 3

[3,1,4,5,6,2] => [[.,.],[[.,[.,[.,.]]],.]] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => 2

[3,1,4,6,2,5] => [[.,.],[[.,[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => 3

[3,1,4,6,5,2] => [[.,.],[[.,[[.,.],.]],.]] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => 2

[3,1,5,2,4,6] => [[.,.],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 4

[3,1,5,2,6,4] => [[.,.],[[.,.],[[.,.],.]]] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 3

[3,1,5,4,2,6] => [[.,.],[[[.,.],.],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 3

[3,1,5,4,6,2] => [[.,.],[[[.,.],[.,.]],.]] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => 2

[3,1,5,6,2,4] => [[.,.],[[.,[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => 3

[3,1,5,6,4,2] => [[.,.],[[[.,[.,.]],.],.]] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0] => 2

[3,1,6,2,4,5] => [[.,.],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 4

[3,1,6,2,5,4] => [[.,.],[[.,.],[[.,.],.]]] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 3

[3,1,6,4,2,5] => [[.,.],[[[.,.],.],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 3

[3,1,6,4,5,2] => [[.,.],[[[.,.],[.,.]],.]] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => 2

[3,1,6,5,2,4] => [[.,.],[[[.,.],.],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 3

[3,1,6,5,4,2] => [[.,.],[[[[.,.],.],.],.]] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 2

[3,2,1,4,5,6] => [[[.,.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => 4

[3,2,1,4,6,5] => [[[.,.],.],[.,[[.,.],.]]] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 3

[3,2,1,5,4,6] => [[[.,.],.],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 3

[3,2,1,5,6,4] => [[[.,.],.],[[.,[.,.]],.]] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0] => 2

[3,2,1,6,4,5] => [[[.,.],.],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 3

[3,2,1,6,5,4] => [[[.,.],.],[[[.,.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 2

[3,2,4,1,5,6] => [[[.,.],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3

[3,2,4,1,6,5] => [[[.,.],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => 2

[3,2,4,5,1,6] => [[[.,.],[.,[.,.]]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2

[3,2,4,5,6,1] => [[[.,.],[.,[.,[.,.]]]],.] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => 1

[3,2,4,6,1,5] => [[[.,.],[.,[.,.]]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2

[3,2,4,6,5,1] => [[[.,.],[.,[[.,.],.]]],.] => [1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => 1

[3,2,5,1,4,6] => [[[.,.],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3

[3,2,5,1,6,4] => [[[.,.],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => 2

[3,2,5,4,1,6] => [[[.,.],[[.,.],.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 2

[3,2,5,4,6,1] => [[[.,.],[[.,.],[.,.]]],.] => [1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,0] => 1

[3,2,5,6,1,4] => [[[.,.],[.,[.,.]]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2

[3,2,5,6,4,1] => [[[.,.],[[.,[.,.]],.]],.] => [1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,0] => 1

[3,2,6,1,4,5] => [[[.,.],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3

[3,2,6,1,5,4] => [[[.,.],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => 2

[3,2,6,4,1,5] => [[[.,.],[[.,.],.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 2

[3,2,6,4,5,1] => [[[.,.],[[.,.],[.,.]]],.] => [1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,0] => 1

[3,2,6,5,1,4] => [[[.,.],[[.,.],.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 2

[3,2,6,5,4,1] => [[[.,.],[[[.,.],.],.]],.] => [1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => 1

[3,4,1,2,5,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => 4

[3,4,1,2,6,5] => [[.,[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3

[3,4,1,5,2,6] => [[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,4,1,5,6,2] => [[.,[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => 2

[3,4,1,6,2,5] => [[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,4,1,6,5,2] => [[.,[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => 2

[3,4,2,1,5,6] => [[[.,[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => 3

[3,4,2,1,6,5] => [[[.,[.,.]],.],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0] => 2

[3,4,2,5,1,6] => [[[.,[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2

[3,4,2,5,6,1] => [[[.,[.,.]],[.,[.,.]]],.] => [1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => 1

[3,4,2,6,1,5] => [[[.,[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2

[3,4,2,6,5,1] => [[[.,[.,.]],[[.,.],.]],.] => [1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => 1

[3,4,5,1,2,6] => [[.,[.,[.,.]]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => 3

[3,4,5,1,6,2] => [[.,[.,[.,.]]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2

[3,4,5,2,1,6] => [[[.,[.,[.,.]]],.],[.,.]] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => 2

[3,4,5,2,6,1] => [[[.,[.,[.,.]]],[.,.]],.] => [1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => 1

[3,4,5,6,1,2] => [[.,[.,[.,[.,.]]]],[.,.]] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => 2

[3,4,5,6,2,1] => [[[.,[.,[.,[.,.]]]],.],.] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1

[3,4,6,1,2,5] => [[.,[.,[.,.]]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => 3

[3,4,6,1,5,2] => [[.,[.,[.,.]]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2

[3,4,6,2,1,5] => [[[.,[.,[.,.]]],.],[.,.]] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => 2

[3,4,6,2,5,1] => [[[.,[.,[.,.]]],[.,.]],.] => [1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => 1

[3,4,6,5,1,2] => [[.,[.,[[.,.],.]]],[.,.]] => [1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => 2

[3,4,6,5,2,1] => [[[.,[.,[[.,.],.]]],.],.] => [1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 1

[3,5,1,2,4,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => 4

[3,5,1,2,6,4] => [[.,[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3

[3,5,1,4,2,6] => [[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,5,1,4,6,2] => [[.,[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => 2

[3,5,1,6,2,4] => [[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,5,1,6,4,2] => [[.,[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => 2

[3,5,2,1,4,6] => [[[.,[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => 3

[3,5,2,1,6,4] => [[[.,[.,.]],.],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0] => 2

[3,5,2,4,1,6] => [[[.,[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2

[3,5,2,4,6,1] => [[[.,[.,.]],[.,[.,.]]],.] => [1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => 1

[3,5,2,6,1,4] => [[[.,[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2

[3,5,2,6,4,1] => [[[.,[.,.]],[[.,.],.]],.] => [1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => 1

[3,5,4,1,2,6] => [[.,[[.,.],.]],[.,[.,.]]] => [1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => 3

[3,5,4,1,6,2] => [[.,[[.,.],.]],[[.,.],.]] => [1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 2

[3,5,4,2,1,6] => [[[.,[[.,.],.]],.],[.,.]] => [1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => 2

[3,5,4,2,6,1] => [[[.,[[.,.],.]],[.,.]],.] => [1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => 1

[3,5,4,6,1,2] => [[.,[[.,.],[.,.]]],[.,.]] => [1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => 2

[3,5,4,6,2,1] => [[[.,[[.,.],[.,.]]],.],.] => [1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,1,1,0,0,0] => 1

[3,5,6,1,2,4] => [[.,[.,[.,.]]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => 3

[3,5,6,1,4,2] => [[.,[.,[.,.]]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2

[3,5,6,2,1,4] => [[[.,[.,[.,.]]],.],[.,.]] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => 2

[3,5,6,2,4,1] => [[[.,[.,[.,.]]],[.,.]],.] => [1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => 1

[3,5,6,4,1,2] => [[.,[[.,[.,.]],.]],[.,.]] => [1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0] => 2

[3,5,6,4,2,1] => [[[.,[[.,[.,.]],.]],.],.] => [1,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => 1

[3,6,1,2,4,5] => [[.,[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => 4

[3,6,1,2,5,4] => [[.,[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3

[3,6,1,4,2,5] => [[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,6,1,4,5,2] => [[.,[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => 2

[3,6,1,5,2,4] => [[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,6,1,5,4,2] => [[.,[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => 2

[3,6,2,1,4,5] => [[[.,[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => 3

[3,6,2,1,5,4] => [[[.,[.,.]],.],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0] => 2

[3,6,2,4,1,5] => [[[.,[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2

[3,6,2,4,5,1] => [[[.,[.,.]],[.,[.,.]]],.] => [1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => 1

[3,6,2,5,1,4] => [[[.,[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2

[3,6,2,5,4,1] => [[[.,[.,.]],[[.,.],.]],.] => [1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => 1

[3,6,4,1,2,5] => [[.,[[.,.],.]],[.,[.,.]]] => [1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => 3

[3,6,4,1,5,2] => [[.,[[.,.],.]],[[.,.],.]] => [1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 2

[3,6,4,2,1,5] => [[[.,[[.,.],.]],.],[.,.]] => [1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => 2

[3,6,4,2,5,1] => [[[.,[[.,.],.]],[.,.]],.] => [1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => 1

[3,6,4,5,1,2] => [[.,[[.,.],[.,.]]],[.,.]] => [1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => 2

[3,6,4,5,2,1] => [[[.,[[.,.],[.,.]]],.],.] => [1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,1,1,0,0,0] => 1

[3,6,5,1,2,4] => [[.,[[.,.],.]],[.,[.,.]]] => [1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => 3

[3,6,5,1,4,2] => [[.,[[.,.],.]],[[.,.],.]] => [1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 2

[3,6,5,2,1,4] => [[[.,[[.,.],.]],.],[.,.]] => [1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => 2

[3,6,5,2,4,1] => [[[.,[[.,.],.]],[.,.]],.] => [1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => 1

[3,6,5,4,1,2] => [[.,[[[.,.],.],.]],[.,.]] => [1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => 2

[3,6,5,4,2,1] => [[[.,[[[.,.],.],.]],.],.] => [1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1

[4,1,2,3,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 5

[4,1,2,3,6,5] => [[.,.],[.,[.,[[.,.],.]]]] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 4

[4,1,2,5,3,6] => [[.,.],[.,[[.,.],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 4

[4,1,2,5,6,3] => [[.,.],[.,[[.,[.,.]],.]]] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => 3

[4,1,2,6,3,5] => [[.,.],[.,[[.,.],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 4

[4,1,2,6,5,3] => [[.,.],[.,[[[.,.],.],.]]] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 3

[4,1,3,2,5,6] => [[.,.],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 4

[4,1,3,2,6,5] => [[.,.],[[.,.],[[.,.],.]]] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 3

[4,1,3,5,2,6] => [[.,.],[[.,[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => 3

[4,1,3,5,6,2] => [[.,.],[[.,[.,[.,.]]],.]] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => 2

[4,1,3,6,2,5] => [[.,.],[[.,[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => 3

[4,1,3,6,5,2] => [[.,.],[[.,[[.,.],.]],.]] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => 2

[4,1,5,2,3,6] => [[.,.],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 4

[4,1,5,2,6,3] => [[.,.],[[.,.],[[.,.],.]]] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 3

[4,1,5,3,2,6] => [[.,.],[[[.,.],.],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 3

[4,1,5,3,6,2] => [[.,.],[[[.,.],[.,.]],.]] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => 2

[4,1,5,6,2,3] => [[.,.],[[.,[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => 3

[4,1,5,6,3,2] => [[.,.],[[[.,[.,.]],.],.]] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0] => 2

[4,1,6,2,3,5] => [[.,.],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 4

[4,1,6,2,5,3] => [[.,.],[[.,.],[[.,.],.]]] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 3

[4,1,6,3,2,5] => [[.,.],[[[.,.],.],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 3

[4,1,6,3,5,2] => [[.,.],[[[.,.],[.,.]],.]] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => 2

[4,1,6,5,2,3] => [[.,.],[[[.,.],.],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 3

[4,1,6,5,3,2] => [[.,.],[[[[.,.],.],.],.]] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 2

[4,2,1,3,5,6] => [[[.,.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => 4

[4,2,1,3,6,5] => [[[.,.],.],[.,[[.,.],.]]] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 3

[4,2,1,5,3,6] => [[[.,.],.],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 3

[4,2,1,5,6,3] => [[[.,.],.],[[.,[.,.]],.]] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0] => 2

[4,2,1,6,3,5] => [[[.,.],.],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 3

[4,2,1,6,5,3] => [[[.,.],.],[[[.,.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 2

[4,2,3,1,5,6] => [[[.,.],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3

[4,2,3,1,6,5] => [[[.,.],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => 2

[4,2,3,5,1,6] => [[[.,.],[.,[.,.]]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2

[4,2,3,5,6,1] => [[[.,.],[.,[.,[.,.]]]],.] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => 1

[4,2,3,6,1,5] => [[[.,.],[.,[.,.]]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2

[4,2,3,6,5,1] => [[[.,.],[.,[[.,.],.]]],.] => [1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => 1

[4,2,5,1,3,6] => [[[.,.],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3

[4,2,5,1,6,3] => [[[.,.],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => 2

[4,2,5,3,1,6] => [[[.,.],[[.,.],.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 2

[4,2,5,3,6,1] => [[[.,.],[[.,.],[.,.]]],.] => [1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,0] => 1

[4,2,5,6,1,3] => [[[.,.],[.,[.,.]]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2

[4,2,5,6,3,1] => [[[.,.],[[.,[.,.]],.]],.] => [1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,0] => 1

[4,2,6,1,3,5] => [[[.,.],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3

[4,2,6,1,5,3] => [[[.,.],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => 2

[4,2,6,3,1,5] => [[[.,.],[[.,.],.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 2

[4,2,6,3,5,1] => [[[.,.],[[.,.],[.,.]]],.] => [1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,0] => 1

[4,2,6,5,1,3] => [[[.,.],[[.,.],.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 2

[4,2,6,5,3,1] => [[[.,.],[[[.,.],.],.]],.] => [1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => 1

[4,3,1,2,5,6] => [[[.,.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => 4

[4,3,1,2,6,5] => [[[.,.],.],[.,[[.,.],.]]] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 3

[4,3,1,5,2,6] => [[[.,.],.],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 3

[4,3,1,5,6,2] => [[[.,.],.],[[.,[.,.]],.]] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0] => 2

[4,3,1,6,2,5] => [[[.,.],.],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 3

[4,3,1,6,5,2] => [[[.,.],.],[[[.,.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 2

[4,3,2,1,5,6] => [[[[.,.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 3

[4,3,2,1,6,5] => [[[[.,.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2

[4,3,2,5,1,6] => [[[[.,.],.],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2

[4,3,2,5,6,1] => [[[[.,.],.],[.,[.,.]]],.] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => 1

[4,3,2,6,1,5] => [[[[.,.],.],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2

[4,3,2,6,5,1] => [[[[.,.],.],[[.,.],.]],.] => [1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => 1

[4,3,5,1,2,6] => [[[.,.],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3

[4,3,5,1,6,2] => [[[.,.],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => 2

[4,3,5,2,1,6] => [[[[.,.],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2

[4,3,5,2,6,1] => [[[[.,.],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 1

[4,3,5,6,1,2] => [[[.,.],[.,[.,.]]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2

[4,3,5,6,2,1] => [[[[.,.],[.,[.,.]]],.],.] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => 1

[4,3,6,1,2,5] => [[[.,.],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3

[4,3,6,1,5,2] => [[[.,.],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => 2

[4,3,6,2,1,5] => [[[[.,.],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2

[4,3,6,2,5,1] => [[[[.,.],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 1

[4,3,6,5,1,2] => [[[.,.],[[.,.],.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 2

[4,3,6,5,2,1] => [[[[.,.],[[.,.],.]],.],.] => [1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => 1

[4,5,1,2,3,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => 4

[4,5,1,2,6,3] => [[.,[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3

[4,5,1,3,2,6] => [[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,5,1,3,6,2] => [[.,[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => 2

[4,5,1,6,2,3] => [[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,5,1,6,3,2] => [[.,[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => 2

[4,5,2,1,3,6] => [[[.,[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => 3

[4,5,2,1,6,3] => [[[.,[.,.]],.],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0] => 2

[4,5,2,3,1,6] => [[[.,[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2

[4,5,2,3,6,1] => [[[.,[.,.]],[.,[.,.]]],.] => [1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => 1

[4,5,2,6,1,3] => [[[.,[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2

[4,5,2,6,3,1] => [[[.,[.,.]],[[.,.],.]],.] => [1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => 1

[4,5,3,1,2,6] => [[[.,[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => 3

[4,5,3,1,6,2] => [[[.,[.,.]],.],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0] => 2

[4,5,3,2,1,6] => [[[[.,[.,.]],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 2

[4,5,3,2,6,1] => [[[[.,[.,.]],.],[.,.]],.] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 1

[4,5,3,6,1,2] => [[[.,[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2

[4,5,3,6,2,1] => [[[[.,[.,.]],[.,.]],.],.] => [1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => 1

[4,5,6,1,2,3] => [[.,[.,[.,.]]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => 3

[4,5,6,1,3,2] => [[.,[.,[.,.]]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2

[4,5,6,2,1,3] => [[[.,[.,[.,.]]],.],[.,.]] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => 2

[4,5,6,2,3,1] => [[[.,[.,[.,.]]],[.,.]],.] => [1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => 1

[4,5,6,3,1,2] => [[[.,[.,[.,.]]],.],[.,.]] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => 2

[4,5,6,3,2,1] => [[[[.,[.,[.,.]]],.],.],.] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1

[4,6,1,2,3,5] => [[.,[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => 4

[4,6,1,2,5,3] => [[.,[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3

[4,6,1,3,2,5] => [[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,6,1,3,5,2] => [[.,[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => 2

[4,6,1,5,2,3] => [[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,6,1,5,3,2] => [[.,[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => 2

[4,6,2,1,3,5] => [[[.,[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => 3

[4,6,2,1,5,3] => [[[.,[.,.]],.],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0] => 2

[4,6,2,3,1,5] => [[[.,[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2

[4,6,2,3,5,1] => [[[.,[.,.]],[.,[.,.]]],.] => [1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => 1

[4,6,2,5,1,3] => [[[.,[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2

[4,6,2,5,3,1] => [[[.,[.,.]],[[.,.],.]],.] => [1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => 1

[4,6,3,1,2,5] => [[[.,[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => 3

[4,6,3,1,5,2] => [[[.,[.,.]],.],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0] => 2

[4,6,3,2,1,5] => [[[[.,[.,.]],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 2

[4,6,3,2,5,1] => [[[[.,[.,.]],.],[.,.]],.] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 1

[4,6,3,5,1,2] => [[[.,[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2

[4,6,3,5,2,1] => [[[[.,[.,.]],[.,.]],.],.] => [1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => 1

[4,6,5,1,2,3] => [[.,[[.,.],.]],[.,[.,.]]] => [1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => 3

[4,6,5,1,3,2] => [[.,[[.,.],.]],[[.,.],.]] => [1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 2

[4,6,5,2,1,3] => [[[.,[[.,.],.]],.],[.,.]] => [1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => 2

[4,6,5,2,3,1] => [[[.,[[.,.],.]],[.,.]],.] => [1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => 1

[4,6,5,3,1,2] => [[[.,[[.,.],.]],.],[.,.]] => [1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => 2

[4,6,5,3,2,1] => [[[[.,[[.,.],.]],.],.],.] => [1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1

[5,1,2,3,4,6] => [[.,.],[.,[.,[.,[.,.]]]]] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 5

[5,1,2,3,6,4] => [[.,.],[.,[.,[[.,.],.]]]] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 4

[5,1,2,4,3,6] => [[.,.],[.,[[.,.],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 4

[5,1,2,4,6,3] => [[.,.],[.,[[.,[.,.]],.]]] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => 3

[5,1,2,6,3,4] => [[.,.],[.,[[.,.],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 4

[5,1,2,6,4,3] => [[.,.],[.,[[[.,.],.],.]]] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 3

[5,1,3,2,4,6] => [[.,.],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 4

[5,1,3,2,6,4] => [[.,.],[[.,.],[[.,.],.]]] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 3

[5,1,3,4,2,6] => [[.,.],[[.,[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => 3

[5,1,3,4,6,2] => [[.,.],[[.,[.,[.,.]]],.]] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => 2

[5,1,3,6,2,4] => [[.,.],[[.,[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => 3

[5,1,3,6,4,2] => [[.,.],[[.,[[.,.],.]],.]] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => 2

[5,1,4,2,3,6] => [[.,.],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 4

[5,1,4,2,6,3] => [[.,.],[[.,.],[[.,.],.]]] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 3

[5,1,4,3,2,6] => [[.,.],[[[.,.],.],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 3

[5,1,4,3,6,2] => [[.,.],[[[.,.],[.,.]],.]] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => 2

[5,1,4,6,2,3] => [[.,.],[[.,[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => 3

[5,1,4,6,3,2] => [[.,.],[[[.,[.,.]],.],.]] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0] => 2

[5,1,6,2,3,4] => [[.,.],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 4

[5,1,6,2,4,3] => [[.,.],[[.,.],[[.,.],.]]] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 3

[5,1,6,3,2,4] => [[.,.],[[[.,.],.],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 3

[5,1,6,3,4,2] => [[.,.],[[[.,.],[.,.]],.]] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => 2

[5,1,6,4,2,3] => [[.,.],[[[.,.],.],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 3

[5,1,6,4,3,2] => [[.,.],[[[[.,.],.],.],.]] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 2

[5,2,1,3,4,6] => [[[.,.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => 4

[5,2,1,3,6,4] => [[[.,.],.],[.,[[.,.],.]]] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 3

[5,2,1,4,3,6] => [[[.,.],.],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 3

[5,2,1,4,6,3] => [[[.,.],.],[[.,[.,.]],.]] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0] => 2

[5,2,1,6,3,4] => [[[.,.],.],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 3

[5,2,1,6,4,3] => [[[.,.],.],[[[.,.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 2

[5,2,3,1,4,6] => [[[.,.],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3

[5,2,3,1,6,4] => [[[.,.],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => 2

[5,2,3,4,1,6] => [[[.,.],[.,[.,.]]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2

[5,2,3,4,6,1] => [[[.,.],[.,[.,[.,.]]]],.] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => 1

[5,2,3,6,1,4] => [[[.,.],[.,[.,.]]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2

[5,2,3,6,4,1] => [[[.,.],[.,[[.,.],.]]],.] => [1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => 1

[5,2,4,1,3,6] => [[[.,.],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3

[5,2,4,1,6,3] => [[[.,.],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => 2

[5,2,4,3,1,6] => [[[.,.],[[.,.],.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 2

[5,2,4,3,6,1] => [[[.,.],[[.,.],[.,.]]],.] => [1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,0] => 1

[5,2,4,6,1,3] => [[[.,.],[.,[.,.]]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2

[5,2,4,6,3,1] => [[[.,.],[[.,[.,.]],.]],.] => [1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,0] => 1

[5,2,6,1,3,4] => [[[.,.],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3

[5,2,6,1,4,3] => [[[.,.],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => 2

[5,2,6,3,1,4] => [[[.,.],[[.,.],.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 2

[5,2,6,3,4,1] => [[[.,.],[[.,.],[.,.]]],.] => [1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,0] => 1

[5,2,6,4,1,3] => [[[.,.],[[.,.],.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 2

[5,2,6,4,3,1] => [[[.,.],[[[.,.],.],.]],.] => [1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => 1

[5,3,1,2,4,6] => [[[.,.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => 4

[5,3,1,2,6,4] => [[[.,.],.],[.,[[.,.],.]]] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 3

[5,3,1,4,2,6] => [[[.,.],.],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 3

[5,3,1,4,6,2] => [[[.,.],.],[[.,[.,.]],.]] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0] => 2

[5,3,1,6,2,4] => [[[.,.],.],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 3

[5,3,1,6,4,2] => [[[.,.],.],[[[.,.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 2

[5,3,2,1,4,6] => [[[[.,.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 3

[5,3,2,1,6,4] => [[[[.,.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2

[5,3,2,4,1,6] => [[[[.,.],.],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2

[5,3,2,4,6,1] => [[[[.,.],.],[.,[.,.]]],.] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => 1

[5,3,2,6,1,4] => [[[[.,.],.],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2

[5,3,2,6,4,1] => [[[[.,.],.],[[.,.],.]],.] => [1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => 1

[5,3,4,1,2,6] => [[[.,.],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3

[5,3,4,1,6,2] => [[[.,.],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => 2

[5,3,4,2,1,6] => [[[[.,.],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2

[5,3,4,2,6,1] => [[[[.,.],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 1

[5,3,4,6,1,2] => [[[.,.],[.,[.,.]]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2

[5,3,4,6,2,1] => [[[[.,.],[.,[.,.]]],.],.] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => 1

[5,3,6,1,2,4] => [[[.,.],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3

[5,3,6,1,4,2] => [[[.,.],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => 2

[5,3,6,2,1,4] => [[[[.,.],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2

[5,3,6,2,4,1] => [[[[.,.],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 1

[5,3,6,4,1,2] => [[[.,.],[[.,.],.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 2

[5,3,6,4,2,1] => [[[[.,.],[[.,.],.]],.],.] => [1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => 1

[5,4,1,2,3,6] => [[[.,.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => 4

[5,4,1,2,6,3] => [[[.,.],.],[.,[[.,.],.]]] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 3

[5,4,1,3,2,6] => [[[.,.],.],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 3

[5,4,1,3,6,2] => [[[.,.],.],[[.,[.,.]],.]] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0] => 2

[5,4,1,6,2,3] => [[[.,.],.],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 3

[5,4,1,6,3,2] => [[[.,.],.],[[[.,.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 2

[5,4,2,1,3,6] => [[[[.,.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 3

[5,4,2,1,6,3] => [[[[.,.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2

[5,4,2,3,1,6] => [[[[.,.],.],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2

[5,4,2,3,6,1] => [[[[.,.],.],[.,[.,.]]],.] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => 1

[5,4,2,6,1,3] => [[[[.,.],.],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2

[5,4,2,6,3,1] => [[[[.,.],.],[[.,.],.]],.] => [1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => 1

[5,4,3,1,2,6] => [[[[.,.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 3

[5,4,3,1,6,2] => [[[[.,.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2

[5,4,3,2,1,6] => [[[[[.,.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2

[5,4,3,2,6,1] => [[[[[.,.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1

[5,4,3,6,1,2] => [[[[.,.],.],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2

[5,4,3,6,2,1] => [[[[[.,.],.],[.,.]],.],.] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1

[5,4,6,1,2,3] => [[[.,.],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3

[5,4,6,1,3,2] => [[[.,.],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => 2

[5,4,6,2,1,3] => [[[[.,.],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2

[5,4,6,2,3,1] => [[[[.,.],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 1

[5,4,6,3,1,2] => [[[[.,.],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2

[5,4,6,3,2,1] => [[[[[.,.],[.,.]],.],.],.] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1

[5,6,1,2,3,4] => [[.,[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => 4

[5,6,1,2,4,3] => [[.,[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3

[5,6,1,3,2,4] => [[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,6,1,3,4,2] => [[.,[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => 2

[5,6,1,4,2,3] => [[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,6,1,4,3,2] => [[.,[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => 2

[5,6,2,1,3,4] => [[[.,[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => 3

[5,6,2,1,4,3] => [[[.,[.,.]],.],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0] => 2

[5,6,2,3,1,4] => [[[.,[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,6,2,3,4,1] => [[[.,[.,.]],[.,[.,.]]],.] => [1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => 1

[5,6,2,4,1,3] => [[[.,[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,6,2,4,3,1] => [[[.,[.,.]],[[.,.],.]],.] => [1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => 1

[5,6,3,1,2,4] => [[[.,[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => 3

[5,6,3,1,4,2] => [[[.,[.,.]],.],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0] => 2

[5,6,3,2,1,4] => [[[[.,[.,.]],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 2

[5,6,3,2,4,1] => [[[[.,[.,.]],.],[.,.]],.] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 1

[5,6,3,4,1,2] => [[[.,[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,6,3,4,2,1] => [[[[.,[.,.]],[.,.]],.],.] => [1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => 1

[5,6,4,1,2,3] => [[[.,[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => 3

[5,6,4,1,3,2] => [[[.,[.,.]],.],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0] => 2

[5,6,4,2,1,3] => [[[[.,[.,.]],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 2

[5,6,4,2,3,1] => [[[[.,[.,.]],.],[.,.]],.] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 1

[5,6,4,3,1,2] => [[[[.,[.,.]],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 2

[5,6,4,3,2,1] => [[[[[.,[.,.]],.],.],.],.] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1

[6,1,2,3,4,5] => [[.,.],[.,[.,[.,[.,.]]]]] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 5

[6,1,2,3,5,4] => [[.,.],[.,[.,[[.,.],.]]]] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 4

[6,1,2,4,3,5] => [[.,.],[.,[[.,.],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 4

[6,1,2,4,5,3] => [[.,.],[.,[[.,[.,.]],.]]] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => 3

[6,1,2,5,3,4] => [[.,.],[.,[[.,.],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 4

[6,1,2,5,4,3] => [[.,.],[.,[[[.,.],.],.]]] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 3

[6,1,3,2,4,5] => [[.,.],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 4

[6,1,3,2,5,4] => [[.,.],[[.,.],[[.,.],.]]] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 3

[6,1,3,4,2,5] => [[.,.],[[.,[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => 3

[6,1,3,4,5,2] => [[.,.],[[.,[.,[.,.]]],.]] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => 2

[6,1,3,5,2,4] => [[.,.],[[.,[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => 3

[6,1,3,5,4,2] => [[.,.],[[.,[[.,.],.]],.]] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => 2

[6,1,4,2,3,5] => [[.,.],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 4

[6,1,4,2,5,3] => [[.,.],[[.,.],[[.,.],.]]] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 3

[6,1,4,3,2,5] => [[.,.],[[[.,.],.],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 3

[6,1,4,3,5,2] => [[.,.],[[[.,.],[.,.]],.]] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => 2

[6,1,4,5,2,3] => [[.,.],[[.,[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => 3

[6,1,4,5,3,2] => [[.,.],[[[.,[.,.]],.],.]] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0] => 2

[6,1,5,2,3,4] => [[.,.],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 4

[6,1,5,2,4,3] => [[.,.],[[.,.],[[.,.],.]]] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 3

[6,1,5,3,2,4] => [[.,.],[[[.,.],.],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 3

[6,1,5,3,4,2] => [[.,.],[[[.,.],[.,.]],.]] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => 2

[6,1,5,4,2,3] => [[.,.],[[[.,.],.],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 3

[6,1,5,4,3,2] => [[.,.],[[[[.,.],.],.],.]] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 2

[6,2,1,3,4,5] => [[[.,.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => 4

[6,2,1,3,5,4] => [[[.,.],.],[.,[[.,.],.]]] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 3

[6,2,1,4,3,5] => [[[.,.],.],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 3

[6,2,1,4,5,3] => [[[.,.],.],[[.,[.,.]],.]] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0] => 2

[6,2,1,5,3,4] => [[[.,.],.],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 3

[6,2,1,5,4,3] => [[[.,.],.],[[[.,.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 2

[6,2,3,1,4,5] => [[[.,.],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3

[6,2,3,1,5,4] => [[[.,.],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => 2

[6,2,3,4,1,5] => [[[.,.],[.,[.,.]]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2

[6,2,3,4,5,1] => [[[.,.],[.,[.,[.,.]]]],.] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => 1

[6,2,3,5,1,4] => [[[.,.],[.,[.,.]]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2

[6,2,3,5,4,1] => [[[.,.],[.,[[.,.],.]]],.] => [1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => 1

[6,2,4,1,3,5] => [[[.,.],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3

[6,2,4,1,5,3] => [[[.,.],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => 2

[6,2,4,3,1,5] => [[[.,.],[[.,.],.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 2

[6,2,4,3,5,1] => [[[.,.],[[.,.],[.,.]]],.] => [1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,0] => 1

[6,2,4,5,1,3] => [[[.,.],[.,[.,.]]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2

[6,2,4,5,3,1] => [[[.,.],[[.,[.,.]],.]],.] => [1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,0] => 1

[6,2,5,1,3,4] => [[[.,.],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3

[6,2,5,1,4,3] => [[[.,.],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => 2

[6,2,5,3,1,4] => [[[.,.],[[.,.],.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 2

[6,2,5,3,4,1] => [[[.,.],[[.,.],[.,.]]],.] => [1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,0] => 1

[6,2,5,4,1,3] => [[[.,.],[[.,.],.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 2

[6,2,5,4,3,1] => [[[.,.],[[[.,.],.],.]],.] => [1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => 1

[6,3,1,2,4,5] => [[[.,.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => 4

[6,3,1,2,5,4] => [[[.,.],.],[.,[[.,.],.]]] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 3

[6,3,1,4,2,5] => [[[.,.],.],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 3

[6,3,1,4,5,2] => [[[.,.],.],[[.,[.,.]],.]] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0] => 2

[6,3,1,5,2,4] => [[[.,.],.],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 3

[6,3,1,5,4,2] => [[[.,.],.],[[[.,.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 2

[6,3,2,1,4,5] => [[[[.,.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 3

[6,3,2,1,5,4] => [[[[.,.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2

[6,3,2,4,1,5] => [[[[.,.],.],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2

[6,3,2,4,5,1] => [[[[.,.],.],[.,[.,.]]],.] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => 1

[6,3,2,5,1,4] => [[[[.,.],.],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2

[6,3,2,5,4,1] => [[[[.,.],.],[[.,.],.]],.] => [1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => 1

[6,3,4,1,2,5] => [[[.,.],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3

[6,3,4,1,5,2] => [[[.,.],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => 2

[6,3,4,2,1,5] => [[[[.,.],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2

[6,3,4,2,5,1] => [[[[.,.],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 1

[6,3,4,5,1,2] => [[[.,.],[.,[.,.]]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2

[6,3,4,5,2,1] => [[[[.,.],[.,[.,.]]],.],.] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => 1

[6,3,5,1,2,4] => [[[.,.],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3

[6,3,5,1,4,2] => [[[.,.],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => 2

[6,3,5,2,1,4] => [[[[.,.],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2

[6,3,5,2,4,1] => [[[[.,.],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 1

[6,3,5,4,1,2] => [[[.,.],[[.,.],.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 2

[6,3,5,4,2,1] => [[[[.,.],[[.,.],.]],.],.] => [1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => 1

[6,4,1,2,3,5] => [[[.,.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => 4

[6,4,1,2,5,3] => [[[.,.],.],[.,[[.,.],.]]] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 3

[6,4,1,3,2,5] => [[[.,.],.],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 3

[6,4,1,3,5,2] => [[[.,.],.],[[.,[.,.]],.]] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0] => 2

[6,4,1,5,2,3] => [[[.,.],.],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 3

[6,4,1,5,3,2] => [[[.,.],.],[[[.,.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 2

[6,4,2,1,3,5] => [[[[.,.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 3

[6,4,2,1,5,3] => [[[[.,.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2

[6,4,2,3,1,5] => [[[[.,.],.],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2

[6,4,2,3,5,1] => [[[[.,.],.],[.,[.,.]]],.] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => 1

[6,4,2,5,1,3] => [[[[.,.],.],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2

[6,4,2,5,3,1] => [[[[.,.],.],[[.,.],.]],.] => [1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => 1

[6,4,3,1,2,5] => [[[[.,.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 3

[6,4,3,1,5,2] => [[[[.,.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2

[6,4,3,2,1,5] => [[[[[.,.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2

[6,4,3,2,5,1] => [[[[[.,.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1

[6,4,3,5,1,2] => [[[[.,.],.],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2

[6,4,3,5,2,1] => [[[[[.,.],.],[.,.]],.],.] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1

[6,4,5,1,2,3] => [[[.,.],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3

[6,4,5,1,3,2] => [[[.,.],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => 2

[6,4,5,2,1,3] => [[[[.,.],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2

[6,4,5,2,3,1] => [[[[.,.],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 1

[6,4,5,3,1,2] => [[[[.,.],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2

[6,4,5,3,2,1] => [[[[[.,.],[.,.]],.],.],.] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1

[6,5,1,2,3,4] => [[[.,.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => 4

[6,5,1,2,4,3] => [[[.,.],.],[.,[[.,.],.]]] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 3

[6,5,1,3,2,4] => [[[.,.],.],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 3

[6,5,1,3,4,2] => [[[.,.],.],[[.,[.,.]],.]] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0] => 2

[6,5,1,4,2,3] => [[[.,.],.],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 3

[6,5,1,4,3,2] => [[[.,.],.],[[[.,.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 2

[6,5,2,1,3,4] => [[[[.,.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 3

[6,5,2,1,4,3] => [[[[.,.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2

[6,5,2,3,1,4] => [[[[.,.],.],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2

[6,5,2,3,4,1] => [[[[.,.],.],[.,[.,.]]],.] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => 1

[6,5,2,4,1,3] => [[[[.,.],.],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2

[6,5,2,4,3,1] => [[[[.,.],.],[[.,.],.]],.] => [1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => 1

[6,5,3,1,2,4] => [[[[.,.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 3

[6,5,3,1,4,2] => [[[[.,.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2

[6,5,3,2,1,4] => [[[[[.,.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2

[6,5,3,2,4,1] => [[[[[.,.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1

[6,5,3,4,1,2] => [[[[.,.],.],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2

[6,5,3,4,2,1] => [[[[[.,.],.],[.,.]],.],.] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1

[6,5,4,1,2,3] => [[[[.,.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 3

[6,5,4,1,3,2] => [[[[.,.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2

[6,5,4,2,1,3] => [[[[[.,.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2

[6,5,4,2,3,1] => [[[[[.,.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1

[6,5,4,3,1,2] => [[[[[.,.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2

[6,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],.] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1

[1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7

[1,2,3,4,5,7,6] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 6

[1,2,3,4,6,5,7] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 6

[1,2,3,4,6,7,5] => [.,[.,[.,[.,[[.,[.,.]],.]]]]] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 5

[1,2,3,4,7,5,6] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 6

[1,2,3,4,7,6,5] => [.,[.,[.,[.,[[[.,.],.],.]]]]] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 5

[1,2,3,5,4,6,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 6

[1,2,3,5,4,7,6] => [.,[.,[.,[[.,.],[[.,.],.]]]]] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 5

[1,2,3,5,6,4,7] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 5

[1,2,3,5,6,7,4] => [.,[.,[.,[[.,[.,[.,.]]],.]]]] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4

[1,2,3,5,7,4,6] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 5

[1,2,3,5,7,6,4] => [.,[.,[.,[[.,[[.,.],.]],.]]]] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 4

[1,2,3,6,4,5,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 6

[1,2,3,6,4,7,5] => [.,[.,[.,[[.,.],[[.,.],.]]]]] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 5

[1,2,3,6,5,4,7] => [.,[.,[.,[[[.,.],.],[.,.]]]]] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 5

[1,2,3,6,5,7,4] => [.,[.,[.,[[[.,.],[.,.]],.]]]] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 4

[1,2,3,6,7,4,5] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 5

[1,2,3,6,7,5,4] => [.,[.,[.,[[[.,[.,.]],.],.]]]] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 4

[1,2,3,7,4,5,6] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 6

[1,2,3,7,4,6,5] => [.,[.,[.,[[.,.],[[.,.],.]]]]] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 5

[1,2,3,7,5,4,6] => [.,[.,[.,[[[.,.],.],[.,.]]]]] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 5

[1,2,3,7,5,6,4] => [.,[.,[.,[[[.,.],[.,.]],.]]]] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 4

[1,2,3,7,6,4,5] => [.,[.,[.,[[[.,.],.],[.,.]]]]] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 5

[1,2,3,7,6,5,4] => [.,[.,[.,[[[[.,.],.],.],.]]]] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 4

[1,2,4,3,5,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 6

[1,2,4,3,5,7,6] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 5

[1,2,4,3,6,5,7] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 5

[1,2,4,3,6,7,5] => [.,[.,[[.,.],[[.,[.,.]],.]]]] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 4

[1,2,4,3,7,5,6] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 5

[1,2,4,3,7,6,5] => [.,[.,[[.,.],[[[.,.],.],.]]]] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 4

[1,2,4,5,3,6,7] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 5

[1,2,4,5,3,7,6] => [.,[.,[[.,[.,.]],[[.,.],.]]]] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 4

[1,2,4,5,6,3,7] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 4

[1,2,4,5,6,7,3] => [.,[.,[[.,[.,[.,[.,.]]]],.]]] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 3

[1,2,4,5,7,3,6] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 4

[1,2,4,5,7,6,3] => [.,[.,[[.,[.,[[.,.],.]]],.]]] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 3

[1,2,4,6,3,5,7] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 5

[1,2,4,6,3,7,5] => [.,[.,[[.,[.,.]],[[.,.],.]]]] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 4

[1,2,4,6,5,3,7] => [.,[.,[[.,[[.,.],.]],[.,.]]]] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 4

[1,2,4,6,5,7,3] => [.,[.,[[.,[[.,.],[.,.]]],.]]] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 3

[1,2,4,6,7,3,5] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 4

[1,2,4,6,7,5,3] => [.,[.,[[.,[[.,[.,.]],.]],.]]] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 3

[1,2,4,7,3,5,6] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 5

[1,2,4,7,3,6,5] => [.,[.,[[.,[.,.]],[[.,.],.]]]] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 4

[1,2,4,7,5,3,6] => [.,[.,[[.,[[.,.],.]],[.,.]]]] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 4

[1,2,4,7,5,6,3] => [.,[.,[[.,[[.,.],[.,.]]],.]]] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 3

[1,2,4,7,6,3,5] => [.,[.,[[.,[[.,.],.]],[.,.]]]] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 4

[1,2,4,7,6,5,3] => [.,[.,[[.,[[[.,.],.],.]],.]]] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 3

[1,2,5,3,4,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 6

[1,2,5,3,4,7,6] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 5

[1,2,5,3,6,4,7] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 5

[1,2,5,3,6,7,4] => [.,[.,[[.,.],[[.,[.,.]],.]]]] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 4

[1,2,5,3,7,4,6] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 5

[1,2,5,3,7,6,4] => [.,[.,[[.,.],[[[.,.],.],.]]]] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 4

[1,2,5,4,3,6,7] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 5

[1,2,5,4,3,7,6] => [.,[.,[[[.,.],.],[[.,.],.]]]] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 4

[1,2,5,4,6,3,7] => [.,[.,[[[.,.],[.,.]],[.,.]]]] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 4

[1,2,5,4,6,7,3] => [.,[.,[[[.,.],[.,[.,.]]],.]]] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 3

[1,2,5,4,7,3,6] => [.,[.,[[[.,.],[.,.]],[.,.]]]] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 4

[1,2,5,4,7,6,3] => [.,[.,[[[.,.],[[.,.],.]],.]]] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 3

[1,2,5,6,3,4,7] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 5

[1,2,5,6,3,7,4] => [.,[.,[[.,[.,.]],[[.,.],.]]]] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 4

[1,2,5,6,4,3,7] => [.,[.,[[[.,[.,.]],.],[.,.]]]] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 4

[1,2,5,6,4,7,3] => [.,[.,[[[.,[.,.]],[.,.]],.]]] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 3

[1,2,5,6,7,3,4] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 4

[1,2,5,6,7,4,3] => [.,[.,[[[.,[.,[.,.]]],.],.]]] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 3

[1,2,5,7,3,4,6] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 5

[1,2,5,7,3,6,4] => [.,[.,[[.,[.,.]],[[.,.],.]]]] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 4

[1,2,5,7,4,3,6] => [.,[.,[[[.,[.,.]],.],[.,.]]]] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 4

[1,2,5,7,4,6,3] => [.,[.,[[[.,[.,.]],[.,.]],.]]] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 3

[1,2,5,7,6,3,4] => [.,[.,[[.,[[.,.],.]],[.,.]]]] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 4

[1,2,5,7,6,4,3] => [.,[.,[[[.,[[.,.],.]],.],.]]] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 3

[1,2,6,3,4,5,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 6

[1,2,6,3,4,7,5] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 5

[1,2,6,3,5,4,7] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 5

[1,2,6,3,5,7,4] => [.,[.,[[.,.],[[.,[.,.]],.]]]] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 4

[1,2,6,3,7,4,5] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 5

[1,2,6,3,7,5,4] => [.,[.,[[.,.],[[[.,.],.],.]]]] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 4

[1,2,6,4,3,5,7] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 5

[1,2,6,4,3,7,5] => [.,[.,[[[.,.],.],[[.,.],.]]]] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 4

[1,2,6,4,5,3,7] => [.,[.,[[[.,.],[.,.]],[.,.]]]] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 4

[1,2,6,4,5,7,3] => [.,[.,[[[.,.],[.,[.,.]]],.]]] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 3

[1,2,6,4,7,3,5] => [.,[.,[[[.,.],[.,.]],[.,.]]]] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 4

[1,2,6,4,7,5,3] => [.,[.,[[[.,.],[[.,.],.]],.]]] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 3

[1,2,6,5,3,4,7] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 5

[1,2,6,5,3,7,4] => [.,[.,[[[.,.],.],[[.,.],.]]]] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 4

[1,2,6,5,4,3,7] => [.,[.,[[[[.,.],.],.],[.,.]]]] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 4

[1,2,6,5,4,7,3] => [.,[.,[[[[.,.],.],[.,.]],.]]] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 3

[1,2,6,5,7,3,4] => [.,[.,[[[.,.],[.,.]],[.,.]]]] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 4

[1,2,6,5,7,4,3] => [.,[.,[[[[.,.],[.,.]],.],.]]] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 3

[1,2,6,7,3,4,5] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 5

[1,2,6,7,3,5,4] => [.,[.,[[.,[.,.]],[[.,.],.]]]] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 4

[1,2,6,7,4,3,5] => [.,[.,[[[.,[.,.]],.],[.,.]]]] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 4

[1,2,6,7,4,5,3] => [.,[.,[[[.,[.,.]],[.,.]],.]]] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 3

[1,2,6,7,5,3,4] => [.,[.,[[[.,[.,.]],.],[.,.]]]] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 4

[1,2,6,7,5,4,3] => [.,[.,[[[[.,[.,.]],.],.],.]]] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 3

[1,2,7,3,4,5,6] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 6

[1,2,7,3,4,6,5] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 5

[1,2,7,3,5,4,6] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 5

[1,2,7,3,5,6,4] => [.,[.,[[.,.],[[.,[.,.]],.]]]] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 4

[1,2,7,3,6,4,5] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 5

[1,2,7,3,6,5,4] => [.,[.,[[.,.],[[[.,.],.],.]]]] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 4

[1,2,7,4,3,5,6] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 5

[1,2,7,4,3,6,5] => [.,[.,[[[.,.],.],[[.,.],.]]]] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 4

[1,2,7,4,5,3,6] => [.,[.,[[[.,.],[.,.]],[.,.]]]] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 4

[1,2,7,4,5,6,3] => [.,[.,[[[.,.],[.,[.,.]]],.]]] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 3

[1,2,7,4,6,3,5] => [.,[.,[[[.,.],[.,.]],[.,.]]]] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 4

[1,2,7,4,6,5,3] => [.,[.,[[[.,.],[[.,.],.]],.]]] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 3

[1,2,7,5,3,4,6] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 5

[1,2,7,5,3,6,4] => [.,[.,[[[.,.],.],[[.,.],.]]]] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 4

[1,2,7,5,4,3,6] => [.,[.,[[[[.,.],.],.],[.,.]]]] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 4

[1,2,7,5,4,6,3] => [.,[.,[[[[.,.],.],[.,.]],.]]] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 3

[1,2,7,5,6,3,4] => [.,[.,[[[.,.],[.,.]],[.,.]]]] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 4

[1,2,7,5,6,4,3] => [.,[.,[[[[.,.],[.,.]],.],.]]] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 3

[1,2,7,6,3,4,5] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 5

[1,2,7,6,3,5,4] => [.,[.,[[[.,.],.],[[.,.],.]]]] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 4

[1,2,7,6,4,3,5] => [.,[.,[[[[.,.],.],.],[.,.]]]] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 4

[1,2,7,6,4,5,3] => [.,[.,[[[[.,.],.],[.,.]],.]]] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 3

[1,2,7,6,5,3,4] => [.,[.,[[[[.,.],.],.],[.,.]]]] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 4

[1,2,7,6,5,4,3] => [.,[.,[[[[[.,.],.],.],.],.]]] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 3

[1,3,2,4,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 6

[1,3,2,4,5,7,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 5

[1,3,2,4,6,5,7] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 5

[1,3,2,4,6,7,5] => [.,[[.,.],[.,[[.,[.,.]],.]]]] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 4

[1,3,2,4,7,5,6] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 5

[1,3,2,4,7,6,5] => [.,[[.,.],[.,[[[.,.],.],.]]]] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 4

[1,3,2,5,4,6,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 5

[1,3,2,5,4,7,6] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 4

[1,3,2,5,6,4,7] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 4

[1,3,2,5,6,7,4] => [.,[[.,.],[[.,[.,[.,.]]],.]]] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 3

[1,3,2,5,7,4,6] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 4

[1,3,2,5,7,6,4] => [.,[[.,.],[[.,[[.,.],.]],.]]] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 3

[1,3,2,6,4,5,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 5

[1,3,2,6,4,7,5] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 4

[1,3,2,6,5,4,7] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 4

[1,3,2,6,5,7,4] => [.,[[.,.],[[[.,.],[.,.]],.]]] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 3

[1,3,2,6,7,4,5] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 4

[1,3,2,6,7,5,4] => [.,[[.,.],[[[.,[.,.]],.],.]]] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 3

[1,3,2,7,4,5,6] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 5

[1,3,2,7,4,6,5] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 4

[1,3,2,7,5,4,6] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 4

[1,3,2,7,5,6,4] => [.,[[.,.],[[[.,.],[.,.]],.]]] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 3

[1,3,2,7,6,4,5] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 4

[1,3,2,7,6,5,4] => [.,[[.,.],[[[[.,.],.],.],.]]] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 3

[1,3,4,2,5,6,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[1,3,4,2,5,7,6] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[1,3,4,2,6,5,7] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[1,3,4,2,6,7,5] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3

[1,3,4,2,7,5,6] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[1,3,4,2,7,6,5] => [.,[[.,[.,.]],[[[.,.],.],.]]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3

[1,3,4,5,2,6,7] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[1,3,4,5,2,7,6] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[1,3,4,5,6,2,7] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 3

[1,3,4,5,6,7,2] => [.,[[.,[.,[.,[.,[.,.]]]]],.]] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2

[1,3,4,5,7,2,6] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 3

[1,3,4,5,7,6,2] => [.,[[.,[.,[.,[[.,.],.]]]],.]] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 2

[1,3,4,6,2,5,7] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[1,3,4,6,2,7,5] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[1,3,4,6,5,2,7] => [.,[[.,[.,[[.,.],.]]],[.,.]]] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 3

[1,3,4,6,5,7,2] => [.,[[.,[.,[[.,.],[.,.]]]],.]] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 2

[1,3,4,6,7,2,5] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 3

[1,3,4,6,7,5,2] => [.,[[.,[.,[[.,[.,.]],.]]],.]] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[1,3,4,7,2,5,6] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[1,3,4,7,2,6,5] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[1,3,4,7,5,2,6] => [.,[[.,[.,[[.,.],.]]],[.,.]]] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 3

[1,3,4,7,5,6,2] => [.,[[.,[.,[[.,.],[.,.]]]],.]] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 2

[1,3,4,7,6,2,5] => [.,[[.,[.,[[.,.],.]]],[.,.]]] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 3

[1,3,4,7,6,5,2] => [.,[[.,[.,[[[.,.],.],.]]],.]] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 2

[1,3,5,2,4,6,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[1,3,5,2,4,7,6] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[1,3,5,2,6,4,7] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[1,3,5,2,6,7,4] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3

[1,3,5,2,7,4,6] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[1,3,5,2,7,6,4] => [.,[[.,[.,.]],[[[.,.],.],.]]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3

[1,3,5,4,2,6,7] => [.,[[.,[[.,.],.]],[.,[.,.]]]] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 4

[1,3,5,4,2,7,6] => [.,[[.,[[.,.],.]],[[.,.],.]]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 3

[1,3,5,4,6,2,7] => [.,[[.,[[.,.],[.,.]]],[.,.]]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 3

[1,3,5,4,6,7,2] => [.,[[.,[[.,.],[.,[.,.]]]],.]] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 2

[1,3,5,4,7,2,6] => [.,[[.,[[.,.],[.,.]]],[.,.]]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 3

[1,3,5,4,7,6,2] => [.,[[.,[[.,.],[[.,.],.]]],.]] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 2

[1,3,5,6,2,4,7] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[1,3,5,6,2,7,4] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[1,3,5,6,4,2,7] => [.,[[.,[[.,[.,.]],.]],[.,.]]] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3

[1,3,5,6,4,7,2] => [.,[[.,[[.,[.,.]],[.,.]]],.]] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 2

[1,3,5,6,7,2,4] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 3

[1,3,5,6,7,4,2] => [.,[[.,[[.,[.,[.,.]]],.]],.]] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 2

[1,3,5,7,2,4,6] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[1,3,5,7,2,6,4] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[1,3,5,7,4,2,6] => [.,[[.,[[.,[.,.]],.]],[.,.]]] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3

[1,3,5,7,4,6,2] => [.,[[.,[[.,[.,.]],[.,.]]],.]] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 2

[1,3,5,7,6,2,4] => [.,[[.,[.,[[.,.],.]]],[.,.]]] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 3

[1,3,5,7,6,4,2] => [.,[[.,[[.,[[.,.],.]],.]],.]] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 2

[1,3,6,2,4,5,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[1,3,6,2,4,7,5] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[1,3,6,2,5,4,7] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[1,3,6,2,5,7,4] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3

[1,3,6,2,7,4,5] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[1,3,6,2,7,5,4] => [.,[[.,[.,.]],[[[.,.],.],.]]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3

[1,3,6,4,2,5,7] => [.,[[.,[[.,.],.]],[.,[.,.]]]] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 4

[1,3,6,4,2,7,5] => [.,[[.,[[.,.],.]],[[.,.],.]]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 3

[1,3,6,4,5,2,7] => [.,[[.,[[.,.],[.,.]]],[.,.]]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 3

[1,3,6,4,5,7,2] => [.,[[.,[[.,.],[.,[.,.]]]],.]] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 2

[1,3,6,4,7,2,5] => [.,[[.,[[.,.],[.,.]]],[.,.]]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 3

[1,3,6,4,7,5,2] => [.,[[.,[[.,.],[[.,.],.]]],.]] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 2

[1,3,6,5,2,4,7] => [.,[[.,[[.,.],.]],[.,[.,.]]]] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 4

[1,3,6,5,2,7,4] => [.,[[.,[[.,.],.]],[[.,.],.]]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 3

[1,3,6,5,4,2,7] => [.,[[.,[[[.,.],.],.]],[.,.]]] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 3

[1,3,6,5,4,7,2] => [.,[[.,[[[.,.],.],[.,.]]],.]] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 2

[1,3,6,5,7,2,4] => [.,[[.,[[.,.],[.,.]]],[.,.]]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 3

[1,3,6,5,7,4,2] => [.,[[.,[[[.,.],[.,.]],.]],.]] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 2

[1,3,6,7,2,4,5] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[1,3,6,7,2,5,4] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[1,3,6,7,4,2,5] => [.,[[.,[[.,[.,.]],.]],[.,.]]] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3

[1,3,6,7,4,5,2] => [.,[[.,[[.,[.,.]],[.,.]]],.]] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 2

[1,3,6,7,5,2,4] => [.,[[.,[[.,[.,.]],.]],[.,.]]] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3

[1,3,6,7,5,4,2] => [.,[[.,[[[.,[.,.]],.],.]],.]] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2

[1,3,7,2,4,5,6] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[1,3,7,2,4,6,5] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[1,3,7,2,5,4,6] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[1,3,7,2,5,6,4] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3

[1,3,7,2,6,4,5] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[1,3,7,2,6,5,4] => [.,[[.,[.,.]],[[[.,.],.],.]]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3

[1,3,7,4,2,5,6] => [.,[[.,[[.,.],.]],[.,[.,.]]]] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 4

[1,3,7,4,2,6,5] => [.,[[.,[[.,.],.]],[[.,.],.]]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 3

[1,3,7,4,5,2,6] => [.,[[.,[[.,.],[.,.]]],[.,.]]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 3

[1,3,7,4,5,6,2] => [.,[[.,[[.,.],[.,[.,.]]]],.]] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 2

[1,3,7,4,6,2,5] => [.,[[.,[[.,.],[.,.]]],[.,.]]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 3

[1,3,7,4,6,5,2] => [.,[[.,[[.,.],[[.,.],.]]],.]] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 2

[1,3,7,5,2,4,6] => [.,[[.,[[.,.],.]],[.,[.,.]]]] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 4

[1,3,7,5,2,6,4] => [.,[[.,[[.,.],.]],[[.,.],.]]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 3

[1,3,7,5,4,2,6] => [.,[[.,[[[.,.],.],.]],[.,.]]] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 3

[1,3,7,5,4,6,2] => [.,[[.,[[[.,.],.],[.,.]]],.]] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 2

[1,3,7,5,6,2,4] => [.,[[.,[[.,.],[.,.]]],[.,.]]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 3

[1,3,7,5,6,4,2] => [.,[[.,[[[.,.],[.,.]],.]],.]] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 2

[1,3,7,6,2,4,5] => [.,[[.,[[.,.],.]],[.,[.,.]]]] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 4

[1,3,7,6,2,5,4] => [.,[[.,[[.,.],.]],[[.,.],.]]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 3

[1,3,7,6,4,2,5] => [.,[[.,[[[.,.],.],.]],[.,.]]] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 3

[1,3,7,6,4,5,2] => [.,[[.,[[[.,.],.],[.,.]]],.]] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 2

[1,3,7,6,5,2,4] => [.,[[.,[[[.,.],.],.]],[.,.]]] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 3

[1,3,7,6,5,4,2] => [.,[[.,[[[[.,.],.],.],.]],.]] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 2

[1,4,2,3,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 6

[1,4,2,3,5,7,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 5

[1,4,2,3,6,5,7] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 5

[1,4,2,3,6,7,5] => [.,[[.,.],[.,[[.,[.,.]],.]]]] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 4

[1,4,2,3,7,5,6] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 5

[1,4,2,3,7,6,5] => [.,[[.,.],[.,[[[.,.],.],.]]]] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 4

[1,4,2,5,3,6,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 5

[1,4,2,5,3,7,6] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 4

[1,4,2,5,6,3,7] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 4

[1,4,2,5,6,7,3] => [.,[[.,.],[[.,[.,[.,.]]],.]]] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 3

[1,4,2,5,7,3,6] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 4

[1,4,2,5,7,6,3] => [.,[[.,.],[[.,[[.,.],.]],.]]] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 3

[1,4,2,6,3,5,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 5

[1,4,2,6,3,7,5] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 4

[1,4,2,6,5,3,7] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 4

[1,4,2,6,5,7,3] => [.,[[.,.],[[[.,.],[.,.]],.]]] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 3

[1,4,2,6,7,3,5] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 4

[1,4,2,6,7,5,3] => [.,[[.,.],[[[.,[.,.]],.],.]]] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 3

[1,4,2,7,3,5,6] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 5

[1,4,2,7,3,6,5] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 4

[1,4,2,7,5,3,6] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 4

[1,4,2,7,5,6,3] => [.,[[.,.],[[[.,.],[.,.]],.]]] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 3

[1,4,2,7,6,3,5] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 4

[1,4,2,7,6,5,3] => [.,[[.,.],[[[[.,.],.],.],.]]] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 3

[1,4,3,2,5,6,7] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 5

[1,4,3,2,5,7,6] => [.,[[[.,.],.],[.,[[.,.],.]]]] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 4

[1,4,3,2,6,5,7] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 4

[1,4,3,2,6,7,5] => [.,[[[.,.],.],[[.,[.,.]],.]]] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3

[1,4,3,2,7,5,6] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 4

[1,4,3,2,7,6,5] => [.,[[[.,.],.],[[[.,.],.],.]]] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 3

[1,4,3,5,2,6,7] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 4

[1,4,3,5,2,7,6] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 3

[1,4,3,5,6,2,7] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 3

[1,4,3,5,6,7,2] => [.,[[[.,.],[.,[.,[.,.]]]],.]] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2

[1,4,3,5,7,2,6] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 3

[1,4,3,5,7,6,2] => [.,[[[.,.],[.,[[.,.],.]]],.]] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 2

[1,4,3,6,2,5,7] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 4

[1,4,3,6,2,7,5] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 3

[1,4,3,6,5,2,7] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 3

[1,4,3,6,5,7,2] => [.,[[[.,.],[[.,.],[.,.]]],.]] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 2

[1,4,3,6,7,2,5] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 3

[1,4,3,6,7,5,2] => [.,[[[.,.],[[.,[.,.]],.]],.]] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 2

[1,4,3,7,2,5,6] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 4

[1,4,3,7,2,6,5] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 3

[1,4,3,7,5,2,6] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 3

[1,4,3,7,5,6,2] => [.,[[[.,.],[[.,.],[.,.]]],.]] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 2

[1,4,3,7,6,2,5] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 3

[1,4,3,7,6,5,2] => [.,[[[.,.],[[[.,.],.],.]],.]] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 2

[1,4,5,2,3,6,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[1,4,5,2,3,7,6] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[1,4,5,2,6,3,7] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[1,4,5,2,6,7,3] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3

[1,4,5,2,7,3,6] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[1,4,5,2,7,6,3] => [.,[[.,[.,.]],[[[.,.],.],.]]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3

[1,4,5,3,2,6,7] => [.,[[[.,[.,.]],.],[.,[.,.]]]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[1,4,5,3,2,7,6] => [.,[[[.,[.,.]],.],[[.,.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3

[1,4,5,3,6,2,7] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[1,4,5,3,6,7,2] => [.,[[[.,[.,.]],[.,[.,.]]],.]] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[1,4,5,3,7,2,6] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[1,4,5,3,7,6,2] => [.,[[[.,[.,.]],[[.,.],.]],.]] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2

[1,4,5,6,2,3,7] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[1,4,5,6,2,7,3] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[1,4,5,6,3,2,7] => [.,[[[.,[.,[.,.]]],.],[.,.]]] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 3

[1,4,5,6,3,7,2] => [.,[[[.,[.,[.,.]]],[.,.]],.]] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2

[1,4,5,6,7,2,3] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 3

[1,4,5,6,7,3,2] => [.,[[[.,[.,[.,[.,.]]]],.],.]] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 2

[1,4,5,7,2,3,6] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[1,4,5,7,2,6,3] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[1,4,5,7,3,2,6] => [.,[[[.,[.,[.,.]]],.],[.,.]]] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 3

[1,4,5,7,3,6,2] => [.,[[[.,[.,[.,.]]],[.,.]],.]] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2

[1,4,5,7,6,2,3] => [.,[[.,[.,[[.,.],.]]],[.,.]]] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 3

[1,4,5,7,6,3,2] => [.,[[[.,[.,[[.,.],.]]],.],.]] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 2

[1,4,6,2,3,5,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[1,4,6,2,3,7,5] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[1,4,6,2,5,3,7] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[1,4,6,2,5,7,3] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3

[1,4,6,2,7,3,5] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[1,4,6,2,7,5,3] => [.,[[.,[.,.]],[[[.,.],.],.]]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3

[1,4,6,3,2,5,7] => [.,[[[.,[.,.]],.],[.,[.,.]]]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[1,4,6,3,2,7,5] => [.,[[[.,[.,.]],.],[[.,.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3

[1,4,6,3,5,2,7] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[1,4,6,3,5,7,2] => [.,[[[.,[.,.]],[.,[.,.]]],.]] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[1,4,6,3,7,2,5] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[1,4,6,3,7,5,2] => [.,[[[.,[.,.]],[[.,.],.]],.]] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2

[1,4,6,5,2,3,7] => [.,[[.,[[.,.],.]],[.,[.,.]]]] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 4

[1,4,6,5,2,7,3] => [.,[[.,[[.,.],.]],[[.,.],.]]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 3

[1,4,6,5,3,2,7] => [.,[[[.,[[.,.],.]],.],[.,.]]] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 3

[1,4,6,5,3,7,2] => [.,[[[.,[[.,.],.]],[.,.]],.]] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 2

[1,4,6,5,7,2,3] => [.,[[.,[[.,.],[.,.]]],[.,.]]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 3

[1,4,6,5,7,3,2] => [.,[[[.,[[.,.],[.,.]]],.],.]] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 2

[1,4,6,7,2,3,5] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[1,4,6,7,2,5,3] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[1,4,6,7,3,2,5] => [.,[[[.,[.,[.,.]]],.],[.,.]]] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 3

[1,4,6,7,3,5,2] => [.,[[[.,[.,[.,.]]],[.,.]],.]] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2

[1,4,6,7,5,2,3] => [.,[[.,[[.,[.,.]],.]],[.,.]]] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3

[1,4,6,7,5,3,2] => [.,[[[.,[[.,[.,.]],.]],.],.]] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2

[1,4,7,2,3,5,6] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[1,4,7,2,3,6,5] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[1,4,7,2,5,3,6] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[1,4,7,2,5,6,3] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3

[1,4,7,2,6,3,5] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[1,4,7,2,6,5,3] => [.,[[.,[.,.]],[[[.,.],.],.]]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3

[1,4,7,3,2,5,6] => [.,[[[.,[.,.]],.],[.,[.,.]]]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[1,4,7,3,2,6,5] => [.,[[[.,[.,.]],.],[[.,.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3

[1,4,7,3,5,2,6] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[1,4,7,3,5,6,2] => [.,[[[.,[.,.]],[.,[.,.]]],.]] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[1,4,7,3,6,2,5] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[1,4,7,3,6,5,2] => [.,[[[.,[.,.]],[[.,.],.]],.]] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2

[1,4,7,5,2,3,6] => [.,[[.,[[.,.],.]],[.,[.,.]]]] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 4

[1,4,7,5,2,6,3] => [.,[[.,[[.,.],.]],[[.,.],.]]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 3

[1,4,7,5,3,2,6] => [.,[[[.,[[.,.],.]],.],[.,.]]] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 3

[1,4,7,5,3,6,2] => [.,[[[.,[[.,.],.]],[.,.]],.]] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 2

[1,4,7,5,6,2,3] => [.,[[.,[[.,.],[.,.]]],[.,.]]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 3

[1,4,7,5,6,3,2] => [.,[[[.,[[.,.],[.,.]]],.],.]] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 2

[1,4,7,6,2,3,5] => [.,[[.,[[.,.],.]],[.,[.,.]]]] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 4

[1,4,7,6,2,5,3] => [.,[[.,[[.,.],.]],[[.,.],.]]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 3

[1,4,7,6,3,2,5] => [.,[[[.,[[.,.],.]],.],[.,.]]] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 3

[1,4,7,6,3,5,2] => [.,[[[.,[[.,.],.]],[.,.]],.]] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 2

[1,4,7,6,5,2,3] => [.,[[.,[[[.,.],.],.]],[.,.]]] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 3

[1,4,7,6,5,3,2] => [.,[[[.,[[[.,.],.],.]],.],.]] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 2

[1,5,2,3,4,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 6

[1,5,2,3,4,7,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 5

[1,5,2,3,6,4,7] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 5

[1,5,2,3,6,7,4] => [.,[[.,.],[.,[[.,[.,.]],.]]]] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 4

[1,5,2,3,7,4,6] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 5

[1,5,2,3,7,6,4] => [.,[[.,.],[.,[[[.,.],.],.]]]] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 4

[1,5,2,4,3,6,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 5

[1,5,2,4,3,7,6] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 4

[1,5,2,4,6,3,7] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 4

[1,5,2,4,6,7,3] => [.,[[.,.],[[.,[.,[.,.]]],.]]] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 3

[1,5,2,4,7,3,6] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 4

[1,5,2,4,7,6,3] => [.,[[.,.],[[.,[[.,.],.]],.]]] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 3

[1,5,2,6,3,4,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 5

[1,5,2,6,3,7,4] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 4

[1,5,2,6,4,3,7] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 4

[1,5,2,6,4,7,3] => [.,[[.,.],[[[.,.],[.,.]],.]]] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 3

[1,5,2,6,7,3,4] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 4

[1,5,2,6,7,4,3] => [.,[[.,.],[[[.,[.,.]],.],.]]] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 3

[1,5,2,7,3,4,6] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 5

[1,5,2,7,3,6,4] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 4

[1,5,2,7,4,3,6] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 4

[1,5,2,7,4,6,3] => [.,[[.,.],[[[.,.],[.,.]],.]]] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 3

[1,5,2,7,6,3,4] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 4

[1,5,2,7,6,4,3] => [.,[[.,.],[[[[.,.],.],.],.]]] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 3

[1,5,3,2,4,6,7] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 5

[1,5,3,2,4,7,6] => [.,[[[.,.],.],[.,[[.,.],.]]]] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 4

[1,5,3,2,6,4,7] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 4

[1,5,3,2,6,7,4] => [.,[[[.,.],.],[[.,[.,.]],.]]] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3

[1,5,3,2,7,4,6] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 4

[1,5,3,2,7,6,4] => [.,[[[.,.],.],[[[.,.],.],.]]] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 3

[1,5,3,4,2,6,7] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 4

[1,5,3,4,2,7,6] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 3

[1,5,3,4,6,2,7] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 3

[1,5,3,4,6,7,2] => [.,[[[.,.],[.,[.,[.,.]]]],.]] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2

[1,5,3,4,7,2,6] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 3

[1,5,3,4,7,6,2] => [.,[[[.,.],[.,[[.,.],.]]],.]] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 2

[1,5,3,6,2,4,7] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 4

[1,5,3,6,2,7,4] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 3

[1,5,3,6,4,2,7] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 3

[1,5,3,6,4,7,2] => [.,[[[.,.],[[.,.],[.,.]]],.]] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 2

[1,5,3,6,7,2,4] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 3

[1,5,3,6,7,4,2] => [.,[[[.,.],[[.,[.,.]],.]],.]] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 2

[1,5,3,7,2,4,6] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 4

[1,5,3,7,2,6,4] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 3

[1,5,3,7,4,2,6] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 3

[1,5,3,7,4,6,2] => [.,[[[.,.],[[.,.],[.,.]]],.]] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 2

[1,5,3,7,6,2,4] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 3

[1,5,3,7,6,4,2] => [.,[[[.,.],[[[.,.],.],.]],.]] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 2

[1,5,4,2,3,6,7] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 5

[1,5,4,2,3,7,6] => [.,[[[.,.],.],[.,[[.,.],.]]]] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 4

[1,5,4,2,6,3,7] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 4

[1,5,4,2,6,7,3] => [.,[[[.,.],.],[[.,[.,.]],.]]] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3

[1,5,4,2,7,3,6] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 4

[1,5,4,2,7,6,3] => [.,[[[.,.],.],[[[.,.],.],.]]] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 3

[1,5,4,3,2,6,7] => [.,[[[[.,.],.],.],[.,[.,.]]]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 4

[1,5,4,3,2,7,6] => [.,[[[[.,.],.],.],[[.,.],.]]] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 3

[1,5,4,3,6,2,7] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 3

[1,5,4,3,6,7,2] => [.,[[[[.,.],.],[.,[.,.]]],.]] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 2

[1,5,4,3,7,2,6] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 3

[1,5,4,3,7,6,2] => [.,[[[[.,.],.],[[.,.],.]],.]] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 2

[1,5,4,6,2,3,7] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 4

[1,5,4,6,2,7,3] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 3

[1,5,4,6,3,2,7] => [.,[[[[.,.],[.,.]],.],[.,.]]] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 3

[1,5,4,6,3,7,2] => [.,[[[[.,.],[.,.]],[.,.]],.]] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 2

[1,5,4,6,7,2,3] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 3

[1,5,4,6,7,3,2] => [.,[[[[.,.],[.,[.,.]]],.],.]] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 2

[1,5,4,7,2,3,6] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 4

[1,5,4,7,2,6,3] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 3

[1,5,4,7,3,2,6] => [.,[[[[.,.],[.,.]],.],[.,.]]] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 3

[1,5,4,7,3,6,2] => [.,[[[[.,.],[.,.]],[.,.]],.]] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 2

[1,5,4,7,6,2,3] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 3

[1,5,4,7,6,3,2] => [.,[[[[.,.],[[.,.],.]],.],.]] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 2

[1,5,6,2,3,4,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[1,5,6,2,3,7,4] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[1,5,6,2,4,3,7] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[1,5,6,2,4,7,3] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3

[1,5,6,2,7,3,4] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[1,5,6,2,7,4,3] => [.,[[.,[.,.]],[[[.,.],.],.]]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3

[1,5,6,3,2,4,7] => [.,[[[.,[.,.]],.],[.,[.,.]]]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[1,5,6,3,2,7,4] => [.,[[[.,[.,.]],.],[[.,.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3

[1,5,6,3,4,2,7] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[1,5,6,3,4,7,2] => [.,[[[.,[.,.]],[.,[.,.]]],.]] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[1,5,6,3,7,2,4] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[1,5,6,3,7,4,2] => [.,[[[.,[.,.]],[[.,.],.]],.]] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2

[1,5,6,4,2,3,7] => [.,[[[.,[.,.]],.],[.,[.,.]]]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[1,5,6,4,2,7,3] => [.,[[[.,[.,.]],.],[[.,.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3

[1,5,6,4,3,2,7] => [.,[[[[.,[.,.]],.],.],[.,.]]] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 3

[1,5,6,4,3,7,2] => [.,[[[[.,[.,.]],.],[.,.]],.]] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 2

[1,5,6,4,7,2,3] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[1,5,6,4,7,3,2] => [.,[[[[.,[.,.]],[.,.]],.],.]] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[1,5,6,7,2,3,4] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[1,5,6,7,2,4,3] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[1,5,6,7,3,2,4] => [.,[[[.,[.,[.,.]]],.],[.,.]]] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 3

[1,5,6,7,3,4,2] => [.,[[[.,[.,[.,.]]],[.,.]],.]] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2

[1,5,6,7,4,2,3] => [.,[[[.,[.,[.,.]]],.],[.,.]]] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 3

[1,5,6,7,4,3,2] => [.,[[[[.,[.,[.,.]]],.],.],.]] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 2

[1,5,7,2,3,4,6] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[1,5,7,2,3,6,4] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[1,5,7,2,4,3,6] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[1,5,7,2,4,6,3] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3

[1,5,7,2,6,3,4] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[1,5,7,2,6,4,3] => [.,[[.,[.,.]],[[[.,.],.],.]]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3

[1,5,7,3,2,4,6] => [.,[[[.,[.,.]],.],[.,[.,.]]]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[1,5,7,3,2,6,4] => [.,[[[.,[.,.]],.],[[.,.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3

[1,5,7,3,4,2,6] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[1,5,7,3,4,6,2] => [.,[[[.,[.,.]],[.,[.,.]]],.]] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[1,5,7,3,6,2,4] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[1,5,7,3,6,4,2] => [.,[[[.,[.,.]],[[.,.],.]],.]] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2

[1,5,7,4,2,3,6] => [.,[[[.,[.,.]],.],[.,[.,.]]]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[1,5,7,4,2,6,3] => [.,[[[.,[.,.]],.],[[.,.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3

[1,5,7,4,3,2,6] => [.,[[[[.,[.,.]],.],.],[.,.]]] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 3

[1,5,7,4,3,6,2] => [.,[[[[.,[.,.]],.],[.,.]],.]] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 2

[1,5,7,4,6,2,3] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[1,5,7,4,6,3,2] => [.,[[[[.,[.,.]],[.,.]],.],.]] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[1,5,7,6,2,3,4] => [.,[[.,[[.,.],.]],[.,[.,.]]]] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 4

[1,5,7,6,2,4,3] => [.,[[.,[[.,.],.]],[[.,.],.]]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 3

[1,5,7,6,3,2,4] => [.,[[[.,[[.,.],.]],.],[.,.]]] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 3

[1,5,7,6,3,4,2] => [.,[[[.,[[.,.],.]],[.,.]],.]] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 2

[1,5,7,6,4,2,3] => [.,[[[.,[[.,.],.]],.],[.,.]]] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 3

[1,5,7,6,4,3,2] => [.,[[[[.,[[.,.],.]],.],.],.]] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 2

[1,6,2,3,4,5,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 6

[1,6,2,3,4,7,5] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 5

[1,6,2,3,5,4,7] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 5

[1,6,2,3,5,7,4] => [.,[[.,.],[.,[[.,[.,.]],.]]]] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 4

[1,6,2,3,7,4,5] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 5

[1,6,2,3,7,5,4] => [.,[[.,.],[.,[[[.,.],.],.]]]] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 4

[1,6,2,4,3,5,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 5

[1,6,2,4,3,7,5] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 4

[1,6,2,4,5,3,7] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 4

[1,6,2,4,5,7,3] => [.,[[.,.],[[.,[.,[.,.]]],.]]] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 3

[1,6,2,4,7,3,5] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 4

[1,6,2,4,7,5,3] => [.,[[.,.],[[.,[[.,.],.]],.]]] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 3

[1,6,2,5,3,4,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 5

[1,6,2,5,3,7,4] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 4

[1,6,2,5,4,3,7] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 4

[1,6,2,5,4,7,3] => [.,[[.,.],[[[.,.],[.,.]],.]]] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 3

[1,6,2,5,7,3,4] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 4

[1,6,2,5,7,4,3] => [.,[[.,.],[[[.,[.,.]],.],.]]] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 3

[1,6,2,7,3,4,5] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 5

[1,6,2,7,3,5,4] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 4

[1,6,2,7,4,3,5] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 4

[1,6,2,7,4,5,3] => [.,[[.,.],[[[.,.],[.,.]],.]]] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 3

[1,6,2,7,5,3,4] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 4

[1,6,2,7,5,4,3] => [.,[[.,.],[[[[.,.],.],.],.]]] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 3

[1,6,3,2,4,5,7] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 5

[1,6,3,2,4,7,5] => [.,[[[.,.],.],[.,[[.,.],.]]]] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 4

[1,6,3,2,5,4,7] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 4

[1,6,3,2,5,7,4] => [.,[[[.,.],.],[[.,[.,.]],.]]] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3

[1,6,3,2,7,4,5] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 4

[1,6,3,2,7,5,4] => [.,[[[.,.],.],[[[.,.],.],.]]] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 3

[1,6,3,4,2,5,7] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 4

[1,6,3,4,2,7,5] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 3

[1,6,3,4,5,2,7] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 3

[1,6,3,4,5,7,2] => [.,[[[.,.],[.,[.,[.,.]]]],.]] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2

[1,6,3,4,7,2,5] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 3

[1,6,3,4,7,5,2] => [.,[[[.,.],[.,[[.,.],.]]],.]] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 2

[1,6,3,5,2,4,7] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 4

[1,6,3,5,2,7,4] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 3

[1,6,3,5,4,2,7] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 3

[1,6,3,5,4,7,2] => [.,[[[.,.],[[.,.],[.,.]]],.]] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 2

[1,6,3,5,7,2,4] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 3

[1,6,3,5,7,4,2] => [.,[[[.,.],[[.,[.,.]],.]],.]] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 2

[1,6,3,7,2,4,5] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 4

[1,6,3,7,2,5,4] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 3

[1,6,3,7,4,2,5] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 3

[1,6,3,7,4,5,2] => [.,[[[.,.],[[.,.],[.,.]]],.]] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 2

[1,6,3,7,5,2,4] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 3

[1,6,3,7,5,4,2] => [.,[[[.,.],[[[.,.],.],.]],.]] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 2

[1,6,4,2,3,5,7] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 5

[1,6,4,2,3,7,5] => [.,[[[.,.],.],[.,[[.,.],.]]]] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 4

[1,6,4,2,5,3,7] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 4

[1,6,4,2,5,7,3] => [.,[[[.,.],.],[[.,[.,.]],.]]] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3

[1,6,4,2,7,3,5] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 4

[1,6,4,2,7,5,3] => [.,[[[.,.],.],[[[.,.],.],.]]] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 3

[1,6,4,3,2,5,7] => [.,[[[[.,.],.],.],[.,[.,.]]]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 4

[1,6,4,3,2,7,5] => [.,[[[[.,.],.],.],[[.,.],.]]] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 3

[1,6,4,3,5,2,7] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 3

[1,6,4,3,5,7,2] => [.,[[[[.,.],.],[.,[.,.]]],.]] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 2

[1,6,4,3,7,2,5] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 3

[1,6,4,3,7,5,2] => [.,[[[[.,.],.],[[.,.],.]],.]] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 2

[1,6,4,5,2,3,7] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 4

[1,6,4,5,2,7,3] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 3

[1,6,4,5,3,2,7] => [.,[[[[.,.],[.,.]],.],[.,.]]] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 3

[1,6,4,5,3,7,2] => [.,[[[[.,.],[.,.]],[.,.]],.]] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 2

[1,6,4,5,7,2,3] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 3

[1,6,4,5,7,3,2] => [.,[[[[.,.],[.,[.,.]]],.],.]] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 2

[1,6,4,7,2,3,5] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 4

[1,6,4,7,2,5,3] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 3

[1,6,4,7,3,2,5] => [.,[[[[.,.],[.,.]],.],[.,.]]] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 3

[1,6,4,7,3,5,2] => [.,[[[[.,.],[.,.]],[.,.]],.]] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 2

[1,6,4,7,5,2,3] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 3

[1,6,4,7,5,3,2] => [.,[[[[.,.],[[.,.],.]],.],.]] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 2

[1,6,5,2,3,4,7] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 5

[1,6,5,2,3,7,4] => [.,[[[.,.],.],[.,[[.,.],.]]]] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 4

[1,6,5,2,4,3,7] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 4

[1,6,5,2,4,7,3] => [.,[[[.,.],.],[[.,[.,.]],.]]] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3

[1,6,5,2,7,3,4] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 4

[1,6,5,2,7,4,3] => [.,[[[.,.],.],[[[.,.],.],.]]] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 3

[1,6,5,3,2,4,7] => [.,[[[[.,.],.],.],[.,[.,.]]]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 4

[1,6,5,3,2,7,4] => [.,[[[[.,.],.],.],[[.,.],.]]] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 3

[1,6,5,3,4,2,7] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 3

[1,6,5,3,4,7,2] => [.,[[[[.,.],.],[.,[.,.]]],.]] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 2

[1,6,5,3,7,2,4] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 3

[1,6,5,3,7,4,2] => [.,[[[[.,.],.],[[.,.],.]],.]] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 2

[1,6,5,4,2,3,7] => [.,[[[[.,.],.],.],[.,[.,.]]]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 4

[1,6,5,4,2,7,3] => [.,[[[[.,.],.],.],[[.,.],.]]] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 3

[1,6,5,4,3,2,7] => [.,[[[[[.,.],.],.],.],[.,.]]] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 3

[1,6,5,4,3,7,2] => [.,[[[[[.,.],.],.],[.,.]],.]] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 2

[1,6,5,4,7,2,3] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 3

[1,6,5,4,7,3,2] => [.,[[[[[.,.],.],[.,.]],.],.]] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 2

[1,6,5,7,2,3,4] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 4

[1,6,5,7,2,4,3] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 3

[1,6,5,7,3,2,4] => [.,[[[[.,.],[.,.]],.],[.,.]]] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 3

[1,6,5,7,3,4,2] => [.,[[[[.,.],[.,.]],[.,.]],.]] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 2

[1,6,5,7,4,2,3] => [.,[[[[.,.],[.,.]],.],[.,.]]] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 3

[1,6,5,7,4,3,2] => [.,[[[[[.,.],[.,.]],.],.],.]] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 2

[1,6,7,2,3,4,5] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[1,6,7,2,3,5,4] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[1,6,7,2,4,3,5] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[1,6,7,2,4,5,3] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3

[1,6,7,2,5,3,4] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[1,6,7,2,5,4,3] => [.,[[.,[.,.]],[[[.,.],.],.]]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3

[1,6,7,3,2,4,5] => [.,[[[.,[.,.]],.],[.,[.,.]]]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[1,6,7,3,2,5,4] => [.,[[[.,[.,.]],.],[[.,.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3

[1,6,7,3,4,2,5] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[1,6,7,3,4,5,2] => [.,[[[.,[.,.]],[.,[.,.]]],.]] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[1,6,7,3,5,2,4] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[1,6,7,3,5,4,2] => [.,[[[.,[.,.]],[[.,.],.]],.]] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2

[1,6,7,4,2,3,5] => [.,[[[.,[.,.]],.],[.,[.,.]]]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[1,6,7,4,2,5,3] => [.,[[[.,[.,.]],.],[[.,.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3

[1,6,7,4,3,2,5] => [.,[[[[.,[.,.]],.],.],[.,.]]] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 3

[1,6,7,4,3,5,2] => [.,[[[[.,[.,.]],.],[.,.]],.]] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 2

[1,6,7,4,5,2,3] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[1,6,7,4,5,3,2] => [.,[[[[.,[.,.]],[.,.]],.],.]] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[1,6,7,5,2,3,4] => [.,[[[.,[.,.]],.],[.,[.,.]]]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[1,6,7,5,2,4,3] => [.,[[[.,[.,.]],.],[[.,.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3

[1,6,7,5,3,2,4] => [.,[[[[.,[.,.]],.],.],[.,.]]] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 3

[1,6,7,5,3,4,2] => [.,[[[[.,[.,.]],.],[.,.]],.]] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 2

[1,6,7,5,4,2,3] => [.,[[[[.,[.,.]],.],.],[.,.]]] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 3

[1,6,7,5,4,3,2] => [.,[[[[[.,[.,.]],.],.],.],.]] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2

[1,7,2,3,4,5,6] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 6

[1,7,2,3,4,6,5] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 5

[1,7,2,3,5,4,6] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 5

[1,7,2,3,5,6,4] => [.,[[.,.],[.,[[.,[.,.]],.]]]] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 4

[1,7,2,3,6,4,5] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 5

[1,7,2,3,6,5,4] => [.,[[.,.],[.,[[[.,.],.],.]]]] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 4

[1,7,2,4,3,5,6] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 5

[1,7,2,4,3,6,5] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 4

[1,7,2,4,5,3,6] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 4

[1,7,2,4,5,6,3] => [.,[[.,.],[[.,[.,[.,.]]],.]]] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 3

[1,7,2,4,6,3,5] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 4

[1,7,2,4,6,5,3] => [.,[[.,.],[[.,[[.,.],.]],.]]] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 3

[1,7,2,5,3,4,6] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 5

[1,7,2,5,3,6,4] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 4

[1,7,2,5,4,3,6] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 4

[1,7,2,5,4,6,3] => [.,[[.,.],[[[.,.],[.,.]],.]]] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 3

[1,7,2,5,6,3,4] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 4

[1,7,2,5,6,4,3] => [.,[[.,.],[[[.,[.,.]],.],.]]] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 3

[1,7,2,6,3,4,5] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 5

[1,7,2,6,3,5,4] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 4

[1,7,2,6,4,3,5] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 4

[1,7,2,6,4,5,3] => [.,[[.,.],[[[.,.],[.,.]],.]]] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 3

[1,7,2,6,5,3,4] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 4

[1,7,2,6,5,4,3] => [.,[[.,.],[[[[.,.],.],.],.]]] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 3

[1,7,3,2,4,5,6] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 5

[1,7,3,2,4,6,5] => [.,[[[.,.],.],[.,[[.,.],.]]]] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 4

[1,7,3,2,5,4,6] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 4

[1,7,3,2,5,6,4] => [.,[[[.,.],.],[[.,[.,.]],.]]] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3

[1,7,3,2,6,4,5] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 4

[1,7,3,2,6,5,4] => [.,[[[.,.],.],[[[.,.],.],.]]] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 3

[1,7,3,4,2,5,6] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 4

[1,7,3,4,2,6,5] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 3

[1,7,3,4,5,2,6] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 3

[1,7,3,4,5,6,2] => [.,[[[.,.],[.,[.,[.,.]]]],.]] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2

[1,7,3,4,6,2,5] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 3

[1,7,3,4,6,5,2] => [.,[[[.,.],[.,[[.,.],.]]],.]] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 2

[1,7,3,5,2,4,6] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 4

[1,7,3,5,2,6,4] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 3

[1,7,3,5,4,2,6] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 3

[1,7,3,5,4,6,2] => [.,[[[.,.],[[.,.],[.,.]]],.]] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 2

[1,7,3,5,6,2,4] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 3

[1,7,3,5,6,4,2] => [.,[[[.,.],[[.,[.,.]],.]],.]] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 2

[1,7,3,6,2,4,5] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 4

[1,7,3,6,2,5,4] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 3

[1,7,3,6,4,2,5] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 3

[1,7,3,6,4,5,2] => [.,[[[.,.],[[.,.],[.,.]]],.]] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 2

[1,7,3,6,5,2,4] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 3

[1,7,3,6,5,4,2] => [.,[[[.,.],[[[.,.],.],.]],.]] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 2

[1,7,4,2,3,5,6] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 5

[1,7,4,2,3,6,5] => [.,[[[.,.],.],[.,[[.,.],.]]]] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 4

[1,7,4,2,5,3,6] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 4

[1,7,4,2,5,6,3] => [.,[[[.,.],.],[[.,[.,.]],.]]] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3

[1,7,4,2,6,3,5] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 4

[1,7,4,2,6,5,3] => [.,[[[.,.],.],[[[.,.],.],.]]] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 3

[1,7,4,3,2,5,6] => [.,[[[[.,.],.],.],[.,[.,.]]]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 4

[1,7,4,3,2,6,5] => [.,[[[[.,.],.],.],[[.,.],.]]] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 3

[1,7,4,3,5,2,6] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 3

[1,7,4,3,5,6,2] => [.,[[[[.,.],.],[.,[.,.]]],.]] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 2

[1,7,4,3,6,2,5] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 3

[1,7,4,3,6,5,2] => [.,[[[[.,.],.],[[.,.],.]],.]] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 2

[1,7,4,5,2,3,6] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 4

[1,7,4,5,2,6,3] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 3

[1,7,4,5,3,2,6] => [.,[[[[.,.],[.,.]],.],[.,.]]] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 3

[1,7,4,5,3,6,2] => [.,[[[[.,.],[.,.]],[.,.]],.]] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 2

[1,7,4,5,6,2,3] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 3

[1,7,4,5,6,3,2] => [.,[[[[.,.],[.,[.,.]]],.],.]] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 2

[1,7,4,6,2,3,5] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 4

[1,7,4,6,2,5,3] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 3

[1,7,4,6,3,2,5] => [.,[[[[.,.],[.,.]],.],[.,.]]] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 3

[1,7,4,6,3,5,2] => [.,[[[[.,.],[.,.]],[.,.]],.]] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 2

[1,7,4,6,5,2,3] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 3

[1,7,4,6,5,3,2] => [.,[[[[.,.],[[.,.],.]],.],.]] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 2

[1,7,5,2,3,4,6] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 5

[1,7,5,2,3,6,4] => [.,[[[.,.],.],[.,[[.,.],.]]]] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 4

[1,7,5,2,4,3,6] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 4

[1,7,5,2,4,6,3] => [.,[[[.,.],.],[[.,[.,.]],.]]] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3

[1,7,5,2,6,3,4] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 4

[1,7,5,2,6,4,3] => [.,[[[.,.],.],[[[.,.],.],.]]] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 3

[1,7,5,3,2,4,6] => [.,[[[[.,.],.],.],[.,[.,.]]]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 4

[1,7,5,3,2,6,4] => [.,[[[[.,.],.],.],[[.,.],.]]] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 3

[1,7,5,3,4,2,6] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 3

[1,7,5,3,4,6,2] => [.,[[[[.,.],.],[.,[.,.]]],.]] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 2

[1,7,5,3,6,2,4] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 3

[1,7,5,3,6,4,2] => [.,[[[[.,.],.],[[.,.],.]],.]] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 2

[1,7,5,4,2,3,6] => [.,[[[[.,.],.],.],[.,[.,.]]]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 4

[1,7,5,4,2,6,3] => [.,[[[[.,.],.],.],[[.,.],.]]] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 3

[1,7,5,4,3,2,6] => [.,[[[[[.,.],.],.],.],[.,.]]] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 3

[1,7,5,4,3,6,2] => [.,[[[[[.,.],.],.],[.,.]],.]] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 2

[1,7,5,4,6,2,3] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 3

[1,7,5,4,6,3,2] => [.,[[[[[.,.],.],[.,.]],.],.]] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 2

[1,7,5,6,2,3,4] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 4

[1,7,5,6,2,4,3] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 3

[1,7,5,6,3,2,4] => [.,[[[[.,.],[.,.]],.],[.,.]]] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 3

[1,7,5,6,3,4,2] => [.,[[[[.,.],[.,.]],[.,.]],.]] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 2

[1,7,5,6,4,2,3] => [.,[[[[.,.],[.,.]],.],[.,.]]] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 3

[1,7,5,6,4,3,2] => [.,[[[[[.,.],[.,.]],.],.],.]] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 2

[1,7,6,2,3,4,5] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 5

[1,7,6,2,3,5,4] => [.,[[[.,.],.],[.,[[.,.],.]]]] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 4

[1,7,6,2,4,3,5] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 4

[1,7,6,2,4,5,3] => [.,[[[.,.],.],[[.,[.,.]],.]]] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3

[1,7,6,2,5,3,4] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 4

[1,7,6,2,5,4,3] => [.,[[[.,.],.],[[[.,.],.],.]]] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 3

[1,7,6,3,2,4,5] => [.,[[[[.,.],.],.],[.,[.,.]]]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 4

[1,7,6,3,2,5,4] => [.,[[[[.,.],.],.],[[.,.],.]]] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 3

[1,7,6,3,4,2,5] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 3

[1,7,6,3,4,5,2] => [.,[[[[.,.],.],[.,[.,.]]],.]] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 2

[1,7,6,3,5,2,4] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 3

[1,7,6,3,5,4,2] => [.,[[[[.,.],.],[[.,.],.]],.]] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 2

[1,7,6,4,2,3,5] => [.,[[[[.,.],.],.],[.,[.,.]]]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 4

[1,7,6,4,2,5,3] => [.,[[[[.,.],.],.],[[.,.],.]]] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 3

[1,7,6,4,3,2,5] => [.,[[[[[.,.],.],.],.],[.,.]]] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 3

[1,7,6,4,3,5,2] => [.,[[[[[.,.],.],.],[.,.]],.]] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 2

[1,7,6,4,5,2,3] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 3

[1,7,6,4,5,3,2] => [.,[[[[[.,.],.],[.,.]],.],.]] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 2

[1,7,6,5,2,3,4] => [.,[[[[.,.],.],.],[.,[.,.]]]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 4

[1,7,6,5,2,4,3] => [.,[[[[.,.],.],.],[[.,.],.]]] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 3

[1,7,6,5,3,2,4] => [.,[[[[[.,.],.],.],.],[.,.]]] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 3

[1,7,6,5,3,4,2] => [.,[[[[[.,.],.],.],[.,.]],.]] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 2

[1,7,6,5,4,2,3] => [.,[[[[[.,.],.],.],.],[.,.]]] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 3

[1,7,6,5,4,3,2] => [.,[[[[[[.,.],.],.],.],.],.]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 2

[2,1,3,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6

[2,1,3,4,5,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 5

[2,1,3,4,6,5,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 5

[2,1,3,4,6,7,5] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 4

[2,1,3,4,7,5,6] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 5

[2,1,3,4,7,6,5] => [[.,.],[.,[.,[[[.,.],.],.]]]] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 4

[2,1,3,5,4,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5

[2,1,3,5,4,7,6] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4

[2,1,3,5,6,4,7] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4

[2,1,3,5,6,7,4] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 3

[2,1,3,5,7,4,6] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4

[2,1,3,5,7,6,4] => [[.,.],[.,[[.,[[.,.],.]],.]]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 3

[2,1,3,6,4,5,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5

[2,1,3,6,4,7,5] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4

[2,1,3,6,5,4,7] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 4

[2,1,3,6,5,7,4] => [[.,.],[.,[[[.,.],[.,.]],.]]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 3

[2,1,3,6,7,4,5] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4

[2,1,3,6,7,5,4] => [[.,.],[.,[[[.,[.,.]],.],.]]] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 3

[2,1,3,7,4,5,6] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5

[2,1,3,7,4,6,5] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4

[2,1,3,7,5,4,6] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 4

[2,1,3,7,5,6,4] => [[.,.],[.,[[[.,.],[.,.]],.]]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 3

[2,1,3,7,6,4,5] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 4

[2,1,3,7,6,5,4] => [[.,.],[.,[[[[.,.],.],.],.]]] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 3

[2,1,4,3,5,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[2,1,4,3,5,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[2,1,4,3,6,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[2,1,4,3,6,7,5] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[2,1,4,3,7,5,6] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[2,1,4,3,7,6,5] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[2,1,4,5,3,6,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[2,1,4,5,3,7,6] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[2,1,4,5,6,3,7] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[2,1,4,5,6,7,3] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2

[2,1,4,5,7,3,6] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[2,1,4,5,7,6,3] => [[.,.],[[.,[.,[[.,.],.]]],.]] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 2

[2,1,4,6,3,5,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[2,1,4,6,3,7,5] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[2,1,4,6,5,3,7] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3

[2,1,4,6,5,7,3] => [[.,.],[[.,[[.,.],[.,.]]],.]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 2

[2,1,4,6,7,3,5] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[2,1,4,6,7,5,3] => [[.,.],[[.,[[.,[.,.]],.]],.]] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 2

[2,1,4,7,3,5,6] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[2,1,4,7,3,6,5] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[2,1,4,7,5,3,6] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3

[2,1,4,7,5,6,3] => [[.,.],[[.,[[.,.],[.,.]]],.]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 2

[2,1,4,7,6,3,5] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3

[2,1,4,7,6,5,3] => [[.,.],[[.,[[[.,.],.],.]],.]] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 2

[2,1,5,3,4,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[2,1,5,3,4,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[2,1,5,3,6,4,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[2,1,5,3,6,7,4] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[2,1,5,3,7,4,6] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[2,1,5,3,7,6,4] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[2,1,5,4,3,6,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[2,1,5,4,3,7,6] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[2,1,5,4,6,3,7] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[2,1,5,4,6,7,3] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 2

[2,1,5,4,7,3,6] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[2,1,5,4,7,6,3] => [[.,.],[[[.,.],[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2

[2,1,5,6,3,4,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[2,1,5,6,3,7,4] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[2,1,5,6,4,3,7] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[2,1,5,6,4,7,3] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2

[2,1,5,6,7,3,4] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[2,1,5,6,7,4,3] => [[.,.],[[[.,[.,[.,.]]],.],.]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2

[2,1,5,7,3,4,6] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[2,1,5,7,3,6,4] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[2,1,5,7,4,3,6] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[2,1,5,7,4,6,3] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2

[2,1,5,7,6,3,4] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3

[2,1,5,7,6,4,3] => [[.,.],[[[.,[[.,.],.]],.],.]] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 2

[2,1,6,3,4,5,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[2,1,6,3,4,7,5] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[2,1,6,3,5,4,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[2,1,6,3,5,7,4] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[2,1,6,3,7,4,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[2,1,6,3,7,5,4] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[2,1,6,4,3,5,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[2,1,6,4,3,7,5] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[2,1,6,4,5,3,7] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[2,1,6,4,5,7,3] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 2

[2,1,6,4,7,3,5] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[2,1,6,4,7,5,3] => [[.,.],[[[.,.],[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2

[2,1,6,5,3,4,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[2,1,6,5,3,7,4] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[2,1,6,5,4,3,7] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[2,1,6,5,4,7,3] => [[.,.],[[[[.,.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2

[2,1,6,5,7,3,4] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[2,1,6,5,7,4,3] => [[.,.],[[[[.,.],[.,.]],.],.]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 2

[2,1,6,7,3,4,5] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[2,1,6,7,3,5,4] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[2,1,6,7,4,3,5] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[2,1,6,7,4,5,3] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2

[2,1,6,7,5,3,4] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[2,1,6,7,5,4,3] => [[.,.],[[[[.,[.,.]],.],.],.]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 2

[2,1,7,3,4,5,6] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[2,1,7,3,4,6,5] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[2,1,7,3,5,4,6] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[2,1,7,3,5,6,4] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[2,1,7,3,6,4,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[2,1,7,3,6,5,4] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[2,1,7,4,3,5,6] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[2,1,7,4,3,6,5] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[2,1,7,4,5,3,6] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[2,1,7,4,5,6,3] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 2

[2,1,7,4,6,3,5] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[2,1,7,4,6,5,3] => [[.,.],[[[.,.],[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2

[2,1,7,5,3,4,6] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[2,1,7,5,3,6,4] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[2,1,7,5,4,3,6] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[2,1,7,5,4,6,3] => [[.,.],[[[[.,.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2

[2,1,7,5,6,3,4] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[2,1,7,5,6,4,3] => [[.,.],[[[[.,.],[.,.]],.],.]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 2

[2,1,7,6,3,4,5] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[2,1,7,6,3,5,4] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[2,1,7,6,4,3,5] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[2,1,7,6,4,5,3] => [[.,.],[[[[.,.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2

[2,1,7,6,5,3,4] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[2,1,7,6,5,4,3] => [[.,.],[[[[[.,.],.],.],.],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2

[2,3,1,4,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[2,3,1,4,5,7,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[2,3,1,4,6,5,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[2,3,1,4,6,7,5] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[2,3,1,4,7,5,6] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[2,3,1,4,7,6,5] => [[.,[.,.]],[.,[[[.,.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[2,3,1,5,4,6,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[2,3,1,5,4,7,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[2,3,1,5,6,4,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[2,3,1,5,6,7,4] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[2,3,1,5,7,4,6] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[2,3,1,5,7,6,4] => [[.,[.,.]],[[.,[[.,.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[2,3,1,6,4,5,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[2,3,1,6,4,7,5] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[2,3,1,6,5,4,7] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[2,3,1,6,5,7,4] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[2,3,1,6,7,4,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[2,3,1,6,7,5,4] => [[.,[.,.]],[[[.,[.,.]],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[2,3,1,7,4,5,6] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[2,3,1,7,4,6,5] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[2,3,1,7,5,4,6] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[2,3,1,7,5,6,4] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[2,3,1,7,6,4,5] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[2,3,1,7,6,5,4] => [[.,[.,.]],[[[[.,.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[2,3,4,1,5,6,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[2,3,4,1,5,7,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[2,3,4,1,6,5,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,3,4,1,6,7,5] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[2,3,4,1,7,5,6] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,3,4,1,7,6,5] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[2,3,4,5,1,6,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[2,3,4,5,1,7,6] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[2,3,4,5,6,1,7] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2

[2,3,4,5,6,7,1] => [[.,[.,[.,[.,[.,[.,.]]]]]],.] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1

[2,3,4,5,7,1,6] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2

[2,3,4,5,7,6,1] => [[.,[.,[.,[.,[[.,.],.]]]]],.] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 1

[2,3,4,6,1,5,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[2,3,4,6,1,7,5] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[2,3,4,6,5,1,7] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 2

[2,3,4,6,5,7,1] => [[.,[.,[.,[[.,.],[.,.]]]]],.] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1

[2,3,4,6,7,1,5] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2

[2,3,4,6,7,5,1] => [[.,[.,[.,[[.,[.,.]],.]]]],.] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 1

[2,3,4,7,1,5,6] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[2,3,4,7,1,6,5] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[2,3,4,7,5,1,6] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 2

[2,3,4,7,5,6,1] => [[.,[.,[.,[[.,.],[.,.]]]]],.] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1

[2,3,4,7,6,1,5] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 2

[2,3,4,7,6,5,1] => [[.,[.,[.,[[[.,.],.],.]]]],.] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 1

[2,3,5,1,4,6,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[2,3,5,1,4,7,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[2,3,5,1,6,4,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,3,5,1,6,7,4] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[2,3,5,1,7,4,6] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,3,5,1,7,6,4] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[2,3,5,4,1,6,7] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 3

[2,3,5,4,1,7,6] => [[.,[.,[[.,.],.]]],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 2

[2,3,5,4,6,1,7] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 2

[2,3,5,4,6,7,1] => [[.,[.,[[.,.],[.,[.,.]]]]],.] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1

[2,3,5,4,7,1,6] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 2

[2,3,5,4,7,6,1] => [[.,[.,[[.,.],[[.,.],.]]]],.] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 1

[2,3,5,6,1,4,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[2,3,5,6,1,7,4] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[2,3,5,6,4,1,7] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 2

[2,3,5,6,4,7,1] => [[.,[.,[[.,[.,.]],[.,.]]]],.] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1

[2,3,5,6,7,1,4] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2

[2,3,5,6,7,4,1] => [[.,[.,[[.,[.,[.,.]]],.]]],.] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 1

[2,3,5,7,1,4,6] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[2,3,5,7,1,6,4] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[2,3,5,7,4,1,6] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 2

[2,3,5,7,4,6,1] => [[.,[.,[[.,[.,.]],[.,.]]]],.] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1

[2,3,5,7,6,1,4] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 2

[2,3,5,7,6,4,1] => [[.,[.,[[.,[[.,.],.]],.]]],.] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1

[2,3,6,1,4,5,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[2,3,6,1,4,7,5] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[2,3,6,1,5,4,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,3,6,1,5,7,4] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[2,3,6,1,7,4,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,3,6,1,7,5,4] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[2,3,6,4,1,5,7] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 3

[2,3,6,4,1,7,5] => [[.,[.,[[.,.],.]]],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 2

[2,3,6,4,5,1,7] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 2

[2,3,6,4,5,7,1] => [[.,[.,[[.,.],[.,[.,.]]]]],.] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1

[2,3,6,4,7,1,5] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 2

[2,3,6,4,7,5,1] => [[.,[.,[[.,.],[[.,.],.]]]],.] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 1

[2,3,6,5,1,4,7] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 3

[2,3,6,5,1,7,4] => [[.,[.,[[.,.],.]]],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 2

[2,3,6,5,4,1,7] => [[.,[.,[[[.,.],.],.]]],[.,.]] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 2

[2,3,6,5,4,7,1] => [[.,[.,[[[.,.],.],[.,.]]]],.] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 1

[2,3,6,5,7,1,4] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 2

[2,3,6,5,7,4,1] => [[.,[.,[[[.,.],[.,.]],.]]],.] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1

[2,3,6,7,1,4,5] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[2,3,6,7,1,5,4] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[2,3,6,7,4,1,5] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 2

[2,3,6,7,4,5,1] => [[.,[.,[[.,[.,.]],[.,.]]]],.] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1

[2,3,6,7,5,1,4] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 2

[2,3,6,7,5,4,1] => [[.,[.,[[[.,[.,.]],.],.]]],.] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 1

[2,3,7,1,4,5,6] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[2,3,7,1,4,6,5] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[2,3,7,1,5,4,6] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,3,7,1,5,6,4] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[2,3,7,1,6,4,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,3,7,1,6,5,4] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[2,3,7,4,1,5,6] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 3

[2,3,7,4,1,6,5] => [[.,[.,[[.,.],.]]],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 2

[2,3,7,4,5,1,6] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 2

[2,3,7,4,5,6,1] => [[.,[.,[[.,.],[.,[.,.]]]]],.] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1

[2,3,7,4,6,1,5] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 2

[2,3,7,4,6,5,1] => [[.,[.,[[.,.],[[.,.],.]]]],.] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 1

[2,3,7,5,1,4,6] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 3

[2,3,7,5,1,6,4] => [[.,[.,[[.,.],.]]],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 2

[2,3,7,5,4,1,6] => [[.,[.,[[[.,.],.],.]]],[.,.]] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 2

[2,3,7,5,4,6,1] => [[.,[.,[[[.,.],.],[.,.]]]],.] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 1

[2,3,7,5,6,1,4] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 2

[2,3,7,5,6,4,1] => [[.,[.,[[[.,.],[.,.]],.]]],.] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1

[2,3,7,6,1,4,5] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 3

[2,3,7,6,1,5,4] => [[.,[.,[[.,.],.]]],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 2

[2,3,7,6,4,1,5] => [[.,[.,[[[.,.],.],.]]],[.,.]] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 2

[2,3,7,6,4,5,1] => [[.,[.,[[[.,.],.],[.,.]]]],.] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 1

[2,3,7,6,5,1,4] => [[.,[.,[[[.,.],.],.]]],[.,.]] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 2

[2,3,7,6,5,4,1] => [[.,[.,[[[[.,.],.],.],.]]],.] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 1

[2,4,1,3,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[2,4,1,3,5,7,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[2,4,1,3,6,5,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[2,4,1,3,6,7,5] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[2,4,1,3,7,5,6] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[2,4,1,3,7,6,5] => [[.,[.,.]],[.,[[[.,.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[2,4,1,5,3,6,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[2,4,1,5,3,7,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[2,4,1,5,6,3,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[2,4,1,5,6,7,3] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[2,4,1,5,7,3,6] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[2,4,1,5,7,6,3] => [[.,[.,.]],[[.,[[.,.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[2,4,1,6,3,5,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[2,4,1,6,3,7,5] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[2,4,1,6,5,3,7] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[2,4,1,6,5,7,3] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[2,4,1,6,7,3,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[2,4,1,6,7,5,3] => [[.,[.,.]],[[[.,[.,.]],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[2,4,1,7,3,5,6] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[2,4,1,7,3,6,5] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[2,4,1,7,5,3,6] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[2,4,1,7,5,6,3] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[2,4,1,7,6,3,5] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[2,4,1,7,6,5,3] => [[.,[.,.]],[[[[.,.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[2,4,3,1,5,6,7] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4

[2,4,3,1,5,7,6] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 3

[2,4,3,1,6,5,7] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[2,4,3,1,6,7,5] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 2

[2,4,3,1,7,5,6] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[2,4,3,1,7,6,5] => [[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2

[2,4,3,5,1,6,7] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[2,4,3,5,1,7,6] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2

[2,4,3,5,6,1,7] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2

[2,4,3,5,6,7,1] => [[.,[[.,.],[.,[.,[.,.]]]]],.] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1

[2,4,3,5,7,1,6] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2

[2,4,3,5,7,6,1] => [[.,[[.,.],[.,[[.,.],.]]]],.] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 1

[2,4,3,6,1,5,7] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[2,4,3,6,1,7,5] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2

[2,4,3,6,5,1,7] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2

[2,4,3,6,5,7,1] => [[.,[[.,.],[[.,.],[.,.]]]],.] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 1

[2,4,3,6,7,1,5] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2

[2,4,3,6,7,5,1] => [[.,[[.,.],[[.,[.,.]],.]]],.] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 1

[2,4,3,7,1,5,6] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[2,4,3,7,1,6,5] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2

[2,4,3,7,5,1,6] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2

[2,4,3,7,5,6,1] => [[.,[[.,.],[[.,.],[.,.]]]],.] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 1

[2,4,3,7,6,1,5] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2

[2,4,3,7,6,5,1] => [[.,[[.,.],[[[.,.],.],.]]],.] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 1

[2,4,5,1,3,6,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[2,4,5,1,3,7,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[2,4,5,1,6,3,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,4,5,1,6,7,3] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[2,4,5,1,7,3,6] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,4,5,1,7,6,3] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[2,4,5,3,1,6,7] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[2,4,5,3,1,7,6] => [[.,[[.,[.,.]],.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[2,4,5,3,6,1,7] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[2,4,5,3,6,7,1] => [[.,[[.,[.,.]],[.,[.,.]]]],.] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1

[2,4,5,3,7,1,6] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[2,4,5,3,7,6,1] => [[.,[[.,[.,.]],[[.,.],.]]],.] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1

[2,4,5,6,1,3,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[2,4,5,6,1,7,3] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[2,4,5,6,3,1,7] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 2

[2,4,5,6,3,7,1] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1

[2,4,5,6,7,1,3] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2

[2,4,5,6,7,3,1] => [[.,[[.,[.,[.,[.,.]]]],.]],.] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 1

[2,4,5,7,1,3,6] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[2,4,5,7,1,6,3] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[2,4,5,7,3,1,6] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 2

[2,4,5,7,3,6,1] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1

[2,4,5,7,6,1,3] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 2

[2,4,5,7,6,3,1] => [[.,[[.,[.,[[.,.],.]]],.]],.] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[2,4,6,1,3,5,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[2,4,6,1,3,7,5] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[2,4,6,1,5,3,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,4,6,1,5,7,3] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[2,4,6,1,7,3,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,4,6,1,7,5,3] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[2,4,6,3,1,5,7] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[2,4,6,3,1,7,5] => [[.,[[.,[.,.]],.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[2,4,6,3,5,1,7] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[2,4,6,3,5,7,1] => [[.,[[.,[.,.]],[.,[.,.]]]],.] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1

[2,4,6,3,7,1,5] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[2,4,6,3,7,5,1] => [[.,[[.,[.,.]],[[.,.],.]]],.] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1

[2,4,6,5,1,3,7] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 3

[2,4,6,5,1,7,3] => [[.,[.,[[.,.],.]]],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 2

[2,4,6,5,3,1,7] => [[.,[[.,[[.,.],.]],.]],[.,.]] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 2

[2,4,6,5,3,7,1] => [[.,[[.,[[.,.],.]],[.,.]]],.] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[2,4,6,5,7,1,3] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 2

[2,4,6,5,7,3,1] => [[.,[[.,[[.,.],[.,.]]],.]],.] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1

[2,4,6,7,1,3,5] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[2,4,6,7,1,5,3] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[2,4,6,7,3,1,5] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 2

[2,4,6,7,3,5,1] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1

[2,4,6,7,5,1,3] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 2

[2,4,6,7,5,3,1] => [[.,[[.,[[.,[.,.]],.]],.]],.] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1

[2,4,7,1,3,5,6] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[2,4,7,1,3,6,5] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[2,4,7,1,5,3,6] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,4,7,1,5,6,3] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[2,4,7,1,6,3,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,4,7,1,6,5,3] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[2,4,7,3,1,5,6] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[2,4,7,3,1,6,5] => [[.,[[.,[.,.]],.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[2,4,7,3,5,1,6] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[2,4,7,3,5,6,1] => [[.,[[.,[.,.]],[.,[.,.]]]],.] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1

[2,4,7,3,6,1,5] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[2,4,7,3,6,5,1] => [[.,[[.,[.,.]],[[.,.],.]]],.] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1

[2,4,7,5,1,3,6] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 3

[2,4,7,5,1,6,3] => [[.,[.,[[.,.],.]]],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 2

[2,4,7,5,3,1,6] => [[.,[[.,[[.,.],.]],.]],[.,.]] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 2

[2,4,7,5,3,6,1] => [[.,[[.,[[.,.],.]],[.,.]]],.] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[2,4,7,5,6,1,3] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 2

[2,4,7,5,6,3,1] => [[.,[[.,[[.,.],[.,.]]],.]],.] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1

[2,4,7,6,1,3,5] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 3

[2,4,7,6,1,5,3] => [[.,[.,[[.,.],.]]],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 2

[2,4,7,6,3,1,5] => [[.,[[.,[[.,.],.]],.]],[.,.]] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 2

[2,4,7,6,3,5,1] => [[.,[[.,[[.,.],.]],[.,.]]],.] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[2,4,7,6,5,1,3] => [[.,[.,[[[.,.],.],.]]],[.,.]] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 2

[2,4,7,6,5,3,1] => [[.,[[.,[[[.,.],.],.]],.]],.] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 1

[2,5,1,3,4,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[2,5,1,3,4,7,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[2,5,1,3,6,4,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[2,5,1,3,6,7,4] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[2,5,1,3,7,4,6] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[2,5,1,3,7,6,4] => [[.,[.,.]],[.,[[[.,.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[2,5,1,4,3,6,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[2,5,1,4,3,7,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[2,5,1,4,6,3,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[2,5,1,4,6,7,3] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[2,5,1,4,7,3,6] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[2,5,1,4,7,6,3] => [[.,[.,.]],[[.,[[.,.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[2,5,1,6,3,4,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[2,5,1,6,3,7,4] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[2,5,1,6,4,3,7] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[2,5,1,6,4,7,3] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[2,5,1,6,7,3,4] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[2,5,1,6,7,4,3] => [[.,[.,.]],[[[.,[.,.]],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[2,5,1,7,3,4,6] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[2,5,1,7,3,6,4] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[2,5,1,7,4,3,6] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[2,5,1,7,4,6,3] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[2,5,1,7,6,3,4] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[2,5,1,7,6,4,3] => [[.,[.,.]],[[[[.,.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[2,5,3,1,4,6,7] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4

[2,5,3,1,4,7,6] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 3

[2,5,3,1,6,4,7] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[2,5,3,1,6,7,4] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 2

[2,5,3,1,7,4,6] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[2,5,3,1,7,6,4] => [[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2

[2,5,3,4,1,6,7] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[2,5,3,4,1,7,6] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2

[2,5,3,4,6,1,7] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2

[2,5,3,4,6,7,1] => [[.,[[.,.],[.,[.,[.,.]]]]],.] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1

[2,5,3,4,7,1,6] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2

[2,5,3,4,7,6,1] => [[.,[[.,.],[.,[[.,.],.]]]],.] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 1

[2,5,3,6,1,4,7] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[2,5,3,6,1,7,4] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2

[2,5,3,6,4,1,7] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2

[2,5,3,6,4,7,1] => [[.,[[.,.],[[.,.],[.,.]]]],.] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 1

[2,5,3,6,7,1,4] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2

[2,5,3,6,7,4,1] => [[.,[[.,.],[[.,[.,.]],.]]],.] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 1

[2,5,3,7,1,4,6] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[2,5,3,7,1,6,4] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2

[2,5,3,7,4,1,6] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2

[2,5,3,7,4,6,1] => [[.,[[.,.],[[.,.],[.,.]]]],.] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 1

[2,5,3,7,6,1,4] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2

[2,5,3,7,6,4,1] => [[.,[[.,.],[[[.,.],.],.]]],.] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 1

[2,5,4,1,3,6,7] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4

[2,5,4,1,3,7,6] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 3

[2,5,4,1,6,3,7] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[2,5,4,1,6,7,3] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 2

[2,5,4,1,7,3,6] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[2,5,4,1,7,6,3] => [[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2

[2,5,4,3,1,6,7] => [[.,[[[.,.],.],.]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 3

[2,5,4,3,1,7,6] => [[.,[[[.,.],.],.]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 2

[2,5,4,3,6,1,7] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 2

[2,5,4,3,6,7,1] => [[.,[[[.,.],.],[.,[.,.]]]],.] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 1

[2,5,4,3,7,1,6] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 2

[2,5,4,3,7,6,1] => [[.,[[[.,.],.],[[.,.],.]]],.] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 1

[2,5,4,6,1,3,7] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[2,5,4,6,1,7,3] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2

[2,5,4,6,3,1,7] => [[.,[[[.,.],[.,.]],.]],[.,.]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2

[2,5,4,6,3,7,1] => [[.,[[[.,.],[.,.]],[.,.]]],.] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1

[2,5,4,6,7,1,3] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2

[2,5,4,6,7,3,1] => [[.,[[[.,.],[.,[.,.]]],.]],.] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[2,5,4,7,1,3,6] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[2,5,4,7,1,6,3] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2

[2,5,4,7,3,1,6] => [[.,[[[.,.],[.,.]],.]],[.,.]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2

[2,5,4,7,3,6,1] => [[.,[[[.,.],[.,.]],[.,.]]],.] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1

[2,5,4,7,6,1,3] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2

[2,5,4,7,6,3,1] => [[.,[[[.,.],[[.,.],.]],.]],.] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 1

[2,5,6,1,3,4,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[2,5,6,1,3,7,4] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[2,5,6,1,4,3,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,5,6,1,4,7,3] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[2,5,6,1,7,3,4] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,5,6,1,7,4,3] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[2,5,6,3,1,4,7] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[2,5,6,3,1,7,4] => [[.,[[.,[.,.]],.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[2,5,6,3,4,1,7] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[2,5,6,3,4,7,1] => [[.,[[.,[.,.]],[.,[.,.]]]],.] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1

[2,5,6,3,7,1,4] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[2,5,6,3,7,4,1] => [[.,[[.,[.,.]],[[.,.],.]]],.] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1

[2,5,6,4,1,3,7] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[2,5,6,4,1,7,3] => [[.,[[.,[.,.]],.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[2,5,6,4,3,1,7] => [[.,[[[.,[.,.]],.],.]],[.,.]] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 2

[2,5,6,4,3,7,1] => [[.,[[[.,[.,.]],.],[.,.]]],.] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1

[2,5,6,4,7,1,3] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[2,5,6,4,7,3,1] => [[.,[[[.,[.,.]],[.,.]],.]],.] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1

[2,5,6,7,1,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[2,5,6,7,1,4,3] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[2,5,6,7,3,1,4] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 2

[2,5,6,7,3,4,1] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1

[2,5,6,7,4,1,3] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 2

[2,5,6,7,4,3,1] => [[.,[[[.,[.,[.,.]]],.],.]],.] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 1

[2,5,7,1,3,4,6] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[2,5,7,1,3,6,4] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[2,5,7,1,4,3,6] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,5,7,1,4,6,3] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[2,5,7,1,6,3,4] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,5,7,1,6,4,3] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[2,5,7,3,1,4,6] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[2,5,7,3,1,6,4] => [[.,[[.,[.,.]],.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[2,5,7,3,4,1,6] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[2,5,7,3,4,6,1] => [[.,[[.,[.,.]],[.,[.,.]]]],.] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1

[2,5,7,3,6,1,4] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[2,5,7,3,6,4,1] => [[.,[[.,[.,.]],[[.,.],.]]],.] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1

[2,5,7,4,1,3,6] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[2,5,7,4,1,6,3] => [[.,[[.,[.,.]],.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[2,5,7,4,3,1,6] => [[.,[[[.,[.,.]],.],.]],[.,.]] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 2

[2,5,7,4,3,6,1] => [[.,[[[.,[.,.]],.],[.,.]]],.] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1

[2,5,7,4,6,1,3] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[2,5,7,4,6,3,1] => [[.,[[[.,[.,.]],[.,.]],.]],.] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1

[2,5,7,6,1,3,4] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 3

[2,5,7,6,1,4,3] => [[.,[.,[[.,.],.]]],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 2

[2,5,7,6,3,1,4] => [[.,[[.,[[.,.],.]],.]],[.,.]] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 2

[2,5,7,6,3,4,1] => [[.,[[.,[[.,.],.]],[.,.]]],.] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[2,5,7,6,4,1,3] => [[.,[[.,[[.,.],.]],.]],[.,.]] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 2

[2,5,7,6,4,3,1] => [[.,[[[.,[[.,.],.]],.],.]],.] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 1

[2,6,1,3,4,5,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[2,6,1,3,4,7,5] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[2,6,1,3,5,4,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[2,6,1,3,5,7,4] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[2,6,1,3,7,4,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[2,6,1,3,7,5,4] => [[.,[.,.]],[.,[[[.,.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[2,6,1,4,3,5,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[2,6,1,4,3,7,5] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[2,6,1,4,5,3,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[2,6,1,4,5,7,3] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[2,6,1,4,7,3,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[2,6,1,4,7,5,3] => [[.,[.,.]],[[.,[[.,.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[2,6,1,5,3,4,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[2,6,1,5,3,7,4] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[2,6,1,5,4,3,7] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[2,6,1,5,4,7,3] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[2,6,1,5,7,3,4] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[2,6,1,5,7,4,3] => [[.,[.,.]],[[[.,[.,.]],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[2,6,1,7,3,4,5] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[2,6,1,7,3,5,4] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[2,6,1,7,4,3,5] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[2,6,1,7,4,5,3] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[2,6,1,7,5,3,4] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[2,6,1,7,5,4,3] => [[.,[.,.]],[[[[.,.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[2,6,3,1,4,5,7] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4

[2,6,3,1,4,7,5] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 3

[2,6,3,1,5,4,7] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[2,6,3,1,5,7,4] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 2

[2,6,3,1,7,4,5] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[2,6,3,1,7,5,4] => [[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2

[2,6,3,4,1,5,7] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[2,6,3,4,1,7,5] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2

[2,6,3,4,5,1,7] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2

[2,6,3,4,5,7,1] => [[.,[[.,.],[.,[.,[.,.]]]]],.] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1

[2,6,3,4,7,1,5] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2

[2,6,3,4,7,5,1] => [[.,[[.,.],[.,[[.,.],.]]]],.] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 1

[2,6,3,5,1,4,7] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[2,6,3,5,1,7,4] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2

[2,6,3,5,4,1,7] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2

[2,6,3,5,4,7,1] => [[.,[[.,.],[[.,.],[.,.]]]],.] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 1

[2,6,3,5,7,1,4] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2

[2,6,3,5,7,4,1] => [[.,[[.,.],[[.,[.,.]],.]]],.] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 1

[2,6,3,7,1,4,5] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[2,6,3,7,1,5,4] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2

[2,6,3,7,4,1,5] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2

[2,6,3,7,4,5,1] => [[.,[[.,.],[[.,.],[.,.]]]],.] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 1

[2,6,3,7,5,1,4] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2

[2,6,3,7,5,4,1] => [[.,[[.,.],[[[.,.],.],.]]],.] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 1

[2,6,4,1,3,5,7] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4

[2,6,4,1,3,7,5] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 3

[2,6,4,1,5,3,7] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[2,6,4,1,5,7,3] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 2

[2,6,4,1,7,3,5] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[2,6,4,1,7,5,3] => [[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2

[2,6,4,3,1,5,7] => [[.,[[[.,.],.],.]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 3

[2,6,4,3,1,7,5] => [[.,[[[.,.],.],.]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 2

[2,6,4,3,5,1,7] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 2

[2,6,4,3,5,7,1] => [[.,[[[.,.],.],[.,[.,.]]]],.] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 1

[2,6,4,3,7,1,5] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 2

[2,6,4,3,7,5,1] => [[.,[[[.,.],.],[[.,.],.]]],.] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 1

[2,6,4,5,1,3,7] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[2,6,4,5,1,7,3] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2

[2,6,4,5,3,1,7] => [[.,[[[.,.],[.,.]],.]],[.,.]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2

[2,6,4,5,3,7,1] => [[.,[[[.,.],[.,.]],[.,.]]],.] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1

[2,6,4,5,7,1,3] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2

[2,6,4,5,7,3,1] => [[.,[[[.,.],[.,[.,.]]],.]],.] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[2,6,4,7,1,3,5] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[2,6,4,7,1,5,3] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2

[2,6,4,7,3,1,5] => [[.,[[[.,.],[.,.]],.]],[.,.]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2

[2,6,4,7,3,5,1] => [[.,[[[.,.],[.,.]],[.,.]]],.] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1

[2,6,4,7,5,1,3] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2

[2,6,4,7,5,3,1] => [[.,[[[.,.],[[.,.],.]],.]],.] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 1

[2,6,5,1,3,4,7] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4

[2,6,5,1,3,7,4] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 3

[2,6,5,1,4,3,7] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[2,6,5,1,4,7,3] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 2

[2,6,5,1,7,3,4] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[2,6,5,1,7,4,3] => [[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2

[2,6,5,3,1,4,7] => [[.,[[[.,.],.],.]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 3

[2,6,5,3,1,7,4] => [[.,[[[.,.],.],.]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 2

[2,6,5,3,4,1,7] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 2

[2,6,5,3,4,7,1] => [[.,[[[.,.],.],[.,[.,.]]]],.] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 1

[2,6,5,3,7,1,4] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 2

[2,6,5,3,7,4,1] => [[.,[[[.,.],.],[[.,.],.]]],.] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 1

[2,6,5,4,1,3,7] => [[.,[[[.,.],.],.]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 3

[2,6,5,4,1,7,3] => [[.,[[[.,.],.],.]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 2

[2,6,5,4,3,1,7] => [[.,[[[[.,.],.],.],.]],[.,.]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 2

[2,6,5,4,3,7,1] => [[.,[[[[.,.],.],.],[.,.]]],.] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 1

[2,6,5,4,7,1,3] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 2

[2,6,5,4,7,3,1] => [[.,[[[[.,.],.],[.,.]],.]],.] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 1

[2,6,5,7,1,3,4] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[2,6,5,7,1,4,3] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2

[2,6,5,7,3,1,4] => [[.,[[[.,.],[.,.]],.]],[.,.]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2

[2,6,5,7,3,4,1] => [[.,[[[.,.],[.,.]],[.,.]]],.] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1

[2,6,5,7,4,1,3] => [[.,[[[.,.],[.,.]],.]],[.,.]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2

[2,6,5,7,4,3,1] => [[.,[[[[.,.],[.,.]],.],.]],.] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[2,6,7,1,3,4,5] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[2,6,7,1,3,5,4] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[2,6,7,1,4,3,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,6,7,1,4,5,3] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[2,6,7,1,5,3,4] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,6,7,1,5,4,3] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[2,6,7,3,1,4,5] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[2,6,7,3,1,5,4] => [[.,[[.,[.,.]],.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[2,6,7,3,4,1,5] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[2,6,7,3,4,5,1] => [[.,[[.,[.,.]],[.,[.,.]]]],.] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1

[2,6,7,3,5,1,4] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[2,6,7,3,5,4,1] => [[.,[[.,[.,.]],[[.,.],.]]],.] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1

[2,6,7,4,1,3,5] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[2,6,7,4,1,5,3] => [[.,[[.,[.,.]],.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[2,6,7,4,3,1,5] => [[.,[[[.,[.,.]],.],.]],[.,.]] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 2

[2,6,7,4,3,5,1] => [[.,[[[.,[.,.]],.],[.,.]]],.] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1

[2,6,7,4,5,1,3] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[2,6,7,4,5,3,1] => [[.,[[[.,[.,.]],[.,.]],.]],.] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1

[2,6,7,5,1,3,4] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[2,6,7,5,1,4,3] => [[.,[[.,[.,.]],.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[2,6,7,5,3,1,4] => [[.,[[[.,[.,.]],.],.]],[.,.]] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 2

[2,6,7,5,3,4,1] => [[.,[[[.,[.,.]],.],[.,.]]],.] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1

[2,6,7,5,4,1,3] => [[.,[[[.,[.,.]],.],.]],[.,.]] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 2

[2,6,7,5,4,3,1] => [[.,[[[[.,[.,.]],.],.],.]],.] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 1

[2,7,1,3,4,5,6] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[2,7,1,3,4,6,5] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[2,7,1,3,5,4,6] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[2,7,1,3,5,6,4] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[2,7,1,3,6,4,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[2,7,1,3,6,5,4] => [[.,[.,.]],[.,[[[.,.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[2,7,1,4,3,5,6] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[2,7,1,4,3,6,5] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[2,7,1,4,5,3,6] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[2,7,1,4,5,6,3] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[2,7,1,4,6,3,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[2,7,1,4,6,5,3] => [[.,[.,.]],[[.,[[.,.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[2,7,1,5,3,4,6] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[2,7,1,5,3,6,4] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[2,7,1,5,4,3,6] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[2,7,1,5,4,6,3] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[2,7,1,5,6,3,4] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[2,7,1,5,6,4,3] => [[.,[.,.]],[[[.,[.,.]],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[2,7,1,6,3,4,5] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[2,7,1,6,3,5,4] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[2,7,1,6,4,3,5] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[2,7,1,6,4,5,3] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[2,7,1,6,5,3,4] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[2,7,1,6,5,4,3] => [[.,[.,.]],[[[[.,.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[2,7,3,1,4,5,6] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4

[2,7,3,1,4,6,5] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 3

[2,7,3,1,5,4,6] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[2,7,3,1,5,6,4] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 2

[2,7,3,1,6,4,5] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[2,7,3,1,6,5,4] => [[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2

[2,7,3,4,1,5,6] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[2,7,3,4,1,6,5] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2

[2,7,3,4,5,1,6] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2

[2,7,3,4,5,6,1] => [[.,[[.,.],[.,[.,[.,.]]]]],.] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1

[2,7,3,4,6,1,5] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2

[2,7,3,4,6,5,1] => [[.,[[.,.],[.,[[.,.],.]]]],.] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 1

[2,7,3,5,1,4,6] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[2,7,3,5,1,6,4] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2

[2,7,3,5,4,1,6] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2

[2,7,3,5,4,6,1] => [[.,[[.,.],[[.,.],[.,.]]]],.] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 1

[2,7,3,5,6,1,4] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2

[2,7,3,5,6,4,1] => [[.,[[.,.],[[.,[.,.]],.]]],.] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 1

[2,7,3,6,1,4,5] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[2,7,3,6,1,5,4] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2

[2,7,3,6,4,1,5] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2

[2,7,3,6,4,5,1] => [[.,[[.,.],[[.,.],[.,.]]]],.] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 1

[2,7,3,6,5,1,4] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2

[2,7,3,6,5,4,1] => [[.,[[.,.],[[[.,.],.],.]]],.] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 1

[2,7,4,1,3,5,6] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4

[2,7,4,1,3,6,5] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 3

[2,7,4,1,5,3,6] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[2,7,4,1,5,6,3] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 2

[2,7,4,1,6,3,5] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[2,7,4,1,6,5,3] => [[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2

[2,7,4,3,1,5,6] => [[.,[[[.,.],.],.]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 3

[2,7,4,3,1,6,5] => [[.,[[[.,.],.],.]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 2

[2,7,4,3,5,1,6] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 2

[2,7,4,3,5,6,1] => [[.,[[[.,.],.],[.,[.,.]]]],.] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 1

[2,7,4,3,6,1,5] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 2

[2,7,4,3,6,5,1] => [[.,[[[.,.],.],[[.,.],.]]],.] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 1

[2,7,4,5,1,3,6] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[2,7,4,5,1,6,3] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2

[2,7,4,5,3,1,6] => [[.,[[[.,.],[.,.]],.]],[.,.]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2

[2,7,4,5,3,6,1] => [[.,[[[.,.],[.,.]],[.,.]]],.] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1

[2,7,4,5,6,1,3] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2

[2,7,4,5,6,3,1] => [[.,[[[.,.],[.,[.,.]]],.]],.] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[2,7,4,6,1,3,5] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[2,7,4,6,1,5,3] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2

[2,7,4,6,3,1,5] => [[.,[[[.,.],[.,.]],.]],[.,.]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2

[2,7,4,6,3,5,1] => [[.,[[[.,.],[.,.]],[.,.]]],.] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1

[2,7,4,6,5,1,3] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2

[2,7,4,6,5,3,1] => [[.,[[[.,.],[[.,.],.]],.]],.] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 1

[2,7,5,1,3,4,6] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4

[2,7,5,1,3,6,4] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 3

[2,7,5,1,4,3,6] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[2,7,5,1,4,6,3] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 2

[2,7,5,1,6,3,4] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[2,7,5,1,6,4,3] => [[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2

[2,7,5,3,1,4,6] => [[.,[[[.,.],.],.]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 3

[2,7,5,3,1,6,4] => [[.,[[[.,.],.],.]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 2

[2,7,5,3,4,1,6] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 2

[2,7,5,3,4,6,1] => [[.,[[[.,.],.],[.,[.,.]]]],.] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 1

[2,7,5,3,6,1,4] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 2

[2,7,5,3,6,4,1] => [[.,[[[.,.],.],[[.,.],.]]],.] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 1

[2,7,5,4,1,3,6] => [[.,[[[.,.],.],.]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 3

[2,7,5,4,1,6,3] => [[.,[[[.,.],.],.]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 2

[2,7,5,4,3,1,6] => [[.,[[[[.,.],.],.],.]],[.,.]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 2

[2,7,5,4,3,6,1] => [[.,[[[[.,.],.],.],[.,.]]],.] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 1

[2,7,5,4,6,1,3] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 2

[2,7,5,4,6,3,1] => [[.,[[[[.,.],.],[.,.]],.]],.] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 1

[2,7,5,6,1,3,4] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[2,7,5,6,1,4,3] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2

[2,7,5,6,3,1,4] => [[.,[[[.,.],[.,.]],.]],[.,.]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2

[2,7,5,6,3,4,1] => [[.,[[[.,.],[.,.]],[.,.]]],.] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1

[2,7,5,6,4,1,3] => [[.,[[[.,.],[.,.]],.]],[.,.]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2

[2,7,5,6,4,3,1] => [[.,[[[[.,.],[.,.]],.],.]],.] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[2,7,6,1,3,4,5] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4

[2,7,6,1,3,5,4] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 3

[2,7,6,1,4,3,5] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[2,7,6,1,4,5,3] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 2

[2,7,6,1,5,3,4] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[2,7,6,1,5,4,3] => [[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2

[2,7,6,3,1,4,5] => [[.,[[[.,.],.],.]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 3

[2,7,6,3,1,5,4] => [[.,[[[.,.],.],.]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 2

[2,7,6,3,4,1,5] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 2

[2,7,6,3,4,5,1] => [[.,[[[.,.],.],[.,[.,.]]]],.] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 1

[2,7,6,3,5,1,4] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 2

[2,7,6,3,5,4,1] => [[.,[[[.,.],.],[[.,.],.]]],.] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 1

[2,7,6,4,1,3,5] => [[.,[[[.,.],.],.]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 3

[2,7,6,4,1,5,3] => [[.,[[[.,.],.],.]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 2

[2,7,6,4,3,1,5] => [[.,[[[[.,.],.],.],.]],[.,.]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 2

[2,7,6,4,3,5,1] => [[.,[[[[.,.],.],.],[.,.]]],.] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 1

[2,7,6,4,5,1,3] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 2

[2,7,6,4,5,3,1] => [[.,[[[[.,.],.],[.,.]],.]],.] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 1

[2,7,6,5,1,3,4] => [[.,[[[.,.],.],.]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 3

[2,7,6,5,1,4,3] => [[.,[[[.,.],.],.]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 2

[2,7,6,5,3,1,4] => [[.,[[[[.,.],.],.],.]],[.,.]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 2

[2,7,6,5,3,4,1] => [[.,[[[[.,.],.],.],[.,.]]],.] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 1

[2,7,6,5,4,1,3] => [[.,[[[[.,.],.],.],.]],[.,.]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 2

[2,7,6,5,4,3,1] => [[.,[[[[[.,.],.],.],.],.]],.] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1

[3,1,2,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6

[3,1,2,4,5,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 5

[3,1,2,4,6,5,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 5

[3,1,2,4,6,7,5] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 4

[3,1,2,4,7,5,6] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 5

[3,1,2,4,7,6,5] => [[.,.],[.,[.,[[[.,.],.],.]]]] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 4

[3,1,2,5,4,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5

[3,1,2,5,4,7,6] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4

[3,1,2,5,6,4,7] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4

[3,1,2,5,6,7,4] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 3

[3,1,2,5,7,4,6] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4

[3,1,2,5,7,6,4] => [[.,.],[.,[[.,[[.,.],.]],.]]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 3

[3,1,2,6,4,5,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5

[3,1,2,6,4,7,5] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4

[3,1,2,6,5,4,7] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 4

[3,1,2,6,5,7,4] => [[.,.],[.,[[[.,.],[.,.]],.]]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 3

[3,1,2,6,7,4,5] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4

[3,1,2,6,7,5,4] => [[.,.],[.,[[[.,[.,.]],.],.]]] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 3

[3,1,2,7,4,5,6] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5

[3,1,2,7,4,6,5] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4

[3,1,2,7,5,4,6] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 4

[3,1,2,7,5,6,4] => [[.,.],[.,[[[.,.],[.,.]],.]]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 3

[3,1,2,7,6,4,5] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 4

[3,1,2,7,6,5,4] => [[.,.],[.,[[[[.,.],.],.],.]]] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 3

[3,1,4,2,5,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[3,1,4,2,5,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[3,1,4,2,6,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[3,1,4,2,6,7,5] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[3,1,4,2,7,5,6] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[3,1,4,2,7,6,5] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[3,1,4,5,2,6,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[3,1,4,5,2,7,6] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[3,1,4,5,6,2,7] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[3,1,4,5,6,7,2] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2

[3,1,4,5,7,2,6] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[3,1,4,5,7,6,2] => [[.,.],[[.,[.,[[.,.],.]]],.]] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 2

[3,1,4,6,2,5,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[3,1,4,6,2,7,5] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[3,1,4,6,5,2,7] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3

[3,1,4,6,5,7,2] => [[.,.],[[.,[[.,.],[.,.]]],.]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 2

[3,1,4,6,7,2,5] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[3,1,4,6,7,5,2] => [[.,.],[[.,[[.,[.,.]],.]],.]] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 2

[3,1,4,7,2,5,6] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[3,1,4,7,2,6,5] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[3,1,4,7,5,2,6] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3

[3,1,4,7,5,6,2] => [[.,.],[[.,[[.,.],[.,.]]],.]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 2

[3,1,4,7,6,2,5] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3

[3,1,4,7,6,5,2] => [[.,.],[[.,[[[.,.],.],.]],.]] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 2

[3,1,5,2,4,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[3,1,5,2,4,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[3,1,5,2,6,4,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[3,1,5,2,6,7,4] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[3,1,5,2,7,4,6] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[3,1,5,2,7,6,4] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[3,1,5,4,2,6,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[3,1,5,4,2,7,6] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[3,1,5,4,6,2,7] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[3,1,5,4,6,7,2] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 2

[3,1,5,4,7,2,6] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[3,1,5,4,7,6,2] => [[.,.],[[[.,.],[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2

[3,1,5,6,2,4,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[3,1,5,6,2,7,4] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[3,1,5,6,4,2,7] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[3,1,5,6,4,7,2] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2

[3,1,5,6,7,2,4] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[3,1,5,6,7,4,2] => [[.,.],[[[.,[.,[.,.]]],.],.]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2

[3,1,5,7,2,4,6] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[3,1,5,7,2,6,4] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[3,1,5,7,4,2,6] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[3,1,5,7,4,6,2] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2

[3,1,5,7,6,2,4] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3

[3,1,5,7,6,4,2] => [[.,.],[[[.,[[.,.],.]],.],.]] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 2

[3,1,6,2,4,5,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[3,1,6,2,4,7,5] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[3,1,6,2,5,4,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[3,1,6,2,5,7,4] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[3,1,6,2,7,4,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[3,1,6,2,7,5,4] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[3,1,6,4,2,5,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[3,1,6,4,2,7,5] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[3,1,6,4,5,2,7] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[3,1,6,4,5,7,2] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 2

[3,1,6,4,7,2,5] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[3,1,6,4,7,5,2] => [[.,.],[[[.,.],[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2

[3,1,6,5,2,4,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[3,1,6,5,2,7,4] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[3,1,6,5,4,2,7] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[3,1,6,5,4,7,2] => [[.,.],[[[[.,.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2

[3,1,6,5,7,2,4] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[3,1,6,5,7,4,2] => [[.,.],[[[[.,.],[.,.]],.],.]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 2

[3,1,6,7,2,4,5] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[3,1,6,7,2,5,4] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[3,1,6,7,4,2,5] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[3,1,6,7,4,5,2] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2

[3,1,6,7,5,2,4] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[3,1,6,7,5,4,2] => [[.,.],[[[[.,[.,.]],.],.],.]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 2

[3,1,7,2,4,5,6] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[3,1,7,2,4,6,5] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[3,1,7,2,5,4,6] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[3,1,7,2,5,6,4] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[3,1,7,2,6,4,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[3,1,7,2,6,5,4] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[3,1,7,4,2,5,6] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[3,1,7,4,2,6,5] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[3,1,7,4,5,2,6] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[3,1,7,4,5,6,2] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 2

[3,1,7,4,6,2,5] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[3,1,7,4,6,5,2] => [[.,.],[[[.,.],[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2

[3,1,7,5,2,4,6] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[3,1,7,5,2,6,4] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[3,1,7,5,4,2,6] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[3,1,7,5,4,6,2] => [[.,.],[[[[.,.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2

[3,1,7,5,6,2,4] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[3,1,7,5,6,4,2] => [[.,.],[[[[.,.],[.,.]],.],.]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 2

[3,1,7,6,2,4,5] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[3,1,7,6,2,5,4] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[3,1,7,6,4,2,5] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[3,1,7,6,4,5,2] => [[.,.],[[[[.,.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2

[3,1,7,6,5,2,4] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[3,1,7,6,5,4,2] => [[.,.],[[[[[.,.],.],.],.],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2

[3,2,1,4,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 5

[3,2,1,4,5,7,6] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 4

[3,2,1,4,6,5,7] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[3,2,1,4,6,7,5] => [[[.,.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 3

[3,2,1,4,7,5,6] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[3,2,1,4,7,6,5] => [[[.,.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 3

[3,2,1,5,4,6,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[3,2,1,5,4,7,6] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[3,2,1,5,6,4,7] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[3,2,1,5,6,7,4] => [[[.,.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 2

[3,2,1,5,7,4,6] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[3,2,1,5,7,6,4] => [[[.,.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 2

[3,2,1,6,4,5,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[3,2,1,6,4,7,5] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[3,2,1,6,5,4,7] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[3,2,1,6,5,7,4] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[3,2,1,6,7,4,5] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[3,2,1,6,7,5,4] => [[[.,.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 2

[3,2,1,7,4,5,6] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[3,2,1,7,4,6,5] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[3,2,1,7,5,4,6] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[3,2,1,7,5,6,4] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[3,2,1,7,6,4,5] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[3,2,1,7,6,5,4] => [[[.,.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2

[3,2,4,1,5,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[3,2,4,1,5,7,6] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[3,2,4,1,6,5,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,2,4,1,6,7,5] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[3,2,4,1,7,5,6] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,2,4,1,7,6,5] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[3,2,4,5,1,6,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[3,2,4,5,1,7,6] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[3,2,4,5,6,1,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[3,2,4,5,6,7,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1

[3,2,4,5,7,1,6] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[3,2,4,5,7,6,1] => [[[.,.],[.,[.,[[.,.],.]]]],.] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 1

[3,2,4,6,1,5,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[3,2,4,6,1,7,5] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[3,2,4,6,5,1,7] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[3,2,4,6,5,7,1] => [[[.,.],[.,[[.,.],[.,.]]]],.] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 1

[3,2,4,6,7,1,5] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[3,2,4,6,7,5,1] => [[[.,.],[.,[[.,[.,.]],.]]],.] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 1

[3,2,4,7,1,5,6] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[3,2,4,7,1,6,5] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[3,2,4,7,5,1,6] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[3,2,4,7,5,6,1] => [[[.,.],[.,[[.,.],[.,.]]]],.] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 1

[3,2,4,7,6,1,5] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[3,2,4,7,6,5,1] => [[[.,.],[.,[[[.,.],.],.]]],.] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 1

[3,2,5,1,4,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[3,2,5,1,4,7,6] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[3,2,5,1,6,4,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,2,5,1,6,7,4] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[3,2,5,1,7,4,6] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,2,5,1,7,6,4] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[3,2,5,4,1,6,7] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[3,2,5,4,1,7,6] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[3,2,5,4,6,1,7] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[3,2,5,4,6,7,1] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 1

[3,2,5,4,7,1,6] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[3,2,5,4,7,6,1] => [[[.,.],[[.,.],[[.,.],.]]],.] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 1

[3,2,5,6,1,4,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[3,2,5,6,1,7,4] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[3,2,5,6,4,1,7] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[3,2,5,6,4,7,1] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 1

[3,2,5,6,7,1,4] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[3,2,5,6,7,4,1] => [[[.,.],[[.,[.,[.,.]]],.]],.] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[3,2,5,7,1,4,6] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[3,2,5,7,1,6,4] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[3,2,5,7,4,1,6] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[3,2,5,7,4,6,1] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 1

[3,2,5,7,6,1,4] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[3,2,5,7,6,4,1] => [[[.,.],[[.,[[.,.],.]],.]],.] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 1

[3,2,6,1,4,5,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[3,2,6,1,4,7,5] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[3,2,6,1,5,4,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,2,6,1,5,7,4] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[3,2,6,1,7,4,5] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,2,6,1,7,5,4] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[3,2,6,4,1,5,7] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[3,2,6,4,1,7,5] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[3,2,6,4,5,1,7] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[3,2,6,4,5,7,1] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 1

[3,2,6,4,7,1,5] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[3,2,6,4,7,5,1] => [[[.,.],[[.,.],[[.,.],.]]],.] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 1

[3,2,6,5,1,4,7] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[3,2,6,5,1,7,4] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[3,2,6,5,4,1,7] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[3,2,6,5,4,7,1] => [[[.,.],[[[.,.],.],[.,.]]],.] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 1

[3,2,6,5,7,1,4] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[3,2,6,5,7,4,1] => [[[.,.],[[[.,.],[.,.]],.]],.] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 1

[3,2,6,7,1,4,5] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[3,2,6,7,1,5,4] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[3,2,6,7,4,1,5] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[3,2,6,7,4,5,1] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 1

[3,2,6,7,5,1,4] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[3,2,6,7,5,4,1] => [[[.,.],[[[.,[.,.]],.],.]],.] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 1

[3,2,7,1,4,5,6] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[3,2,7,1,4,6,5] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[3,2,7,1,5,4,6] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,2,7,1,5,6,4] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[3,2,7,1,6,4,5] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,2,7,1,6,5,4] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[3,2,7,4,1,5,6] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[3,2,7,4,1,6,5] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[3,2,7,4,5,1,6] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[3,2,7,4,5,6,1] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 1

[3,2,7,4,6,1,5] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[3,2,7,4,6,5,1] => [[[.,.],[[.,.],[[.,.],.]]],.] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 1

[3,2,7,5,1,4,6] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[3,2,7,5,1,6,4] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[3,2,7,5,4,1,6] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[3,2,7,5,4,6,1] => [[[.,.],[[[.,.],.],[.,.]]],.] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 1

[3,2,7,5,6,1,4] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[3,2,7,5,6,4,1] => [[[.,.],[[[.,.],[.,.]],.]],.] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 1

[3,2,7,6,1,4,5] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[3,2,7,6,1,5,4] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[3,2,7,6,4,1,5] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[3,2,7,6,4,5,1] => [[[.,.],[[[.,.],.],[.,.]]],.] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 1

[3,2,7,6,5,1,4] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[3,2,7,6,5,4,1] => [[[.,.],[[[[.,.],.],.],.]],.] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1

[3,4,1,2,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[3,4,1,2,5,7,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[3,4,1,2,6,5,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[3,4,1,2,6,7,5] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[3,4,1,2,7,5,6] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[3,4,1,2,7,6,5] => [[.,[.,.]],[.,[[[.,.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[3,4,1,5,2,6,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[3,4,1,5,2,7,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[3,4,1,5,6,2,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[3,4,1,5,6,7,2] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[3,4,1,5,7,2,6] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[3,4,1,5,7,6,2] => [[.,[.,.]],[[.,[[.,.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[3,4,1,6,2,5,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[3,4,1,6,2,7,5] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[3,4,1,6,5,2,7] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[3,4,1,6,5,7,2] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[3,4,1,6,7,2,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[3,4,1,6,7,5,2] => [[.,[.,.]],[[[.,[.,.]],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[3,4,1,7,2,5,6] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[3,4,1,7,2,6,5] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[3,4,1,7,5,2,6] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[3,4,1,7,5,6,2] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[3,4,1,7,6,2,5] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[3,4,1,7,6,5,2] => [[.,[.,.]],[[[[.,.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[3,4,2,1,5,6,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[3,4,2,1,5,7,6] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[3,4,2,1,6,5,7] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[3,4,2,1,6,7,5] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[3,4,2,1,7,5,6] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[3,4,2,1,7,6,5] => [[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[3,4,2,5,1,6,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[3,4,2,5,1,7,6] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[3,4,2,5,6,1,7] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[3,4,2,5,6,7,1] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1

[3,4,2,5,7,1,6] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[3,4,2,5,7,6,1] => [[[.,[.,.]],[.,[[.,.],.]]],.] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[3,4,2,6,1,5,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[3,4,2,6,1,7,5] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[3,4,2,6,5,1,7] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[3,4,2,6,5,7,1] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[3,4,2,6,7,1,5] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[3,4,2,6,7,5,1] => [[[.,[.,.]],[[.,[.,.]],.]],.] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[3,4,2,7,1,5,6] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[3,4,2,7,1,6,5] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[3,4,2,7,5,1,6] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[3,4,2,7,5,6,1] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[3,4,2,7,6,1,5] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[3,4,2,7,6,5,1] => [[[.,[.,.]],[[[.,.],.],.]],.] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1

[3,4,5,1,2,6,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[3,4,5,1,2,7,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[3,4,5,1,6,2,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,4,5,1,6,7,2] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[3,4,5,1,7,2,6] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,4,5,1,7,6,2] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[3,4,5,2,1,6,7] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[3,4,5,2,1,7,6] => [[[.,[.,[.,.]]],.],[[.,.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[3,4,5,2,6,1,7] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[3,4,5,2,6,7,1] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1

[3,4,5,2,7,1,6] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[3,4,5,2,7,6,1] => [[[.,[.,[.,.]]],[[.,.],.]],.] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 1

[3,4,5,6,1,2,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[3,4,5,6,1,7,2] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[3,4,5,6,2,1,7] => [[[.,[.,[.,[.,.]]]],.],[.,.]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 2

[3,4,5,6,2,7,1] => [[[.,[.,[.,[.,.]]]],[.,.]],.] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 1

[3,4,5,6,7,1,2] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2

[3,4,5,6,7,2,1] => [[[.,[.,[.,[.,[.,.]]]]],.],.] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1

[3,4,5,7,1,2,6] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[3,4,5,7,1,6,2] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[3,4,5,7,2,1,6] => [[[.,[.,[.,[.,.]]]],.],[.,.]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 2

[3,4,5,7,2,6,1] => [[[.,[.,[.,[.,.]]]],[.,.]],.] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 1

[3,4,5,7,6,1,2] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 2

[3,4,5,7,6,2,1] => [[[.,[.,[.,[[.,.],.]]]],.],.] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 1

[3,4,6,1,2,5,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[3,4,6,1,2,7,5] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[3,4,6,1,5,2,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,4,6,1,5,7,2] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[3,4,6,1,7,2,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,4,6,1,7,5,2] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[3,4,6,2,1,5,7] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[3,4,6,2,1,7,5] => [[[.,[.,[.,.]]],.],[[.,.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[3,4,6,2,5,1,7] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[3,4,6,2,5,7,1] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1

[3,4,6,2,7,1,5] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[3,4,6,2,7,5,1] => [[[.,[.,[.,.]]],[[.,.],.]],.] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 1

[3,4,6,5,1,2,7] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 3

[3,4,6,5,1,7,2] => [[.,[.,[[.,.],.]]],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 2

[3,4,6,5,2,1,7] => [[[.,[.,[[.,.],.]]],.],[.,.]] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 2

[3,4,6,5,2,7,1] => [[[.,[.,[[.,.],.]]],[.,.]],.] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[3,4,6,5,7,1,2] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 2

[3,4,6,5,7,2,1] => [[[.,[.,[[.,.],[.,.]]]],.],.] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 1

[3,4,6,7,1,2,5] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[3,4,6,7,1,5,2] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[3,4,6,7,2,1,5] => [[[.,[.,[.,[.,.]]]],.],[.,.]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 2

[3,4,6,7,2,5,1] => [[[.,[.,[.,[.,.]]]],[.,.]],.] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 1

[3,4,6,7,5,1,2] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 2

[3,4,6,7,5,2,1] => [[[.,[.,[[.,[.,.]],.]]],.],.] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1

[3,4,7,1,2,5,6] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[3,4,7,1,2,6,5] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[3,4,7,1,5,2,6] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,4,7,1,5,6,2] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[3,4,7,1,6,2,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,4,7,1,6,5,2] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[3,4,7,2,1,5,6] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[3,4,7,2,1,6,5] => [[[.,[.,[.,.]]],.],[[.,.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[3,4,7,2,5,1,6] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[3,4,7,2,5,6,1] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1

[3,4,7,2,6,1,5] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[3,4,7,2,6,5,1] => [[[.,[.,[.,.]]],[[.,.],.]],.] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 1

[3,4,7,5,1,2,6] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 3

[3,4,7,5,1,6,2] => [[.,[.,[[.,.],.]]],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 2

[3,4,7,5,2,1,6] => [[[.,[.,[[.,.],.]]],.],[.,.]] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 2

[3,4,7,5,2,6,1] => [[[.,[.,[[.,.],.]]],[.,.]],.] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[3,4,7,5,6,1,2] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 2

[3,4,7,5,6,2,1] => [[[.,[.,[[.,.],[.,.]]]],.],.] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 1

[3,4,7,6,1,2,5] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 3

[3,4,7,6,1,5,2] => [[.,[.,[[.,.],.]]],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 2

[3,4,7,6,2,1,5] => [[[.,[.,[[.,.],.]]],.],[.,.]] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 2

[3,4,7,6,2,5,1] => [[[.,[.,[[.,.],.]]],[.,.]],.] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[3,4,7,6,5,1,2] => [[.,[.,[[[.,.],.],.]]],[.,.]] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 2

[3,4,7,6,5,2,1] => [[[.,[.,[[[.,.],.],.]]],.],.] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 1

[3,5,1,2,4,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[3,5,1,2,4,7,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[3,5,1,2,6,4,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[3,5,1,2,6,7,4] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[3,5,1,2,7,4,6] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[3,5,1,2,7,6,4] => [[.,[.,.]],[.,[[[.,.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[3,5,1,4,2,6,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[3,5,1,4,2,7,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[3,5,1,4,6,2,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[3,5,1,4,6,7,2] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[3,5,1,4,7,2,6] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[3,5,1,4,7,6,2] => [[.,[.,.]],[[.,[[.,.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[3,5,1,6,2,4,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[3,5,1,6,2,7,4] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[3,5,1,6,4,2,7] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[3,5,1,6,4,7,2] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[3,5,1,6,7,2,4] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[3,5,1,6,7,4,2] => [[.,[.,.]],[[[.,[.,.]],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[3,5,1,7,2,4,6] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[3,5,1,7,2,6,4] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[3,5,1,7,4,2,6] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[3,5,1,7,4,6,2] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[3,5,1,7,6,2,4] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[3,5,1,7,6,4,2] => [[.,[.,.]],[[[[.,.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[3,5,2,1,4,6,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[3,5,2,1,4,7,6] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[3,5,2,1,6,4,7] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[3,5,2,1,6,7,4] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[3,5,2,1,7,4,6] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[3,5,2,1,7,6,4] => [[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[3,5,2,4,1,6,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[3,5,2,4,1,7,6] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[3,5,2,4,6,1,7] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[3,5,2,4,6,7,1] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1

[3,5,2,4,7,1,6] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[3,5,2,4,7,6,1] => [[[.,[.,.]],[.,[[.,.],.]]],.] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[3,5,2,6,1,4,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[3,5,2,6,1,7,4] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[3,5,2,6,4,1,7] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[3,5,2,6,4,7,1] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[3,5,2,6,7,1,4] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[3,5,2,6,7,4,1] => [[[.,[.,.]],[[.,[.,.]],.]],.] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[3,5,2,7,1,4,6] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[3,5,2,7,1,6,4] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[3,5,2,7,4,1,6] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[3,5,2,7,4,6,1] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[3,5,2,7,6,1,4] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[3,5,2,7,6,4,1] => [[[.,[.,.]],[[[.,.],.],.]],.] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1

[3,5,4,1,2,6,7] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4

[3,5,4,1,2,7,6] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 3

[3,5,4,1,6,2,7] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[3,5,4,1,6,7,2] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 2

[3,5,4,1,7,2,6] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[3,5,4,1,7,6,2] => [[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2

[3,5,4,2,1,6,7] => [[[.,[[.,.],.]],.],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 3

[3,5,4,2,1,7,6] => [[[.,[[.,.],.]],.],[[.,.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 2

[3,5,4,2,6,1,7] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[3,5,4,2,6,7,1] => [[[.,[[.,.],.]],[.,[.,.]]],.] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 1

[3,5,4,2,7,1,6] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[3,5,4,2,7,6,1] => [[[.,[[.,.],.]],[[.,.],.]],.] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[3,5,4,6,1,2,7] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[3,5,4,6,1,7,2] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2

[3,5,4,6,2,1,7] => [[[.,[[.,.],[.,.]]],.],[.,.]] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 2

[3,5,4,6,2,7,1] => [[[.,[[.,.],[.,.]]],[.,.]],.] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[3,5,4,6,7,1,2] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2

[3,5,4,6,7,2,1] => [[[.,[[.,.],[.,[.,.]]]],.],.] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 1

[3,5,4,7,1,2,6] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[3,5,4,7,1,6,2] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2

[3,5,4,7,2,1,6] => [[[.,[[.,.],[.,.]]],.],[.,.]] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 2

[3,5,4,7,2,6,1] => [[[.,[[.,.],[.,.]]],[.,.]],.] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[3,5,4,7,6,1,2] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2

[3,5,4,7,6,2,1] => [[[.,[[.,.],[[.,.],.]]],.],.] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 1

[3,5,6,1,2,4,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[3,5,6,1,2,7,4] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[3,5,6,1,4,2,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,5,6,1,4,7,2] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[3,5,6,1,7,2,4] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,5,6,1,7,4,2] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[3,5,6,2,1,4,7] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[3,5,6,2,1,7,4] => [[[.,[.,[.,.]]],.],[[.,.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[3,5,6,2,4,1,7] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[3,5,6,2,4,7,1] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1

[3,5,6,2,7,1,4] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[3,5,6,2,7,4,1] => [[[.,[.,[.,.]]],[[.,.],.]],.] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 1

[3,5,6,4,1,2,7] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[3,5,6,4,1,7,2] => [[.,[[.,[.,.]],.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[3,5,6,4,2,1,7] => [[[.,[[.,[.,.]],.]],.],[.,.]] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 2

[3,5,6,4,2,7,1] => [[[.,[[.,[.,.]],.]],[.,.]],.] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[3,5,6,4,7,1,2] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[3,5,6,4,7,2,1] => [[[.,[[.,[.,.]],[.,.]]],.],.] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1

[3,5,6,7,1,2,4] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[3,5,6,7,1,4,2] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[3,5,6,7,2,1,4] => [[[.,[.,[.,[.,.]]]],.],[.,.]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 2

[3,5,6,7,2,4,1] => [[[.,[.,[.,[.,.]]]],[.,.]],.] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 1

[3,5,6,7,4,1,2] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 2

[3,5,6,7,4,2,1] => [[[.,[[.,[.,[.,.]]],.]],.],.] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 1

[3,5,7,1,2,4,6] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[3,5,7,1,2,6,4] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[3,5,7,1,4,2,6] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,5,7,1,4,6,2] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[3,5,7,1,6,2,4] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,5,7,1,6,4,2] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[3,5,7,2,1,4,6] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[3,5,7,2,1,6,4] => [[[.,[.,[.,.]]],.],[[.,.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[3,5,7,2,4,1,6] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[3,5,7,2,4,6,1] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1

[3,5,7,2,6,1,4] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[3,5,7,2,6,4,1] => [[[.,[.,[.,.]]],[[.,.],.]],.] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 1

[3,5,7,4,1,2,6] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[3,5,7,4,1,6,2] => [[.,[[.,[.,.]],.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[3,5,7,4,2,1,6] => [[[.,[[.,[.,.]],.]],.],[.,.]] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 2

[3,5,7,4,2,6,1] => [[[.,[[.,[.,.]],.]],[.,.]],.] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[3,5,7,4,6,1,2] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[3,5,7,4,6,2,1] => [[[.,[[.,[.,.]],[.,.]]],.],.] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1

[3,5,7,6,1,2,4] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 3

[3,5,7,6,1,4,2] => [[.,[.,[[.,.],.]]],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 2

[3,5,7,6,2,1,4] => [[[.,[.,[[.,.],.]]],.],[.,.]] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 2

[3,5,7,6,2,4,1] => [[[.,[.,[[.,.],.]]],[.,.]],.] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[3,5,7,6,4,1,2] => [[.,[[.,[[.,.],.]],.]],[.,.]] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 2

[3,5,7,6,4,2,1] => [[[.,[[.,[[.,.],.]],.]],.],.] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[3,6,1,2,4,5,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[3,6,1,2,4,7,5] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[3,6,1,2,5,4,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[3,6,1,2,5,7,4] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[3,6,1,2,7,4,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[3,6,1,2,7,5,4] => [[.,[.,.]],[.,[[[.,.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[3,6,1,4,2,5,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[3,6,1,4,2,7,5] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[3,6,1,4,5,2,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[3,6,1,4,5,7,2] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[3,6,1,4,7,2,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[3,6,1,4,7,5,2] => [[.,[.,.]],[[.,[[.,.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[3,6,1,5,2,4,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[3,6,1,5,2,7,4] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[3,6,1,5,4,2,7] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[3,6,1,5,4,7,2] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[3,6,1,5,7,2,4] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[3,6,1,5,7,4,2] => [[.,[.,.]],[[[.,[.,.]],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[3,6,1,7,2,4,5] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[3,6,1,7,2,5,4] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[3,6,1,7,4,2,5] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[3,6,1,7,4,5,2] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[3,6,1,7,5,2,4] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[3,6,1,7,5,4,2] => [[.,[.,.]],[[[[.,.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[3,6,2,1,4,5,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[3,6,2,1,4,7,5] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[3,6,2,1,5,4,7] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[3,6,2,1,5,7,4] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[3,6,2,1,7,4,5] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[3,6,2,1,7,5,4] => [[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[3,6,2,4,1,5,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[3,6,2,4,1,7,5] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[3,6,2,4,5,1,7] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[3,6,2,4,5,7,1] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1

[3,6,2,4,7,1,5] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[3,6,2,4,7,5,1] => [[[.,[.,.]],[.,[[.,.],.]]],.] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[3,6,2,5,1,4,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[3,6,2,5,1,7,4] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[3,6,2,5,4,1,7] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[3,6,2,5,4,7,1] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[3,6,2,5,7,1,4] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[3,6,2,5,7,4,1] => [[[.,[.,.]],[[.,[.,.]],.]],.] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[3,6,2,7,1,4,5] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[3,6,2,7,1,5,4] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[3,6,2,7,4,1,5] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[3,6,2,7,4,5,1] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[3,6,2,7,5,1,4] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[3,6,2,7,5,4,1] => [[[.,[.,.]],[[[.,.],.],.]],.] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1

[3,6,4,1,2,5,7] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4

[3,6,4,1,2,7,5] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 3

[3,6,4,1,5,2,7] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[3,6,4,1,5,7,2] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 2

[3,6,4,1,7,2,5] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[3,6,4,1,7,5,2] => [[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2

[3,6,4,2,1,5,7] => [[[.,[[.,.],.]],.],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 3

[3,6,4,2,1,7,5] => [[[.,[[.,.],.]],.],[[.,.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 2

[3,6,4,2,5,1,7] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[3,6,4,2,5,7,1] => [[[.,[[.,.],.]],[.,[.,.]]],.] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 1

[3,6,4,2,7,1,5] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[3,6,4,2,7,5,1] => [[[.,[[.,.],.]],[[.,.],.]],.] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[3,6,4,5,1,2,7] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[3,6,4,5,1,7,2] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2

[3,6,4,5,2,1,7] => [[[.,[[.,.],[.,.]]],.],[.,.]] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 2

[3,6,4,5,2,7,1] => [[[.,[[.,.],[.,.]]],[.,.]],.] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[3,6,4,5,7,1,2] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2

[3,6,4,5,7,2,1] => [[[.,[[.,.],[.,[.,.]]]],.],.] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 1

[3,6,4,7,1,2,5] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[3,6,4,7,1,5,2] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2

[3,6,4,7,2,1,5] => [[[.,[[.,.],[.,.]]],.],[.,.]] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 2

[3,6,4,7,2,5,1] => [[[.,[[.,.],[.,.]]],[.,.]],.] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[3,6,4,7,5,1,2] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2

[3,6,4,7,5,2,1] => [[[.,[[.,.],[[.,.],.]]],.],.] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 1

[3,6,5,1,2,4,7] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4

[3,6,5,1,2,7,4] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 3

[3,6,5,1,4,2,7] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[3,6,5,1,4,7,2] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 2

[3,6,5,1,7,2,4] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[3,6,5,1,7,4,2] => [[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2

[3,6,5,2,1,4,7] => [[[.,[[.,.],.]],.],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 3

[3,6,5,2,1,7,4] => [[[.,[[.,.],.]],.],[[.,.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 2

[3,6,5,2,4,1,7] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[3,6,5,2,4,7,1] => [[[.,[[.,.],.]],[.,[.,.]]],.] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 1

[3,6,5,2,7,1,4] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[3,6,5,2,7,4,1] => [[[.,[[.,.],.]],[[.,.],.]],.] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[3,6,5,4,1,2,7] => [[.,[[[.,.],.],.]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 3

[3,6,5,4,1,7,2] => [[.,[[[.,.],.],.]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 2

[3,6,5,4,2,1,7] => [[[.,[[[.,.],.],.]],.],[.,.]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 2

[3,6,5,4,2,7,1] => [[[.,[[[.,.],.],.]],[.,.]],.] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1

[3,6,5,4,7,1,2] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 2

[3,6,5,4,7,2,1] => [[[.,[[[.,.],.],[.,.]]],.],.] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 1

[3,6,5,7,1,2,4] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[3,6,5,7,1,4,2] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2

[3,6,5,7,2,1,4] => [[[.,[[.,.],[.,.]]],.],[.,.]] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 2

[3,6,5,7,2,4,1] => [[[.,[[.,.],[.,.]]],[.,.]],.] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[3,6,5,7,4,1,2] => [[.,[[[.,.],[.,.]],.]],[.,.]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2

[3,6,5,7,4,2,1] => [[[.,[[[.,.],[.,.]],.]],.],.] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[3,6,7,1,2,4,5] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[3,6,7,1,2,5,4] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[3,6,7,1,4,2,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,6,7,1,4,5,2] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[3,6,7,1,5,2,4] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,6,7,1,5,4,2] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[3,6,7,2,1,4,5] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[3,6,7,2,1,5,4] => [[[.,[.,[.,.]]],.],[[.,.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[3,6,7,2,4,1,5] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[3,6,7,2,4,5,1] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1

[3,6,7,2,5,1,4] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[3,6,7,2,5,4,1] => [[[.,[.,[.,.]]],[[.,.],.]],.] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 1

[3,6,7,4,1,2,5] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[3,6,7,4,1,5,2] => [[.,[[.,[.,.]],.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[3,6,7,4,2,1,5] => [[[.,[[.,[.,.]],.]],.],[.,.]] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 2

[3,6,7,4,2,5,1] => [[[.,[[.,[.,.]],.]],[.,.]],.] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[3,6,7,4,5,1,2] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[3,6,7,4,5,2,1] => [[[.,[[.,[.,.]],[.,.]]],.],.] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1

[3,6,7,5,1,2,4] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[3,6,7,5,1,4,2] => [[.,[[.,[.,.]],.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[3,6,7,5,2,1,4] => [[[.,[[.,[.,.]],.]],.],[.,.]] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 2

[3,6,7,5,2,4,1] => [[[.,[[.,[.,.]],.]],[.,.]],.] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[3,6,7,5,4,1,2] => [[.,[[[.,[.,.]],.],.]],[.,.]] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 2

[3,6,7,5,4,2,1] => [[[.,[[[.,[.,.]],.],.]],.],.] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 1

[3,7,1,2,4,5,6] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[3,7,1,2,4,6,5] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[3,7,1,2,5,4,6] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[3,7,1,2,5,6,4] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[3,7,1,2,6,4,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[3,7,1,2,6,5,4] => [[.,[.,.]],[.,[[[.,.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[3,7,1,4,2,5,6] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[3,7,1,4,2,6,5] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[3,7,1,4,5,2,6] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[3,7,1,4,5,6,2] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[3,7,1,4,6,2,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[3,7,1,4,6,5,2] => [[.,[.,.]],[[.,[[.,.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[3,7,1,5,2,4,6] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[3,7,1,5,2,6,4] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[3,7,1,5,4,2,6] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[3,7,1,5,4,6,2] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[3,7,1,5,6,2,4] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[3,7,1,5,6,4,2] => [[.,[.,.]],[[[.,[.,.]],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[3,7,1,6,2,4,5] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[3,7,1,6,2,5,4] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[3,7,1,6,4,2,5] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[3,7,1,6,4,5,2] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[3,7,1,6,5,2,4] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[3,7,1,6,5,4,2] => [[.,[.,.]],[[[[.,.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[3,7,2,1,4,5,6] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[3,7,2,1,4,6,5] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[3,7,2,1,5,4,6] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[3,7,2,1,5,6,4] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[3,7,2,1,6,4,5] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[3,7,2,1,6,5,4] => [[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[3,7,2,4,1,5,6] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[3,7,2,4,1,6,5] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[3,7,2,4,5,1,6] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[3,7,2,4,5,6,1] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1

[3,7,2,4,6,1,5] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[3,7,2,4,6,5,1] => [[[.,[.,.]],[.,[[.,.],.]]],.] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[3,7,2,5,1,4,6] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[3,7,2,5,1,6,4] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[3,7,2,5,4,1,6] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[3,7,2,5,4,6,1] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[3,7,2,5,6,1,4] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[3,7,2,5,6,4,1] => [[[.,[.,.]],[[.,[.,.]],.]],.] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[3,7,2,6,1,4,5] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[3,7,2,6,1,5,4] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[3,7,2,6,4,1,5] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[3,7,2,6,4,5,1] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[3,7,2,6,5,1,4] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[3,7,2,6,5,4,1] => [[[.,[.,.]],[[[.,.],.],.]],.] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1

[3,7,4,1,2,5,6] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4

[3,7,4,1,2,6,5] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 3

[3,7,4,1,5,2,6] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[3,7,4,1,5,6,2] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 2

[3,7,4,1,6,2,5] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[3,7,4,1,6,5,2] => [[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2

[3,7,4,2,1,5,6] => [[[.,[[.,.],.]],.],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 3

[3,7,4,2,1,6,5] => [[[.,[[.,.],.]],.],[[.,.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 2

[3,7,4,2,5,1,6] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[3,7,4,2,5,6,1] => [[[.,[[.,.],.]],[.,[.,.]]],.] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 1

[3,7,4,2,6,1,5] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[3,7,4,2,6,5,1] => [[[.,[[.,.],.]],[[.,.],.]],.] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[3,7,4,5,1,2,6] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[3,7,4,5,1,6,2] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2

[3,7,4,5,2,1,6] => [[[.,[[.,.],[.,.]]],.],[.,.]] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 2

[3,7,4,5,2,6,1] => [[[.,[[.,.],[.,.]]],[.,.]],.] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[3,7,4,5,6,1,2] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2

[3,7,4,5,6,2,1] => [[[.,[[.,.],[.,[.,.]]]],.],.] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 1

[3,7,4,6,1,2,5] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[3,7,4,6,1,5,2] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2

[3,7,4,6,2,1,5] => [[[.,[[.,.],[.,.]]],.],[.,.]] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 2

[3,7,4,6,2,5,1] => [[[.,[[.,.],[.,.]]],[.,.]],.] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[3,7,4,6,5,1,2] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2

[3,7,4,6,5,2,1] => [[[.,[[.,.],[[.,.],.]]],.],.] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 1

[3,7,5,1,2,4,6] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4

[3,7,5,1,2,6,4] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 3

[3,7,5,1,4,2,6] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[3,7,5,1,4,6,2] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 2

[3,7,5,1,6,2,4] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[3,7,5,1,6,4,2] => [[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2

[3,7,5,2,1,4,6] => [[[.,[[.,.],.]],.],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 3

[3,7,5,2,1,6,4] => [[[.,[[.,.],.]],.],[[.,.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 2

[3,7,5,2,4,1,6] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[3,7,5,2,4,6,1] => [[[.,[[.,.],.]],[.,[.,.]]],.] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 1

[3,7,5,2,6,1,4] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[3,7,5,2,6,4,1] => [[[.,[[.,.],.]],[[.,.],.]],.] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[3,7,5,4,1,2,6] => [[.,[[[.,.],.],.]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 3

[3,7,5,4,1,6,2] => [[.,[[[.,.],.],.]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 2

[3,7,5,4,2,1,6] => [[[.,[[[.,.],.],.]],.],[.,.]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 2

[3,7,5,4,2,6,1] => [[[.,[[[.,.],.],.]],[.,.]],.] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1

[3,7,5,4,6,1,2] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 2

[3,7,5,4,6,2,1] => [[[.,[[[.,.],.],[.,.]]],.],.] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 1

[3,7,5,6,1,2,4] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[3,7,5,6,1,4,2] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2

[3,7,5,6,2,1,4] => [[[.,[[.,.],[.,.]]],.],[.,.]] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 2

[3,7,5,6,2,4,1] => [[[.,[[.,.],[.,.]]],[.,.]],.] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[3,7,5,6,4,1,2] => [[.,[[[.,.],[.,.]],.]],[.,.]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2

[3,7,5,6,4,2,1] => [[[.,[[[.,.],[.,.]],.]],.],.] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[3,7,6,1,2,4,5] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4

[3,7,6,1,2,5,4] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 3

[3,7,6,1,4,2,5] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[3,7,6,1,4,5,2] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 2

[3,7,6,1,5,2,4] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[3,7,6,1,5,4,2] => [[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2

[3,7,6,2,1,4,5] => [[[.,[[.,.],.]],.],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 3

[3,7,6,2,1,5,4] => [[[.,[[.,.],.]],.],[[.,.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 2

[3,7,6,2,4,1,5] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[3,7,6,2,4,5,1] => [[[.,[[.,.],.]],[.,[.,.]]],.] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 1

[3,7,6,2,5,1,4] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[3,7,6,2,5,4,1] => [[[.,[[.,.],.]],[[.,.],.]],.] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[3,7,6,4,1,2,5] => [[.,[[[.,.],.],.]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 3

[3,7,6,4,1,5,2] => [[.,[[[.,.],.],.]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 2

[3,7,6,4,2,1,5] => [[[.,[[[.,.],.],.]],.],[.,.]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 2

[3,7,6,4,2,5,1] => [[[.,[[[.,.],.],.]],[.,.]],.] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1

[3,7,6,4,5,1,2] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 2

[3,7,6,4,5,2,1] => [[[.,[[[.,.],.],[.,.]]],.],.] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 1

[3,7,6,5,1,2,4] => [[.,[[[.,.],.],.]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 3

[3,7,6,5,1,4,2] => [[.,[[[.,.],.],.]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 2

[3,7,6,5,2,1,4] => [[[.,[[[.,.],.],.]],.],[.,.]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 2

[3,7,6,5,2,4,1] => [[[.,[[[.,.],.],.]],[.,.]],.] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1

[3,7,6,5,4,1,2] => [[.,[[[[.,.],.],.],.]],[.,.]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 2

[3,7,6,5,4,2,1] => [[[.,[[[[.,.],.],.],.]],.],.] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1

[4,1,2,3,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6

[4,1,2,3,5,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 5

[4,1,2,3,6,5,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 5

[4,1,2,3,6,7,5] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 4

[4,1,2,3,7,5,6] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 5

[4,1,2,3,7,6,5] => [[.,.],[.,[.,[[[.,.],.],.]]]] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 4

[4,1,2,5,3,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5

[4,1,2,5,3,7,6] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4

[4,1,2,5,6,3,7] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4

[4,1,2,5,6,7,3] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 3

[4,1,2,5,7,3,6] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4

[4,1,2,5,7,6,3] => [[.,.],[.,[[.,[[.,.],.]],.]]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 3

[4,1,2,6,3,5,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5

[4,1,2,6,3,7,5] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4

[4,1,2,6,5,3,7] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 4

[4,1,2,6,5,7,3] => [[.,.],[.,[[[.,.],[.,.]],.]]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 3

[4,1,2,6,7,3,5] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4

[4,1,2,6,7,5,3] => [[.,.],[.,[[[.,[.,.]],.],.]]] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 3

[4,1,2,7,3,5,6] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5

[4,1,2,7,3,6,5] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4

[4,1,2,7,5,3,6] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 4

[4,1,2,7,5,6,3] => [[.,.],[.,[[[.,.],[.,.]],.]]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 3

[4,1,2,7,6,3,5] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 4

[4,1,2,7,6,5,3] => [[.,.],[.,[[[[.,.],.],.],.]]] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 3

[4,1,3,2,5,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[4,1,3,2,5,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[4,1,3,2,6,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[4,1,3,2,6,7,5] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[4,1,3,2,7,5,6] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[4,1,3,2,7,6,5] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[4,1,3,5,2,6,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[4,1,3,5,2,7,6] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[4,1,3,5,6,2,7] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[4,1,3,5,6,7,2] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2

[4,1,3,5,7,2,6] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[4,1,3,5,7,6,2] => [[.,.],[[.,[.,[[.,.],.]]],.]] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 2

[4,1,3,6,2,5,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[4,1,3,6,2,7,5] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[4,1,3,6,5,2,7] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3

[4,1,3,6,5,7,2] => [[.,.],[[.,[[.,.],[.,.]]],.]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 2

[4,1,3,6,7,2,5] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[4,1,3,6,7,5,2] => [[.,.],[[.,[[.,[.,.]],.]],.]] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 2

[4,1,3,7,2,5,6] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[4,1,3,7,2,6,5] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[4,1,3,7,5,2,6] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3

[4,1,3,7,5,6,2] => [[.,.],[[.,[[.,.],[.,.]]],.]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 2

[4,1,3,7,6,2,5] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3

[4,1,3,7,6,5,2] => [[.,.],[[.,[[[.,.],.],.]],.]] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 2

[4,1,5,2,3,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[4,1,5,2,3,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[4,1,5,2,6,3,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[4,1,5,2,6,7,3] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[4,1,5,2,7,3,6] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[4,1,5,2,7,6,3] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[4,1,5,3,2,6,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[4,1,5,3,2,7,6] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[4,1,5,3,6,2,7] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[4,1,5,3,6,7,2] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 2

[4,1,5,3,7,2,6] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[4,1,5,3,7,6,2] => [[.,.],[[[.,.],[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2

[4,1,5,6,2,3,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[4,1,5,6,2,7,3] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[4,1,5,6,3,2,7] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[4,1,5,6,3,7,2] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2

[4,1,5,6,7,2,3] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[4,1,5,6,7,3,2] => [[.,.],[[[.,[.,[.,.]]],.],.]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2

[4,1,5,7,2,3,6] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[4,1,5,7,2,6,3] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[4,1,5,7,3,2,6] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[4,1,5,7,3,6,2] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2

[4,1,5,7,6,2,3] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3

[4,1,5,7,6,3,2] => [[.,.],[[[.,[[.,.],.]],.],.]] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 2

[4,1,6,2,3,5,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[4,1,6,2,3,7,5] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[4,1,6,2,5,3,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[4,1,6,2,5,7,3] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[4,1,6,2,7,3,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[4,1,6,2,7,5,3] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[4,1,6,3,2,5,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[4,1,6,3,2,7,5] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[4,1,6,3,5,2,7] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[4,1,6,3,5,7,2] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 2

[4,1,6,3,7,2,5] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[4,1,6,3,7,5,2] => [[.,.],[[[.,.],[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2

[4,1,6,5,2,3,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[4,1,6,5,2,7,3] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[4,1,6,5,3,2,7] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[4,1,6,5,3,7,2] => [[.,.],[[[[.,.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2

[4,1,6,5,7,2,3] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[4,1,6,5,7,3,2] => [[.,.],[[[[.,.],[.,.]],.],.]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 2

[4,1,6,7,2,3,5] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[4,1,6,7,2,5,3] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[4,1,6,7,3,2,5] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[4,1,6,7,3,5,2] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2

[4,1,6,7,5,2,3] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[4,1,6,7,5,3,2] => [[.,.],[[[[.,[.,.]],.],.],.]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 2

[4,1,7,2,3,5,6] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[4,1,7,2,3,6,5] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[4,1,7,2,5,3,6] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[4,1,7,2,5,6,3] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[4,1,7,2,6,3,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[4,1,7,2,6,5,3] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[4,1,7,3,2,5,6] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[4,1,7,3,2,6,5] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[4,1,7,3,5,2,6] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[4,1,7,3,5,6,2] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 2

[4,1,7,3,6,2,5] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[4,1,7,3,6,5,2] => [[.,.],[[[.,.],[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2

[4,1,7,5,2,3,6] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[4,1,7,5,2,6,3] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[4,1,7,5,3,2,6] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[4,1,7,5,3,6,2] => [[.,.],[[[[.,.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2

[4,1,7,5,6,2,3] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[4,1,7,5,6,3,2] => [[.,.],[[[[.,.],[.,.]],.],.]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 2

[4,1,7,6,2,3,5] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[4,1,7,6,2,5,3] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[4,1,7,6,3,2,5] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[4,1,7,6,3,5,2] => [[.,.],[[[[.,.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2

[4,1,7,6,5,2,3] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[4,1,7,6,5,3,2] => [[.,.],[[[[[.,.],.],.],.],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2

[4,2,1,3,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 5

[4,2,1,3,5,7,6] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 4

[4,2,1,3,6,5,7] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[4,2,1,3,6,7,5] => [[[.,.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 3

[4,2,1,3,7,5,6] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[4,2,1,3,7,6,5] => [[[.,.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 3

[4,2,1,5,3,6,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[4,2,1,5,3,7,6] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[4,2,1,5,6,3,7] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[4,2,1,5,6,7,3] => [[[.,.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 2

[4,2,1,5,7,3,6] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[4,2,1,5,7,6,3] => [[[.,.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 2

[4,2,1,6,3,5,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[4,2,1,6,3,7,5] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[4,2,1,6,5,3,7] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[4,2,1,6,5,7,3] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[4,2,1,6,7,3,5] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[4,2,1,6,7,5,3] => [[[.,.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 2

[4,2,1,7,3,5,6] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[4,2,1,7,3,6,5] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[4,2,1,7,5,3,6] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[4,2,1,7,5,6,3] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[4,2,1,7,6,3,5] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[4,2,1,7,6,5,3] => [[[.,.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2

[4,2,3,1,5,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[4,2,3,1,5,7,6] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[4,2,3,1,6,5,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,2,3,1,6,7,5] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[4,2,3,1,7,5,6] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,2,3,1,7,6,5] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[4,2,3,5,1,6,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[4,2,3,5,1,7,6] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[4,2,3,5,6,1,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[4,2,3,5,6,7,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1

[4,2,3,5,7,1,6] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[4,2,3,5,7,6,1] => [[[.,.],[.,[.,[[.,.],.]]]],.] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 1

[4,2,3,6,1,5,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[4,2,3,6,1,7,5] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[4,2,3,6,5,1,7] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[4,2,3,6,5,7,1] => [[[.,.],[.,[[.,.],[.,.]]]],.] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 1

[4,2,3,6,7,1,5] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[4,2,3,6,7,5,1] => [[[.,.],[.,[[.,[.,.]],.]]],.] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 1

[4,2,3,7,1,5,6] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[4,2,3,7,1,6,5] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[4,2,3,7,5,1,6] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[4,2,3,7,5,6,1] => [[[.,.],[.,[[.,.],[.,.]]]],.] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 1

[4,2,3,7,6,1,5] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[4,2,3,7,6,5,1] => [[[.,.],[.,[[[.,.],.],.]]],.] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 1

[4,2,5,1,3,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[4,2,5,1,3,7,6] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[4,2,5,1,6,3,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,2,5,1,6,7,3] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[4,2,5,1,7,3,6] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,2,5,1,7,6,3] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[4,2,5,3,1,6,7] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[4,2,5,3,1,7,6] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[4,2,5,3,6,1,7] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[4,2,5,3,6,7,1] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 1

[4,2,5,3,7,1,6] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[4,2,5,3,7,6,1] => [[[.,.],[[.,.],[[.,.],.]]],.] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 1

[4,2,5,6,1,3,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[4,2,5,6,1,7,3] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[4,2,5,6,3,1,7] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[4,2,5,6,3,7,1] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 1

[4,2,5,6,7,1,3] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[4,2,5,6,7,3,1] => [[[.,.],[[.,[.,[.,.]]],.]],.] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[4,2,5,7,1,3,6] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[4,2,5,7,1,6,3] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[4,2,5,7,3,1,6] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[4,2,5,7,3,6,1] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 1

[4,2,5,7,6,1,3] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[4,2,5,7,6,3,1] => [[[.,.],[[.,[[.,.],.]],.]],.] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 1

[4,2,6,1,3,5,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[4,2,6,1,3,7,5] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[4,2,6,1,5,3,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,2,6,1,5,7,3] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[4,2,6,1,7,3,5] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,2,6,1,7,5,3] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[4,2,6,3,1,5,7] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[4,2,6,3,1,7,5] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[4,2,6,3,5,1,7] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[4,2,6,3,5,7,1] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 1

[4,2,6,3,7,1,5] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[4,2,6,3,7,5,1] => [[[.,.],[[.,.],[[.,.],.]]],.] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 1

[4,2,6,5,1,3,7] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[4,2,6,5,1,7,3] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[4,2,6,5,3,1,7] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[4,2,6,5,3,7,1] => [[[.,.],[[[.,.],.],[.,.]]],.] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 1

[4,2,6,5,7,1,3] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[4,2,6,5,7,3,1] => [[[.,.],[[[.,.],[.,.]],.]],.] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 1

[4,2,6,7,1,3,5] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[4,2,6,7,1,5,3] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[4,2,6,7,3,1,5] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[4,2,6,7,3,5,1] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 1

[4,2,6,7,5,1,3] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[4,2,6,7,5,3,1] => [[[.,.],[[[.,[.,.]],.],.]],.] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 1

[4,2,7,1,3,5,6] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[4,2,7,1,3,6,5] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[4,2,7,1,5,3,6] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,2,7,1,5,6,3] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[4,2,7,1,6,3,5] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,2,7,1,6,5,3] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[4,2,7,3,1,5,6] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[4,2,7,3,1,6,5] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[4,2,7,3,5,1,6] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[4,2,7,3,5,6,1] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 1

[4,2,7,3,6,1,5] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[4,2,7,3,6,5,1] => [[[.,.],[[.,.],[[.,.],.]]],.] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 1

[4,2,7,5,1,3,6] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[4,2,7,5,1,6,3] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[4,2,7,5,3,1,6] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[4,2,7,5,3,6,1] => [[[.,.],[[[.,.],.],[.,.]]],.] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 1

[4,2,7,5,6,1,3] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[4,2,7,5,6,3,1] => [[[.,.],[[[.,.],[.,.]],.]],.] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 1

[4,2,7,6,1,3,5] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[4,2,7,6,1,5,3] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[4,2,7,6,3,1,5] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[4,2,7,6,3,5,1] => [[[.,.],[[[.,.],.],[.,.]]],.] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 1

[4,2,7,6,5,1,3] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[4,2,7,6,5,3,1] => [[[.,.],[[[[.,.],.],.],.]],.] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1

[4,3,1,2,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 5

[4,3,1,2,5,7,6] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 4

[4,3,1,2,6,5,7] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[4,3,1,2,6,7,5] => [[[.,.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 3

[4,3,1,2,7,5,6] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[4,3,1,2,7,6,5] => [[[.,.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 3

[4,3,1,5,2,6,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[4,3,1,5,2,7,6] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[4,3,1,5,6,2,7] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[4,3,1,5,6,7,2] => [[[.,.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 2

[4,3,1,5,7,2,6] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[4,3,1,5,7,6,2] => [[[.,.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 2

[4,3,1,6,2,5,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[4,3,1,6,2,7,5] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[4,3,1,6,5,2,7] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[4,3,1,6,5,7,2] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[4,3,1,6,7,2,5] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[4,3,1,6,7,5,2] => [[[.,.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 2

[4,3,1,7,2,5,6] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[4,3,1,7,2,6,5] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[4,3,1,7,5,2,6] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[4,3,1,7,5,6,2] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[4,3,1,7,6,2,5] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[4,3,1,7,6,5,2] => [[[.,.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2

[4,3,2,1,5,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4

[4,3,2,1,5,7,6] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 3

[4,3,2,1,6,5,7] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[4,3,2,1,6,7,5] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 2

[4,3,2,1,7,5,6] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[4,3,2,1,7,6,5] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2

[4,3,2,5,1,6,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[4,3,2,5,1,7,6] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[4,3,2,5,6,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[4,3,2,5,6,7,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1

[4,3,2,5,7,1,6] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[4,3,2,5,7,6,1] => [[[[.,.],.],[.,[[.,.],.]]],.] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 1

[4,3,2,6,1,5,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[4,3,2,6,1,7,5] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[4,3,2,6,5,1,7] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[4,3,2,6,5,7,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 1

[4,3,2,6,7,1,5] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[4,3,2,6,7,5,1] => [[[[.,.],.],[[.,[.,.]],.]],.] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 1

[4,3,2,7,1,5,6] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[4,3,2,7,1,6,5] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[4,3,2,7,5,1,6] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[4,3,2,7,5,6,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 1

[4,3,2,7,6,1,5] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[4,3,2,7,6,5,1] => [[[[.,.],.],[[[.,.],.],.]],.] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 1

[4,3,5,1,2,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[4,3,5,1,2,7,6] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[4,3,5,1,6,2,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,3,5,1,6,7,2] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[4,3,5,1,7,2,6] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,3,5,1,7,6,2] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[4,3,5,2,1,6,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3

[4,3,5,2,1,7,6] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[4,3,5,2,6,1,7] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[4,3,5,2,6,7,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1

[4,3,5,2,7,1,6] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[4,3,5,2,7,6,1] => [[[[.,.],[.,.]],[[.,.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 1

[4,3,5,6,1,2,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[4,3,5,6,1,7,2] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[4,3,5,6,2,1,7] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2

[4,3,5,6,2,7,1] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[4,3,5,6,7,1,2] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[4,3,5,6,7,2,1] => [[[[.,.],[.,[.,[.,.]]]],.],.] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1

[4,3,5,7,1,2,6] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[4,3,5,7,1,6,2] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[4,3,5,7,2,1,6] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2

[4,3,5,7,2,6,1] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[4,3,5,7,6,1,2] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[4,3,5,7,6,2,1] => [[[[.,.],[.,[[.,.],.]]],.],.] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 1

[4,3,6,1,2,5,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[4,3,6,1,2,7,5] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[4,3,6,1,5,2,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,3,6,1,5,7,2] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[4,3,6,1,7,2,5] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,3,6,1,7,5,2] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[4,3,6,2,1,5,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3

[4,3,6,2,1,7,5] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[4,3,6,2,5,1,7] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[4,3,6,2,5,7,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1

[4,3,6,2,7,1,5] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[4,3,6,2,7,5,1] => [[[[.,.],[.,.]],[[.,.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 1

[4,3,6,5,1,2,7] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[4,3,6,5,1,7,2] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[4,3,6,5,2,1,7] => [[[[.,.],[[.,.],.]],.],[.,.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2

[4,3,6,5,2,7,1] => [[[[.,.],[[.,.],.]],[.,.]],.] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 1

[4,3,6,5,7,1,2] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[4,3,6,5,7,2,1] => [[[[.,.],[[.,.],[.,.]]],.],.] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 1

[4,3,6,7,1,2,5] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[4,3,6,7,1,5,2] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[4,3,6,7,2,1,5] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2

[4,3,6,7,2,5,1] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[4,3,6,7,5,1,2] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[4,3,6,7,5,2,1] => [[[[.,.],[[.,[.,.]],.]],.],.] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 1

[4,3,7,1,2,5,6] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[4,3,7,1,2,6,5] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[4,3,7,1,5,2,6] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,3,7,1,5,6,2] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[4,3,7,1,6,2,5] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,3,7,1,6,5,2] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[4,3,7,2,1,5,6] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3

[4,3,7,2,1,6,5] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[4,3,7,2,5,1,6] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[4,3,7,2,5,6,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1

[4,3,7,2,6,1,5] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[4,3,7,2,6,5,1] => [[[[.,.],[.,.]],[[.,.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 1

[4,3,7,5,1,2,6] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[4,3,7,5,1,6,2] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[4,3,7,5,2,1,6] => [[[[.,.],[[.,.],.]],.],[.,.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2

[4,3,7,5,2,6,1] => [[[[.,.],[[.,.],.]],[.,.]],.] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 1

[4,3,7,5,6,1,2] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[4,3,7,5,6,2,1] => [[[[.,.],[[.,.],[.,.]]],.],.] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 1

[4,3,7,6,1,2,5] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[4,3,7,6,1,5,2] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[4,3,7,6,2,1,5] => [[[[.,.],[[.,.],.]],.],[.,.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2

[4,3,7,6,2,5,1] => [[[[.,.],[[.,.],.]],[.,.]],.] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 1

[4,3,7,6,5,1,2] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[4,3,7,6,5,2,1] => [[[[.,.],[[[.,.],.],.]],.],.] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 1

[4,5,1,2,3,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[4,5,1,2,3,7,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[4,5,1,2,6,3,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[4,5,1,2,6,7,3] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[4,5,1,2,7,3,6] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[4,5,1,2,7,6,3] => [[.,[.,.]],[.,[[[.,.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[4,5,1,3,2,6,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[4,5,1,3,2,7,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[4,5,1,3,6,2,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[4,5,1,3,6,7,2] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[4,5,1,3,7,2,6] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[4,5,1,3,7,6,2] => [[.,[.,.]],[[.,[[.,.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[4,5,1,6,2,3,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[4,5,1,6,2,7,3] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[4,5,1,6,3,2,7] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[4,5,1,6,3,7,2] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[4,5,1,6,7,2,3] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[4,5,1,6,7,3,2] => [[.,[.,.]],[[[.,[.,.]],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[4,5,1,7,2,3,6] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[4,5,1,7,2,6,3] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[4,5,1,7,3,2,6] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[4,5,1,7,3,6,2] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[4,5,1,7,6,2,3] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[4,5,1,7,6,3,2] => [[.,[.,.]],[[[[.,.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[4,5,2,1,3,6,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[4,5,2,1,3,7,6] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[4,5,2,1,6,3,7] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[4,5,2,1,6,7,3] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[4,5,2,1,7,3,6] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[4,5,2,1,7,6,3] => [[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[4,5,2,3,1,6,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[4,5,2,3,1,7,6] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[4,5,2,3,6,1,7] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[4,5,2,3,6,7,1] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1

[4,5,2,3,7,1,6] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[4,5,2,3,7,6,1] => [[[.,[.,.]],[.,[[.,.],.]]],.] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[4,5,2,6,1,3,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[4,5,2,6,1,7,3] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[4,5,2,6,3,1,7] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[4,5,2,6,3,7,1] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[4,5,2,6,7,1,3] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[4,5,2,6,7,3,1] => [[[.,[.,.]],[[.,[.,.]],.]],.] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[4,5,2,7,1,3,6] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[4,5,2,7,1,6,3] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[4,5,2,7,3,1,6] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[4,5,2,7,3,6,1] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[4,5,2,7,6,1,3] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[4,5,2,7,6,3,1] => [[[.,[.,.]],[[[.,.],.],.]],.] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1

[4,5,3,1,2,6,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[4,5,3,1,2,7,6] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[4,5,3,1,6,2,7] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[4,5,3,1,6,7,2] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[4,5,3,1,7,2,6] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[4,5,3,1,7,6,2] => [[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[4,5,3,2,1,6,7] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3

[4,5,3,2,1,7,6] => [[[[.,[.,.]],.],.],[[.,.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[4,5,3,2,6,1,7] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[4,5,3,2,6,7,1] => [[[[.,[.,.]],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1

[4,5,3,2,7,1,6] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[4,5,3,2,7,6,1] => [[[[.,[.,.]],.],[[.,.],.]],.] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1

[4,5,3,6,1,2,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[4,5,3,6,1,7,2] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[4,5,3,6,2,1,7] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[4,5,3,6,2,7,1] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[4,5,3,6,7,1,2] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[4,5,3,6,7,2,1] => [[[[.,[.,.]],[.,[.,.]]],.],.] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1

[4,5,3,7,1,2,6] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[4,5,3,7,1,6,2] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[4,5,3,7,2,1,6] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[4,5,3,7,2,6,1] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[4,5,3,7,6,1,2] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[4,5,3,7,6,2,1] => [[[[.,[.,.]],[[.,.],.]],.],.] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

[4,5,6,1,2,3,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[4,5,6,1,2,7,3] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[4,5,6,1,3,2,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,5,6,1,3,7,2] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[4,5,6,1,7,2,3] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,5,6,1,7,3,2] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[4,5,6,2,1,3,7] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[4,5,6,2,1,7,3] => [[[.,[.,[.,.]]],.],[[.,.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[4,5,6,2,3,1,7] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[4,5,6,2,3,7,1] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1

[4,5,6,2,7,1,3] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[4,5,6,2,7,3,1] => [[[.,[.,[.,.]]],[[.,.],.]],.] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 1

[4,5,6,3,1,2,7] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[4,5,6,3,1,7,2] => [[[.,[.,[.,.]]],.],[[.,.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[4,5,6,3,2,1,7] => [[[[.,[.,[.,.]]],.],.],[.,.]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2

[4,5,6,3,2,7,1] => [[[[.,[.,[.,.]]],.],[.,.]],.] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1

[4,5,6,3,7,1,2] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[4,5,6,3,7,2,1] => [[[[.,[.,[.,.]]],[.,.]],.],.] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1

[4,5,6,7,1,2,3] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[4,5,6,7,1,3,2] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[4,5,6,7,2,1,3] => [[[.,[.,[.,[.,.]]]],.],[.,.]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 2

[4,5,6,7,2,3,1] => [[[.,[.,[.,[.,.]]]],[.,.]],.] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 1

[4,5,6,7,3,1,2] => [[[.,[.,[.,[.,.]]]],.],[.,.]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 2

[4,5,6,7,3,2,1] => [[[[.,[.,[.,[.,.]]]],.],.],.] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1

[4,5,7,1,2,3,6] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[4,5,7,1,2,6,3] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[4,5,7,1,3,2,6] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,5,7,1,3,6,2] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[4,5,7,1,6,2,3] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,5,7,1,6,3,2] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[4,5,7,2,1,3,6] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[4,5,7,2,1,6,3] => [[[.,[.,[.,.]]],.],[[.,.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[4,5,7,2,3,1,6] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[4,5,7,2,3,6,1] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1

[4,5,7,2,6,1,3] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[4,5,7,2,6,3,1] => [[[.,[.,[.,.]]],[[.,.],.]],.] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 1

[4,5,7,3,1,2,6] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[4,5,7,3,1,6,2] => [[[.,[.,[.,.]]],.],[[.,.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[4,5,7,3,2,1,6] => [[[[.,[.,[.,.]]],.],.],[.,.]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2

[4,5,7,3,2,6,1] => [[[[.,[.,[.,.]]],.],[.,.]],.] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1

[4,5,7,3,6,1,2] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[4,5,7,3,6,2,1] => [[[[.,[.,[.,.]]],[.,.]],.],.] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1

[4,5,7,6,1,2,3] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 3

[4,5,7,6,1,3,2] => [[.,[.,[[.,.],.]]],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 2

[4,5,7,6,2,1,3] => [[[.,[.,[[.,.],.]]],.],[.,.]] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 2

[4,5,7,6,2,3,1] => [[[.,[.,[[.,.],.]]],[.,.]],.] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[4,5,7,6,3,1,2] => [[[.,[.,[[.,.],.]]],.],[.,.]] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 2

[4,5,7,6,3,2,1] => [[[[.,[.,[[.,.],.]]],.],.],.] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1

[4,6,1,2,3,5,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[4,6,1,2,3,7,5] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[4,6,1,2,5,3,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[4,6,1,2,5,7,3] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[4,6,1,2,7,3,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[4,6,1,2,7,5,3] => [[.,[.,.]],[.,[[[.,.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[4,6,1,3,2,5,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[4,6,1,3,2,7,5] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[4,6,1,3,5,2,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[4,6,1,3,5,7,2] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[4,6,1,3,7,2,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[4,6,1,3,7,5,2] => [[.,[.,.]],[[.,[[.,.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[4,6,1,5,2,3,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[4,6,1,5,2,7,3] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[4,6,1,5,3,2,7] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[4,6,1,5,3,7,2] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[4,6,1,5,7,2,3] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[4,6,1,5,7,3,2] => [[.,[.,.]],[[[.,[.,.]],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[4,6,1,7,2,3,5] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[4,6,1,7,2,5,3] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[4,6,1,7,3,2,5] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[4,6,1,7,3,5,2] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[4,6,1,7,5,2,3] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[4,6,1,7,5,3,2] => [[.,[.,.]],[[[[.,.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[4,6,2,1,3,5,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[4,6,2,1,3,7,5] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[4,6,2,1,5,3,7] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[4,6,2,1,5,7,3] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[4,6,2,1,7,3,5] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[4,6,2,1,7,5,3] => [[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[4,6,2,3,1,5,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[4,6,2,3,1,7,5] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[4,6,2,3,5,1,7] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[4,6,2,3,5,7,1] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1

[4,6,2,3,7,1,5] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[4,6,2,3,7,5,1] => [[[.,[.,.]],[.,[[.,.],.]]],.] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[4,6,2,5,1,3,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[4,6,2,5,1,7,3] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[4,6,2,5,3,1,7] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[4,6,2,5,3,7,1] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[4,6,2,5,7,1,3] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[4,6,2,5,7,3,1] => [[[.,[.,.]],[[.,[.,.]],.]],.] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[4,6,2,7,1,3,5] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[4,6,2,7,1,5,3] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[4,6,2,7,3,1,5] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[4,6,2,7,3,5,1] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[4,6,2,7,5,1,3] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[4,6,2,7,5,3,1] => [[[.,[.,.]],[[[.,.],.],.]],.] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1

[4,6,3,1,2,5,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[4,6,3,1,2,7,5] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[4,6,3,1,5,2,7] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[4,6,3,1,5,7,2] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[4,6,3,1,7,2,5] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[4,6,3,1,7,5,2] => [[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[4,6,3,2,1,5,7] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3

[4,6,3,2,1,7,5] => [[[[.,[.,.]],.],.],[[.,.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[4,6,3,2,5,1,7] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[4,6,3,2,5,7,1] => [[[[.,[.,.]],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1

[4,6,3,2,7,1,5] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[4,6,3,2,7,5,1] => [[[[.,[.,.]],.],[[.,.],.]],.] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1

[4,6,3,5,1,2,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[4,6,3,5,1,7,2] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[4,6,3,5,2,1,7] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[4,6,3,5,2,7,1] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[4,6,3,5,7,1,2] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[4,6,3,5,7,2,1] => [[[[.,[.,.]],[.,[.,.]]],.],.] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1

[4,6,3,7,1,2,5] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[4,6,3,7,1,5,2] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[4,6,3,7,2,1,5] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[4,6,3,7,2,5,1] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[4,6,3,7,5,1,2] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[4,6,3,7,5,2,1] => [[[[.,[.,.]],[[.,.],.]],.],.] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

[4,6,5,1,2,3,7] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4

[4,6,5,1,2,7,3] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 3

[4,6,5,1,3,2,7] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[4,6,5,1,3,7,2] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 2

[4,6,5,1,7,2,3] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[4,6,5,1,7,3,2] => [[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2

[4,6,5,2,1,3,7] => [[[.,[[.,.],.]],.],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 3

[4,6,5,2,1,7,3] => [[[.,[[.,.],.]],.],[[.,.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 2

[4,6,5,2,3,1,7] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[4,6,5,2,3,7,1] => [[[.,[[.,.],.]],[.,[.,.]]],.] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 1

[4,6,5,2,7,1,3] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[4,6,5,2,7,3,1] => [[[.,[[.,.],.]],[[.,.],.]],.] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[4,6,5,3,1,2,7] => [[[.,[[.,.],.]],.],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 3

[4,6,5,3,1,7,2] => [[[.,[[.,.],.]],.],[[.,.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 2

[4,6,5,3,2,1,7] => [[[[.,[[.,.],.]],.],.],[.,.]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 2

[4,6,5,3,2,7,1] => [[[[.,[[.,.],.]],.],[.,.]],.] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[4,6,5,3,7,1,2] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[4,6,5,3,7,2,1] => [[[[.,[[.,.],.]],[.,.]],.],.] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[4,6,5,7,1,2,3] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[4,6,5,7,1,3,2] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2

[4,6,5,7,2,1,3] => [[[.,[[.,.],[.,.]]],.],[.,.]] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 2

[4,6,5,7,2,3,1] => [[[.,[[.,.],[.,.]]],[.,.]],.] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[4,6,5,7,3,1,2] => [[[.,[[.,.],[.,.]]],.],[.,.]] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 2

[4,6,5,7,3,2,1] => [[[[.,[[.,.],[.,.]]],.],.],.] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1

[4,6,7,1,2,3,5] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[4,6,7,1,2,5,3] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[4,6,7,1,3,2,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,6,7,1,3,5,2] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[4,6,7,1,5,2,3] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,6,7,1,5,3,2] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[4,6,7,2,1,3,5] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[4,6,7,2,1,5,3] => [[[.,[.,[.,.]]],.],[[.,.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[4,6,7,2,3,1,5] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[4,6,7,2,3,5,1] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1

[4,6,7,2,5,1,3] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[4,6,7,2,5,3,1] => [[[.,[.,[.,.]]],[[.,.],.]],.] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 1

[4,6,7,3,1,2,5] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[4,6,7,3,1,5,2] => [[[.,[.,[.,.]]],.],[[.,.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[4,6,7,3,2,1,5] => [[[[.,[.,[.,.]]],.],.],[.,.]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2

[4,6,7,3,2,5,1] => [[[[.,[.,[.,.]]],.],[.,.]],.] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1

[4,6,7,3,5,1,2] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[4,6,7,3,5,2,1] => [[[[.,[.,[.,.]]],[.,.]],.],.] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1

[4,6,7,5,1,2,3] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[4,6,7,5,1,3,2] => [[.,[[.,[.,.]],.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[4,6,7,5,2,1,3] => [[[.,[[.,[.,.]],.]],.],[.,.]] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 2

[4,6,7,5,2,3,1] => [[[.,[[.,[.,.]],.]],[.,.]],.] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[4,6,7,5,3,1,2] => [[[.,[[.,[.,.]],.]],.],[.,.]] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 2

[4,6,7,5,3,2,1] => [[[[.,[[.,[.,.]],.]],.],.],.] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 1

[4,7,1,2,3,5,6] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[4,7,1,2,3,6,5] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[4,7,1,2,5,3,6] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[4,7,1,2,5,6,3] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[4,7,1,2,6,3,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[4,7,1,2,6,5,3] => [[.,[.,.]],[.,[[[.,.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[4,7,1,3,2,5,6] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[4,7,1,3,2,6,5] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[4,7,1,3,5,2,6] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[4,7,1,3,5,6,2] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[4,7,1,3,6,2,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[4,7,1,3,6,5,2] => [[.,[.,.]],[[.,[[.,.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[4,7,1,5,2,3,6] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[4,7,1,5,2,6,3] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[4,7,1,5,3,2,6] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[4,7,1,5,3,6,2] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[4,7,1,5,6,2,3] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[4,7,1,5,6,3,2] => [[.,[.,.]],[[[.,[.,.]],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[4,7,1,6,2,3,5] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[4,7,1,6,2,5,3] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[4,7,1,6,3,2,5] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[4,7,1,6,3,5,2] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[4,7,1,6,5,2,3] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[4,7,1,6,5,3,2] => [[.,[.,.]],[[[[.,.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[4,7,2,1,3,5,6] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[4,7,2,1,3,6,5] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[4,7,2,1,5,3,6] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[4,7,2,1,5,6,3] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[4,7,2,1,6,3,5] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[4,7,2,1,6,5,3] => [[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[4,7,2,3,1,5,6] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[4,7,2,3,1,6,5] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[4,7,2,3,5,1,6] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[4,7,2,3,5,6,1] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1

[4,7,2,3,6,1,5] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[4,7,2,3,6,5,1] => [[[.,[.,.]],[.,[[.,.],.]]],.] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[4,7,2,5,1,3,6] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[4,7,2,5,1,6,3] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[4,7,2,5,3,1,6] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[4,7,2,5,3,6,1] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[4,7,2,5,6,1,3] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[4,7,2,5,6,3,1] => [[[.,[.,.]],[[.,[.,.]],.]],.] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[4,7,2,6,1,3,5] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[4,7,2,6,1,5,3] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[4,7,2,6,3,1,5] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[4,7,2,6,3,5,1] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[4,7,2,6,5,1,3] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[4,7,2,6,5,3,1] => [[[.,[.,.]],[[[.,.],.],.]],.] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1

[4,7,3,1,2,5,6] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[4,7,3,1,2,6,5] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[4,7,3,1,5,2,6] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[4,7,3,1,5,6,2] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[4,7,3,1,6,2,5] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[4,7,3,1,6,5,2] => [[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[4,7,3,2,1,5,6] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3

[4,7,3,2,1,6,5] => [[[[.,[.,.]],.],.],[[.,.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[4,7,3,2,5,1,6] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[4,7,3,2,5,6,1] => [[[[.,[.,.]],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1

[4,7,3,2,6,1,5] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[4,7,3,2,6,5,1] => [[[[.,[.,.]],.],[[.,.],.]],.] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1

[4,7,3,5,1,2,6] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[4,7,3,5,1,6,2] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[4,7,3,5,2,1,6] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[4,7,3,5,2,6,1] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[4,7,3,5,6,1,2] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[4,7,3,5,6,2,1] => [[[[.,[.,.]],[.,[.,.]]],.],.] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1

[4,7,3,6,1,2,5] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[4,7,3,6,1,5,2] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[4,7,3,6,2,1,5] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[4,7,3,6,2,5,1] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[4,7,3,6,5,1,2] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[4,7,3,6,5,2,1] => [[[[.,[.,.]],[[.,.],.]],.],.] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

[4,7,5,1,2,3,6] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4

[4,7,5,1,2,6,3] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 3

[4,7,5,1,3,2,6] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[4,7,5,1,3,6,2] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 2

[4,7,5,1,6,2,3] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[4,7,5,1,6,3,2] => [[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2

[4,7,5,2,1,3,6] => [[[.,[[.,.],.]],.],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 3

[4,7,5,2,1,6,3] => [[[.,[[.,.],.]],.],[[.,.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 2

[4,7,5,2,3,1,6] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[4,7,5,2,3,6,1] => [[[.,[[.,.],.]],[.,[.,.]]],.] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 1

[4,7,5,2,6,1,3] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[4,7,5,2,6,3,1] => [[[.,[[.,.],.]],[[.,.],.]],.] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[4,7,5,3,1,2,6] => [[[.,[[.,.],.]],.],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 3

[4,7,5,3,1,6,2] => [[[.,[[.,.],.]],.],[[.,.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 2

[4,7,5,3,2,1,6] => [[[[.,[[.,.],.]],.],.],[.,.]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 2

[4,7,5,3,2,6,1] => [[[[.,[[.,.],.]],.],[.,.]],.] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[4,7,5,3,6,1,2] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[4,7,5,3,6,2,1] => [[[[.,[[.,.],.]],[.,.]],.],.] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[4,7,5,6,1,2,3] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[4,7,5,6,1,3,2] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2

[4,7,5,6,2,1,3] => [[[.,[[.,.],[.,.]]],.],[.,.]] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 2

[4,7,5,6,2,3,1] => [[[.,[[.,.],[.,.]]],[.,.]],.] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[4,7,5,6,3,1,2] => [[[.,[[.,.],[.,.]]],.],[.,.]] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 2

[4,7,5,6,3,2,1] => [[[[.,[[.,.],[.,.]]],.],.],.] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1

[4,7,6,1,2,3,5] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4

[4,7,6,1,2,5,3] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 3

[4,7,6,1,3,2,5] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[4,7,6,1,3,5,2] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 2

[4,7,6,1,5,2,3] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[4,7,6,1,5,3,2] => [[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2

[4,7,6,2,1,3,5] => [[[.,[[.,.],.]],.],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 3

[4,7,6,2,1,5,3] => [[[.,[[.,.],.]],.],[[.,.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 2

[4,7,6,2,3,1,5] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[4,7,6,2,3,5,1] => [[[.,[[.,.],.]],[.,[.,.]]],.] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 1

[4,7,6,2,5,1,3] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[4,7,6,2,5,3,1] => [[[.,[[.,.],.]],[[.,.],.]],.] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[4,7,6,3,1,2,5] => [[[.,[[.,.],.]],.],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 3

[4,7,6,3,1,5,2] => [[[.,[[.,.],.]],.],[[.,.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 2

[4,7,6,3,2,1,5] => [[[[.,[[.,.],.]],.],.],[.,.]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 2

[4,7,6,3,2,5,1] => [[[[.,[[.,.],.]],.],[.,.]],.] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[4,7,6,3,5,1,2] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[4,7,6,3,5,2,1] => [[[[.,[[.,.],.]],[.,.]],.],.] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[4,7,6,5,1,2,3] => [[.,[[[.,.],.],.]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 3

[4,7,6,5,1,3,2] => [[.,[[[.,.],.],.]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 2

[4,7,6,5,2,1,3] => [[[.,[[[.,.],.],.]],.],[.,.]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 2

[4,7,6,5,2,3,1] => [[[.,[[[.,.],.],.]],[.,.]],.] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1

[4,7,6,5,3,1,2] => [[[.,[[[.,.],.],.]],.],[.,.]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 2

[4,7,6,5,3,2,1] => [[[[.,[[[.,.],.],.]],.],.],.] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1

[5,1,2,3,4,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6

[5,1,2,3,4,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 5

[5,1,2,3,6,4,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 5

[5,1,2,3,6,7,4] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 4

[5,1,2,3,7,4,6] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 5

[5,1,2,3,7,6,4] => [[.,.],[.,[.,[[[.,.],.],.]]]] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 4

[5,1,2,4,3,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5

[5,1,2,4,3,7,6] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4

[5,1,2,4,6,3,7] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4

[5,1,2,4,6,7,3] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 3

[5,1,2,4,7,3,6] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4

[5,1,2,4,7,6,3] => [[.,.],[.,[[.,[[.,.],.]],.]]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 3

[5,1,2,6,3,4,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5

[5,1,2,6,3,7,4] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4

[5,1,2,6,4,3,7] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 4

[5,1,2,6,4,7,3] => [[.,.],[.,[[[.,.],[.,.]],.]]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 3

[5,1,2,6,7,3,4] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4

[5,1,2,6,7,4,3] => [[.,.],[.,[[[.,[.,.]],.],.]]] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 3

[5,1,2,7,3,4,6] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5

[5,1,2,7,3,6,4] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4

[5,1,2,7,4,3,6] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 4

[5,1,2,7,4,6,3] => [[.,.],[.,[[[.,.],[.,.]],.]]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 3

[5,1,2,7,6,3,4] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 4

[5,1,2,7,6,4,3] => [[.,.],[.,[[[[.,.],.],.],.]]] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 3

[5,1,3,2,4,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[5,1,3,2,4,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[5,1,3,2,6,4,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[5,1,3,2,6,7,4] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[5,1,3,2,7,4,6] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[5,1,3,2,7,6,4] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[5,1,3,4,2,6,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[5,1,3,4,2,7,6] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[5,1,3,4,6,2,7] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[5,1,3,4,6,7,2] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2

[5,1,3,4,7,2,6] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[5,1,3,4,7,6,2] => [[.,.],[[.,[.,[[.,.],.]]],.]] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 2

[5,1,3,6,2,4,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[5,1,3,6,2,7,4] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[5,1,3,6,4,2,7] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3

[5,1,3,6,4,7,2] => [[.,.],[[.,[[.,.],[.,.]]],.]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 2

[5,1,3,6,7,2,4] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[5,1,3,6,7,4,2] => [[.,.],[[.,[[.,[.,.]],.]],.]] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 2

[5,1,3,7,2,4,6] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[5,1,3,7,2,6,4] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[5,1,3,7,4,2,6] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3

[5,1,3,7,4,6,2] => [[.,.],[[.,[[.,.],[.,.]]],.]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 2

[5,1,3,7,6,2,4] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3

[5,1,3,7,6,4,2] => [[.,.],[[.,[[[.,.],.],.]],.]] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 2

[5,1,4,2,3,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[5,1,4,2,3,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[5,1,4,2,6,3,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[5,1,4,2,6,7,3] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[5,1,4,2,7,3,6] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[5,1,4,2,7,6,3] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[5,1,4,3,2,6,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[5,1,4,3,2,7,6] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[5,1,4,3,6,2,7] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[5,1,4,3,6,7,2] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 2

[5,1,4,3,7,2,6] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[5,1,4,3,7,6,2] => [[.,.],[[[.,.],[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2

[5,1,4,6,2,3,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[5,1,4,6,2,7,3] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[5,1,4,6,3,2,7] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[5,1,4,6,3,7,2] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2

[5,1,4,6,7,2,3] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[5,1,4,6,7,3,2] => [[.,.],[[[.,[.,[.,.]]],.],.]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2

[5,1,4,7,2,3,6] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[5,1,4,7,2,6,3] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[5,1,4,7,3,2,6] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[5,1,4,7,3,6,2] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2

[5,1,4,7,6,2,3] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3

[5,1,4,7,6,3,2] => [[.,.],[[[.,[[.,.],.]],.],.]] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 2

[5,1,6,2,3,4,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[5,1,6,2,3,7,4] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[5,1,6,2,4,3,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[5,1,6,2,4,7,3] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[5,1,6,2,7,3,4] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[5,1,6,2,7,4,3] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[5,1,6,3,2,4,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[5,1,6,3,2,7,4] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[5,1,6,3,4,2,7] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[5,1,6,3,4,7,2] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 2

[5,1,6,3,7,2,4] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[5,1,6,3,7,4,2] => [[.,.],[[[.,.],[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2

[5,1,6,4,2,3,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[5,1,6,4,2,7,3] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[5,1,6,4,3,2,7] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[5,1,6,4,3,7,2] => [[.,.],[[[[.,.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2

[5,1,6,4,7,2,3] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[5,1,6,4,7,3,2] => [[.,.],[[[[.,.],[.,.]],.],.]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 2

[5,1,6,7,2,3,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[5,1,6,7,2,4,3] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[5,1,6,7,3,2,4] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[5,1,6,7,3,4,2] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2

[5,1,6,7,4,2,3] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[5,1,6,7,4,3,2] => [[.,.],[[[[.,[.,.]],.],.],.]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 2

[5,1,7,2,3,4,6] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[5,1,7,2,3,6,4] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[5,1,7,2,4,3,6] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[5,1,7,2,4,6,3] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[5,1,7,2,6,3,4] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[5,1,7,2,6,4,3] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[5,1,7,3,2,4,6] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[5,1,7,3,2,6,4] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[5,1,7,3,4,2,6] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[5,1,7,3,4,6,2] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 2

[5,1,7,3,6,2,4] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[5,1,7,3,6,4,2] => [[.,.],[[[.,.],[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2

[5,1,7,4,2,3,6] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[5,1,7,4,2,6,3] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[5,1,7,4,3,2,6] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[5,1,7,4,3,6,2] => [[.,.],[[[[.,.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2

[5,1,7,4,6,2,3] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[5,1,7,4,6,3,2] => [[.,.],[[[[.,.],[.,.]],.],.]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 2

[5,1,7,6,2,3,4] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[5,1,7,6,2,4,3] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[5,1,7,6,3,2,4] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[5,1,7,6,3,4,2] => [[.,.],[[[[.,.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2

[5,1,7,6,4,2,3] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[5,1,7,6,4,3,2] => [[.,.],[[[[[.,.],.],.],.],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2

[5,2,1,3,4,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 5

[5,2,1,3,4,7,6] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 4

[5,2,1,3,6,4,7] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[5,2,1,3,6,7,4] => [[[.,.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 3

[5,2,1,3,7,4,6] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[5,2,1,3,7,6,4] => [[[.,.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 3

[5,2,1,4,3,6,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[5,2,1,4,3,7,6] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[5,2,1,4,6,3,7] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[5,2,1,4,6,7,3] => [[[.,.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 2

[5,2,1,4,7,3,6] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[5,2,1,4,7,6,3] => [[[.,.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 2

[5,2,1,6,3,4,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[5,2,1,6,3,7,4] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[5,2,1,6,4,3,7] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[5,2,1,6,4,7,3] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[5,2,1,6,7,3,4] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[5,2,1,6,7,4,3] => [[[.,.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 2

[5,2,1,7,3,4,6] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[5,2,1,7,3,6,4] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[5,2,1,7,4,3,6] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[5,2,1,7,4,6,3] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[5,2,1,7,6,3,4] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[5,2,1,7,6,4,3] => [[[.,.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2

[5,2,3,1,4,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[5,2,3,1,4,7,6] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[5,2,3,1,6,4,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,2,3,1,6,7,4] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[5,2,3,1,7,4,6] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,2,3,1,7,6,4] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[5,2,3,4,1,6,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[5,2,3,4,1,7,6] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[5,2,3,4,6,1,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[5,2,3,4,6,7,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1

[5,2,3,4,7,1,6] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[5,2,3,4,7,6,1] => [[[.,.],[.,[.,[[.,.],.]]]],.] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 1

[5,2,3,6,1,4,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[5,2,3,6,1,7,4] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[5,2,3,6,4,1,7] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[5,2,3,6,4,7,1] => [[[.,.],[.,[[.,.],[.,.]]]],.] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 1

[5,2,3,6,7,1,4] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[5,2,3,6,7,4,1] => [[[.,.],[.,[[.,[.,.]],.]]],.] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 1

[5,2,3,7,1,4,6] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[5,2,3,7,1,6,4] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[5,2,3,7,4,1,6] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[5,2,3,7,4,6,1] => [[[.,.],[.,[[.,.],[.,.]]]],.] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 1

[5,2,3,7,6,1,4] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[5,2,3,7,6,4,1] => [[[.,.],[.,[[[.,.],.],.]]],.] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 1

[5,2,4,1,3,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[5,2,4,1,3,7,6] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[5,2,4,1,6,3,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,2,4,1,6,7,3] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[5,2,4,1,7,3,6] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,2,4,1,7,6,3] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[5,2,4,3,1,6,7] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[5,2,4,3,1,7,6] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[5,2,4,3,6,1,7] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[5,2,4,3,6,7,1] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 1

[5,2,4,3,7,1,6] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[5,2,4,3,7,6,1] => [[[.,.],[[.,.],[[.,.],.]]],.] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 1

[5,2,4,6,1,3,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[5,2,4,6,1,7,3] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[5,2,4,6,3,1,7] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[5,2,4,6,3,7,1] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 1

[5,2,4,6,7,1,3] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[5,2,4,6,7,3,1] => [[[.,.],[[.,[.,[.,.]]],.]],.] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[5,2,4,7,1,3,6] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[5,2,4,7,1,6,3] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[5,2,4,7,3,1,6] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[5,2,4,7,3,6,1] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 1

[5,2,4,7,6,1,3] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[5,2,4,7,6,3,1] => [[[.,.],[[.,[[.,.],.]],.]],.] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 1

[5,2,6,1,3,4,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[5,2,6,1,3,7,4] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[5,2,6,1,4,3,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,2,6,1,4,7,3] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[5,2,6,1,7,3,4] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,2,6,1,7,4,3] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[5,2,6,3,1,4,7] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[5,2,6,3,1,7,4] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[5,2,6,3,4,1,7] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[5,2,6,3,4,7,1] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 1

[5,2,6,3,7,1,4] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[5,2,6,3,7,4,1] => [[[.,.],[[.,.],[[.,.],.]]],.] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 1

[5,2,6,4,1,3,7] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[5,2,6,4,1,7,3] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[5,2,6,4,3,1,7] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[5,2,6,4,3,7,1] => [[[.,.],[[[.,.],.],[.,.]]],.] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 1

[5,2,6,4,7,1,3] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[5,2,6,4,7,3,1] => [[[.,.],[[[.,.],[.,.]],.]],.] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 1

[5,2,6,7,1,3,4] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[5,2,6,7,1,4,3] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[5,2,6,7,3,1,4] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[5,2,6,7,3,4,1] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 1

[5,2,6,7,4,1,3] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[5,2,6,7,4,3,1] => [[[.,.],[[[.,[.,.]],.],.]],.] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 1

[5,2,7,1,3,4,6] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[5,2,7,1,3,6,4] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[5,2,7,1,4,3,6] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,2,7,1,4,6,3] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[5,2,7,1,6,3,4] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,2,7,1,6,4,3] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[5,2,7,3,1,4,6] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[5,2,7,3,1,6,4] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[5,2,7,3,4,1,6] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[5,2,7,3,4,6,1] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 1

[5,2,7,3,6,1,4] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[5,2,7,3,6,4,1] => [[[.,.],[[.,.],[[.,.],.]]],.] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 1

[5,2,7,4,1,3,6] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[5,2,7,4,1,6,3] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[5,2,7,4,3,1,6] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[5,2,7,4,3,6,1] => [[[.,.],[[[.,.],.],[.,.]]],.] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 1

[5,2,7,4,6,1,3] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[5,2,7,4,6,3,1] => [[[.,.],[[[.,.],[.,.]],.]],.] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 1

[5,2,7,6,1,3,4] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[5,2,7,6,1,4,3] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[5,2,7,6,3,1,4] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[5,2,7,6,3,4,1] => [[[.,.],[[[.,.],.],[.,.]]],.] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 1

[5,2,7,6,4,1,3] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[5,2,7,6,4,3,1] => [[[.,.],[[[[.,.],.],.],.]],.] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1

[5,3,1,2,4,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 5

[5,3,1,2,4,7,6] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 4

[5,3,1,2,6,4,7] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[5,3,1,2,6,7,4] => [[[.,.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 3

[5,3,1,2,7,4,6] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[5,3,1,2,7,6,4] => [[[.,.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 3

[5,3,1,4,2,6,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[5,3,1,4,2,7,6] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[5,3,1,4,6,2,7] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[5,3,1,4,6,7,2] => [[[.,.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 2

[5,3,1,4,7,2,6] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[5,3,1,4,7,6,2] => [[[.,.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 2

[5,3,1,6,2,4,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[5,3,1,6,2,7,4] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[5,3,1,6,4,2,7] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[5,3,1,6,4,7,2] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[5,3,1,6,7,2,4] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[5,3,1,6,7,4,2] => [[[.,.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 2

[5,3,1,7,2,4,6] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[5,3,1,7,2,6,4] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[5,3,1,7,4,2,6] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[5,3,1,7,4,6,2] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[5,3,1,7,6,2,4] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[5,3,1,7,6,4,2] => [[[.,.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2

[5,3,2,1,4,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4

[5,3,2,1,4,7,6] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 3

[5,3,2,1,6,4,7] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[5,3,2,1,6,7,4] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 2

[5,3,2,1,7,4,6] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[5,3,2,1,7,6,4] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2

[5,3,2,4,1,6,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[5,3,2,4,1,7,6] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[5,3,2,4,6,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[5,3,2,4,6,7,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1

[5,3,2,4,7,1,6] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[5,3,2,4,7,6,1] => [[[[.,.],.],[.,[[.,.],.]]],.] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 1

[5,3,2,6,1,4,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[5,3,2,6,1,7,4] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[5,3,2,6,4,1,7] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[5,3,2,6,4,7,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 1

[5,3,2,6,7,1,4] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[5,3,2,6,7,4,1] => [[[[.,.],.],[[.,[.,.]],.]],.] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 1

[5,3,2,7,1,4,6] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[5,3,2,7,1,6,4] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[5,3,2,7,4,1,6] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[5,3,2,7,4,6,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 1

[5,3,2,7,6,1,4] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[5,3,2,7,6,4,1] => [[[[.,.],.],[[[.,.],.],.]],.] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 1

[5,3,4,1,2,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[5,3,4,1,2,7,6] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[5,3,4,1,6,2,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,3,4,1,6,7,2] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[5,3,4,1,7,2,6] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,3,4,1,7,6,2] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[5,3,4,2,1,6,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3

[5,3,4,2,1,7,6] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[5,3,4,2,6,1,7] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,3,4,2,6,7,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1

[5,3,4,2,7,1,6] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,3,4,2,7,6,1] => [[[[.,.],[.,.]],[[.,.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 1

[5,3,4,6,1,2,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[5,3,4,6,1,7,2] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[5,3,4,6,2,1,7] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2

[5,3,4,6,2,7,1] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[5,3,4,6,7,1,2] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[5,3,4,6,7,2,1] => [[[[.,.],[.,[.,[.,.]]]],.],.] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1

[5,3,4,7,1,2,6] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[5,3,4,7,1,6,2] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[5,3,4,7,2,1,6] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2

[5,3,4,7,2,6,1] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[5,3,4,7,6,1,2] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[5,3,4,7,6,2,1] => [[[[.,.],[.,[[.,.],.]]],.],.] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 1

[5,3,6,1,2,4,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[5,3,6,1,2,7,4] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[5,3,6,1,4,2,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,3,6,1,4,7,2] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[5,3,6,1,7,2,4] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,3,6,1,7,4,2] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[5,3,6,2,1,4,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3

[5,3,6,2,1,7,4] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[5,3,6,2,4,1,7] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,3,6,2,4,7,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1

[5,3,6,2,7,1,4] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,3,6,2,7,4,1] => [[[[.,.],[.,.]],[[.,.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 1

[5,3,6,4,1,2,7] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[5,3,6,4,1,7,2] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[5,3,6,4,2,1,7] => [[[[.,.],[[.,.],.]],.],[.,.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2

[5,3,6,4,2,7,1] => [[[[.,.],[[.,.],.]],[.,.]],.] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 1

[5,3,6,4,7,1,2] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[5,3,6,4,7,2,1] => [[[[.,.],[[.,.],[.,.]]],.],.] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 1

[5,3,6,7,1,2,4] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[5,3,6,7,1,4,2] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[5,3,6,7,2,1,4] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2

[5,3,6,7,2,4,1] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[5,3,6,7,4,1,2] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[5,3,6,7,4,2,1] => [[[[.,.],[[.,[.,.]],.]],.],.] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 1

[5,3,7,1,2,4,6] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[5,3,7,1,2,6,4] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[5,3,7,1,4,2,6] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,3,7,1,4,6,2] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[5,3,7,1,6,2,4] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,3,7,1,6,4,2] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[5,3,7,2,1,4,6] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3

[5,3,7,2,1,6,4] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[5,3,7,2,4,1,6] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,3,7,2,4,6,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1

[5,3,7,2,6,1,4] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,3,7,2,6,4,1] => [[[[.,.],[.,.]],[[.,.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 1

[5,3,7,4,1,2,6] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[5,3,7,4,1,6,2] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[5,3,7,4,2,1,6] => [[[[.,.],[[.,.],.]],.],[.,.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2

[5,3,7,4,2,6,1] => [[[[.,.],[[.,.],.]],[.,.]],.] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 1

[5,3,7,4,6,1,2] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[5,3,7,4,6,2,1] => [[[[.,.],[[.,.],[.,.]]],.],.] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 1

[5,3,7,6,1,2,4] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[5,3,7,6,1,4,2] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[5,3,7,6,2,1,4] => [[[[.,.],[[.,.],.]],.],[.,.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2

[5,3,7,6,2,4,1] => [[[[.,.],[[.,.],.]],[.,.]],.] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 1

[5,3,7,6,4,1,2] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[5,3,7,6,4,2,1] => [[[[.,.],[[[.,.],.],.]],.],.] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 1

[5,4,1,2,3,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 5

[5,4,1,2,3,7,6] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 4

[5,4,1,2,6,3,7] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[5,4,1,2,6,7,3] => [[[.,.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 3

[5,4,1,2,7,3,6] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[5,4,1,2,7,6,3] => [[[.,.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 3

[5,4,1,3,2,6,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[5,4,1,3,2,7,6] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[5,4,1,3,6,2,7] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[5,4,1,3,6,7,2] => [[[.,.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 2

[5,4,1,3,7,2,6] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[5,4,1,3,7,6,2] => [[[.,.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 2

[5,4,1,6,2,3,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[5,4,1,6,2,7,3] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[5,4,1,6,3,2,7] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[5,4,1,6,3,7,2] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[5,4,1,6,7,2,3] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[5,4,1,6,7,3,2] => [[[.,.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 2

[5,4,1,7,2,3,6] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[5,4,1,7,2,6,3] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[5,4,1,7,3,2,6] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[5,4,1,7,3,6,2] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[5,4,1,7,6,2,3] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[5,4,1,7,6,3,2] => [[[.,.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2

[5,4,2,1,3,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4

[5,4,2,1,3,7,6] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 3

[5,4,2,1,6,3,7] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[5,4,2,1,6,7,3] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 2

[5,4,2,1,7,3,6] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[5,4,2,1,7,6,3] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2

[5,4,2,3,1,6,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[5,4,2,3,1,7,6] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[5,4,2,3,6,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[5,4,2,3,6,7,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1

[5,4,2,3,7,1,6] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[5,4,2,3,7,6,1] => [[[[.,.],.],[.,[[.,.],.]]],.] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 1

[5,4,2,6,1,3,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[5,4,2,6,1,7,3] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[5,4,2,6,3,1,7] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[5,4,2,6,3,7,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 1

[5,4,2,6,7,1,3] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[5,4,2,6,7,3,1] => [[[[.,.],.],[[.,[.,.]],.]],.] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 1

[5,4,2,7,1,3,6] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[5,4,2,7,1,6,3] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[5,4,2,7,3,1,6] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[5,4,2,7,3,6,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 1

[5,4,2,7,6,1,3] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[5,4,2,7,6,3,1] => [[[[.,.],.],[[[.,.],.],.]],.] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 1

[5,4,3,1,2,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4

[5,4,3,1,2,7,6] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 3

[5,4,3,1,6,2,7] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[5,4,3,1,6,7,2] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 2

[5,4,3,1,7,2,6] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[5,4,3,1,7,6,2] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2

[5,4,3,2,1,6,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 3

[5,4,3,2,1,7,6] => [[[[[.,.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2

[5,4,3,2,6,1,7] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2

[5,4,3,2,6,7,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1

[5,4,3,2,7,1,6] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2

[5,4,3,2,7,6,1] => [[[[[.,.],.],.],[[.,.],.]],.] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 1

[5,4,3,6,1,2,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[5,4,3,6,1,7,2] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[5,4,3,6,2,1,7] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[5,4,3,6,2,7,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1

[5,4,3,6,7,1,2] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[5,4,3,6,7,2,1] => [[[[[.,.],.],[.,[.,.]]],.],.] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1

[5,4,3,7,1,2,6] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[5,4,3,7,1,6,2] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[5,4,3,7,2,1,6] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[5,4,3,7,2,6,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1

[5,4,3,7,6,1,2] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[5,4,3,7,6,2,1] => [[[[[.,.],.],[[.,.],.]],.],.] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 1

[5,4,6,1,2,3,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[5,4,6,1,2,7,3] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[5,4,6,1,3,2,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,4,6,1,3,7,2] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[5,4,6,1,7,2,3] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,4,6,1,7,3,2] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[5,4,6,2,1,3,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3

[5,4,6,2,1,7,3] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[5,4,6,2,3,1,7] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,4,6,2,3,7,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1

[5,4,6,2,7,1,3] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,4,6,2,7,3,1] => [[[[.,.],[.,.]],[[.,.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 1

[5,4,6,3,1,2,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3

[5,4,6,3,1,7,2] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[5,4,6,3,2,1,7] => [[[[[.,.],[.,.]],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2

[5,4,6,3,2,7,1] => [[[[[.,.],[.,.]],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1

[5,4,6,3,7,1,2] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,4,6,3,7,2,1] => [[[[[.,.],[.,.]],[.,.]],.],.] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1

[5,4,6,7,1,2,3] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[5,4,6,7,1,3,2] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[5,4,6,7,2,1,3] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2

[5,4,6,7,2,3,1] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[5,4,6,7,3,1,2] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2

[5,4,6,7,3,2,1] => [[[[[.,.],[.,[.,.]]],.],.],.] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1

[5,4,7,1,2,3,6] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[5,4,7,1,2,6,3] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[5,4,7,1,3,2,6] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,4,7,1,3,6,2] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[5,4,7,1,6,2,3] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,4,7,1,6,3,2] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[5,4,7,2,1,3,6] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3

[5,4,7,2,1,6,3] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[5,4,7,2,3,1,6] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,4,7,2,3,6,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1

[5,4,7,2,6,1,3] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,4,7,2,6,3,1] => [[[[.,.],[.,.]],[[.,.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 1

[5,4,7,3,1,2,6] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3

[5,4,7,3,1,6,2] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[5,4,7,3,2,1,6] => [[[[[.,.],[.,.]],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2

[5,4,7,3,2,6,1] => [[[[[.,.],[.,.]],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1

[5,4,7,3,6,1,2] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,4,7,3,6,2,1] => [[[[[.,.],[.,.]],[.,.]],.],.] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1

[5,4,7,6,1,2,3] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[5,4,7,6,1,3,2] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[5,4,7,6,2,1,3] => [[[[.,.],[[.,.],.]],.],[.,.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2

[5,4,7,6,2,3,1] => [[[[.,.],[[.,.],.]],[.,.]],.] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 1

[5,4,7,6,3,1,2] => [[[[.,.],[[.,.],.]],.],[.,.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2

[5,4,7,6,3,2,1] => [[[[[.,.],[[.,.],.]],.],.],.] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 1

[5,6,1,2,3,4,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[5,6,1,2,3,7,4] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[5,6,1,2,4,3,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[5,6,1,2,4,7,3] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[5,6,1,2,7,3,4] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[5,6,1,2,7,4,3] => [[.,[.,.]],[.,[[[.,.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[5,6,1,3,2,4,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[5,6,1,3,2,7,4] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[5,6,1,3,4,2,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[5,6,1,3,4,7,2] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[5,6,1,3,7,2,4] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[5,6,1,3,7,4,2] => [[.,[.,.]],[[.,[[.,.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[5,6,1,4,2,3,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[5,6,1,4,2,7,3] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[5,6,1,4,3,2,7] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[5,6,1,4,3,7,2] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[5,6,1,4,7,2,3] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[5,6,1,4,7,3,2] => [[.,[.,.]],[[[.,[.,.]],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[5,6,1,7,2,3,4] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[5,6,1,7,2,4,3] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[5,6,1,7,3,2,4] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[5,6,1,7,3,4,2] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[5,6,1,7,4,2,3] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[5,6,1,7,4,3,2] => [[.,[.,.]],[[[[.,.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[5,6,2,1,3,4,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[5,6,2,1,3,7,4] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[5,6,2,1,4,3,7] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[5,6,2,1,4,7,3] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[5,6,2,1,7,3,4] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[5,6,2,1,7,4,3] => [[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[5,6,2,3,1,4,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[5,6,2,3,1,7,4] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[5,6,2,3,4,1,7] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[5,6,2,3,4,7,1] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1

[5,6,2,3,7,1,4] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[5,6,2,3,7,4,1] => [[[.,[.,.]],[.,[[.,.],.]]],.] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[5,6,2,4,1,3,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[5,6,2,4,1,7,3] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[5,6,2,4,3,1,7] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[5,6,2,4,3,7,1] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[5,6,2,4,7,1,3] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[5,6,2,4,7,3,1] => [[[.,[.,.]],[[.,[.,.]],.]],.] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[5,6,2,7,1,3,4] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[5,6,2,7,1,4,3] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[5,6,2,7,3,1,4] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[5,6,2,7,3,4,1] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[5,6,2,7,4,1,3] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[5,6,2,7,4,3,1] => [[[.,[.,.]],[[[.,.],.],.]],.] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1

[5,6,3,1,2,4,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[5,6,3,1,2,7,4] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[5,6,3,1,4,2,7] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[5,6,3,1,4,7,2] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[5,6,3,1,7,2,4] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[5,6,3,1,7,4,2] => [[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[5,6,3,2,1,4,7] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3

[5,6,3,2,1,7,4] => [[[[.,[.,.]],.],.],[[.,.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[5,6,3,2,4,1,7] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[5,6,3,2,4,7,1] => [[[[.,[.,.]],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1

[5,6,3,2,7,1,4] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[5,6,3,2,7,4,1] => [[[[.,[.,.]],.],[[.,.],.]],.] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1

[5,6,3,4,1,2,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[5,6,3,4,1,7,2] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[5,6,3,4,2,1,7] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[5,6,3,4,2,7,1] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[5,6,3,4,7,1,2] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[5,6,3,4,7,2,1] => [[[[.,[.,.]],[.,[.,.]]],.],.] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1

[5,6,3,7,1,2,4] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[5,6,3,7,1,4,2] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[5,6,3,7,2,1,4] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[5,6,3,7,2,4,1] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[5,6,3,7,4,1,2] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[5,6,3,7,4,2,1] => [[[[.,[.,.]],[[.,.],.]],.],.] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

[5,6,4,1,2,3,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[5,6,4,1,2,7,3] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[5,6,4,1,3,2,7] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[5,6,4,1,3,7,2] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[5,6,4,1,7,2,3] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[5,6,4,1,7,3,2] => [[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[5,6,4,2,1,3,7] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3

[5,6,4,2,1,7,3] => [[[[.,[.,.]],.],.],[[.,.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[5,6,4,2,3,1,7] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[5,6,4,2,3,7,1] => [[[[.,[.,.]],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1

[5,6,4,2,7,1,3] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[5,6,4,2,7,3,1] => [[[[.,[.,.]],.],[[.,.],.]],.] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1

[5,6,4,3,1,2,7] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3

[5,6,4,3,1,7,2] => [[[[.,[.,.]],.],.],[[.,.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[5,6,4,3,2,1,7] => [[[[[.,[.,.]],.],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2

[5,6,4,3,2,7,1] => [[[[[.,[.,.]],.],.],[.,.]],.] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1

[5,6,4,3,7,1,2] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[5,6,4,3,7,2,1] => [[[[[.,[.,.]],.],[.,.]],.],.] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1

[5,6,4,7,1,2,3] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[5,6,4,7,1,3,2] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[5,6,4,7,2,1,3] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[5,6,4,7,2,3,1] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[5,6,4,7,3,1,2] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[5,6,4,7,3,2,1] => [[[[[.,[.,.]],[.,.]],.],.],.] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1

[5,6,7,1,2,3,4] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[5,6,7,1,2,4,3] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[5,6,7,1,3,2,4] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,6,7,1,3,4,2] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[5,6,7,1,4,2,3] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,6,7,1,4,3,2] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[5,6,7,2,1,3,4] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[5,6,7,2,1,4,3] => [[[.,[.,[.,.]]],.],[[.,.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[5,6,7,2,3,1,4] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,6,7,2,3,4,1] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1

[5,6,7,2,4,1,3] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,6,7,2,4,3,1] => [[[.,[.,[.,.]]],[[.,.],.]],.] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 1

[5,6,7,3,1,2,4] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[5,6,7,3,1,4,2] => [[[.,[.,[.,.]]],.],[[.,.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[5,6,7,3,2,1,4] => [[[[.,[.,[.,.]]],.],.],[.,.]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2

[5,6,7,3,2,4,1] => [[[[.,[.,[.,.]]],.],[.,.]],.] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1

[5,6,7,3,4,1,2] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,6,7,3,4,2,1] => [[[[.,[.,[.,.]]],[.,.]],.],.] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1

[5,6,7,4,1,2,3] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[5,6,7,4,1,3,2] => [[[.,[.,[.,.]]],.],[[.,.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[5,6,7,4,2,1,3] => [[[[.,[.,[.,.]]],.],.],[.,.]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2

[5,6,7,4,2,3,1] => [[[[.,[.,[.,.]]],.],[.,.]],.] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1

[5,6,7,4,3,1,2] => [[[[.,[.,[.,.]]],.],.],[.,.]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2

[5,6,7,4,3,2,1] => [[[[[.,[.,[.,.]]],.],.],.],.] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1

[5,7,1,2,3,4,6] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[5,7,1,2,3,6,4] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[5,7,1,2,4,3,6] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[5,7,1,2,4,6,3] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[5,7,1,2,6,3,4] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[5,7,1,2,6,4,3] => [[.,[.,.]],[.,[[[.,.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[5,7,1,3,2,4,6] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[5,7,1,3,2,6,4] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[5,7,1,3,4,2,6] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[5,7,1,3,4,6,2] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[5,7,1,3,6,2,4] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[5,7,1,3,6,4,2] => [[.,[.,.]],[[.,[[.,.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[5,7,1,4,2,3,6] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[5,7,1,4,2,6,3] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[5,7,1,4,3,2,6] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[5,7,1,4,3,6,2] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[5,7,1,4,6,2,3] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[5,7,1,4,6,3,2] => [[.,[.,.]],[[[.,[.,.]],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[5,7,1,6,2,3,4] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[5,7,1,6,2,4,3] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[5,7,1,6,3,2,4] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[5,7,1,6,3,4,2] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[5,7,1,6,4,2,3] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[5,7,1,6,4,3,2] => [[.,[.,.]],[[[[.,.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[5,7,2,1,3,4,6] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[5,7,2,1,3,6,4] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[5,7,2,1,4,3,6] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[5,7,2,1,4,6,3] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[5,7,2,1,6,3,4] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[5,7,2,1,6,4,3] => [[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[5,7,2,3,1,4,6] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[5,7,2,3,1,6,4] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[5,7,2,3,4,1,6] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[5,7,2,3,4,6,1] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1

[5,7,2,3,6,1,4] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[5,7,2,3,6,4,1] => [[[.,[.,.]],[.,[[.,.],.]]],.] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[5,7,2,4,1,3,6] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[5,7,2,4,1,6,3] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[5,7,2,4,3,1,6] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[5,7,2,4,3,6,1] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[5,7,2,4,6,1,3] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[5,7,2,4,6,3,1] => [[[.,[.,.]],[[.,[.,.]],.]],.] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[5,7,2,6,1,3,4] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[5,7,2,6,1,4,3] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[5,7,2,6,3,1,4] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[5,7,2,6,3,4,1] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[5,7,2,6,4,1,3] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[5,7,2,6,4,3,1] => [[[.,[.,.]],[[[.,.],.],.]],.] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1

[5,7,3,1,2,4,6] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[5,7,3,1,2,6,4] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[5,7,3,1,4,2,6] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[5,7,3,1,4,6,2] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[5,7,3,1,6,2,4] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[5,7,3,1,6,4,2] => [[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[5,7,3,2,1,4,6] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3

[5,7,3,2,1,6,4] => [[[[.,[.,.]],.],.],[[.,.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[5,7,3,2,4,1,6] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[5,7,3,2,4,6,1] => [[[[.,[.,.]],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1

[5,7,3,2,6,1,4] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[5,7,3,2,6,4,1] => [[[[.,[.,.]],.],[[.,.],.]],.] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1

[5,7,3,4,1,2,6] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[5,7,3,4,1,6,2] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[5,7,3,4,2,1,6] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[5,7,3,4,2,6,1] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[5,7,3,4,6,1,2] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[5,7,3,4,6,2,1] => [[[[.,[.,.]],[.,[.,.]]],.],.] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1

[5,7,3,6,1,2,4] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[5,7,3,6,1,4,2] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[5,7,3,6,2,1,4] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[5,7,3,6,2,4,1] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[5,7,3,6,4,1,2] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[5,7,3,6,4,2,1] => [[[[.,[.,.]],[[.,.],.]],.],.] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

[5,7,4,1,2,3,6] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[5,7,4,1,2,6,3] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[5,7,4,1,3,2,6] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[5,7,4,1,3,6,2] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[5,7,4,1,6,2,3] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[5,7,4,1,6,3,2] => [[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[5,7,4,2,1,3,6] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3

[5,7,4,2,1,6,3] => [[[[.,[.,.]],.],.],[[.,.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[5,7,4,2,3,1,6] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[5,7,4,2,3,6,1] => [[[[.,[.,.]],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1

[5,7,4,2,6,1,3] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[5,7,4,2,6,3,1] => [[[[.,[.,.]],.],[[.,.],.]],.] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1

[5,7,4,3,1,2,6] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3

[5,7,4,3,1,6,2] => [[[[.,[.,.]],.],.],[[.,.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[5,7,4,3,2,1,6] => [[[[[.,[.,.]],.],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2

[5,7,4,3,2,6,1] => [[[[[.,[.,.]],.],.],[.,.]],.] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1

[5,7,4,3,6,1,2] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[5,7,4,3,6,2,1] => [[[[[.,[.,.]],.],[.,.]],.],.] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1

[5,7,4,6,1,2,3] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[5,7,4,6,1,3,2] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[5,7,4,6,2,1,3] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[5,7,4,6,2,3,1] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[5,7,4,6,3,1,2] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[5,7,4,6,3,2,1] => [[[[[.,[.,.]],[.,.]],.],.],.] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1

[5,7,6,1,2,3,4] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4

[5,7,6,1,2,4,3] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 3

[5,7,6,1,3,2,4] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[5,7,6,1,3,4,2] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 2

[5,7,6,1,4,2,3] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[5,7,6,1,4,3,2] => [[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2

[5,7,6,2,1,3,4] => [[[.,[[.,.],.]],.],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 3

[5,7,6,2,1,4,3] => [[[.,[[.,.],.]],.],[[.,.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 2

[5,7,6,2,3,1,4] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[5,7,6,2,3,4,1] => [[[.,[[.,.],.]],[.,[.,.]]],.] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 1

[5,7,6,2,4,1,3] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[5,7,6,2,4,3,1] => [[[.,[[.,.],.]],[[.,.],.]],.] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[5,7,6,3,1,2,4] => [[[.,[[.,.],.]],.],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 3

[5,7,6,3,1,4,2] => [[[.,[[.,.],.]],.],[[.,.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 2

[5,7,6,3,2,1,4] => [[[[.,[[.,.],.]],.],.],[.,.]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 2

[5,7,6,3,2,4,1] => [[[[.,[[.,.],.]],.],[.,.]],.] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[5,7,6,3,4,1,2] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[5,7,6,3,4,2,1] => [[[[.,[[.,.],.]],[.,.]],.],.] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[5,7,6,4,1,2,3] => [[[.,[[.,.],.]],.],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 3

[5,7,6,4,1,3,2] => [[[.,[[.,.],.]],.],[[.,.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 2

[5,7,6,4,2,1,3] => [[[[.,[[.,.],.]],.],.],[.,.]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 2

[5,7,6,4,2,3,1] => [[[[.,[[.,.],.]],.],[.,.]],.] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[5,7,6,4,3,1,2] => [[[[.,[[.,.],.]],.],.],[.,.]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 2

[5,7,6,4,3,2,1] => [[[[[.,[[.,.],.]],.],.],.],.] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1

[6,1,2,3,4,5,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6

[6,1,2,3,4,7,5] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 5

[6,1,2,3,5,4,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 5

[6,1,2,3,5,7,4] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 4

[6,1,2,3,7,4,5] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 5

[6,1,2,3,7,5,4] => [[.,.],[.,[.,[[[.,.],.],.]]]] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 4

[6,1,2,4,3,5,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5

[6,1,2,4,3,7,5] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4

[6,1,2,4,5,3,7] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4

[6,1,2,4,5,7,3] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 3

[6,1,2,4,7,3,5] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4

[6,1,2,4,7,5,3] => [[.,.],[.,[[.,[[.,.],.]],.]]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 3

[6,1,2,5,3,4,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5

[6,1,2,5,3,7,4] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4

[6,1,2,5,4,3,7] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 4

[6,1,2,5,4,7,3] => [[.,.],[.,[[[.,.],[.,.]],.]]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 3

[6,1,2,5,7,3,4] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4

[6,1,2,5,7,4,3] => [[.,.],[.,[[[.,[.,.]],.],.]]] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 3

[6,1,2,7,3,4,5] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5

[6,1,2,7,3,5,4] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4

[6,1,2,7,4,3,5] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 4

[6,1,2,7,4,5,3] => [[.,.],[.,[[[.,.],[.,.]],.]]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 3

[6,1,2,7,5,3,4] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 4

[6,1,2,7,5,4,3] => [[.,.],[.,[[[[.,.],.],.],.]]] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 3

[6,1,3,2,4,5,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[6,1,3,2,4,7,5] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[6,1,3,2,5,4,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[6,1,3,2,5,7,4] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[6,1,3,2,7,4,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[6,1,3,2,7,5,4] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[6,1,3,4,2,5,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[6,1,3,4,2,7,5] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[6,1,3,4,5,2,7] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[6,1,3,4,5,7,2] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2

[6,1,3,4,7,2,5] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[6,1,3,4,7,5,2] => [[.,.],[[.,[.,[[.,.],.]]],.]] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 2

[6,1,3,5,2,4,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[6,1,3,5,2,7,4] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[6,1,3,5,4,2,7] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3

[6,1,3,5,4,7,2] => [[.,.],[[.,[[.,.],[.,.]]],.]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 2

[6,1,3,5,7,2,4] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[6,1,3,5,7,4,2] => [[.,.],[[.,[[.,[.,.]],.]],.]] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 2

[6,1,3,7,2,4,5] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[6,1,3,7,2,5,4] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[6,1,3,7,4,2,5] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3

[6,1,3,7,4,5,2] => [[.,.],[[.,[[.,.],[.,.]]],.]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 2

[6,1,3,7,5,2,4] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3

[6,1,3,7,5,4,2] => [[.,.],[[.,[[[.,.],.],.]],.]] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 2

[6,1,4,2,3,5,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[6,1,4,2,3,7,5] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[6,1,4,2,5,3,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[6,1,4,2,5,7,3] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[6,1,4,2,7,3,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[6,1,4,2,7,5,3] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[6,1,4,3,2,5,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[6,1,4,3,2,7,5] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[6,1,4,3,5,2,7] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[6,1,4,3,5,7,2] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 2

[6,1,4,3,7,2,5] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[6,1,4,3,7,5,2] => [[.,.],[[[.,.],[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2

[6,1,4,5,2,3,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[6,1,4,5,2,7,3] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[6,1,4,5,3,2,7] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[6,1,4,5,3,7,2] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2

[6,1,4,5,7,2,3] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[6,1,4,5,7,3,2] => [[.,.],[[[.,[.,[.,.]]],.],.]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2

[6,1,4,7,2,3,5] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[6,1,4,7,2,5,3] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[6,1,4,7,3,2,5] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[6,1,4,7,3,5,2] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2

[6,1,4,7,5,2,3] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3

[6,1,4,7,5,3,2] => [[.,.],[[[.,[[.,.],.]],.],.]] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 2

[6,1,5,2,3,4,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[6,1,5,2,3,7,4] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[6,1,5,2,4,3,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[6,1,5,2,4,7,3] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[6,1,5,2,7,3,4] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[6,1,5,2,7,4,3] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[6,1,5,3,2,4,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[6,1,5,3,2,7,4] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[6,1,5,3,4,2,7] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[6,1,5,3,4,7,2] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 2

[6,1,5,3,7,2,4] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[6,1,5,3,7,4,2] => [[.,.],[[[.,.],[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2

[6,1,5,4,2,3,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[6,1,5,4,2,7,3] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[6,1,5,4,3,2,7] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[6,1,5,4,3,7,2] => [[.,.],[[[[.,.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2

[6,1,5,4,7,2,3] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[6,1,5,4,7,3,2] => [[.,.],[[[[.,.],[.,.]],.],.]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 2

[6,1,5,7,2,3,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[6,1,5,7,2,4,3] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[6,1,5,7,3,2,4] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[6,1,5,7,3,4,2] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2

[6,1,5,7,4,2,3] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[6,1,5,7,4,3,2] => [[.,.],[[[[.,[.,.]],.],.],.]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 2

[6,1,7,2,3,4,5] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[6,1,7,2,3,5,4] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[6,1,7,2,4,3,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[6,1,7,2,4,5,3] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[6,1,7,2,5,3,4] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[6,1,7,2,5,4,3] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[6,1,7,3,2,4,5] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[6,1,7,3,2,5,4] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[6,1,7,3,4,2,5] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[6,1,7,3,4,5,2] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 2

[6,1,7,3,5,2,4] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[6,1,7,3,5,4,2] => [[.,.],[[[.,.],[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2

[6,1,7,4,2,3,5] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[6,1,7,4,2,5,3] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[6,1,7,4,3,2,5] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[6,1,7,4,3,5,2] => [[.,.],[[[[.,.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2

[6,1,7,4,5,2,3] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[6,1,7,4,5,3,2] => [[.,.],[[[[.,.],[.,.]],.],.]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 2

[6,1,7,5,2,3,4] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[6,1,7,5,2,4,3] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[6,1,7,5,3,2,4] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[6,1,7,5,3,4,2] => [[.,.],[[[[.,.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2

[6,1,7,5,4,2,3] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[6,1,7,5,4,3,2] => [[.,.],[[[[[.,.],.],.],.],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2

[6,2,1,3,4,5,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 5

[6,2,1,3,4,7,5] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 4

[6,2,1,3,5,4,7] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[6,2,1,3,5,7,4] => [[[.,.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 3

[6,2,1,3,7,4,5] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[6,2,1,3,7,5,4] => [[[.,.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 3

[6,2,1,4,3,5,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[6,2,1,4,3,7,5] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[6,2,1,4,5,3,7] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[6,2,1,4,5,7,3] => [[[.,.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 2

[6,2,1,4,7,3,5] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[6,2,1,4,7,5,3] => [[[.,.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 2

[6,2,1,5,3,4,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[6,2,1,5,3,7,4] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[6,2,1,5,4,3,7] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[6,2,1,5,4,7,3] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[6,2,1,5,7,3,4] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[6,2,1,5,7,4,3] => [[[.,.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 2

[6,2,1,7,3,4,5] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[6,2,1,7,3,5,4] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[6,2,1,7,4,3,5] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[6,2,1,7,4,5,3] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[6,2,1,7,5,3,4] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[6,2,1,7,5,4,3] => [[[.,.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2

[6,2,3,1,4,5,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[6,2,3,1,4,7,5] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[6,2,3,1,5,4,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,2,3,1,5,7,4] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[6,2,3,1,7,4,5] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,2,3,1,7,5,4] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[6,2,3,4,1,5,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[6,2,3,4,1,7,5] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[6,2,3,4,5,1,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[6,2,3,4,5,7,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1

[6,2,3,4,7,1,5] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[6,2,3,4,7,5,1] => [[[.,.],[.,[.,[[.,.],.]]]],.] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 1

[6,2,3,5,1,4,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[6,2,3,5,1,7,4] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[6,2,3,5,4,1,7] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[6,2,3,5,4,7,1] => [[[.,.],[.,[[.,.],[.,.]]]],.] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 1

[6,2,3,5,7,1,4] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[6,2,3,5,7,4,1] => [[[.,.],[.,[[.,[.,.]],.]]],.] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 1

[6,2,3,7,1,4,5] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[6,2,3,7,1,5,4] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[6,2,3,7,4,1,5] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[6,2,3,7,4,5,1] => [[[.,.],[.,[[.,.],[.,.]]]],.] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 1

[6,2,3,7,5,1,4] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[6,2,3,7,5,4,1] => [[[.,.],[.,[[[.,.],.],.]]],.] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 1

[6,2,4,1,3,5,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[6,2,4,1,3,7,5] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[6,2,4,1,5,3,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,2,4,1,5,7,3] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[6,2,4,1,7,3,5] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,2,4,1,7,5,3] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[6,2,4,3,1,5,7] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[6,2,4,3,1,7,5] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[6,2,4,3,5,1,7] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[6,2,4,3,5,7,1] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 1

[6,2,4,3,7,1,5] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[6,2,4,3,7,5,1] => [[[.,.],[[.,.],[[.,.],.]]],.] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 1

[6,2,4,5,1,3,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[6,2,4,5,1,7,3] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[6,2,4,5,3,1,7] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[6,2,4,5,3,7,1] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 1

[6,2,4,5,7,1,3] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[6,2,4,5,7,3,1] => [[[.,.],[[.,[.,[.,.]]],.]],.] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[6,2,4,7,1,3,5] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[6,2,4,7,1,5,3] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[6,2,4,7,3,1,5] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[6,2,4,7,3,5,1] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 1

[6,2,4,7,5,1,3] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[6,2,4,7,5,3,1] => [[[.,.],[[.,[[.,.],.]],.]],.] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 1

[6,2,5,1,3,4,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[6,2,5,1,3,7,4] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[6,2,5,1,4,3,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,2,5,1,4,7,3] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[6,2,5,1,7,3,4] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,2,5,1,7,4,3] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[6,2,5,3,1,4,7] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[6,2,5,3,1,7,4] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[6,2,5,3,4,1,7] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[6,2,5,3,4,7,1] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 1

[6,2,5,3,7,1,4] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[6,2,5,3,7,4,1] => [[[.,.],[[.,.],[[.,.],.]]],.] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 1

[6,2,5,4,1,3,7] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[6,2,5,4,1,7,3] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[6,2,5,4,3,1,7] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[6,2,5,4,3,7,1] => [[[.,.],[[[.,.],.],[.,.]]],.] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 1

[6,2,5,4,7,1,3] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[6,2,5,4,7,3,1] => [[[.,.],[[[.,.],[.,.]],.]],.] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 1

[6,2,5,7,1,3,4] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[6,2,5,7,1,4,3] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[6,2,5,7,3,1,4] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[6,2,5,7,3,4,1] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 1

[6,2,5,7,4,1,3] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[6,2,5,7,4,3,1] => [[[.,.],[[[.,[.,.]],.],.]],.] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 1

[6,2,7,1,3,4,5] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[6,2,7,1,3,5,4] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[6,2,7,1,4,3,5] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,2,7,1,4,5,3] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[6,2,7,1,5,3,4] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,2,7,1,5,4,3] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[6,2,7,3,1,4,5] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[6,2,7,3,1,5,4] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[6,2,7,3,4,1,5] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[6,2,7,3,4,5,1] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 1

[6,2,7,3,5,1,4] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[6,2,7,3,5,4,1] => [[[.,.],[[.,.],[[.,.],.]]],.] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 1

[6,2,7,4,1,3,5] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[6,2,7,4,1,5,3] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[6,2,7,4,3,1,5] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[6,2,7,4,3,5,1] => [[[.,.],[[[.,.],.],[.,.]]],.] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 1

[6,2,7,4,5,1,3] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[6,2,7,4,5,3,1] => [[[.,.],[[[.,.],[.,.]],.]],.] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 1

[6,2,7,5,1,3,4] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[6,2,7,5,1,4,3] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[6,2,7,5,3,1,4] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[6,2,7,5,3,4,1] => [[[.,.],[[[.,.],.],[.,.]]],.] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 1

[6,2,7,5,4,1,3] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[6,2,7,5,4,3,1] => [[[.,.],[[[[.,.],.],.],.]],.] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1

[6,3,1,2,4,5,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 5

[6,3,1,2,4,7,5] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 4

[6,3,1,2,5,4,7] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[6,3,1,2,5,7,4] => [[[.,.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 3

[6,3,1,2,7,4,5] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[6,3,1,2,7,5,4] => [[[.,.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 3

[6,3,1,4,2,5,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[6,3,1,4,2,7,5] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[6,3,1,4,5,2,7] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[6,3,1,4,5,7,2] => [[[.,.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 2

[6,3,1,4,7,2,5] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[6,3,1,4,7,5,2] => [[[.,.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 2

[6,3,1,5,2,4,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[6,3,1,5,2,7,4] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[6,3,1,5,4,2,7] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[6,3,1,5,4,7,2] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[6,3,1,5,7,2,4] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[6,3,1,5,7,4,2] => [[[.,.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 2

[6,3,1,7,2,4,5] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[6,3,1,7,2,5,4] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[6,3,1,7,4,2,5] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[6,3,1,7,4,5,2] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[6,3,1,7,5,2,4] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[6,3,1,7,5,4,2] => [[[.,.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2

[6,3,2,1,4,5,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4

[6,3,2,1,4,7,5] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 3

[6,3,2,1,5,4,7] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[6,3,2,1,5,7,4] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 2

[6,3,2,1,7,4,5] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[6,3,2,1,7,5,4] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2

[6,3,2,4,1,5,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[6,3,2,4,1,7,5] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[6,3,2,4,5,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[6,3,2,4,5,7,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1

[6,3,2,4,7,1,5] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[6,3,2,4,7,5,1] => [[[[.,.],.],[.,[[.,.],.]]],.] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 1

[6,3,2,5,1,4,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[6,3,2,5,1,7,4] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[6,3,2,5,4,1,7] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[6,3,2,5,4,7,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 1

[6,3,2,5,7,1,4] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[6,3,2,5,7,4,1] => [[[[.,.],.],[[.,[.,.]],.]],.] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 1

[6,3,2,7,1,4,5] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[6,3,2,7,1,5,4] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[6,3,2,7,4,1,5] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[6,3,2,7,4,5,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 1

[6,3,2,7,5,1,4] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[6,3,2,7,5,4,1] => [[[[.,.],.],[[[.,.],.],.]],.] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 1

[6,3,4,1,2,5,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[6,3,4,1,2,7,5] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[6,3,4,1,5,2,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,3,4,1,5,7,2] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[6,3,4,1,7,2,5] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,3,4,1,7,5,2] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[6,3,4,2,1,5,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3

[6,3,4,2,1,7,5] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[6,3,4,2,5,1,7] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,3,4,2,5,7,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1

[6,3,4,2,7,1,5] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,3,4,2,7,5,1] => [[[[.,.],[.,.]],[[.,.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 1

[6,3,4,5,1,2,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[6,3,4,5,1,7,2] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[6,3,4,5,2,1,7] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2

[6,3,4,5,2,7,1] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[6,3,4,5,7,1,2] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[6,3,4,5,7,2,1] => [[[[.,.],[.,[.,[.,.]]]],.],.] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1

[6,3,4,7,1,2,5] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[6,3,4,7,1,5,2] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[6,3,4,7,2,1,5] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2

[6,3,4,7,2,5,1] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[6,3,4,7,5,1,2] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[6,3,4,7,5,2,1] => [[[[.,.],[.,[[.,.],.]]],.],.] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 1

[6,3,5,1,2,4,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[6,3,5,1,2,7,4] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[6,3,5,1,4,2,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,3,5,1,4,7,2] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[6,3,5,1,7,2,4] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,3,5,1,7,4,2] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[6,3,5,2,1,4,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3

[6,3,5,2,1,7,4] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[6,3,5,2,4,1,7] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,3,5,2,4,7,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1

[6,3,5,2,7,1,4] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,3,5,2,7,4,1] => [[[[.,.],[.,.]],[[.,.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 1

[6,3,5,4,1,2,7] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[6,3,5,4,1,7,2] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[6,3,5,4,2,1,7] => [[[[.,.],[[.,.],.]],.],[.,.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2

[6,3,5,4,2,7,1] => [[[[.,.],[[.,.],.]],[.,.]],.] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 1

[6,3,5,4,7,1,2] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[6,3,5,4,7,2,1] => [[[[.,.],[[.,.],[.,.]]],.],.] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 1

[6,3,5,7,1,2,4] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[6,3,5,7,1,4,2] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[6,3,5,7,2,1,4] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2

[6,3,5,7,2,4,1] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[6,3,5,7,4,1,2] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[6,3,5,7,4,2,1] => [[[[.,.],[[.,[.,.]],.]],.],.] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 1

[6,3,7,1,2,4,5] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[6,3,7,1,2,5,4] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[6,3,7,1,4,2,5] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,3,7,1,4,5,2] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[6,3,7,1,5,2,4] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,3,7,1,5,4,2] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[6,3,7,2,1,4,5] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3

[6,3,7,2,1,5,4] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[6,3,7,2,4,1,5] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,3,7,2,4,5,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1

[6,3,7,2,5,1,4] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,3,7,2,5,4,1] => [[[[.,.],[.,.]],[[.,.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 1

[6,3,7,4,1,2,5] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[6,3,7,4,1,5,2] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[6,3,7,4,2,1,5] => [[[[.,.],[[.,.],.]],.],[.,.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2

[6,3,7,4,2,5,1] => [[[[.,.],[[.,.],.]],[.,.]],.] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 1

[6,3,7,4,5,1,2] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[6,3,7,4,5,2,1] => [[[[.,.],[[.,.],[.,.]]],.],.] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 1

[6,3,7,5,1,2,4] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[6,3,7,5,1,4,2] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[6,3,7,5,2,1,4] => [[[[.,.],[[.,.],.]],.],[.,.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2

[6,3,7,5,2,4,1] => [[[[.,.],[[.,.],.]],[.,.]],.] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 1

[6,3,7,5,4,1,2] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[6,3,7,5,4,2,1] => [[[[.,.],[[[.,.],.],.]],.],.] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 1

[6,4,1,2,3,5,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 5

[6,4,1,2,3,7,5] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 4

[6,4,1,2,5,3,7] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[6,4,1,2,5,7,3] => [[[.,.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 3

[6,4,1,2,7,3,5] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[6,4,1,2,7,5,3] => [[[.,.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 3

[6,4,1,3,2,5,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[6,4,1,3,2,7,5] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[6,4,1,3,5,2,7] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[6,4,1,3,5,7,2] => [[[.,.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 2

[6,4,1,3,7,2,5] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[6,4,1,3,7,5,2] => [[[.,.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 2

[6,4,1,5,2,3,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[6,4,1,5,2,7,3] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[6,4,1,5,3,2,7] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[6,4,1,5,3,7,2] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[6,4,1,5,7,2,3] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[6,4,1,5,7,3,2] => [[[.,.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 2

[6,4,1,7,2,3,5] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[6,4,1,7,2,5,3] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[6,4,1,7,3,2,5] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[6,4,1,7,3,5,2] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[6,4,1,7,5,2,3] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[6,4,1,7,5,3,2] => [[[.,.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2

[6,4,2,1,3,5,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4

[6,4,2,1,3,7,5] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 3

[6,4,2,1,5,3,7] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[6,4,2,1,5,7,3] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 2

[6,4,2,1,7,3,5] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[6,4,2,1,7,5,3] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2

[6,4,2,3,1,5,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[6,4,2,3,1,7,5] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[6,4,2,3,5,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[6,4,2,3,5,7,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1

[6,4,2,3,7,1,5] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[6,4,2,3,7,5,1] => [[[[.,.],.],[.,[[.,.],.]]],.] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 1

[6,4,2,5,1,3,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[6,4,2,5,1,7,3] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[6,4,2,5,3,1,7] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[6,4,2,5,3,7,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 1

[6,4,2,5,7,1,3] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[6,4,2,5,7,3,1] => [[[[.,.],.],[[.,[.,.]],.]],.] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 1

[6,4,2,7,1,3,5] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[6,4,2,7,1,5,3] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[6,4,2,7,3,1,5] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[6,4,2,7,3,5,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 1

[6,4,2,7,5,1,3] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[6,4,2,7,5,3,1] => [[[[.,.],.],[[[.,.],.],.]],.] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 1

[6,4,3,1,2,5,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4

[6,4,3,1,2,7,5] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 3

[6,4,3,1,5,2,7] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[6,4,3,1,5,7,2] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 2

[6,4,3,1,7,2,5] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[6,4,3,1,7,5,2] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2

[6,4,3,2,1,5,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 3

[6,4,3,2,1,7,5] => [[[[[.,.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2

[6,4,3,2,5,1,7] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2

[6,4,3,2,5,7,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1

[6,4,3,2,7,1,5] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2

[6,4,3,2,7,5,1] => [[[[[.,.],.],.],[[.,.],.]],.] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 1

[6,4,3,5,1,2,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[6,4,3,5,1,7,2] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[6,4,3,5,2,1,7] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[6,4,3,5,2,7,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1

[6,4,3,5,7,1,2] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[6,4,3,5,7,2,1] => [[[[[.,.],.],[.,[.,.]]],.],.] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1

[6,4,3,7,1,2,5] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[6,4,3,7,1,5,2] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[6,4,3,7,2,1,5] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[6,4,3,7,2,5,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1

[6,4,3,7,5,1,2] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[6,4,3,7,5,2,1] => [[[[[.,.],.],[[.,.],.]],.],.] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 1

[6,4,5,1,2,3,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[6,4,5,1,2,7,3] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[6,4,5,1,3,2,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,4,5,1,3,7,2] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[6,4,5,1,7,2,3] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,4,5,1,7,3,2] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[6,4,5,2,1,3,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3

[6,4,5,2,1,7,3] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[6,4,5,2,3,1,7] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,4,5,2,3,7,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1

[6,4,5,2,7,1,3] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,4,5,2,7,3,1] => [[[[.,.],[.,.]],[[.,.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 1

[6,4,5,3,1,2,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3

[6,4,5,3,1,7,2] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[6,4,5,3,2,1,7] => [[[[[.,.],[.,.]],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2

[6,4,5,3,2,7,1] => [[[[[.,.],[.,.]],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1

[6,4,5,3,7,1,2] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,4,5,3,7,2,1] => [[[[[.,.],[.,.]],[.,.]],.],.] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1

[6,4,5,7,1,2,3] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[6,4,5,7,1,3,2] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[6,4,5,7,2,1,3] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2

[6,4,5,7,2,3,1] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[6,4,5,7,3,1,2] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2

[6,4,5,7,3,2,1] => [[[[[.,.],[.,[.,.]]],.],.],.] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1

[6,4,7,1,2,3,5] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[6,4,7,1,2,5,3] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[6,4,7,1,3,2,5] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,4,7,1,3,5,2] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[6,4,7,1,5,2,3] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,4,7,1,5,3,2] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[6,4,7,2,1,3,5] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3

[6,4,7,2,1,5,3] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[6,4,7,2,3,1,5] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,4,7,2,3,5,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1

[6,4,7,2,5,1,3] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,4,7,2,5,3,1] => [[[[.,.],[.,.]],[[.,.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 1

[6,4,7,3,1,2,5] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3

[6,4,7,3,1,5,2] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[6,4,7,3,2,1,5] => [[[[[.,.],[.,.]],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2

[6,4,7,3,2,5,1] => [[[[[.,.],[.,.]],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1

[6,4,7,3,5,1,2] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,4,7,3,5,2,1] => [[[[[.,.],[.,.]],[.,.]],.],.] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1

[6,4,7,5,1,2,3] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[6,4,7,5,1,3,2] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[6,4,7,5,2,1,3] => [[[[.,.],[[.,.],.]],.],[.,.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2

[6,4,7,5,2,3,1] => [[[[.,.],[[.,.],.]],[.,.]],.] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 1

[6,4,7,5,3,1,2] => [[[[.,.],[[.,.],.]],.],[.,.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2

[6,4,7,5,3,2,1] => [[[[[.,.],[[.,.],.]],.],.],.] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 1

[6,5,1,2,3,4,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 5

[6,5,1,2,3,7,4] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 4

[6,5,1,2,4,3,7] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[6,5,1,2,4,7,3] => [[[.,.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 3

[6,5,1,2,7,3,4] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[6,5,1,2,7,4,3] => [[[.,.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 3

[6,5,1,3,2,4,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[6,5,1,3,2,7,4] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[6,5,1,3,4,2,7] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[6,5,1,3,4,7,2] => [[[.,.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 2

[6,5,1,3,7,2,4] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[6,5,1,3,7,4,2] => [[[.,.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 2

[6,5,1,4,2,3,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[6,5,1,4,2,7,3] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[6,5,1,4,3,2,7] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[6,5,1,4,3,7,2] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[6,5,1,4,7,2,3] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[6,5,1,4,7,3,2] => [[[.,.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 2

[6,5,1,7,2,3,4] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[6,5,1,7,2,4,3] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[6,5,1,7,3,2,4] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[6,5,1,7,3,4,2] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[6,5,1,7,4,2,3] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[6,5,1,7,4,3,2] => [[[.,.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2

[6,5,2,1,3,4,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4

[6,5,2,1,3,7,4] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 3

[6,5,2,1,4,3,7] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[6,5,2,1,4,7,3] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 2

[6,5,2,1,7,3,4] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[6,5,2,1,7,4,3] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2

[6,5,2,3,1,4,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[6,5,2,3,1,7,4] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[6,5,2,3,4,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[6,5,2,3,4,7,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1

[6,5,2,3,7,1,4] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[6,5,2,3,7,4,1] => [[[[.,.],.],[.,[[.,.],.]]],.] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 1

[6,5,2,4,1,3,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[6,5,2,4,1,7,3] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[6,5,2,4,3,1,7] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[6,5,2,4,3,7,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 1

[6,5,2,4,7,1,3] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[6,5,2,4,7,3,1] => [[[[.,.],.],[[.,[.,.]],.]],.] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 1

[6,5,2,7,1,3,4] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[6,5,2,7,1,4,3] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[6,5,2,7,3,1,4] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[6,5,2,7,3,4,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 1

[6,5,2,7,4,1,3] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[6,5,2,7,4,3,1] => [[[[.,.],.],[[[.,.],.],.]],.] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 1

[6,5,3,1,2,4,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4

[6,5,3,1,2,7,4] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 3

[6,5,3,1,4,2,7] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[6,5,3,1,4,7,2] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 2

[6,5,3,1,7,2,4] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[6,5,3,1,7,4,2] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2

[6,5,3,2,1,4,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 3

[6,5,3,2,1,7,4] => [[[[[.,.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2

[6,5,3,2,4,1,7] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2

[6,5,3,2,4,7,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1

[6,5,3,2,7,1,4] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2

[6,5,3,2,7,4,1] => [[[[[.,.],.],.],[[.,.],.]],.] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 1

[6,5,3,4,1,2,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[6,5,3,4,1,7,2] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[6,5,3,4,2,1,7] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[6,5,3,4,2,7,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1

[6,5,3,4,7,1,2] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[6,5,3,4,7,2,1] => [[[[[.,.],.],[.,[.,.]]],.],.] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1

[6,5,3,7,1,2,4] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[6,5,3,7,1,4,2] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[6,5,3,7,2,1,4] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[6,5,3,7,2,4,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1

[6,5,3,7,4,1,2] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[6,5,3,7,4,2,1] => [[[[[.,.],.],[[.,.],.]],.],.] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 1

[6,5,4,1,2,3,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4

[6,5,4,1,2,7,3] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 3

[6,5,4,1,3,2,7] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[6,5,4,1,3,7,2] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 2

[6,5,4,1,7,2,3] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[6,5,4,1,7,3,2] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2

[6,5,4,2,1,3,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 3

[6,5,4,2,1,7,3] => [[[[[.,.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2

[6,5,4,2,3,1,7] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2

[6,5,4,2,3,7,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1

[6,5,4,2,7,1,3] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2

[6,5,4,2,7,3,1] => [[[[[.,.],.],.],[[.,.],.]],.] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 1

[6,5,4,3,1,2,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 3

[6,5,4,3,1,7,2] => [[[[[.,.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2

[6,5,4,3,2,1,7] => [[[[[[.,.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 2

[6,5,4,3,2,7,1] => [[[[[[.,.],.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1

[6,5,4,3,7,1,2] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2

[6,5,4,3,7,2,1] => [[[[[[.,.],.],.],[.,.]],.],.] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1

[6,5,4,7,1,2,3] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[6,5,4,7,1,3,2] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[6,5,4,7,2,1,3] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[6,5,4,7,2,3,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1

[6,5,4,7,3,1,2] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[6,5,4,7,3,2,1] => [[[[[[.,.],.],[.,.]],.],.],.] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1

[6,5,7,1,2,3,4] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[6,5,7,1,2,4,3] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[6,5,7,1,3,2,4] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,5,7,1,3,4,2] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[6,5,7,1,4,2,3] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,5,7,1,4,3,2] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[6,5,7,2,1,3,4] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3

[6,5,7,2,1,4,3] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[6,5,7,2,3,1,4] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,5,7,2,3,4,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1

[6,5,7,2,4,1,3] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,5,7,2,4,3,1] => [[[[.,.],[.,.]],[[.,.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 1

[6,5,7,3,1,2,4] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3

[6,5,7,3,1,4,2] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[6,5,7,3,2,1,4] => [[[[[.,.],[.,.]],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2

[6,5,7,3,2,4,1] => [[[[[.,.],[.,.]],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1

[6,5,7,3,4,1,2] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,5,7,3,4,2,1] => [[[[[.,.],[.,.]],[.,.]],.],.] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1

[6,5,7,4,1,2,3] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3

[6,5,7,4,1,3,2] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[6,5,7,4,2,1,3] => [[[[[.,.],[.,.]],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2

[6,5,7,4,2,3,1] => [[[[[.,.],[.,.]],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1

[6,5,7,4,3,1,2] => [[[[[.,.],[.,.]],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2

[6,5,7,4,3,2,1] => [[[[[[.,.],[.,.]],.],.],.],.] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1

[6,7,1,2,3,4,5] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[6,7,1,2,3,5,4] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[6,7,1,2,4,3,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[6,7,1,2,4,5,3] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[6,7,1,2,5,3,4] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[6,7,1,2,5,4,3] => [[.,[.,.]],[.,[[[.,.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[6,7,1,3,2,4,5] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[6,7,1,3,2,5,4] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[6,7,1,3,4,2,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[6,7,1,3,4,5,2] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[6,7,1,3,5,2,4] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[6,7,1,3,5,4,2] => [[.,[.,.]],[[.,[[.,.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[6,7,1,4,2,3,5] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[6,7,1,4,2,5,3] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[6,7,1,4,3,2,5] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[6,7,1,4,3,5,2] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[6,7,1,4,5,2,3] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[6,7,1,4,5,3,2] => [[.,[.,.]],[[[.,[.,.]],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[6,7,1,5,2,3,4] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[6,7,1,5,2,4,3] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[6,7,1,5,3,2,4] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[6,7,1,5,3,4,2] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[6,7,1,5,4,2,3] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[6,7,1,5,4,3,2] => [[.,[.,.]],[[[[.,.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[6,7,2,1,3,4,5] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[6,7,2,1,3,5,4] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[6,7,2,1,4,3,5] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[6,7,2,1,4,5,3] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[6,7,2,1,5,3,4] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[6,7,2,1,5,4,3] => [[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[6,7,2,3,1,4,5] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[6,7,2,3,1,5,4] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[6,7,2,3,4,1,5] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[6,7,2,3,4,5,1] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1

[6,7,2,3,5,1,4] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[6,7,2,3,5,4,1] => [[[.,[.,.]],[.,[[.,.],.]]],.] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[6,7,2,4,1,3,5] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[6,7,2,4,1,5,3] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[6,7,2,4,3,1,5] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[6,7,2,4,3,5,1] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[6,7,2,4,5,1,3] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[6,7,2,4,5,3,1] => [[[.,[.,.]],[[.,[.,.]],.]],.] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[6,7,2,5,1,3,4] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[6,7,2,5,1,4,3] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[6,7,2,5,3,1,4] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[6,7,2,5,3,4,1] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[6,7,2,5,4,1,3] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[6,7,2,5,4,3,1] => [[[.,[.,.]],[[[.,.],.],.]],.] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1

[6,7,3,1,2,4,5] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[6,7,3,1,2,5,4] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[6,7,3,1,4,2,5] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[6,7,3,1,4,5,2] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[6,7,3,1,5,2,4] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[6,7,3,1,5,4,2] => [[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[6,7,3,2,1,4,5] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3

[6,7,3,2,1,5,4] => [[[[.,[.,.]],.],.],[[.,.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[6,7,3,2,4,1,5] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[6,7,3,2,4,5,1] => [[[[.,[.,.]],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1

[6,7,3,2,5,1,4] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[6,7,3,2,5,4,1] => [[[[.,[.,.]],.],[[.,.],.]],.] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1

[6,7,3,4,1,2,5] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[6,7,3,4,1,5,2] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[6,7,3,4,2,1,5] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[6,7,3,4,2,5,1] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[6,7,3,4,5,1,2] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[6,7,3,4,5,2,1] => [[[[.,[.,.]],[.,[.,.]]],.],.] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1

[6,7,3,5,1,2,4] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[6,7,3,5,1,4,2] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[6,7,3,5,2,1,4] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[6,7,3,5,2,4,1] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[6,7,3,5,4,1,2] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[6,7,3,5,4,2,1] => [[[[.,[.,.]],[[.,.],.]],.],.] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

[6,7,4,1,2,3,5] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[6,7,4,1,2,5,3] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[6,7,4,1,3,2,5] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[6,7,4,1,3,5,2] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[6,7,4,1,5,2,3] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[6,7,4,1,5,3,2] => [[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[6,7,4,2,1,3,5] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3

[6,7,4,2,1,5,3] => [[[[.,[.,.]],.],.],[[.,.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[6,7,4,2,3,1,5] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[6,7,4,2,3,5,1] => [[[[.,[.,.]],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1

[6,7,4,2,5,1,3] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[6,7,4,2,5,3,1] => [[[[.,[.,.]],.],[[.,.],.]],.] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1

[6,7,4,3,1,2,5] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3

[6,7,4,3,1,5,2] => [[[[.,[.,.]],.],.],[[.,.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[6,7,4,3,2,1,5] => [[[[[.,[.,.]],.],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2

[6,7,4,3,2,5,1] => [[[[[.,[.,.]],.],.],[.,.]],.] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1

[6,7,4,3,5,1,2] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[6,7,4,3,5,2,1] => [[[[[.,[.,.]],.],[.,.]],.],.] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1

[6,7,4,5,1,2,3] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[6,7,4,5,1,3,2] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[6,7,4,5,2,1,3] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[6,7,4,5,2,3,1] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[6,7,4,5,3,1,2] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[6,7,4,5,3,2,1] => [[[[[.,[.,.]],[.,.]],.],.],.] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1

[6,7,5,1,2,3,4] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[6,7,5,1,2,4,3] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[6,7,5,1,3,2,4] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[6,7,5,1,3,4,2] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[6,7,5,1,4,2,3] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[6,7,5,1,4,3,2] => [[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[6,7,5,2,1,3,4] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3

[6,7,5,2,1,4,3] => [[[[.,[.,.]],.],.],[[.,.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[6,7,5,2,3,1,4] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[6,7,5,2,3,4,1] => [[[[.,[.,.]],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1

[6,7,5,2,4,1,3] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[6,7,5,2,4,3,1] => [[[[.,[.,.]],.],[[.,.],.]],.] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1

[6,7,5,3,1,2,4] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3

[6,7,5,3,1,4,2] => [[[[.,[.,.]],.],.],[[.,.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[6,7,5,3,2,1,4] => [[[[[.,[.,.]],.],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2

[6,7,5,3,2,4,1] => [[[[[.,[.,.]],.],.],[.,.]],.] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1

[6,7,5,3,4,1,2] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[6,7,5,3,4,2,1] => [[[[[.,[.,.]],.],[.,.]],.],.] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1

[6,7,5,4,1,2,3] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3

[6,7,5,4,1,3,2] => [[[[.,[.,.]],.],.],[[.,.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[6,7,5,4,2,1,3] => [[[[[.,[.,.]],.],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2

[6,7,5,4,2,3,1] => [[[[[.,[.,.]],.],.],[.,.]],.] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1

[6,7,5,4,3,1,2] => [[[[[.,[.,.]],.],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2

[6,7,5,4,3,2,1] => [[[[[[.,[.,.]],.],.],.],.],.] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1

[7,1,2,3,4,5,6] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6

[7,1,2,3,4,6,5] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 5

[7,1,2,3,5,4,6] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 5

[7,1,2,3,5,6,4] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 4

[7,1,2,3,6,4,5] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 5

[7,1,2,3,6,5,4] => [[.,.],[.,[.,[[[.,.],.],.]]]] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 4

[7,1,2,4,3,5,6] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5

[7,1,2,4,3,6,5] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4

[7,1,2,4,5,3,6] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4

[7,1,2,4,5,6,3] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 3

[7,1,2,4,6,3,5] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4

[7,1,2,4,6,5,3] => [[.,.],[.,[[.,[[.,.],.]],.]]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 3

[7,1,2,5,3,4,6] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5

[7,1,2,5,3,6,4] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4

[7,1,2,5,4,3,6] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 4

[7,1,2,5,4,6,3] => [[.,.],[.,[[[.,.],[.,.]],.]]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 3

[7,1,2,5,6,3,4] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4

[7,1,2,5,6,4,3] => [[.,.],[.,[[[.,[.,.]],.],.]]] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 3

[7,1,2,6,3,4,5] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5

[7,1,2,6,3,5,4] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4

[7,1,2,6,4,3,5] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 4

[7,1,2,6,4,5,3] => [[.,.],[.,[[[.,.],[.,.]],.]]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 3

[7,1,2,6,5,3,4] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 4

[7,1,2,6,5,4,3] => [[.,.],[.,[[[[.,.],.],.],.]]] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 3

[7,1,3,2,4,5,6] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[7,1,3,2,4,6,5] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[7,1,3,2,5,4,6] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[7,1,3,2,5,6,4] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[7,1,3,2,6,4,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[7,1,3,2,6,5,4] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[7,1,3,4,2,5,6] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[7,1,3,4,2,6,5] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[7,1,3,4,5,2,6] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[7,1,3,4,5,6,2] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2

[7,1,3,4,6,2,5] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[7,1,3,4,6,5,2] => [[.,.],[[.,[.,[[.,.],.]]],.]] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 2

[7,1,3,5,2,4,6] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[7,1,3,5,2,6,4] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[7,1,3,5,4,2,6] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3

[7,1,3,5,4,6,2] => [[.,.],[[.,[[.,.],[.,.]]],.]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 2

[7,1,3,5,6,2,4] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[7,1,3,5,6,4,2] => [[.,.],[[.,[[.,[.,.]],.]],.]] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 2

[7,1,3,6,2,4,5] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[7,1,3,6,2,5,4] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[7,1,3,6,4,2,5] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3

[7,1,3,6,4,5,2] => [[.,.],[[.,[[.,.],[.,.]]],.]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 2

[7,1,3,6,5,2,4] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3

[7,1,3,6,5,4,2] => [[.,.],[[.,[[[.,.],.],.]],.]] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 2

[7,1,4,2,3,5,6] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[7,1,4,2,3,6,5] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[7,1,4,2,5,3,6] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[7,1,4,2,5,6,3] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[7,1,4,2,6,3,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[7,1,4,2,6,5,3] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[7,1,4,3,2,5,6] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[7,1,4,3,2,6,5] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[7,1,4,3,5,2,6] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[7,1,4,3,5,6,2] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 2

[7,1,4,3,6,2,5] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[7,1,4,3,6,5,2] => [[.,.],[[[.,.],[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2

[7,1,4,5,2,3,6] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[7,1,4,5,2,6,3] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[7,1,4,5,3,2,6] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[7,1,4,5,3,6,2] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2

[7,1,4,5,6,2,3] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[7,1,4,5,6,3,2] => [[.,.],[[[.,[.,[.,.]]],.],.]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2

[7,1,4,6,2,3,5] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[7,1,4,6,2,5,3] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[7,1,4,6,3,2,5] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[7,1,4,6,3,5,2] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2

[7,1,4,6,5,2,3] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3

[7,1,4,6,5,3,2] => [[.,.],[[[.,[[.,.],.]],.],.]] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 2

[7,1,5,2,3,4,6] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[7,1,5,2,3,6,4] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[7,1,5,2,4,3,6] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[7,1,5,2,4,6,3] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[7,1,5,2,6,3,4] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[7,1,5,2,6,4,3] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[7,1,5,3,2,4,6] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[7,1,5,3,2,6,4] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[7,1,5,3,4,2,6] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[7,1,5,3,4,6,2] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 2

[7,1,5,3,6,2,4] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[7,1,5,3,6,4,2] => [[.,.],[[[.,.],[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2

[7,1,5,4,2,3,6] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[7,1,5,4,2,6,3] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[7,1,5,4,3,2,6] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[7,1,5,4,3,6,2] => [[.,.],[[[[.,.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2

[7,1,5,4,6,2,3] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[7,1,5,4,6,3,2] => [[.,.],[[[[.,.],[.,.]],.],.]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 2

[7,1,5,6,2,3,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[7,1,5,6,2,4,3] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[7,1,5,6,3,2,4] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[7,1,5,6,3,4,2] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2

[7,1,5,6,4,2,3] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[7,1,5,6,4,3,2] => [[.,.],[[[[.,[.,.]],.],.],.]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 2

[7,1,6,2,3,4,5] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[7,1,6,2,3,5,4] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[7,1,6,2,4,3,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[7,1,6,2,4,5,3] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[7,1,6,2,5,3,4] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[7,1,6,2,5,4,3] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[7,1,6,3,2,4,5] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[7,1,6,3,2,5,4] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[7,1,6,3,4,2,5] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[7,1,6,3,4,5,2] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 2

[7,1,6,3,5,2,4] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[7,1,6,3,5,4,2] => [[.,.],[[[.,.],[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2

[7,1,6,4,2,3,5] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[7,1,6,4,2,5,3] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[7,1,6,4,3,2,5] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[7,1,6,4,3,5,2] => [[.,.],[[[[.,.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2

[7,1,6,4,5,2,3] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[7,1,6,4,5,3,2] => [[.,.],[[[[.,.],[.,.]],.],.]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 2

[7,1,6,5,2,3,4] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[7,1,6,5,2,4,3] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[7,1,6,5,3,2,4] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[7,1,6,5,3,4,2] => [[.,.],[[[[.,.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2

[7,1,6,5,4,2,3] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[7,1,6,5,4,3,2] => [[.,.],[[[[[.,.],.],.],.],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2

[7,2,1,3,4,5,6] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 5

[7,2,1,3,4,6,5] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 4

[7,2,1,3,5,4,6] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[7,2,1,3,5,6,4] => [[[.,.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 3

[7,2,1,3,6,4,5] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[7,2,1,3,6,5,4] => [[[.,.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 3

[7,2,1,4,3,5,6] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[7,2,1,4,3,6,5] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[7,2,1,4,5,3,6] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[7,2,1,4,5,6,3] => [[[.,.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 2

[7,2,1,4,6,3,5] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[7,2,1,4,6,5,3] => [[[.,.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 2

[7,2,1,5,3,4,6] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[7,2,1,5,3,6,4] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[7,2,1,5,4,3,6] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[7,2,1,5,4,6,3] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[7,2,1,5,6,3,4] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[7,2,1,5,6,4,3] => [[[.,.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 2

[7,2,1,6,3,4,5] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[7,2,1,6,3,5,4] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[7,2,1,6,4,3,5] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[7,2,1,6,4,5,3] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[7,2,1,6,5,3,4] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[7,2,1,6,5,4,3] => [[[.,.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2

[7,2,3,1,4,5,6] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[7,2,3,1,4,6,5] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[7,2,3,1,5,4,6] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[7,2,3,1,5,6,4] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[7,2,3,1,6,4,5] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[7,2,3,1,6,5,4] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[7,2,3,4,1,5,6] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[7,2,3,4,1,6,5] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[7,2,3,4,5,1,6] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[7,2,3,4,5,6,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1

[7,2,3,4,6,1,5] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[7,2,3,4,6,5,1] => [[[.,.],[.,[.,[[.,.],.]]]],.] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 1

[7,2,3,5,1,4,6] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[7,2,3,5,1,6,4] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[7,2,3,5,4,1,6] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[7,2,3,5,4,6,1] => [[[.,.],[.,[[.,.],[.,.]]]],.] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 1

[7,2,3,5,6,1,4] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[7,2,3,5,6,4,1] => [[[.,.],[.,[[.,[.,.]],.]]],.] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 1

[7,2,3,6,1,4,5] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[7,2,3,6,1,5,4] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[7,2,3,6,4,1,5] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[7,2,3,6,4,5,1] => [[[.,.],[.,[[.,.],[.,.]]]],.] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 1

[7,2,3,6,5,1,4] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[7,2,3,6,5,4,1] => [[[.,.],[.,[[[.,.],.],.]]],.] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 1

[7,2,4,1,3,5,6] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[7,2,4,1,3,6,5] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[7,2,4,1,5,3,6] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[7,2,4,1,5,6,3] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[7,2,4,1,6,3,5] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[7,2,4,1,6,5,3] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[7,2,4,3,1,5,6] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[7,2,4,3,1,6,5] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[7,2,4,3,5,1,6] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[7,2,4,3,5,6,1] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 1

[7,2,4,3,6,1,5] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[7,2,4,3,6,5,1] => [[[.,.],[[.,.],[[.,.],.]]],.] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 1

[7,2,4,5,1,3,6] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[7,2,4,5,1,6,3] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[7,2,4,5,3,1,6] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[7,2,4,5,3,6,1] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 1

[7,2,4,5,6,1,3] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[7,2,4,5,6,3,1] => [[[.,.],[[.,[.,[.,.]]],.]],.] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[7,2,4,6,1,3,5] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[7,2,4,6,1,5,3] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[7,2,4,6,3,1,5] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[7,2,4,6,3,5,1] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 1

[7,2,4,6,5,1,3] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[7,2,4,6,5,3,1] => [[[.,.],[[.,[[.,.],.]],.]],.] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 1

[7,2,5,1,3,4,6] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[7,2,5,1,3,6,4] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[7,2,5,1,4,3,6] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[7,2,5,1,4,6,3] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[7,2,5,1,6,3,4] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[7,2,5,1,6,4,3] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[7,2,5,3,1,4,6] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[7,2,5,3,1,6,4] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[7,2,5,3,4,1,6] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[7,2,5,3,4,6,1] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 1

[7,2,5,3,6,1,4] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[7,2,5,3,6,4,1] => [[[.,.],[[.,.],[[.,.],.]]],.] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 1

[7,2,5,4,1,3,6] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[7,2,5,4,1,6,3] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[7,2,5,4,3,1,6] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[7,2,5,4,3,6,1] => [[[.,.],[[[.,.],.],[.,.]]],.] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 1

[7,2,5,4,6,1,3] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[7,2,5,4,6,3,1] => [[[.,.],[[[.,.],[.,.]],.]],.] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 1

[7,2,5,6,1,3,4] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[7,2,5,6,1,4,3] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[7,2,5,6,3,1,4] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[7,2,5,6,3,4,1] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 1

[7,2,5,6,4,1,3] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[7,2,5,6,4,3,1] => [[[.,.],[[[.,[.,.]],.],.]],.] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 1

[7,2,6,1,3,4,5] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[7,2,6,1,3,5,4] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[7,2,6,1,4,3,5] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[7,2,6,1,4,5,3] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[7,2,6,1,5,3,4] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[7,2,6,1,5,4,3] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[7,2,6,3,1,4,5] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[7,2,6,3,1,5,4] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[7,2,6,3,4,1,5] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[7,2,6,3,4,5,1] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 1

[7,2,6,3,5,1,4] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[7,2,6,3,5,4,1] => [[[.,.],[[.,.],[[.,.],.]]],.] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 1

[7,2,6,4,1,3,5] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[7,2,6,4,1,5,3] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[7,2,6,4,3,1,5] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[7,2,6,4,3,5,1] => [[[.,.],[[[.,.],.],[.,.]]],.] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 1

[7,2,6,4,5,1,3] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[7,2,6,4,5,3,1] => [[[.,.],[[[.,.],[.,.]],.]],.] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 1

[7,2,6,5,1,3,4] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[7,2,6,5,1,4,3] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[7,2,6,5,3,1,4] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[7,2,6,5,3,4,1] => [[[.,.],[[[.,.],.],[.,.]]],.] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 1

[7,2,6,5,4,1,3] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[7,2,6,5,4,3,1] => [[[.,.],[[[[.,.],.],.],.]],.] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1

[7,3,1,2,4,5,6] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 5

[7,3,1,2,4,6,5] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 4

[7,3,1,2,5,4,6] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[7,3,1,2,5,6,4] => [[[.,.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 3

[7,3,1,2,6,4,5] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[7,3,1,2,6,5,4] => [[[.,.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 3

[7,3,1,4,2,5,6] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[7,3,1,4,2,6,5] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[7,3,1,4,5,2,6] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[7,3,1,4,5,6,2] => [[[.,.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 2

[7,3,1,4,6,2,5] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[7,3,1,4,6,5,2] => [[[.,.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 2

[7,3,1,5,2,4,6] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[7,3,1,5,2,6,4] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[7,3,1,5,4,2,6] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[7,3,1,5,4,6,2] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[7,3,1,5,6,2,4] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[7,3,1,5,6,4,2] => [[[.,.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 2

[7,3,1,6,2,4,5] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[7,3,1,6,2,5,4] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[7,3,1,6,4,2,5] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[7,3,1,6,4,5,2] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[7,3,1,6,5,2,4] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[7,3,1,6,5,4,2] => [[[.,.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2

[7,3,2,1,4,5,6] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4

[7,3,2,1,4,6,5] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 3

[7,3,2,1,5,4,6] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[7,3,2,1,5,6,4] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 2

[7,3,2,1,6,4,5] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[7,3,2,1,6,5,4] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2

[7,3,2,4,1,5,6] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[7,3,2,4,1,6,5] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[7,3,2,4,5,1,6] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[7,3,2,4,5,6,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1

[7,3,2,4,6,1,5] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[7,3,2,4,6,5,1] => [[[[.,.],.],[.,[[.,.],.]]],.] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 1

[7,3,2,5,1,4,6] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[7,3,2,5,1,6,4] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[7,3,2,5,4,1,6] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[7,3,2,5,4,6,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 1

[7,3,2,5,6,1,4] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[7,3,2,5,6,4,1] => [[[[.,.],.],[[.,[.,.]],.]],.] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 1

[7,3,2,6,1,4,5] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[7,3,2,6,1,5,4] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[7,3,2,6,4,1,5] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[7,3,2,6,4,5,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 1

[7,3,2,6,5,1,4] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[7,3,2,6,5,4,1] => [[[[.,.],.],[[[.,.],.],.]],.] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 1

[7,3,4,1,2,5,6] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[7,3,4,1,2,6,5] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[7,3,4,1,5,2,6] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[7,3,4,1,5,6,2] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[7,3,4,1,6,2,5] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[7,3,4,1,6,5,2] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[7,3,4,2,1,5,6] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3

[7,3,4,2,1,6,5] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[7,3,4,2,5,1,6] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[7,3,4,2,5,6,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1

[7,3,4,2,6,1,5] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[7,3,4,2,6,5,1] => [[[[.,.],[.,.]],[[.,.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 1

[7,3,4,5,1,2,6] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[7,3,4,5,1,6,2] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[7,3,4,5,2,1,6] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2

[7,3,4,5,2,6,1] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[7,3,4,5,6,1,2] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[7,3,4,5,6,2,1] => [[[[.,.],[.,[.,[.,.]]]],.],.] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1

[7,3,4,6,1,2,5] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[7,3,4,6,1,5,2] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[7,3,4,6,2,1,5] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2

[7,3,4,6,2,5,1] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[7,3,4,6,5,1,2] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[7,3,4,6,5,2,1] => [[[[.,.],[.,[[.,.],.]]],.],.] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 1

[7,3,5,1,2,4,6] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[7,3,5,1,2,6,4] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[7,3,5,1,4,2,6] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[7,3,5,1,4,6,2] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[7,3,5,1,6,2,4] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[7,3,5,1,6,4,2] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[7,3,5,2,1,4,6] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3

[7,3,5,2,1,6,4] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[7,3,5,2,4,1,6] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[7,3,5,2,4,6,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1

[7,3,5,2,6,1,4] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[7,3,5,2,6,4,1] => [[[[.,.],[.,.]],[[.,.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 1

[7,3,5,4,1,2,6] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[7,3,5,4,1,6,2] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[7,3,5,4,2,1,6] => [[[[.,.],[[.,.],.]],.],[.,.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2

[7,3,5,4,2,6,1] => [[[[.,.],[[.,.],.]],[.,.]],.] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 1

[7,3,5,4,6,1,2] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[7,3,5,4,6,2,1] => [[[[.,.],[[.,.],[.,.]]],.],.] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 1

[7,3,5,6,1,2,4] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[7,3,5,6,1,4,2] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[7,3,5,6,2,1,4] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2

[7,3,5,6,2,4,1] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[7,3,5,6,4,1,2] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[7,3,5,6,4,2,1] => [[[[.,.],[[.,[.,.]],.]],.],.] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 1

[7,3,6,1,2,4,5] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[7,3,6,1,2,5,4] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[7,3,6,1,4,2,5] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[7,3,6,1,4,5,2] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[7,3,6,1,5,2,4] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[7,3,6,1,5,4,2] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[7,3,6,2,1,4,5] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3

[7,3,6,2,1,5,4] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[7,3,6,2,4,1,5] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[7,3,6,2,4,5,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1

[7,3,6,2,5,1,4] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[7,3,6,2,5,4,1] => [[[[.,.],[.,.]],[[.,.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 1

[7,3,6,4,1,2,5] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[7,3,6,4,1,5,2] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[7,3,6,4,2,1,5] => [[[[.,.],[[.,.],.]],.],[.,.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2

[7,3,6,4,2,5,1] => [[[[.,.],[[.,.],.]],[.,.]],.] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 1

[7,3,6,4,5,1,2] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[7,3,6,4,5,2,1] => [[[[.,.],[[.,.],[.,.]]],.],.] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 1

[7,3,6,5,1,2,4] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[7,3,6,5,1,4,2] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[7,3,6,5,2,1,4] => [[[[.,.],[[.,.],.]],.],[.,.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2

[7,3,6,5,2,4,1] => [[[[.,.],[[.,.],.]],[.,.]],.] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 1

[7,3,6,5,4,1,2] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[7,3,6,5,4,2,1] => [[[[.,.],[[[.,.],.],.]],.],.] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 1

[7,4,1,2,3,5,6] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 5

[7,4,1,2,3,6,5] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 4

[7,4,1,2,5,3,6] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[7,4,1,2,5,6,3] => [[[.,.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 3

[7,4,1,2,6,3,5] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[7,4,1,2,6,5,3] => [[[.,.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 3

[7,4,1,3,2,5,6] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[7,4,1,3,2,6,5] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[7,4,1,3,5,2,6] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[7,4,1,3,5,6,2] => [[[.,.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 2

[7,4,1,3,6,2,5] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[7,4,1,3,6,5,2] => [[[.,.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 2

[7,4,1,5,2,3,6] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[7,4,1,5,2,6,3] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[7,4,1,5,3,2,6] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[7,4,1,5,3,6,2] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[7,4,1,5,6,2,3] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[7,4,1,5,6,3,2] => [[[.,.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 2

[7,4,1,6,2,3,5] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[7,4,1,6,2,5,3] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[7,4,1,6,3,2,5] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[7,4,1,6,3,5,2] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[7,4,1,6,5,2,3] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[7,4,1,6,5,3,2] => [[[.,.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2

[7,4,2,1,3,5,6] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4

[7,4,2,1,3,6,5] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 3

[7,4,2,1,5,3,6] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[7,4,2,1,5,6,3] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 2

[7,4,2,1,6,3,5] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[7,4,2,1,6,5,3] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2

[7,4,2,3,1,5,6] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[7,4,2,3,1,6,5] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[7,4,2,3,5,1,6] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[7,4,2,3,5,6,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1

[7,4,2,3,6,1,5] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[7,4,2,3,6,5,1] => [[[[.,.],.],[.,[[.,.],.]]],.] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 1

[7,4,2,5,1,3,6] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[7,4,2,5,1,6,3] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[7,4,2,5,3,1,6] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[7,4,2,5,3,6,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 1

[7,4,2,5,6,1,3] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[7,4,2,5,6,3,1] => [[[[.,.],.],[[.,[.,.]],.]],.] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 1

[7,4,2,6,1,3,5] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[7,4,2,6,1,5,3] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[7,4,2,6,3,1,5] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[7,4,2,6,3,5,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 1

[7,4,2,6,5,1,3] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[7,4,2,6,5,3,1] => [[[[.,.],.],[[[.,.],.],.]],.] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 1

[7,4,3,1,2,5,6] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4

[7,4,3,1,2,6,5] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 3

[7,4,3,1,5,2,6] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[7,4,3,1,5,6,2] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 2

[7,4,3,1,6,2,5] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[7,4,3,1,6,5,2] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2

[7,4,3,2,1,5,6] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 3

[7,4,3,2,1,6,5] => [[[[[.,.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2

[7,4,3,2,5,1,6] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2

[7,4,3,2,5,6,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1

[7,4,3,2,6,1,5] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2

[7,4,3,2,6,5,1] => [[[[[.,.],.],.],[[.,.],.]],.] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 1

[7,4,3,5,1,2,6] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[7,4,3,5,1,6,2] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[7,4,3,5,2,1,6] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[7,4,3,5,2,6,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1

[7,4,3,5,6,1,2] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[7,4,3,5,6,2,1] => [[[[[.,.],.],[.,[.,.]]],.],.] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1

[7,4,3,6,1,2,5] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[7,4,3,6,1,5,2] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[7,4,3,6,2,1,5] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[7,4,3,6,2,5,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1

[7,4,3,6,5,1,2] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[7,4,3,6,5,2,1] => [[[[[.,.],.],[[.,.],.]],.],.] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 1

[7,4,5,1,2,3,6] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[7,4,5,1,2,6,3] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[7,4,5,1,3,2,6] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[7,4,5,1,3,6,2] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[7,4,5,1,6,2,3] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[7,4,5,1,6,3,2] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[7,4,5,2,1,3,6] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3

[7,4,5,2,1,6,3] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[7,4,5,2,3,1,6] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[7,4,5,2,3,6,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1

[7,4,5,2,6,1,3] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[7,4,5,2,6,3,1] => [[[[.,.],[.,.]],[[.,.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 1

[7,4,5,3,1,2,6] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3

[7,4,5,3,1,6,2] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[7,4,5,3,2,1,6] => [[[[[.,.],[.,.]],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2

[7,4,5,3,2,6,1] => [[[[[.,.],[.,.]],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1

[7,4,5,3,6,1,2] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[7,4,5,3,6,2,1] => [[[[[.,.],[.,.]],[.,.]],.],.] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1

[7,4,5,6,1,2,3] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[7,4,5,6,1,3,2] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[7,4,5,6,2,1,3] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2

[7,4,5,6,2,3,1] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[7,4,5,6,3,1,2] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2

[7,4,5,6,3,2,1] => [[[[[.,.],[.,[.,.]]],.],.],.] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1

[7,4,6,1,2,3,5] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[7,4,6,1,2,5,3] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[7,4,6,1,3,2,5] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[7,4,6,1,3,5,2] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[7,4,6,1,5,2,3] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[7,4,6,1,5,3,2] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[7,4,6,2,1,3,5] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3

[7,4,6,2,1,5,3] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[7,4,6,2,3,1,5] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[7,4,6,2,3,5,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1

[7,4,6,2,5,1,3] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[7,4,6,2,5,3,1] => [[[[.,.],[.,.]],[[.,.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 1

[7,4,6,3,1,2,5] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3

[7,4,6,3,1,5,2] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[7,4,6,3,2,1,5] => [[[[[.,.],[.,.]],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2

[7,4,6,3,2,5,1] => [[[[[.,.],[.,.]],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1

[7,4,6,3,5,1,2] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[7,4,6,3,5,2,1] => [[[[[.,.],[.,.]],[.,.]],.],.] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1

[7,4,6,5,1,2,3] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[7,4,6,5,1,3,2] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[7,4,6,5,2,1,3] => [[[[.,.],[[.,.],.]],.],[.,.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2

[7,4,6,5,2,3,1] => [[[[.,.],[[.,.],.]],[.,.]],.] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 1

[7,4,6,5,3,1,2] => [[[[.,.],[[.,.],.]],.],[.,.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2

[7,4,6,5,3,2,1] => [[[[[.,.],[[.,.],.]],.],.],.] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 1

[7,5,1,2,3,4,6] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 5

[7,5,1,2,3,6,4] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 4

[7,5,1,2,4,3,6] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[7,5,1,2,4,6,3] => [[[.,.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 3

[7,5,1,2,6,3,4] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[7,5,1,2,6,4,3] => [[[.,.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 3

[7,5,1,3,2,4,6] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[7,5,1,3,2,6,4] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[7,5,1,3,4,2,6] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[7,5,1,3,4,6,2] => [[[.,.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 2

[7,5,1,3,6,2,4] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[7,5,1,3,6,4,2] => [[[.,.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 2

[7,5,1,4,2,3,6] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[7,5,1,4,2,6,3] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[7,5,1,4,3,2,6] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[7,5,1,4,3,6,2] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[7,5,1,4,6,2,3] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[7,5,1,4,6,3,2] => [[[.,.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 2

[7,5,1,6,2,3,4] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[7,5,1,6,2,4,3] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[7,5,1,6,3,2,4] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[7,5,1,6,3,4,2] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[7,5,1,6,4,2,3] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[7,5,1,6,4,3,2] => [[[.,.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2

[7,5,2,1,3,4,6] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4

[7,5,2,1,3,6,4] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 3

[7,5,2,1,4,3,6] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[7,5,2,1,4,6,3] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 2

[7,5,2,1,6,3,4] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[7,5,2,1,6,4,3] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2

[7,5,2,3,1,4,6] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[7,5,2,3,1,6,4] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[7,5,2,3,4,1,6] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[7,5,2,3,4,6,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1

[7,5,2,3,6,1,4] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[7,5,2,3,6,4,1] => [[[[.,.],.],[.,[[.,.],.]]],.] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 1

[7,5,2,4,1,3,6] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[7,5,2,4,1,6,3] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[7,5,2,4,3,1,6] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[7,5,2,4,3,6,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 1

[7,5,2,4,6,1,3] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[7,5,2,4,6,3,1] => [[[[.,.],.],[[.,[.,.]],.]],.] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 1

[7,5,2,6,1,3,4] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[7,5,2,6,1,4,3] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[7,5,2,6,3,1,4] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[7,5,2,6,3,4,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 1

[7,5,2,6,4,1,3] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[7,5,2,6,4,3,1] => [[[[.,.],.],[[[.,.],.],.]],.] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 1

[7,5,3,1,2,4,6] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4

[7,5,3,1,2,6,4] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 3

[7,5,3,1,4,2,6] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[7,5,3,1,4,6,2] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 2

[7,5,3,1,6,2,4] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[7,5,3,1,6,4,2] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2

[7,5,3,2,1,4,6] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 3

[7,5,3,2,1,6,4] => [[[[[.,.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2

[7,5,3,2,4,1,6] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2

[7,5,3,2,4,6,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1

[7,5,3,2,6,1,4] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2

[7,5,3,2,6,4,1] => [[[[[.,.],.],.],[[.,.],.]],.] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 1

[7,5,3,4,1,2,6] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[7,5,3,4,1,6,2] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[7,5,3,4,2,1,6] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[7,5,3,4,2,6,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1

[7,5,3,4,6,1,2] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[7,5,3,4,6,2,1] => [[[[[.,.],.],[.,[.,.]]],.],.] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1

[7,5,3,6,1,2,4] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[7,5,3,6,1,4,2] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[7,5,3,6,2,1,4] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[7,5,3,6,2,4,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1

[7,5,3,6,4,1,2] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[7,5,3,6,4,2,1] => [[[[[.,.],.],[[.,.],.]],.],.] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 1

[7,5,4,1,2,3,6] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4

[7,5,4,1,2,6,3] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 3

[7,5,4,1,3,2,6] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[7,5,4,1,3,6,2] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 2

[7,5,4,1,6,2,3] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[7,5,4,1,6,3,2] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2

[7,5,4,2,1,3,6] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 3

[7,5,4,2,1,6,3] => [[[[[.,.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2

[7,5,4,2,3,1,6] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2

[7,5,4,2,3,6,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1

[7,5,4,2,6,1,3] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2

[7,5,4,2,6,3,1] => [[[[[.,.],.],.],[[.,.],.]],.] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 1

[7,5,4,3,1,2,6] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 3

[7,5,4,3,1,6,2] => [[[[[.,.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2

[7,5,4,3,2,1,6] => [[[[[[.,.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 2

[7,5,4,3,2,6,1] => [[[[[[.,.],.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1

[7,5,4,3,6,1,2] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2

[7,5,4,3,6,2,1] => [[[[[[.,.],.],.],[.,.]],.],.] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1

[7,5,4,6,1,2,3] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[7,5,4,6,1,3,2] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[7,5,4,6,2,1,3] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[7,5,4,6,2,3,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1

[7,5,4,6,3,1,2] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[7,5,4,6,3,2,1] => [[[[[[.,.],.],[.,.]],.],.],.] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1

[7,5,6,1,2,3,4] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[7,5,6,1,2,4,3] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[7,5,6,1,3,2,4] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[7,5,6,1,3,4,2] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[7,5,6,1,4,2,3] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[7,5,6,1,4,3,2] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[7,5,6,2,1,3,4] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3

[7,5,6,2,1,4,3] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[7,5,6,2,3,1,4] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[7,5,6,2,3,4,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1

[7,5,6,2,4,1,3] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[7,5,6,2,4,3,1] => [[[[.,.],[.,.]],[[.,.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 1

[7,5,6,3,1,2,4] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3

[7,5,6,3,1,4,2] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[7,5,6,3,2,1,4] => [[[[[.,.],[.,.]],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2

[7,5,6,3,2,4,1] => [[[[[.,.],[.,.]],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1

[7,5,6,3,4,1,2] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[7,5,6,3,4,2,1] => [[[[[.,.],[.,.]],[.,.]],.],.] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1

[7,5,6,4,1,2,3] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3

[7,5,6,4,1,3,2] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[7,5,6,4,2,1,3] => [[[[[.,.],[.,.]],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2

[7,5,6,4,2,3,1] => [[[[[.,.],[.,.]],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1

[7,5,6,4,3,1,2] => [[[[[.,.],[.,.]],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2

[7,5,6,4,3,2,1] => [[[[[[.,.],[.,.]],.],.],.],.] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1

[7,6,1,2,3,4,5] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 5

[7,6,1,2,3,5,4] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 4

[7,6,1,2,4,3,5] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[7,6,1,2,4,5,3] => [[[.,.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 3

[7,6,1,2,5,3,4] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[7,6,1,2,5,4,3] => [[[.,.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 3

[7,6,1,3,2,4,5] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[7,6,1,3,2,5,4] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[7,6,1,3,4,2,5] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[7,6,1,3,4,5,2] => [[[.,.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 2

[7,6,1,3,5,2,4] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[7,6,1,3,5,4,2] => [[[.,.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 2

[7,6,1,4,2,3,5] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[7,6,1,4,2,5,3] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[7,6,1,4,3,2,5] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[7,6,1,4,3,5,2] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[7,6,1,4,5,2,3] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[7,6,1,4,5,3,2] => [[[.,.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 2

[7,6,1,5,2,3,4] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[7,6,1,5,2,4,3] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[7,6,1,5,3,2,4] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[7,6,1,5,3,4,2] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[7,6,1,5,4,2,3] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[7,6,1,5,4,3,2] => [[[.,.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2

[7,6,2,1,3,4,5] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4

[7,6,2,1,3,5,4] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 3

[7,6,2,1,4,3,5] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[7,6,2,1,4,5,3] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 2

[7,6,2,1,5,3,4] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[7,6,2,1,5,4,3] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2

[7,6,2,3,1,4,5] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[7,6,2,3,1,5,4] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[7,6,2,3,4,1,5] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[7,6,2,3,4,5,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1

[7,6,2,3,5,1,4] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[7,6,2,3,5,4,1] => [[[[.,.],.],[.,[[.,.],.]]],.] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 1

[7,6,2,4,1,3,5] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[7,6,2,4,1,5,3] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[7,6,2,4,3,1,5] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[7,6,2,4,3,5,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 1

[7,6,2,4,5,1,3] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[7,6,2,4,5,3,1] => [[[[.,.],.],[[.,[.,.]],.]],.] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 1

[7,6,2,5,1,3,4] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[7,6,2,5,1,4,3] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[7,6,2,5,3,1,4] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[7,6,2,5,3,4,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 1

[7,6,2,5,4,1,3] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[7,6,2,5,4,3,1] => [[[[.,.],.],[[[.,.],.],.]],.] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 1

[7,6,3,1,2,4,5] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4

[7,6,3,1,2,5,4] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 3

[7,6,3,1,4,2,5] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[7,6,3,1,4,5,2] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 2

[7,6,3,1,5,2,4] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[7,6,3,1,5,4,2] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2

[7,6,3,2,1,4,5] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 3

[7,6,3,2,1,5,4] => [[[[[.,.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2

[7,6,3,2,4,1,5] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2

[7,6,3,2,4,5,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1

[7,6,3,2,5,1,4] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2

[7,6,3,2,5,4,1] => [[[[[.,.],.],.],[[.,.],.]],.] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 1

[7,6,3,4,1,2,5] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[7,6,3,4,1,5,2] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[7,6,3,4,2,1,5] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[7,6,3,4,2,5,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1

[7,6,3,4,5,1,2] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[7,6,3,4,5,2,1] => [[[[[.,.],.],[.,[.,.]]],.],.] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1

[7,6,3,5,1,2,4] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[7,6,3,5,1,4,2] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[7,6,3,5,2,1,4] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[7,6,3,5,2,4,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1

[7,6,3,5,4,1,2] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[7,6,3,5,4,2,1] => [[[[[.,.],.],[[.,.],.]],.],.] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 1

[7,6,4,1,2,3,5] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4

[7,6,4,1,2,5,3] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 3

[7,6,4,1,3,2,5] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[7,6,4,1,3,5,2] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 2

[7,6,4,1,5,2,3] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[7,6,4,1,5,3,2] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2

[7,6,4,2,1,3,5] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 3

[7,6,4,2,1,5,3] => [[[[[.,.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2

[7,6,4,2,3,1,5] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2

[7,6,4,2,3,5,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1

[7,6,4,2,5,1,3] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2

[7,6,4,2,5,3,1] => [[[[[.,.],.],.],[[.,.],.]],.] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 1

[7,6,4,3,1,2,5] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 3

[7,6,4,3,1,5,2] => [[[[[.,.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2

[7,6,4,3,2,1,5] => [[[[[[.,.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 2

[7,6,4,3,2,5,1] => [[[[[[.,.],.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1

[7,6,4,3,5,1,2] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2

[7,6,4,3,5,2,1] => [[[[[[.,.],.],.],[.,.]],.],.] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1

[7,6,4,5,1,2,3] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[7,6,4,5,1,3,2] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[7,6,4,5,2,1,3] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[7,6,4,5,2,3,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1

[7,6,4,5,3,1,2] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[7,6,4,5,3,2,1] => [[[[[[.,.],.],[.,.]],.],.],.] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1

[7,6,5,1,2,3,4] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4

[7,6,5,1,2,4,3] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 3

[7,6,5,1,3,2,4] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[7,6,5,1,3,4,2] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 2

[7,6,5,1,4,2,3] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[7,6,5,1,4,3,2] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2

[7,6,5,2,1,3,4] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 3

[7,6,5,2,1,4,3] => [[[[[.,.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2

[7,6,5,2,3,1,4] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2

[7,6,5,2,3,4,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1

[7,6,5,2,4,1,3] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2

[7,6,5,2,4,3,1] => [[[[[.,.],.],.],[[.,.],.]],.] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 1

[7,6,5,3,1,2,4] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 3

[7,6,5,3,1,4,2] => [[[[[.,.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2

[7,6,5,3,2,1,4] => [[[[[[.,.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 2

[7,6,5,3,2,4,1] => [[[[[[.,.],.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1

[7,6,5,3,4,1,2] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2

[7,6,5,3,4,2,1] => [[[[[[.,.],.],.],[.,.]],.],.] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1

[7,6,5,4,1,2,3] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 3

[7,6,5,4,1,3,2] => [[[[[.,.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2

[7,6,5,4,2,1,3] => [[[[[[.,.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 2

[7,6,5,4,2,3,1] => [[[[[[.,.],.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1

[7,6,5,4,3,1,2] => [[[[[[.,.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 2

[7,6,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],.] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1

[7,8,6,5,4,3,2,1] => [[[[[[[.,[.,.]],.],.],.],.],.],.] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1

[8,6,7,5,4,3,2,1] => [[[[[[[.,.],[.,.]],.],.],.],.],.] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1

[7,6,8,5,4,3,2,1] => [[[[[[[.,.],[.,.]],.],.],.],.],.] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1

[6,7,8,5,4,3,2,1] => [[[[[[.,[.,[.,.]]],.],.],.],.],.] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1

[7,8,5,6,4,3,2,1] => [[[[[[.,[.,.]],[.,.]],.],.],.],.] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1

[8,5,6,7,4,3,2,1] => [[[[[[.,.],[.,[.,.]]],.],.],.],.] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1

[6,7,5,8,4,3,2,1] => [[[[[[.,[.,.]],[.,.]],.],.],.],.] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1

[7,5,6,8,4,3,2,1] => [[[[[[.,.],[.,[.,.]]],.],.],.],.] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1

[6,5,7,8,4,3,2,1] => [[[[[[.,.],[.,[.,.]]],.],.],.],.] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1

[5,6,7,8,4,3,2,1] => [[[[[.,[.,[.,[.,.]]]],.],.],.],.] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1

[7,8,6,4,5,3,2,1] => [[[[[[.,[.,.]],.],[.,.]],.],.],.] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1

[8,6,7,4,5,3,2,1] => [[[[[[.,.],[.,.]],[.,.]],.],.],.] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1

[8,5,6,4,7,3,2,1] => [[[[[[.,.],[.,.]],[.,.]],.],.],.] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1

[8,4,5,6,7,3,2,1] => [[[[[.,.],[.,[.,[.,.]]]],.],.],.] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1

[6,7,5,4,8,3,2,1] => [[[[[[.,[.,.]],.],[.,.]],.],.],.] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1

[7,5,6,4,8,3,2,1] => [[[[[[.,.],[.,.]],[.,.]],.],.],.] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1

[6,5,7,4,8,3,2,1] => [[[[[[.,.],[.,.]],[.,.]],.],.],.] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1

[5,6,7,4,8,3,2,1] => [[[[[.,[.,[.,.]]],[.,.]],.],.],.] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1

[6,7,4,5,8,3,2,1] => [[[[[.,[.,.]],[.,[.,.]]],.],.],.] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1

[7,4,5,6,8,3,2,1] => [[[[[.,.],[.,[.,[.,.]]]],.],.],.] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1

[5,6,4,7,8,3,2,1] => [[[[[.,[.,.]],[.,[.,.]]],.],.],.] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1

[6,4,5,7,8,3,2,1] => [[[[[.,.],[.,[.,[.,.]]]],.],.],.] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1

[5,4,6,7,8,3,2,1] => [[[[[.,.],[.,[.,[.,.]]]],.],.],.] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1

[4,5,6,7,8,3,2,1] => [[[[.,[.,[.,[.,[.,.]]]]],.],.],.] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1

[7,8,6,5,3,4,2,1] => [[[[[[.,[.,.]],.],.],[.,.]],.],.] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1

[8,6,7,5,3,4,2,1] => [[[[[[.,.],[.,.]],.],[.,.]],.],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1

[7,6,8,5,3,4,2,1] => [[[[[[.,.],[.,.]],.],[.,.]],.],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1

[7,8,5,6,3,4,2,1] => [[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1

[8,5,6,7,3,4,2,1] => [[[[[.,.],[.,[.,.]]],[.,.]],.],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1

[6,7,5,8,3,4,2,1] => [[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1

[6,5,7,8,3,4,2,1] => [[[[[.,.],[.,[.,.]]],[.,.]],.],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1

[5,6,7,8,3,4,2,1] => [[[[.,[.,[.,[.,.]]]],[.,.]],.],.] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1

[7,8,6,4,3,5,2,1] => [[[[[[.,[.,.]],.],.],[.,.]],.],.] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1

[7,6,8,4,3,5,2,1] => [[[[[[.,.],[.,.]],.],[.,.]],.],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1

[6,7,8,4,3,5,2,1] => [[[[[.,[.,[.,.]]],.],[.,.]],.],.] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1

[7,8,6,3,4,5,2,1] => [[[[[.,[.,.]],.],[.,[.,.]]],.],.] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1

[8,6,7,3,4,5,2,1] => [[[[[.,.],[.,.]],[.,[.,.]]],.],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1

[7,6,8,3,4,5,2,1] => [[[[[.,.],[.,.]],[.,[.,.]]],.],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1

[6,7,8,3,4,5,2,1] => [[[[.,[.,[.,.]]],[.,[.,.]]],.],.] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1

[7,8,5,4,3,6,2,1] => [[[[[[.,[.,.]],.],.],[.,.]],.],.] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1

[7,8,5,3,4,6,2,1] => [[[[[.,[.,.]],.],[.,[.,.]]],.],.] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1

[7,8,3,4,5,6,2,1] => [[[[.,[.,.]],[.,[.,[.,.]]]],.],.] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1

[8,3,4,5,6,7,2,1] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1

[6,7,5,4,3,8,2,1] => [[[[[[.,[.,.]],.],.],[.,.]],.],.] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1

[7,5,6,4,3,8,2,1] => [[[[[[.,.],[.,.]],.],[.,.]],.],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1

[5,6,7,4,3,8,2,1] => [[[[[.,[.,[.,.]]],.],[.,.]],.],.] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1

[6,7,4,5,3,8,2,1] => [[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1

[7,4,5,6,3,8,2,1] => [[[[[.,.],[.,[.,.]]],[.,.]],.],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1

[6,4,5,7,3,8,2,1] => [[[[[.,.],[.,[.,.]]],[.,.]],.],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1

[5,4,6,7,3,8,2,1] => [[[[[.,.],[.,[.,.]]],[.,.]],.],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1

[4,5,6,7,3,8,2,1] => [[[[.,[.,[.,[.,.]]]],[.,.]],.],.] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1

[7,3,4,5,6,8,2,1] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1

[6,3,4,5,7,8,2,1] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1

[5,3,4,6,7,8,2,1] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1

[4,3,5,6,7,8,2,1] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1

[3,4,5,6,7,8,2,1] => [[[.,[.,[.,[.,[.,[.,.]]]]]],.],.] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1

[7,8,6,5,4,2,3,1] => [[[[[[.,[.,.]],.],.],.],[.,.]],.] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1

[8,6,7,5,4,2,3,1] => [[[[[[.,.],[.,.]],.],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1

[7,6,8,5,4,2,3,1] => [[[[[[.,.],[.,.]],.],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1

[8,5,6,7,4,2,3,1] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1

[6,7,5,8,4,2,3,1] => [[[[[.,[.,.]],[.,.]],.],[.,.]],.] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1

[7,5,6,8,4,2,3,1] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1

[5,6,7,8,4,2,3,1] => [[[[.,[.,[.,[.,.]]]],.],[.,.]],.] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1

[8,6,7,4,5,2,3,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[7,6,8,4,5,2,3,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[6,7,8,4,5,2,3,1] => [[[[.,[.,[.,.]]],[.,.]],[.,.]],.] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[7,8,4,5,6,2,3,1] => [[[[.,[.,.]],[.,[.,.]]],[.,.]],.] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[8,5,6,4,7,2,3,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[8,4,5,6,7,2,3,1] => [[[[.,.],[.,[.,[.,.]]]],[.,.]],.] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 1

[7,5,6,4,8,2,3,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[6,5,7,4,8,2,3,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[6,7,4,5,8,2,3,1] => [[[[.,[.,.]],[.,[.,.]]],[.,.]],.] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[4,5,6,7,8,2,3,1] => [[[.,[.,[.,[.,[.,.]]]]],[.,.]],.] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 1

[7,8,6,5,3,2,4,1] => [[[[[[.,[.,.]],.],.],.],[.,.]],.] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1

[8,6,7,5,3,2,4,1] => [[[[[[.,.],[.,.]],.],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1

[7,6,8,5,3,2,4,1] => [[[[[[.,.],[.,.]],.],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1

[6,7,8,5,3,2,4,1] => [[[[[.,[.,[.,.]]],.],.],[.,.]],.] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1

[8,5,6,7,3,2,4,1] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1

[6,7,5,8,3,2,4,1] => [[[[[.,[.,.]],[.,.]],.],[.,.]],.] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1

[5,6,7,8,3,2,4,1] => [[[[.,[.,[.,[.,.]]]],.],[.,.]],.] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1

[8,6,7,5,2,3,4,1] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1

[7,6,8,5,2,3,4,1] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1

[6,7,8,5,2,3,4,1] => [[[[.,[.,[.,.]]],.],[.,[.,.]]],.] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1

[7,8,5,6,2,3,4,1] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1

[8,5,6,7,2,3,4,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1

[6,7,5,8,2,3,4,1] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1

[6,5,7,8,2,3,4,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1

[5,6,7,8,2,3,4,1] => [[[.,[.,[.,[.,.]]]],[.,[.,.]]],.] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1

[7,6,8,4,3,2,5,1] => [[[[[[.,.],[.,.]],.],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1

[7,8,6,3,4,2,5,1] => [[[[[.,[.,.]],.],[.,.]],[.,.]],.] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1

[8,6,7,3,4,2,5,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[7,6,8,3,4,2,5,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[6,7,8,3,4,2,5,1] => [[[[.,[.,[.,.]]],[.,.]],[.,.]],.] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[6,7,8,4,2,3,5,1] => [[[[.,[.,[.,.]]],.],[.,[.,.]]],.] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1

[7,8,6,3,2,4,5,1] => [[[[[.,[.,.]],.],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1

[8,6,7,3,2,4,5,1] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1

[6,7,8,3,2,4,5,1] => [[[[.,[.,[.,.]]],.],[.,[.,.]]],.] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1

[7,8,6,2,3,4,5,1] => [[[[.,[.,.]],.],[.,[.,[.,.]]]],.] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1

[8,6,7,2,3,4,5,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1

[7,6,8,2,3,4,5,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1

[6,7,8,2,3,4,5,1] => [[[.,[.,[.,.]]],[.,[.,[.,.]]]],.] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1

[7,8,5,4,3,2,6,1] => [[[[[[.,[.,.]],.],.],.],[.,.]],.] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1

[7,8,5,3,4,2,6,1] => [[[[[.,[.,.]],.],[.,.]],[.,.]],.] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1

[7,8,4,3,5,2,6,1] => [[[[[.,[.,.]],.],[.,.]],[.,.]],.] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1

[7,8,4,3,2,5,6,1] => [[[[[.,[.,.]],.],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1

[7,8,3,4,2,5,6,1] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1

[7,8,4,2,3,5,6,1] => [[[[.,[.,.]],.],[.,[.,[.,.]]]],.] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1

[7,8,3,2,4,5,6,1] => [[[[.,[.,.]],.],[.,[.,[.,.]]]],.] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1

[7,8,2,3,4,5,6,1] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1

[8,5,6,3,4,2,7,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[8,4,5,3,6,2,7,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[8,5,6,4,2,3,7,1] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1

[8,4,5,3,2,6,7,1] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1

[8,3,4,5,2,6,7,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1

[8,3,4,2,5,6,7,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1

[8,2,3,4,5,6,7,1] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1

[6,7,5,4,3,2,8,1] => [[[[[[.,[.,.]],.],.],.],[.,.]],.] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1

[6,5,7,4,3,2,8,1] => [[[[[[.,.],[.,.]],.],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1

[6,7,4,5,3,2,8,1] => [[[[[.,[.,.]],[.,.]],.],[.,.]],.] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1

[7,4,5,6,3,2,8,1] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1

[6,4,5,7,3,2,8,1] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1

[4,5,6,7,3,2,8,1] => [[[[.,[.,[.,[.,.]]]],.],[.,.]],.] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1

[7,5,6,3,4,2,8,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[6,5,7,3,4,2,8,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[7,4,5,3,6,2,8,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[7,3,4,5,6,2,8,1] => [[[[.,.],[.,[.,[.,.]]]],[.,.]],.] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 1

[6,4,5,3,7,2,8,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[5,4,6,3,7,2,8,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[4,5,6,3,7,2,8,1] => [[[[.,[.,[.,.]]],[.,.]],[.,.]],.] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[5,6,3,4,7,2,8,1] => [[[[.,[.,.]],[.,[.,.]]],[.,.]],.] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[6,3,4,5,7,2,8,1] => [[[[.,.],[.,[.,[.,.]]]],[.,.]],.] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 1

[4,5,3,6,7,2,8,1] => [[[[.,[.,.]],[.,[.,.]]],[.,.]],.] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[3,4,5,6,7,2,8,1] => [[[.,[.,[.,[.,[.,.]]]]],[.,.]],.] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 1

[6,7,5,4,2,3,8,1] => [[[[[.,[.,.]],.],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1

[7,5,6,4,2,3,8,1] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1

[6,5,7,4,2,3,8,1] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1

[5,6,7,4,2,3,8,1] => [[[[.,[.,[.,.]]],.],[.,[.,.]]],.] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1

[6,7,4,5,2,3,8,1] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1

[7,4,5,6,2,3,8,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1

[5,6,4,7,2,3,8,1] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1

[5,4,6,7,2,3,8,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1

[4,5,6,7,2,3,8,1] => [[[.,[.,[.,[.,.]]]],[.,[.,.]]],.] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1

[6,7,5,3,2,4,8,1] => [[[[[.,[.,.]],.],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1

[6,5,7,3,2,4,8,1] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1

[7,5,6,2,3,4,8,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1

[5,6,7,2,3,4,8,1] => [[[.,[.,[.,.]]],[.,[.,[.,.]]]],.] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1

[6,7,4,3,2,5,8,1] => [[[[[.,[.,.]],.],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1

[6,7,3,2,4,5,8,1] => [[[[.,[.,.]],.],[.,[.,[.,.]]]],.] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1

[6,7,2,3,4,5,8,1] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1

[7,4,5,2,3,6,8,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1

[7,2,3,4,5,6,8,1] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1

[4,5,6,3,2,7,8,1] => [[[[.,[.,[.,.]]],.],[.,[.,.]]],.] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1

[6,3,4,5,2,7,8,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1

[4,3,5,6,2,7,8,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1

[3,4,5,6,2,7,8,1] => [[[.,[.,[.,[.,.]]]],[.,[.,.]]],.] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1

[6,4,5,2,3,7,8,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1

[4,5,6,2,3,7,8,1] => [[[.,[.,[.,.]]],[.,[.,[.,.]]]],.] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1

[6,2,3,4,5,7,8,1] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1

[4,5,3,2,6,7,8,1] => [[[[.,[.,.]],.],[.,[.,[.,.]]]],.] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1

[5,3,4,2,6,7,8,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1

[4,3,5,2,6,7,8,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1

[3,4,5,2,6,7,8,1] => [[[.,[.,[.,.]]],[.,[.,[.,.]]]],.] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1

[4,5,2,3,6,7,8,1] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1

[5,2,3,4,6,7,8,1] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1

[3,4,2,5,6,7,8,1] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1

[4,2,3,5,6,7,8,1] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1

[3,2,4,5,6,7,8,1] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1

[2,3,4,5,6,7,8,1] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1

[7,8,6,5,4,3,1,2] => [[[[[[.,[.,.]],.],.],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 2

[8,6,7,5,4,3,1,2] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2

[7,6,8,5,4,3,1,2] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2

[6,7,8,5,4,3,1,2] => [[[[[.,[.,[.,.]]],.],.],.],[.,.]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2

[7,8,5,6,4,3,1,2] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2

[6,7,5,8,4,3,1,2] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2

[7,5,6,8,4,3,1,2] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2

[6,5,7,8,4,3,1,2] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2

[5,6,7,8,4,3,1,2] => [[[[.,[.,[.,[.,.]]]],.],.],[.,.]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2

[7,8,6,4,5,3,1,2] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[8,6,7,4,5,3,1,2] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[6,7,8,4,5,3,1,2] => [[[[.,[.,[.,.]]],[.,.]],.],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[7,8,4,5,6,3,1,2] => [[[[.,[.,.]],[.,[.,.]]],.],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2

[8,5,6,4,7,3,1,2] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[7,5,6,4,8,3,1,2] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[6,5,7,4,8,3,1,2] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[6,7,4,5,8,3,1,2] => [[[[.,[.,.]],[.,[.,.]]],.],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2

[5,6,4,7,8,3,1,2] => [[[[.,[.,.]],[.,[.,.]]],.],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2

[5,4,6,7,8,3,1,2] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 2

[4,5,6,7,8,3,1,2] => [[[.,[.,[.,[.,[.,.]]]]],.],[.,.]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 2

[7,8,6,5,3,4,1,2] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2

[7,6,8,5,3,4,1,2] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[6,7,8,5,3,4,1,2] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[7,8,5,6,3,4,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[8,5,6,7,3,4,1,2] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,7,5,8,3,4,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[7,5,6,8,3,4,1,2] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,5,7,8,3,4,1,2] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,6,7,8,3,4,1,2] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,7,8,4,3,5,1,2] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[7,8,6,3,4,5,1,2] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[8,6,7,3,4,5,1,2] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[7,8,5,4,3,6,1,2] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2

[7,8,4,5,3,6,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[7,8,5,3,4,6,1,2] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[7,8,4,3,5,6,1,2] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[7,8,3,4,5,6,1,2] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[8,3,4,5,6,7,1,2] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2

[7,5,6,4,3,8,1,2] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[5,6,7,4,3,8,1,2] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[6,7,4,5,3,8,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,6,4,7,3,8,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,4,5,7,3,8,1,2] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[4,5,6,7,3,8,1,2] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[7,3,4,5,6,8,1,2] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2

[5,6,4,3,7,8,1,2] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[5,4,6,3,7,8,1,2] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[4,5,6,3,7,8,1,2] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[5,6,3,4,7,8,1,2] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[6,3,4,5,7,8,1,2] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2

[4,5,3,6,7,8,1,2] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[5,3,4,6,7,8,1,2] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2

[4,3,5,6,7,8,1,2] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2

[3,4,5,6,7,8,1,2] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2

[7,8,6,5,4,2,1,3] => [[[[[[.,[.,.]],.],.],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 2

[8,6,7,5,4,2,1,3] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2

[7,6,8,5,4,2,1,3] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2

[6,7,8,5,4,2,1,3] => [[[[[.,[.,[.,.]]],.],.],.],[.,.]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2

[7,8,5,6,4,2,1,3] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2

[6,7,5,8,4,2,1,3] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2

[7,5,6,8,4,2,1,3] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2

[6,5,7,8,4,2,1,3] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2

[5,6,7,8,4,2,1,3] => [[[[.,[.,[.,[.,.]]]],.],.],[.,.]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2

[7,6,8,4,5,2,1,3] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[8,4,5,6,7,2,1,3] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 2

[6,7,5,4,8,2,1,3] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[6,5,7,4,8,2,1,3] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[5,6,7,4,8,2,1,3] => [[[[.,[.,[.,.]]],[.,.]],.],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[7,4,5,6,8,2,1,3] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 2

[5,4,6,7,8,2,1,3] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 2

[4,5,6,7,8,2,1,3] => [[[.,[.,[.,[.,[.,.]]]]],.],[.,.]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 2

[7,8,6,5,4,1,2,3] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 3

[7,6,8,5,4,1,2,3] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3

[6,7,8,5,4,1,2,3] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3

[7,8,5,6,4,1,2,3] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3

[8,5,6,7,4,1,2,3] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[6,7,5,8,4,1,2,3] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3

[7,5,6,8,4,1,2,3] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[6,5,7,8,4,1,2,3] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[5,6,7,8,4,1,2,3] => [[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[8,6,7,4,5,1,2,3] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[6,7,8,4,5,1,2,3] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[7,8,5,4,6,1,2,3] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[7,8,4,5,6,1,2,3] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[8,5,6,4,7,1,2,3] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[8,4,5,6,7,1,2,3] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[6,7,5,4,8,1,2,3] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[7,5,6,4,8,1,2,3] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[6,5,7,4,8,1,2,3] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[5,6,7,4,8,1,2,3] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[6,7,4,5,8,1,2,3] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[7,4,5,6,8,1,2,3] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[5,6,4,7,8,1,2,3] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[6,4,5,7,8,1,2,3] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[5,4,6,7,8,1,2,3] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[4,5,6,7,8,1,2,3] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[7,8,6,5,3,2,1,4] => [[[[[[.,[.,.]],.],.],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 2

[8,6,7,5,3,2,1,4] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2

[7,6,8,5,3,2,1,4] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2

[6,7,8,5,3,2,1,4] => [[[[[.,[.,[.,.]]],.],.],.],[.,.]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2

[7,8,5,6,3,2,1,4] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2

[8,5,6,7,3,2,1,4] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2

[6,7,5,8,3,2,1,4] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2

[7,5,6,8,3,2,1,4] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2

[6,5,7,8,3,2,1,4] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2

[5,6,7,8,3,2,1,4] => [[[[.,[.,[.,[.,.]]]],.],.],[.,.]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2

[7,8,6,5,2,3,1,4] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2

[8,6,7,5,2,3,1,4] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[7,6,8,5,2,3,1,4] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[6,7,8,5,2,3,1,4] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[7,8,5,6,2,3,1,4] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[8,5,6,7,2,3,1,4] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,7,5,8,2,3,1,4] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[7,5,6,8,2,3,1,4] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,5,7,8,2,3,1,4] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,6,7,8,2,3,1,4] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[7,8,6,5,3,1,2,4] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 3

[8,6,7,5,3,1,2,4] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3

[7,6,8,5,3,1,2,4] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3

[7,8,5,6,3,1,2,4] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3

[6,7,5,8,3,1,2,4] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3

[7,5,6,8,3,1,2,4] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[6,5,7,8,3,1,2,4] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[5,6,7,8,3,1,2,4] => [[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[7,8,6,5,2,1,3,4] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 3

[7,6,8,5,2,1,3,4] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3

[6,7,8,5,2,1,3,4] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3

[7,8,5,6,2,1,3,4] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3

[8,5,6,7,2,1,3,4] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[6,7,5,8,2,1,3,4] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3

[7,5,6,8,2,1,3,4] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[6,5,7,8,2,1,3,4] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[5,6,7,8,2,1,3,4] => [[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[7,8,6,5,1,2,3,4] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4

[8,6,7,5,1,2,3,4] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[7,6,8,5,1,2,3,4] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[6,7,8,5,1,2,3,4] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[7,8,5,6,1,2,3,4] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[8,5,6,7,1,2,3,4] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[6,7,5,8,1,2,3,4] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[7,5,6,8,1,2,3,4] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[6,5,7,8,1,2,3,4] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[5,6,7,8,1,2,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[7,8,6,4,3,2,1,5] => [[[[[[.,[.,.]],.],.],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 2

[8,6,7,4,3,2,1,5] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2

[7,6,8,4,3,2,1,5] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2

[6,7,8,4,3,2,1,5] => [[[[[.,[.,[.,.]]],.],.],.],[.,.]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2

[7,8,6,3,4,2,1,5] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[6,7,8,3,4,2,1,5] => [[[[.,[.,[.,.]]],[.,.]],.],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[6,7,8,4,2,3,1,5] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[8,6,7,3,2,4,1,5] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[6,7,8,3,2,4,1,5] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[8,6,7,2,3,4,1,5] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[7,6,8,2,3,4,1,5] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[6,7,8,2,3,4,1,5] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[6,7,8,4,3,1,2,5] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3

[7,8,6,3,4,1,2,5] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[8,6,7,3,4,1,2,5] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[6,7,8,3,4,1,2,5] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[7,8,6,4,2,1,3,5] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 3

[8,6,7,4,2,1,3,5] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3

[6,7,8,4,2,1,3,5] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3

[7,8,6,4,1,2,3,5] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4

[7,6,8,4,1,2,3,5] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[6,7,8,4,1,2,3,5] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[7,8,6,3,2,1,4,5] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 3

[8,6,7,3,2,1,4,5] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3

[7,6,8,3,2,1,4,5] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3

[6,7,8,3,2,1,4,5] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3

[7,8,6,2,3,1,4,5] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[8,6,7,2,3,1,4,5] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[7,6,8,2,3,1,4,5] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[6,7,8,2,3,1,4,5] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[7,8,6,3,1,2,4,5] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4

[8,6,7,3,1,2,4,5] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[7,6,8,3,1,2,4,5] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[6,7,8,3,1,2,4,5] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[7,8,6,2,1,3,4,5] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4

[8,6,7,2,1,3,4,5] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[6,7,8,2,1,3,4,5] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[7,8,6,1,2,3,4,5] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 5

[8,6,7,1,2,3,4,5] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[7,6,8,1,2,3,4,5] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[6,7,8,1,2,3,4,5] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[7,8,5,4,3,2,1,6] => [[[[[[.,[.,.]],.],.],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 2

[7,8,4,5,3,2,1,6] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2

[7,8,3,4,5,2,1,6] => [[[[.,[.,.]],[.,[.,.]]],.],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2

[7,8,4,5,2,3,1,6] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[7,8,5,2,3,4,1,6] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[7,8,4,3,2,5,1,6] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2

[7,8,3,4,2,5,1,6] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[7,8,2,3,4,5,1,6] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[7,8,5,4,3,1,2,6] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 3

[7,8,3,4,5,1,2,6] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[7,8,5,4,2,1,3,6] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 3

[7,8,5,4,1,2,3,6] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4

[7,8,4,5,1,2,3,6] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[7,8,5,3,2,1,4,6] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 3

[7,8,5,3,1,2,4,6] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4

[7,8,5,2,1,3,4,6] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4

[7,8,5,1,2,3,4,6] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 5

[7,8,4,3,2,1,5,6] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 3

[7,8,3,4,2,1,5,6] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3

[7,8,4,2,3,1,5,6] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[7,8,3,2,4,1,5,6] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[7,8,2,3,4,1,5,6] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[7,8,4,3,1,2,5,6] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4

[7,8,3,4,1,2,5,6] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[7,8,4,2,1,3,5,6] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4

[7,8,3,2,1,4,5,6] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4

[7,8,2,3,1,4,5,6] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[7,8,3,1,2,4,5,6] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 5

[7,8,2,1,3,4,5,6] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 5

[7,8,1,2,3,4,5,6] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6

[8,5,6,4,3,2,1,7] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2

[8,4,5,6,3,2,1,7] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2

[8,5,6,3,4,2,1,7] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[8,4,5,3,6,2,1,7] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[8,3,4,5,6,2,1,7] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 2

[8,5,6,4,2,3,1,7] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[8,4,5,6,2,3,1,7] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[8,5,6,2,3,4,1,7] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[8,4,5,2,3,6,1,7] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[8,2,3,4,5,6,1,7] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2

[8,5,6,3,4,1,2,7] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[8,3,4,5,6,1,2,7] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[8,5,6,4,2,1,3,7] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3

[8,4,5,6,2,1,3,7] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[8,5,6,4,1,2,3,7] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[8,4,5,6,1,2,3,7] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[8,5,6,3,2,1,4,7] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3

[8,5,6,2,3,1,4,7] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[8,5,6,3,1,2,4,7] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[8,5,6,2,1,3,4,7] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[8,5,6,1,2,3,4,7] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[8,4,5,3,2,1,6,7] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3

[8,3,4,5,2,1,6,7] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[8,4,5,2,3,1,6,7] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[8,2,3,4,5,1,6,7] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[8,3,4,5,1,2,6,7] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[8,4,5,1,2,3,6,7] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[8,3,4,2,1,5,6,7] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[8,2,3,4,1,5,6,7] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[8,3,4,1,2,5,6,7] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[8,2,3,1,4,5,6,7] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[8,1,2,3,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7

[6,7,5,4,3,2,1,8] => [[[[[[.,[.,.]],.],.],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 2

[7,5,6,4,3,2,1,8] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2

[6,5,7,4,3,2,1,8] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2

[5,6,7,4,3,2,1,8] => [[[[[.,[.,[.,.]]],.],.],.],[.,.]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2

[6,7,4,5,3,2,1,8] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2

[7,4,5,6,3,2,1,8] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2

[5,6,4,7,3,2,1,8] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2

[5,4,6,7,3,2,1,8] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2

[4,5,6,7,3,2,1,8] => [[[[.,[.,[.,[.,.]]]],.],.],[.,.]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2

[6,7,5,3,4,2,1,8] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[7,5,6,3,4,2,1,8] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[6,5,7,3,4,2,1,8] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[5,6,7,3,4,2,1,8] => [[[[.,[.,[.,.]]],[.,.]],.],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[6,7,4,3,5,2,1,8] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[5,6,4,3,7,2,1,8] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[5,4,6,3,7,2,1,8] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[3,4,5,6,7,2,1,8] => [[[.,[.,[.,[.,[.,.]]]]],.],[.,.]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 2

[6,7,5,4,2,3,1,8] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2

[7,5,6,4,2,3,1,8] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[5,6,7,4,2,3,1,8] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[6,7,4,5,2,3,1,8] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,6,4,7,2,3,1,8] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,4,6,7,2,3,1,8] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[4,5,6,7,2,3,1,8] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,5,7,3,2,4,1,8] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[5,6,7,3,2,4,1,8] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[6,7,5,2,3,4,1,8] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[7,5,6,2,3,4,1,8] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[6,5,7,2,3,4,1,8] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[5,6,7,2,3,4,1,8] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[6,7,4,3,2,5,1,8] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2

[6,7,3,4,2,5,1,8] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,7,4,2,3,5,1,8] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[6,7,3,2,4,5,1,8] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[6,7,2,3,4,5,1,8] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[7,4,5,3,2,6,1,8] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[7,2,3,4,5,6,1,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2

[5,6,4,3,2,7,1,8] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2

[5,6,3,4,2,7,1,8] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,3,4,5,2,7,1,8] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[4,5,3,6,2,7,1,8] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,3,4,6,2,7,1,8] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[4,3,5,6,2,7,1,8] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[3,4,5,6,2,7,1,8] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,4,6,2,3,7,1,8] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[4,5,2,3,6,7,1,8] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[5,2,3,4,6,7,1,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2

[3,4,2,5,6,7,1,8] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[4,2,3,5,6,7,1,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2

[3,2,4,5,6,7,1,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2

[2,3,4,5,6,7,1,8] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2

[6,7,5,4,3,1,2,8] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 3

[7,5,6,4,3,1,2,8] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3

[5,4,6,7,3,1,2,8] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[4,5,6,7,3,1,2,8] => [[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[6,5,7,3,4,1,2,8] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[6,7,3,4,5,1,2,8] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[5,6,3,4,7,1,2,8] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[6,3,4,5,7,1,2,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[4,3,5,6,7,1,2,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[3,4,5,6,7,1,2,8] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[6,5,7,4,2,1,3,8] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3

[5,4,6,7,2,1,3,8] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[4,5,6,7,2,1,3,8] => [[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[5,6,7,4,1,2,3,8] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[7,4,5,6,1,2,3,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[5,6,4,7,1,2,3,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[5,4,6,7,1,2,3,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[4,5,6,7,1,2,3,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[6,7,5,2,3,1,4,8] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[7,5,6,2,3,1,4,8] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[6,5,7,2,3,1,4,8] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[5,6,7,2,3,1,4,8] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[5,6,7,3,1,2,4,8] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[7,5,6,2,1,3,4,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[5,6,7,2,1,3,4,8] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[6,7,5,1,2,3,4,8] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 5

[7,5,6,1,2,3,4,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[6,5,7,1,2,3,4,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[5,6,7,1,2,3,4,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[6,7,4,3,2,1,5,8] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 3

[6,7,3,4,2,1,5,8] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3

[6,7,4,2,3,1,5,8] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[6,7,2,3,4,1,5,8] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[6,7,3,2,1,4,5,8] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4

[6,7,2,3,1,4,5,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[6,7,3,1,2,4,5,8] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 5

[6,7,1,2,3,4,5,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6

[7,4,5,3,2,1,6,8] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3

[7,3,4,5,2,1,6,8] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[7,2,3,4,5,1,6,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[7,4,5,1,2,3,6,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[7,2,3,4,1,5,6,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[7,3,4,1,2,5,6,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[7,2,3,1,4,5,6,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[7,1,2,3,4,5,6,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7

[5,6,4,3,2,1,7,8] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 3

[5,4,6,3,2,1,7,8] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3

[4,5,6,3,2,1,7,8] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3

[5,6,3,4,2,1,7,8] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3

[6,3,4,5,2,1,7,8] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[3,4,5,6,2,1,7,8] => [[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[5,4,6,2,3,1,7,8] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[5,6,3,2,4,1,7,8] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[5,6,2,3,4,1,7,8] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[6,2,3,4,5,1,7,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[4,5,3,2,6,1,7,8] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[4,3,5,2,6,1,7,8] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[3,4,5,2,6,1,7,8] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[5,2,3,4,6,1,7,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[3,4,2,5,6,1,7,8] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[4,2,3,5,6,1,7,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[3,2,4,5,6,1,7,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[2,3,4,5,6,1,7,8] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[5,6,4,3,1,2,7,8] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4

[5,4,6,3,1,2,7,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[5,6,3,4,1,2,7,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[4,3,5,6,1,2,7,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[3,4,5,6,1,2,7,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[5,6,4,2,1,3,7,8] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4

[6,4,5,2,1,3,7,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[5,4,6,2,1,3,7,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[4,5,6,2,1,3,7,8] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[4,5,6,1,2,3,7,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[5,6,3,2,1,4,7,8] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4

[5,6,2,1,3,4,7,8] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 5

[6,3,4,2,1,5,7,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[6,2,3,1,4,5,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[6,1,2,3,4,5,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7

[4,5,3,2,1,6,7,8] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4

[5,3,4,2,1,6,7,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[4,3,5,2,1,6,7,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[3,4,5,2,1,6,7,8] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[4,5,2,3,1,6,7,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[5,2,3,4,1,6,7,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[3,4,2,5,1,6,7,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[4,2,3,5,1,6,7,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[3,2,4,5,1,6,7,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[2,3,4,5,1,6,7,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[4,3,5,1,2,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[3,4,5,1,2,6,7,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[4,5,2,1,3,6,7,8] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 5

[4,5,1,2,3,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6

[5,2,3,1,4,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[5,1,2,3,4,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7

[3,4,2,1,5,6,7,8] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 5

[4,2,3,1,5,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[3,2,4,1,5,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[2,3,4,1,5,6,7,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[3,4,1,2,5,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6

[4,1,2,3,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7

[2,3,1,4,5,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6

[3,1,2,4,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7

[2,1,3,4,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7

[1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 8

[5,7,8,6,4,3,2,1] => [[[[[.,[[.,[.,.]],.]],.],.],.],.] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1

[4,7,8,6,5,3,2,1] => [[[[.,[[[.,[.,.]],.],.]],.],.],.] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1

[4,6,7,5,8,3,2,1] => [[[[.,[[.,[.,.]],[.,.]]],.],.],.] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1

[4,6,5,7,8,3,2,1] => [[[[.,[[.,.],[.,[.,.]]]],.],.],.] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1

[3,7,8,6,5,4,2,1] => [[[.,[[[[.,[.,.]],.],.],.]],.],.] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1

[3,5,7,8,6,4,2,1] => [[[.,[[.,[[.,[.,.]],.]],.]],.],.] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[3,5,6,7,8,4,2,1] => [[[.,[[.,[.,[.,[.,.]]]],.]],.],.] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 1

[4,3,6,7,8,5,2,1] => [[[[.,.],[[.,[.,[.,.]]],.]],.],.] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => 1

[3,4,6,7,8,5,2,1] => [[[.,[.,[[.,[.,[.,.]]],.]]],.],.] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1

[4,5,3,7,8,6,2,1] => [[[[.,[.,.]],[[.,[.,.]],.]],.],.] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 1

[4,3,5,7,8,6,2,1] => [[[[.,.],[.,[[.,[.,.]],.]]],.],.] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1

[3,4,5,7,8,6,2,1] => [[[.,[.,[.,[[.,[.,.]],.]]]],.],.] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 1

[5,6,4,3,8,7,2,1] => [[[[[.,[.,.]],.],[[.,.],.]],.],.] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 1

[4,5,6,3,8,7,2,1] => [[[[.,[.,[.,.]]],[[.,.],.]],.],.] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

[4,5,3,6,8,7,2,1] => [[[[.,[.,.]],[.,[[.,.],.]]],.],.] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 1

[3,5,6,7,4,8,2,1] => [[[.,[[.,[.,[.,.]]],[.,.]]],.],.] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1

[3,4,6,7,5,8,2,1] => [[[.,[.,[[.,[.,.]],[.,.]]]],.],.] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 1

[3,5,6,4,7,8,2,1] => [[[.,[[.,[.,.]],[.,[.,.]]]],.],.] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 1

[3,5,4,6,7,8,2,1] => [[[.,[[.,.],[.,[.,[.,.]]]]],.],.] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1

[2,7,8,6,5,4,3,1] => [[.,[[[[[.,[.,.]],.],.],.],.]],.] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1

[2,6,7,8,5,4,3,1] => [[.,[[[[.,[.,[.,.]]],.],.],.]],.] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 1

[2,6,7,5,8,4,3,1] => [[.,[[[[.,[.,.]],[.,.]],.],.]],.] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[2,5,6,7,8,4,3,1] => [[.,[[[.,[.,[.,[.,.]]]],.],.]],.] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 1

[2,4,7,8,6,5,3,1] => [[.,[[.,[[[.,[.,.]],.],.]],.]],.] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 1

[2,4,6,7,8,5,3,1] => [[.,[[.,[[.,[.,[.,.]]],.]],.]],.] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1

[2,4,5,7,8,6,3,1] => [[.,[[.,[.,[[.,[.,.]],.]]],.]],.] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[2,5,6,4,8,7,3,1] => [[.,[[[.,[.,.]],[[.,.],.]],.]],.] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 1

[2,5,6,7,4,8,3,1] => [[.,[[[.,[.,[.,.]]],[.,.]],.]],.] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1

[2,4,6,7,5,8,3,1] => [[.,[[.,[[.,[.,.]],[.,.]]],.]],.] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1

[2,5,6,4,7,8,3,1] => [[.,[[[.,[.,.]],[.,[.,.]]],.]],.] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[2,5,4,6,7,8,3,1] => [[.,[[[.,.],[.,[.,[.,.]]]],.]],.] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[2,4,5,6,7,8,3,1] => [[.,[[.,[.,[.,[.,[.,.]]]]],.]],.] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 1

[3,2,5,7,8,6,4,1] => [[[.,.],[[.,[[.,[.,.]],.]],.]],.] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1

[3,2,6,7,5,8,4,1] => [[[.,.],[[[.,[.,.]],[.,.]],.]],.] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1

[3,2,5,6,7,8,4,1] => [[[.,.],[[.,[.,[.,[.,.]]]],.]],.] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 1

[2,3,6,7,8,5,4,1] => [[.,[.,[[[.,[.,[.,.]]],.],.]]],.] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 1

[2,3,5,7,8,6,4,1] => [[.,[.,[[.,[[.,[.,.]],.]],.]]],.] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1

[2,3,5,6,7,8,4,1] => [[.,[.,[[.,[.,[.,[.,.]]]],.]]],.] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 1

[3,4,2,8,7,6,5,1] => [[[.,[.,.]],[[[[.,.],.],.],.]],.] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1

[3,4,2,7,8,6,5,1] => [[[.,[.,.]],[[[.,[.,.]],.],.]],.] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 1

[3,2,4,7,8,6,5,1] => [[[.,.],[.,[[[.,[.,.]],.],.]]],.] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 1

[2,3,4,6,7,8,5,1] => [[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 1

[4,5,3,2,8,7,6,1] => [[[[.,[.,.]],.],[[[.,.],.],.]],.] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 1

[4,3,5,2,8,7,6,1] => [[[[.,.],[.,.]],[[[.,.],.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1

[3,4,5,2,7,8,6,1] => [[[.,[.,[.,.]]],[[.,[.,.]],.]],.] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[2,4,5,3,8,7,6,1] => [[.,[[.,[.,.]],[[[.,.],.],.]]],.] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 1

[2,4,5,3,7,8,6,1] => [[.,[[.,[.,.]],[[.,[.,.]],.]]],.] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 1

[3,4,2,5,8,7,6,1] => [[[.,[.,.]],[.,[[[.,.],.],.]]],.] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 1

[3,4,2,5,7,8,6,1] => [[[.,[.,.]],[.,[[.,[.,.]],.]]],.] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 1

[3,2,4,5,7,8,6,1] => [[[.,.],[.,[.,[[.,[.,.]],.]]]],.] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 1

[2,3,4,5,7,8,6,1] => [[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 1

[5,4,6,3,2,8,7,1] => [[[[[.,.],[.,.]],.],[[.,.],.]],.] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1

[3,5,6,4,2,8,7,1] => [[[.,[[.,[.,.]],.]],[[.,.],.]],.] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[4,5,3,6,2,8,7,1] => [[[[.,[.,.]],[.,.]],[[.,.],.]],.] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 1

[2,4,5,6,3,8,7,1] => [[.,[[.,[.,[.,.]]],[[.,.],.]]],.] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1

[2,3,5,6,4,8,7,1] => [[.,[.,[[.,[.,.]],[[.,.],.]]]],.] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 1

[3,4,2,6,5,8,7,1] => [[[.,[.,.]],[[.,.],[[.,.],.]]],.] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 1

[2,4,5,3,6,8,7,1] => [[.,[[.,[.,.]],[.,[[.,.],.]]]],.] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 1

[3,4,2,5,6,8,7,1] => [[[.,[.,.]],[.,[.,[[.,.],.]]]],.] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 1

[4,6,7,5,3,2,8,1] => [[[[.,[[.,[.,.]],.]],.],[.,.]],.] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[3,5,6,7,4,2,8,1] => [[[.,[[.,[.,[.,.]]],.]],[.,.]],.] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[3,4,6,7,5,2,8,1] => [[[.,[.,[[.,[.,.]],.]]],[.,.]],.] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[3,5,6,4,7,2,8,1] => [[[.,[[.,[.,.]],[.,.]]],[.,.]],.] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[3,5,4,6,7,2,8,1] => [[[.,[[.,.],[.,[.,.]]]],[.,.]],.] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[2,5,6,7,4,3,8,1] => [[.,[[[.,[.,[.,.]]],.],[.,.]]],.] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1

[2,4,6,7,5,3,8,1] => [[.,[[.,[[.,[.,.]],.]],[.,.]]],.] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[2,4,5,6,7,3,8,1] => [[.,[[.,[.,[.,[.,.]]]],[.,.]]],.] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1

[3,2,6,7,5,4,8,1] => [[[.,.],[[[.,[.,.]],.],[.,.]]],.] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1

[3,2,5,6,7,4,8,1] => [[[.,.],[[.,[.,[.,.]]],[.,.]]],.] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1

[2,3,5,6,7,4,8,1] => [[.,[.,[[.,[.,[.,.]]],[.,.]]]],.] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1

[3,4,2,7,6,5,8,1] => [[[.,[.,.]],[[[.,.],.],[.,.]]],.] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 1

[3,4,2,6,7,5,8,1] => [[[.,[.,.]],[[.,[.,.]],[.,.]]],.] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 1

[2,3,4,6,7,5,8,1] => [[.,[.,[.,[[.,[.,.]],[.,.]]]]],.] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1

[4,3,5,2,7,6,8,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[3,4,5,2,7,6,8,1] => [[[.,[.,[.,.]]],[[.,.],[.,.]]],.] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[3,4,2,5,7,6,8,1] => [[[.,[.,.]],[.,[[.,.],[.,.]]]],.] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 1

[3,5,6,4,2,7,8,1] => [[[.,[[.,[.,.]],.]],[.,[.,.]]],.] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 1

[2,5,6,4,3,7,8,1] => [[.,[[[.,[.,.]],.],[.,[.,.]]]],.] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 1

[2,4,5,6,3,7,8,1] => [[.,[[.,[.,[.,.]]],[.,[.,.]]]],.] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1

[3,2,5,6,4,7,8,1] => [[[.,.],[[.,[.,.]],[.,[.,.]]]],.] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1

[2,3,5,6,4,7,8,1] => [[.,[.,[[.,[.,.]],[.,[.,.]]]]],.] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1

[3,4,2,6,5,7,8,1] => [[[.,[.,.]],[[.,.],[.,[.,.]]]],.] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 1

[2,4,5,3,6,7,8,1] => [[.,[[.,[.,.]],[.,[.,[.,.]]]]],.] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1

[2,4,3,5,6,7,8,1] => [[.,[[.,.],[.,[.,[.,[.,.]]]]]],.] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1

[1,7,8,6,5,4,3,2] => [.,[[[[[[.,[.,.]],.],.],.],.],.]] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 2

[1,6,7,8,5,4,3,2] => [.,[[[[[.,[.,[.,.]]],.],.],.],.]] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2

[1,6,7,5,8,4,3,2] => [.,[[[[[.,[.,.]],[.,.]],.],.],.]] => [1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 2

[1,5,6,7,8,4,3,2] => [.,[[[[.,[.,[.,[.,.]]]],.],.],.]] => [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 2

[1,4,7,8,6,5,3,2] => [.,[[[.,[[[.,[.,.]],.],.]],.],.]] => [1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 2

[1,4,6,7,8,5,3,2] => [.,[[[.,[[.,[.,[.,.]]],.]],.],.]] => [1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2

[1,4,6,7,5,8,3,2] => [.,[[[.,[[.,[.,.]],[.,.]]],.],.]] => [1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 2

[1,5,4,6,7,8,3,2] => [.,[[[[.,.],[.,[.,[.,.]]]],.],.]] => [1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2

[1,4,5,6,7,8,3,2] => [.,[[[.,[.,[.,[.,[.,.]]]]],.],.]] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 2

[1,3,7,8,6,5,4,2] => [.,[[.,[[[[.,[.,.]],.],.],.]],.]] => [1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 2

[1,3,6,7,8,5,4,2] => [.,[[.,[[[.,[.,[.,.]]],.],.]],.]] => [1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2

[1,3,5,7,8,6,4,2] => [.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => [1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 2

[1,3,6,7,5,8,4,2] => [.,[[.,[[[.,[.,.]],[.,.]],.]],.]] => [1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 2

[1,3,5,6,7,8,4,2] => [.,[[.,[[.,[.,[.,[.,.]]]],.]],.]] => [1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 2

[1,3,4,6,7,8,5,2] => [.,[[.,[.,[[.,[.,[.,.]]],.]]],.]] => [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[1,4,5,3,8,7,6,2] => [.,[[[.,[.,.]],[[[.,.],.],.]],.]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 2

[1,4,5,3,7,8,6,2] => [.,[[[.,[.,.]],[[.,[.,.]],.]],.]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 2

[1,3,4,5,7,8,6,2] => [.,[[.,[.,[.,[[.,[.,.]],.]]]],.]] => [1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 2

[1,5,6,4,3,8,7,2] => [.,[[[[.,[.,.]],.],[[.,.],.]],.]] => [1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 2

[1,4,5,6,3,8,7,2] => [.,[[[.,[.,[.,.]]],[[.,.],.]],.]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2

[1,4,5,3,6,8,7,2] => [.,[[[.,[.,.]],[.,[[.,.],.]]],.]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 2

[1,6,7,5,4,3,8,2] => [.,[[[[[.,[.,.]],.],.],[.,.]],.]] => [1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 2

[1,4,6,7,5,3,8,2] => [.,[[[.,[[.,[.,.]],.]],[.,.]],.]] => [1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 2

[1,5,6,4,7,3,8,2] => [.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 2

[1,4,5,6,7,3,8,2] => [.,[[[.,[.,[.,[.,.]]]],[.,.]],.]] => [1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2

[1,3,5,6,7,4,8,2] => [.,[[.,[[.,[.,[.,.]]],[.,.]]],.]] => [1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 2

[1,3,4,6,7,5,8,2] => [.,[[.,[.,[[.,[.,.]],[.,.]]]],.]] => [1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 2

[1,4,5,3,6,7,8,2] => [.,[[[.,[.,.]],[.,[.,[.,.]]]],.]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2

[1,4,3,5,6,7,8,2] => [.,[[[.,.],[.,[.,[.,[.,.]]]]],.]] => [1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2

[1,3,4,5,6,7,8,2] => [.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2

[2,1,7,8,6,5,4,3] => [[.,.],[[[[[.,[.,.]],.],.],.],.]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2

[2,1,6,7,8,5,4,3] => [[.,.],[[[[.,[.,[.,.]]],.],.],.]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => 2

[2,1,5,7,8,6,4,3] => [[.,.],[[[.,[[.,[.,.]],.]],.],.]] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2

[2,1,6,7,5,8,4,3] => [[.,.],[[[[.,[.,.]],[.,.]],.],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[2,1,5,6,7,8,4,3] => [[.,.],[[[.,[.,[.,[.,.]]]],.],.]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => 2

[2,1,4,7,8,6,5,3] => [[.,.],[[.,[[[.,[.,.]],.],.]],.]] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2

[2,1,4,6,7,8,5,3] => [[.,.],[[.,[[.,[.,[.,.]]],.]],.]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => 2

[2,1,4,5,7,8,6,3] => [[.,.],[[.,[.,[[.,[.,.]],.]]],.]] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[2,1,5,6,4,8,7,3] => [[.,.],[[[.,[.,.]],[[.,.],.]],.]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2

[2,1,6,7,5,4,8,3] => [[.,.],[[[[.,[.,.]],.],[.,.]],.]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 2

[2,1,5,6,7,4,8,3] => [[.,.],[[[.,[.,[.,.]]],[.,.]],.]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2

[2,1,4,6,7,5,8,3] => [[.,.],[[.,[[.,[.,.]],[.,.]]],.]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 2

[2,1,5,6,4,7,8,3] => [[.,.],[[[.,[.,.]],[.,[.,.]]],.]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[2,1,4,5,6,7,8,3] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2

[1,2,7,8,6,5,4,3] => [.,[.,[[[[[.,[.,.]],.],.],.],.]]] => [1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 3

[1,2,6,7,8,5,4,3] => [.,[.,[[[[.,[.,[.,.]]],.],.],.]]] => [1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 3

[1,2,5,6,7,8,4,3] => [.,[.,[[[.,[.,[.,[.,.]]]],.],.]]] => [1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 3

[1,2,4,7,8,6,5,3] => [.,[.,[[.,[[[.,[.,.]],.],.]],.]]] => [1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 3

[1,2,4,6,7,8,5,3] => [.,[.,[[.,[[.,[.,[.,.]]],.]],.]]] => [1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 3

[1,2,4,5,7,8,6,3] => [.,[.,[[.,[.,[[.,[.,.]],.]]],.]]] => [1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 3

[1,2,5,6,7,4,8,3] => [.,[.,[[[.,[.,[.,.]]],[.,.]],.]]] => [1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 3

[1,2,4,5,6,7,8,3] => [.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 3

[2,3,1,8,7,6,5,4] => [[.,[.,.]],[[[[[.,.],.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2

[2,3,1,6,8,7,5,4] => [[.,[.,.]],[[[.,[[.,.],.]],.],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 2

[2,3,1,7,6,8,5,4] => [[.,[.,.]],[[[[.,.],[.,.]],.],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 2

[2,3,1,6,7,8,5,4] => [[.,[.,.]],[[[.,[.,[.,.]]],.],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2

[2,3,1,5,7,8,6,4] => [[.,[.,.]],[[.,[[.,[.,.]],.]],.]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 2

[2,3,1,6,5,8,7,4] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2

[2,3,1,7,6,5,8,4] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2

[2,3,1,6,7,5,8,4] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2

[2,3,1,5,7,6,8,4] => [[.,[.,.]],[[.,[[.,.],[.,.]]],.]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 2

[2,3,1,5,6,7,8,4] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2

[1,3,2,5,6,7,8,4] => [.,[[.,.],[[.,[.,[.,[.,.]]]],.]]] => [1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 3

[2,1,3,7,8,6,5,4] => [[.,.],[.,[[[[.,[.,.]],.],.],.]]] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 3

[2,1,3,5,6,7,8,4] => [[.,.],[.,[[.,[.,[.,[.,.]]]],.]]] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 3

[1,2,3,7,8,6,5,4] => [.,[.,[.,[[[[.,[.,.]],.],.],.]]]] => [1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 4

[1,2,3,6,7,8,5,4] => [.,[.,[.,[[[.,[.,[.,.]]],.],.]]]] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 4

[1,2,3,5,7,8,6,4] => [.,[.,[.,[[.,[[.,[.,.]],.]],.]]]] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 4

[1,2,3,6,7,5,8,4] => [.,[.,[.,[[[.,[.,.]],[.,.]],.]]]] => [1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 4

[1,2,3,5,6,7,8,4] => [.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4

[3,4,2,1,8,7,6,5] => [[[.,[.,.]],.],[[[[.,.],.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2

[3,4,2,1,7,8,6,5] => [[[.,[.,.]],.],[[[.,[.,.]],.],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 2

[3,4,2,1,6,8,7,5] => [[[.,[.,.]],.],[[.,[[.,.],.]],.]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 2

[3,4,2,1,7,6,8,5] => [[[.,[.,.]],.],[[[.,.],[.,.]],.]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[3,4,2,1,6,7,8,5] => [[[.,[.,.]],.],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 2

[3,2,4,1,8,7,6,5] => [[[.,.],[.,.]],[[[[.,.],.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[3,2,4,1,7,8,6,5] => [[[.,.],[.,.]],[[[.,[.,.]],.],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[3,2,4,1,6,8,7,5] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[3,2,4,1,7,6,8,5] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[3,2,4,1,6,7,8,5] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[2,3,4,1,8,7,6,5] => [[.,[.,[.,.]]],[[[[.,.],.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[2,3,4,1,7,8,6,5] => [[.,[.,[.,.]]],[[[.,[.,.]],.],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[2,3,4,1,6,8,7,5] => [[.,[.,[.,.]]],[[.,[[.,.],.]],.]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[2,3,4,1,7,6,8,5] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[2,3,4,1,6,7,8,5] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[1,3,4,2,8,7,6,5] => [.,[[.,[.,.]],[[[[.,.],.],.],.]]] => [1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 3

[1,3,4,2,7,8,6,5] => [.,[[.,[.,.]],[[[.,[.,.]],.],.]]] => [1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 3

[1,3,4,2,6,8,7,5] => [.,[[.,[.,.]],[[.,[[.,.],.]],.]]] => [1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 3

[1,3,4,2,7,6,8,5] => [.,[[.,[.,.]],[[[.,.],[.,.]],.]]] => [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 3

[1,3,4,2,6,7,8,5] => [.,[[.,[.,.]],[[.,[.,[.,.]]],.]]] => [1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 3

[2,3,1,4,8,7,6,5] => [[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 3

[2,3,1,4,7,8,6,5] => [[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 3

[2,3,1,4,7,6,8,5] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 3

[2,3,1,4,6,7,8,5] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 3

[2,1,3,4,7,8,6,5] => [[.,.],[.,[.,[[[.,[.,.]],.],.]]]] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => 4

[2,1,3,4,6,7,8,5] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4

[1,2,3,4,7,8,6,5] => [.,[.,[.,[.,[[[.,[.,.]],.],.]]]]] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 5

[1,2,3,4,6,7,8,5] => [.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 5

[4,5,3,2,1,8,7,6] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2

[4,3,5,2,1,8,7,6] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[3,4,5,2,1,8,7,6] => [[[.,[.,[.,.]]],.],[[[.,.],.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[2,4,5,3,1,8,7,6] => [[.,[[.,[.,.]],.]],[[[.,.],.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2

[2,4,5,3,1,7,8,6] => [[.,[[.,[.,.]],.]],[[.,[.,.]],.]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 2

[3,4,2,5,1,8,7,6] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[3,4,2,5,1,7,8,6] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[3,2,4,5,1,8,7,6] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[2,3,4,5,1,8,7,6] => [[.,[.,[.,[.,.]]]],[[[.,.],.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[2,3,4,5,1,7,8,6] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[1,4,5,3,2,8,7,6] => [.,[[[.,[.,.]],.],[[[.,.],.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 3

[1,4,5,3,2,7,8,6] => [.,[[[.,[.,.]],.],[[.,[.,.]],.]]] => [1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3

[1,3,4,5,2,8,7,6] => [.,[[.,[.,[.,.]]],[[[.,.],.],.]]] => [1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3

[1,3,4,5,2,7,8,6] => [.,[[.,[.,[.,.]]],[[.,[.,.]],.]]] => [1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3

[2,1,4,5,3,8,7,6] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3

[1,2,4,5,3,8,7,6] => [.,[.,[[.,[.,.]],[[[.,.],.],.]]]] => [1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 4

[1,2,4,5,3,7,8,6] => [.,[.,[[.,[.,.]],[[.,[.,.]],.]]]] => [1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 4

[3,2,4,1,5,8,7,6] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[3,2,4,1,5,7,8,6] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[2,3,4,1,5,8,7,6] => [[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[2,3,4,1,5,7,8,6] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[1,3,4,2,5,7,8,6] => [.,[[.,[.,.]],[.,[[.,[.,.]],.]]]] => [1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 4

[2,3,1,4,5,7,8,6] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 4

[2,1,3,4,5,7,8,6] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 5

[1,2,3,4,5,7,8,6] => [.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 6

[5,6,4,3,2,1,8,7] => [[[[[.,[.,.]],.],.],.],[[.,.],.]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2

[5,4,6,3,2,1,8,7] => [[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[4,5,6,3,2,1,8,7] => [[[[.,[.,[.,.]]],.],.],[[.,.],.]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[3,5,6,4,2,1,8,7] => [[[.,[[.,[.,.]],.]],.],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 2

[4,5,3,6,2,1,8,7] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[4,3,5,6,2,1,8,7] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[3,4,5,6,2,1,8,7] => [[[.,[.,[.,[.,.]]]],.],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[2,5,6,4,3,1,8,7] => [[.,[[[.,[.,.]],.],.]],[[.,.],.]] => [1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 2

[3,2,5,6,4,1,8,7] => [[[.,.],[[.,[.,.]],.]],[[.,.],.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[2,3,5,6,4,1,8,7] => [[.,[.,[[.,[.,.]],.]]],[[.,.],.]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 2

[3,4,2,6,5,1,8,7] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[4,3,5,2,6,1,8,7] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[3,4,5,2,6,1,8,7] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[2,4,5,3,6,1,8,7] => [[.,[[.,[.,.]],[.,.]]],[[.,.],.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2

[3,4,2,5,6,1,8,7] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[2,4,3,5,6,1,8,7] => [[.,[[.,.],[.,[.,.]]]],[[.,.],.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[2,3,4,5,6,1,8,7] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[1,5,6,4,3,2,8,7] => [.,[[[[.,[.,.]],.],.],[[.,.],.]]] => [1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 3

[1,3,4,5,6,2,8,7] => [.,[[.,[.,[.,[.,.]]]],[[.,.],.]]] => [1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[2,1,5,6,4,3,8,7] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3

[2,1,4,5,6,3,8,7] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[1,2,4,5,6,3,8,7] => [.,[.,[[.,[.,[.,.]]],[[.,.],.]]]] => [1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 4

[2,3,1,6,5,4,8,7] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[2,1,3,5,6,4,8,7] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 4

[1,2,3,5,6,4,8,7] => [.,[.,[.,[[.,[.,.]],[[.,.],.]]]]] => [1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 5

[3,4,2,1,6,5,8,7] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[3,2,4,1,6,5,8,7] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[2,3,4,1,6,5,8,7] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[1,3,4,2,6,5,8,7] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 4

[2,3,1,4,6,5,8,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4

[4,5,3,2,1,6,8,7] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 3

[4,3,5,2,1,6,8,7] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[3,4,5,2,1,6,8,7] => [[[.,[.,[.,.]]],.],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[2,4,5,3,1,6,8,7] => [[.,[[.,[.,.]],.]],[.,[[.,.],.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 3

[2,3,4,5,1,6,8,7] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[1,4,5,3,2,6,8,7] => [.,[[[.,[.,.]],.],[.,[[.,.],.]]]] => [1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 4

[2,1,4,5,3,6,8,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[3,2,4,1,5,6,8,7] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[2,3,4,1,5,6,8,7] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[1,3,4,2,5,6,8,7] => [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => [1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 5

[2,3,1,4,5,6,8,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 5

[3,5,6,7,4,2,1,8] => [[[.,[[.,[.,[.,.]]],.]],.],[.,.]] => [1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 2

[3,5,6,4,7,2,1,8] => [[[.,[[.,[.,.]],[.,.]]],.],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 2

[2,6,7,5,4,3,1,8] => [[.,[[[[.,[.,.]],.],.],.]],[.,.]] => [1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 2

[2,5,6,7,4,3,1,8] => [[.,[[[.,[.,[.,.]]],.],.]],[.,.]] => [1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 2

[2,4,6,7,5,3,1,8] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => [1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 2

[2,5,6,4,7,3,1,8] => [[.,[[[.,[.,.]],[.,.]],.]],[.,.]] => [1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2

[2,4,5,6,7,3,1,8] => [[.,[[.,[.,[.,[.,.]]]],.]],[.,.]] => [1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 2

[3,2,6,7,5,4,1,8] => [[[.,.],[[[.,[.,.]],.],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => 2

[3,2,5,6,7,4,1,8] => [[[.,.],[[.,[.,[.,.]]],.]],[.,.]] => [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => 2

[2,3,6,7,5,4,1,8] => [[.,[.,[[[.,[.,.]],.],.]]],[.,.]] => [1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 2

[2,3,5,6,7,4,1,8] => [[.,[.,[[.,[.,[.,.]]],.]]],[.,.]] => [1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 2

[3,4,2,6,7,5,1,8] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[3,2,4,6,7,5,1,8] => [[[.,.],[.,[[.,[.,.]],.]]],[.,.]] => [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => 2

[2,3,4,6,7,5,1,8] => [[.,[.,[.,[[.,[.,.]],.]]]],[.,.]] => [1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 2

[4,5,3,2,7,6,1,8] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[4,3,5,2,7,6,1,8] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[3,4,5,2,7,6,1,8] => [[[.,[.,[.,.]]],[[.,.],.]],[.,.]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[3,4,2,5,7,6,1,8] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[3,5,6,4,2,7,1,8] => [[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => [1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[2,4,5,6,3,7,1,8] => [[.,[[.,[.,[.,.]]],[.,.]]],[.,.]] => [1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[2,3,5,6,4,7,1,8] => [[.,[.,[[.,[.,.]],[.,.]]]],[.,.]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 2

[3,4,2,6,5,7,1,8] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[2,4,3,5,6,7,1,8] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[1,6,7,5,4,3,2,8] => [.,[[[[[.,[.,.]],.],.],.],[.,.]]] => [1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 3

[1,5,6,7,4,3,2,8] => [.,[[[[.,[.,[.,.]]],.],.],[.,.]]] => [1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 3

[1,4,6,7,5,3,2,8] => [.,[[[.,[[.,[.,.]],.]],.],[.,.]]] => [1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 3

[1,5,6,4,7,3,2,8] => [.,[[[[.,[.,.]],[.,.]],.],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 3

[1,3,6,7,5,4,2,8] => [.,[[.,[[[.,[.,.]],.],.]],[.,.]]] => [1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 3

[1,3,5,6,7,4,2,8] => [.,[[.,[[.,[.,[.,.]]],.]],[.,.]]] => [1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3

[1,3,4,6,7,5,2,8] => [.,[[.,[.,[[.,[.,.]],.]]],[.,.]]] => [1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 3

[1,4,5,6,3,7,2,8] => [.,[[[.,[.,[.,.]]],[.,.]],[.,.]]] => [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[1,3,5,6,4,7,2,8] => [.,[[.,[[.,[.,.]],[.,.]]],[.,.]]] => [1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 3

[1,4,5,3,6,7,2,8] => [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 3

[1,4,3,5,6,7,2,8] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[1,3,4,5,6,7,2,8] => [.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]] => [1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 3

[2,1,6,7,5,4,3,8] => [[.,.],[[[[.,[.,.]],.],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => 3

[2,1,5,6,7,4,3,8] => [[.,.],[[[.,[.,[.,.]]],.],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => 3

[2,1,4,5,6,7,3,8] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 3

[1,2,6,7,5,4,3,8] => [.,[.,[[[[.,[.,.]],.],.],[.,.]]]] => [1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 4

[1,2,5,6,7,4,3,8] => [.,[.,[[[.,[.,[.,.]]],.],[.,.]]]] => [1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 4

[1,2,4,6,7,5,3,8] => [.,[.,[[.,[[.,[.,.]],.]],[.,.]]]] => [1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 4

[1,2,5,6,4,7,3,8] => [.,[.,[[[.,[.,.]],[.,.]],[.,.]]]] => [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 4

[1,2,4,5,6,7,3,8] => [.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]] => [1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 4

[2,3,1,6,7,5,4,8] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[2,3,1,6,5,7,4,8] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[2,3,1,5,6,7,4,8] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[2,1,3,6,7,5,4,8] => [[.,.],[.,[[[.,[.,.]],.],[.,.]]]] => [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => 4

[1,2,3,6,7,5,4,8] => [.,[.,[.,[[[.,[.,.]],.],[.,.]]]]] => [1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 5

[1,2,3,5,6,7,4,8] => [.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 5

[3,2,4,1,7,6,5,8] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[3,2,4,1,6,7,5,8] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[2,3,4,1,7,6,5,8] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[2,3,4,1,6,7,5,8] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[1,3,4,2,6,7,5,8] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 4

[2,3,1,4,6,7,5,8] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4

[1,2,3,4,6,7,5,8] => [.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 6

[4,5,3,2,1,7,6,8] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[3,4,5,2,1,7,6,8] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[2,4,5,3,1,7,6,8] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[3,4,2,5,1,7,6,8] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,3,4,5,1,7,6,8] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[1,4,5,3,2,7,6,8] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 4

[1,3,4,5,2,7,6,8] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[1,2,4,5,3,7,6,8] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => [1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 5

[2,3,1,5,4,7,6,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[3,2,4,1,5,7,6,8] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[2,3,4,1,5,7,6,8] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[1,3,4,2,5,7,6,8] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 5

[2,3,1,4,5,7,6,8] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 5

[2,4,5,6,3,1,7,8] => [[.,[[.,[.,[.,.]]],.]],[.,[.,.]]] => [1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[2,3,5,6,4,1,7,8] => [[.,[.,[[.,[.,.]],.]]],[.,[.,.]]] => [1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 3

[1,5,6,4,3,2,7,8] => [.,[[[[.,[.,.]],.],.],[.,[.,.]]]] => [1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 4

[1,4,5,6,3,2,7,8] => [.,[[[.,[.,[.,.]]],.],[.,[.,.]]]] => [1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[1,3,5,6,4,2,7,8] => [.,[[.,[[.,[.,.]],.]],[.,[.,.]]]] => [1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 4

[1,4,5,3,6,2,7,8] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 4

[1,3,4,5,6,2,7,8] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[2,1,5,6,4,3,7,8] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[1,2,4,5,6,3,7,8] => [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 5

[2,3,1,6,5,4,7,8] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[2,3,1,5,6,4,7,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[1,2,3,5,6,4,7,8] => [.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 6

[3,2,4,1,6,5,7,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[2,3,4,1,6,5,7,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[2,4,5,3,1,6,7,8] => [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4

[2,4,3,5,1,6,7,8] => [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[1,4,5,3,2,6,7,8] => [.,[[[.,[.,.]],.],[.,[.,[.,.]]]]] => [1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 5

[1,3,4,5,2,6,7,8] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[2,1,4,5,3,6,7,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[1,2,4,5,3,6,7,8] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => [1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 6

[2,3,1,5,4,6,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[1,3,4,2,5,6,7,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 6

[1,3,2,4,5,6,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 7

[1,3,4,2,8,6,7,5] => [.,[[.,[.,.]],[[[.,.],[.,.]],.]]] => [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 3

[1,5,3,4,6,7,2,8] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[1,5,3,4,6,7,8,2] => [.,[[[.,.],[.,[.,[.,[.,.]]]]],.]] => [1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2

[1,7,3,4,5,6,2,8] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[1,7,3,4,5,6,8,2] => [.,[[[.,.],[.,[.,[.,[.,.]]]]],.]] => [1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2

[1,8,3,4,5,6,7,2] => [.,[[[.,.],[.,[.,[.,[.,.]]]]],.]] => [1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2

[1,8,4,5,6,7,3,2] => [.,[[[[.,.],[.,[.,[.,.]]]],.],.]] => [1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2

[2,3,1,7,5,6,4,8] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[2,3,1,8,5,6,7,4] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 2

[2,3,1,8,6,7,5,4] => [[.,[.,.]],[[[[.,.],[.,.]],.],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 2

[2,3,4,1,8,6,7,5] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[2,5,3,4,1,6,7,8] => [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[2,5,3,4,6,7,8,1] => [[.,[[.,.],[.,[.,[.,[.,.]]]]]],.] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1

[2,6,3,4,5,1,7,8] => [[.,[[.,.],[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[2,6,3,4,5,7,8,1] => [[.,[[.,.],[.,[.,[.,[.,.]]]]]],.] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1

[2,7,3,4,5,6,1,8] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[2,8,3,4,5,6,7,1] => [[.,[[.,.],[.,[.,[.,[.,.]]]]]],.] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1

[2,8,4,5,6,7,3,1] => [[.,[[[.,.],[.,[.,[.,.]]]],.]],.] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[3,2,4,1,8,6,7,5] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[4,2,3,1,5,7,6,8] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[4,2,3,1,5,7,8,6] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[4,2,3,1,5,8,7,6] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[4,2,3,1,6,5,7,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[4,2,3,1,6,5,8,7] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[4,2,3,1,6,7,8,5] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[4,2,3,1,6,8,7,5] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[4,2,3,1,7,6,5,8] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[4,2,3,1,7,6,8,5] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[4,2,3,1,8,6,7,5] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[4,2,3,1,8,7,6,5] => [[[.,.],[.,.]],[[[[.,.],.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[4,2,3,5,1,8,7,6] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[4,2,3,5,6,1,8,7] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[5,2,3,4,1,6,8,7] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[5,2,3,4,1,7,8,6] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[5,2,3,4,1,8,7,6] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[5,2,3,4,6,1,8,7] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[6,2,3,4,5,1,8,7] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[7,2,3,5,6,4,1,8] => [[[.,.],[.,[[.,[.,.]],.]]],[.,.]] => [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => 2

[8,2,3,5,6,7,4,1] => [[[.,.],[.,[[.,[.,[.,.]]],.]]],.] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => 1

[6,2,4,5,3,1,7,8] => [[[.,.],[[.,[.,.]],.]],[.,[.,.]]] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[7,2,4,5,3,6,1,8] => [[[.,.],[[.,[.,.]],[.,.]]],[.,.]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[7,2,4,5,3,6,8,1] => [[[.,.],[[.,[.,.]],[.,[.,.]]]],.] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1

[8,2,4,5,3,7,6,1] => [[[.,.],[[.,[.,.]],[[.,.],.]]],.] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1

[8,2,4,5,6,7,3,1] => [[[.,.],[[.,[.,[.,[.,.]]]],.]],.] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 1

[5,3,4,2,1,6,8,7] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[5,3,4,2,1,7,8,6] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[5,3,4,2,1,8,7,6] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[5,3,4,2,6,1,8,7] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[5,3,4,2,7,6,1,8] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[5,3,4,2,7,6,8,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[5,3,4,2,8,6,7,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[6,3,4,2,5,1,8,7] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[7,3,4,2,6,5,1,8] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[7,3,4,2,6,5,8,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[8,3,4,2,6,5,7,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[6,3,4,5,2,1,8,7] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[6,3,4,5,2,8,7,1] => [[[[.,.],[.,[.,.]]],[[.,.],.]],.] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => 1

[8,3,4,5,2,7,6,1] => [[[[.,.],[.,[.,.]]],[[.,.],.]],.] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => 1

[2,4,1,3,6,5,8,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4

[2,1,4,6,3,5,8,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[2,4,1,6,3,5,8,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[2,4,6,1,3,5,8,7] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[2,4,1,3,6,8,5,7] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4

[2,1,4,6,3,8,5,7] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[2,4,1,6,3,8,5,7] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[2,4,6,1,3,8,5,7] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[2,1,4,6,8,3,5,7] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[2,4,1,6,8,3,5,7] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[2,4,6,1,8,3,5,7] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[2,4,6,8,1,3,5,7] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[2,4,1,3,6,5,7,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5

[2,1,4,6,3,5,7,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[2,4,1,6,3,5,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[2,4,6,1,3,5,7,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[2,1,4,6,3,7,5,8] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[2,4,1,6,3,7,5,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[2,4,6,1,3,7,5,8] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[2,4,6,7,1,3,5,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[2,4,1,3,6,7,8,5] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 3

[2,1,4,6,3,7,8,5] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3

[2,4,1,6,3,7,8,5] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[2,1,4,6,7,3,8,5] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[2,4,1,6,7,3,8,5] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[2,4,6,1,7,3,8,5] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[2,4,6,7,1,3,8,5] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[2,1,4,6,7,8,3,5] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 3

[2,4,1,6,7,8,3,5] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[2,4,6,7,8,1,3,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[2,4,1,3,7,5,8,6] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4

[2,1,4,7,3,5,8,6] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[2,4,1,7,3,5,8,6] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[2,4,1,3,7,8,5,6] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4

[2,4,1,7,3,8,5,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[2,1,4,7,8,3,5,6] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[2,4,1,7,8,3,5,6] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[2,4,7,1,8,3,5,6] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[2,4,7,8,1,3,5,6] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[2,4,1,5,3,7,6,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[2,4,5,1,3,7,6,8] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[2,4,5,1,7,3,6,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[2,4,1,3,5,7,8,6] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 4

[2,4,1,5,3,7,8,6] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[2,4,5,1,3,7,8,6] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[2,1,4,5,7,3,8,6] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[2,4,1,5,7,3,8,6] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[2,4,5,1,7,3,8,6] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[2,4,5,1,7,8,3,6] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[2,4,5,7,8,1,3,6] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[2,4,1,3,8,5,6,7] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5

[2,1,4,8,3,5,6,7] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[2,4,1,8,3,5,6,7] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[2,4,8,1,3,5,6,7] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[2,4,1,5,3,8,6,7] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[2,1,4,5,8,3,6,7] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[2,4,1,5,8,3,6,7] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[2,4,5,1,8,3,6,7] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[2,4,1,5,3,6,8,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[2,4,1,5,6,3,8,7] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[2,4,5,1,6,3,8,7] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[2,4,5,6,1,3,8,7] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[2,1,4,5,6,8,3,7] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 3

[2,4,1,5,6,8,3,7] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[2,4,5,1,6,8,3,7] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[2,4,5,6,1,8,3,7] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,4,5,6,8,1,3,7] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[2,4,1,3,5,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6

[2,4,1,5,3,6,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[2,4,5,1,3,6,7,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[2,4,1,5,6,3,7,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[2,4,5,1,6,3,7,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[2,4,5,6,1,3,7,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[2,4,1,5,6,7,3,8] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[2,4,5,6,1,7,3,8] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,4,5,6,7,1,3,8] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[2,4,1,5,6,7,8,3] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2

[2,4,5,1,6,7,8,3] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[2,4,5,6,1,7,8,3] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[2,4,5,6,7,1,8,3] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[2,4,5,6,7,8,1,3] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2

[2,5,1,3,6,4,8,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4

[2,1,5,6,3,4,8,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[2,5,1,6,3,4,8,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[2,5,6,1,3,4,8,7] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[2,5,1,3,6,8,4,7] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4

[2,5,6,1,3,8,4,7] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[2,1,5,6,8,3,4,7] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[2,5,1,6,8,3,4,7] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[2,5,6,8,1,3,4,7] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[2,5,1,3,6,4,7,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5

[2,1,5,6,3,7,4,8] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[2,5,1,6,3,7,4,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[2,5,6,1,3,7,4,8] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[2,1,5,6,7,3,4,8] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[2,5,1,6,7,3,4,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[2,5,1,3,6,7,8,4] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 3

[2,1,5,6,3,7,8,4] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3

[2,5,1,6,3,7,8,4] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[2,5,6,1,3,7,8,4] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[2,1,5,6,7,3,8,4] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[2,5,1,6,7,3,8,4] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[2,5,6,7,1,3,8,4] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[2,1,5,6,7,8,3,4] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 3

[2,5,1,6,7,8,3,4] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[2,5,6,1,7,8,3,4] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[2,5,6,7,1,8,3,4] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,5,6,7,8,1,3,4] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[2,5,1,3,7,4,8,6] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4

[2,1,5,7,3,4,8,6] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[2,5,1,7,3,4,8,6] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[2,5,7,1,3,4,8,6] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[2,5,1,3,7,8,4,6] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4

[2,1,5,7,3,8,4,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[2,1,5,7,8,3,4,6] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[2,5,1,7,8,3,4,6] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[2,5,7,1,8,3,4,6] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[2,5,7,8,1,3,4,6] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[2,1,5,7,3,4,6,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[2,3,5,1,4,7,6,8] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[2,3,5,7,1,4,6,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[2,3,5,1,7,4,8,6] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[2,3,1,5,7,8,4,6] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[2,3,5,7,8,1,4,6] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[2,5,1,3,8,4,6,7] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5

[2,1,5,8,3,4,6,7] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[2,5,1,8,3,4,6,7] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[2,3,5,1,4,8,6,7] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[2,1,3,5,8,4,6,7] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 5

[2,3,5,1,8,4,6,7] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[2,3,5,8,1,4,6,7] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[2,3,5,1,6,4,8,7] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[2,3,1,5,6,8,4,7] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[2,3,5,1,6,8,4,7] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[2,3,5,6,1,8,4,7] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,3,5,6,8,1,4,7] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[2,5,1,3,4,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6

[2,3,5,1,4,6,7,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[2,3,5,6,1,4,7,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[2,3,5,6,1,7,4,8] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,3,5,6,7,1,4,8] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[2,3,5,1,6,7,8,4] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[2,3,5,6,1,7,8,4] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[2,3,5,6,7,8,1,4] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2

[2,6,1,3,7,4,8,5] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4

[2,1,6,7,3,4,8,5] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[2,6,1,7,3,4,8,5] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[2,6,7,1,3,4,8,5] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[2,6,1,3,7,8,4,5] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4

[2,6,1,7,3,8,4,5] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[2,1,6,7,8,3,4,5] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[2,6,1,7,8,3,4,5] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[2,6,7,1,8,3,4,5] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[2,6,7,8,1,3,4,5] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[2,6,1,7,3,4,5,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[2,6,1,3,4,7,5,8] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 5

[2,3,1,6,4,7,5,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[2,6,1,3,4,7,8,5] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 4

[2,3,6,1,4,7,8,5] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[2,1,3,6,7,4,8,5] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 4

[2,1,3,6,7,8,4,5] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 4

[2,3,1,6,7,8,4,5] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[2,3,6,1,7,8,4,5] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[2,3,6,7,1,8,4,5] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,3,6,7,8,1,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[2,6,1,3,8,4,5,7] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5

[2,1,6,8,3,4,5,7] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[2,6,1,8,3,4,5,7] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[2,6,8,1,3,4,5,7] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[2,6,1,3,4,8,5,7] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 5

[2,3,1,6,4,8,5,7] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[2,3,6,1,4,8,5,7] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[2,3,1,6,8,4,5,7] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[2,3,6,1,8,4,5,7] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[2,6,1,3,4,5,8,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 5

[2,3,6,1,4,5,8,7] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[2,3,4,1,6,8,5,7] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[2,3,4,6,1,8,5,7] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,3,4,6,8,1,5,7] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[2,6,1,3,4,5,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6

[2,3,1,6,4,5,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[2,3,6,1,4,5,7,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[2,3,4,6,1,5,7,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[2,3,4,6,1,7,5,8] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,3,4,6,7,1,5,8] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[2,3,4,6,1,7,8,5] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[2,3,4,6,7,8,1,5] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2

[2,7,1,3,8,4,5,6] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5

[2,1,7,8,3,4,5,6] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[2,7,1,8,3,4,5,6] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[2,7,8,1,3,4,5,6] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[2,3,1,7,4,8,5,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[2,1,3,7,8,4,5,6] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 5

[2,3,1,7,8,4,5,6] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[2,3,7,8,1,4,5,6] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[2,7,1,3,4,5,8,6] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 5

[2,3,1,7,4,5,8,6] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[2,3,7,1,4,5,8,6] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[2,3,4,1,7,5,8,6] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[2,3,4,7,1,5,8,6] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[2,1,3,4,7,8,5,6] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => 5

[2,3,1,4,7,8,5,6] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4

[2,3,4,1,7,8,5,6] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[2,3,4,7,1,8,5,6] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,3,4,7,8,1,5,6] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[2,7,1,3,4,5,6,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6

[2,3,7,1,4,5,6,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[2,3,1,4,7,5,6,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5

[2,3,4,1,7,5,6,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[2,3,4,7,1,5,6,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[2,3,4,5,7,1,6,8] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[2,3,4,5,7,1,8,6] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[2,3,4,5,7,8,1,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2

[2,8,1,3,4,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6

[2,3,1,8,4,5,6,7] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[2,3,8,1,4,5,6,7] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[2,3,1,4,8,5,6,7] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5

[2,3,4,1,8,5,6,7] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[2,3,4,8,1,5,6,7] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[2,3,1,4,5,8,6,7] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 5

[2,3,4,1,5,8,6,7] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[2,3,4,5,1,8,6,7] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,3,4,5,8,1,6,7] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[2,3,4,5,6,8,1,7] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2

[3,4,1,2,6,5,8,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4

[3,1,4,6,2,5,8,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[3,4,1,6,2,5,8,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[3,4,6,1,2,5,8,7] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[3,4,1,2,6,8,5,7] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4

[3,1,4,6,2,8,5,7] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[3,4,1,6,2,8,5,7] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[3,1,4,6,8,2,5,7] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[3,4,1,6,8,2,5,7] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[3,4,6,8,1,2,5,7] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[3,4,1,2,6,5,7,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5

[3,4,1,2,6,7,5,8] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4

[3,4,1,6,2,7,5,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[3,4,6,1,2,7,5,8] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[3,4,1,6,7,2,5,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[3,4,6,7,1,2,5,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[3,4,1,2,6,7,8,5] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 3

[3,1,4,6,2,7,8,5] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3

[3,4,1,6,2,7,8,5] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[3,4,6,1,2,7,8,5] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[3,1,4,6,7,2,8,5] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[3,4,1,6,7,2,8,5] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[3,4,6,1,7,2,8,5] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[3,4,6,7,1,2,8,5] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[3,1,4,6,7,8,2,5] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 3

[3,4,1,6,7,8,2,5] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[3,4,6,1,7,8,2,5] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[3,4,6,7,1,8,2,5] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,4,6,7,8,1,2,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[3,4,1,2,7,5,8,6] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4

[3,1,4,7,2,5,8,6] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[3,4,7,1,2,5,8,6] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[3,4,1,2,7,8,5,6] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4

[3,4,7,1,8,2,5,6] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[3,4,7,8,1,2,5,6] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[3,4,1,2,7,5,6,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5

[3,4,1,2,5,7,6,8] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 5

[3,1,4,5,2,7,6,8] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[3,4,1,5,2,7,6,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[3,4,1,5,7,2,6,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[3,4,5,7,1,2,6,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[3,4,1,2,5,7,8,6] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 4

[3,1,4,5,2,7,8,6] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3

[3,4,5,1,2,7,8,6] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[3,1,4,5,7,2,8,6] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[3,4,1,5,7,2,8,6] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[3,4,5,7,1,2,8,6] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[3,1,4,5,7,8,2,6] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 3

[3,4,1,5,7,8,2,6] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[3,4,5,1,7,8,2,6] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[3,4,5,7,8,1,2,6] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[3,4,1,2,8,5,6,7] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5

[3,1,4,8,2,5,6,7] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[3,4,1,8,2,5,6,7] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[3,4,8,1,2,5,6,7] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[3,4,1,2,5,8,6,7] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 5

[3,4,1,5,2,8,6,7] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[3,4,5,1,2,8,6,7] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[3,1,4,5,8,2,6,7] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[3,4,1,5,8,2,6,7] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[3,4,5,8,1,2,6,7] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[3,4,1,2,5,6,8,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 5

[3,4,5,1,2,6,8,7] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[3,1,4,5,6,2,8,7] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[3,4,1,5,6,2,8,7] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[3,4,5,1,6,2,8,7] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[3,4,5,6,1,2,8,7] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[3,1,4,5,6,8,2,7] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 3

[3,4,1,5,6,8,2,7] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[3,4,5,6,1,8,2,7] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,4,5,6,8,1,2,7] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[3,1,4,5,2,6,7,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[3,4,1,5,2,6,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[3,4,1,5,6,2,7,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[3,4,5,1,6,2,7,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[3,1,4,5,6,7,2,8] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 3

[3,4,1,5,6,7,2,8] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[3,4,5,1,6,7,2,8] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[3,4,5,6,1,7,2,8] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,1,4,5,6,7,8,2] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2

[3,4,1,5,6,7,8,2] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2

[3,4,5,1,6,7,8,2] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[3,4,5,6,1,7,8,2] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[3,4,5,6,7,1,8,2] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[3,5,1,2,6,4,8,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4

[3,1,5,6,2,4,8,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[3,5,1,6,2,4,8,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[3,5,6,1,2,4,8,7] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[3,5,1,2,6,8,4,7] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4

[3,1,5,6,2,8,4,7] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[3,5,6,1,2,8,4,7] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[3,1,5,6,8,2,4,7] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[3,5,1,6,8,2,4,7] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[3,5,6,1,8,2,4,7] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[3,5,6,8,1,2,4,7] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[3,1,5,6,2,4,7,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[3,5,1,6,2,4,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[3,5,6,1,2,4,7,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[3,5,1,2,6,7,4,8] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4

[3,5,1,6,2,7,4,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[3,5,6,1,2,7,4,8] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[3,5,1,6,7,2,4,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[3,5,6,1,7,2,4,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[3,5,6,7,1,2,4,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[3,5,1,2,6,7,8,4] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 3

[3,1,5,6,2,7,8,4] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3

[3,5,1,6,2,7,8,4] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[3,5,6,1,2,7,8,4] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[3,1,5,6,7,2,8,4] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[3,5,1,6,7,2,8,4] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[3,5,6,1,7,2,8,4] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[3,5,6,7,1,2,8,4] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[3,1,5,6,7,8,2,4] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 3

[3,5,1,6,7,8,2,4] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[3,5,6,1,7,8,2,4] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[3,5,6,7,1,8,2,4] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,5,6,7,8,1,2,4] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[3,5,1,2,7,4,8,6] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4

[3,1,5,7,2,4,8,6] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[3,5,7,1,2,4,8,6] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[3,5,1,2,7,8,4,6] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4

[3,1,5,7,2,8,4,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[3,5,1,7,2,8,4,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[3,1,5,7,8,2,4,6] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[3,5,1,7,8,2,4,6] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[3,5,7,8,1,2,4,6] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[3,5,1,2,7,4,6,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5

[3,1,5,7,2,4,6,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[3,5,1,7,2,4,6,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[3,5,7,1,2,4,6,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[3,5,1,2,4,7,6,8] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 5

[1,3,5,2,4,7,6,8] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 5

[3,1,2,5,7,4,6,8] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 5

[1,3,5,2,7,4,6,8] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 5

[1,3,5,7,2,4,6,8] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[3,5,1,2,4,7,8,6] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 4

[3,1,2,5,7,4,8,6] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 4

[1,3,5,2,7,4,8,6] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 4

[1,3,5,7,2,4,8,6] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[1,3,5,2,7,8,4,6] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 4

[1,3,5,7,2,8,4,6] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[1,3,5,7,8,2,4,6] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[3,5,1,2,8,4,6,7] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5

[3,1,5,8,2,4,6,7] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[3,5,1,8,2,4,6,7] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[3,5,1,2,4,8,6,7] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 5

[1,3,5,2,4,8,6,7] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 5

[3,1,2,5,8,4,6,7] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 5

[1,3,5,2,8,4,6,7] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 5

[1,3,5,8,2,4,6,7] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[3,5,1,2,4,6,8,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 5

[1,3,5,2,4,6,8,7] => [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => [1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 5

[1,3,5,2,6,4,8,7] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 4

[1,3,5,6,2,4,8,7] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[3,1,2,5,6,8,4,7] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 4

[1,3,5,2,6,8,4,7] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 4

[1,3,5,6,2,8,4,7] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[1,3,5,6,8,2,4,7] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[3,5,1,2,4,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6

[1,3,5,2,4,6,7,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 6

[1,3,5,6,2,4,7,8] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[3,1,2,5,6,7,4,8] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 4

[1,3,5,2,6,7,4,8] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 4

[1,3,5,6,2,7,4,8] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[1,3,5,6,7,2,4,8] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[3,1,2,5,6,7,8,4] => [[.,.],[.,[[.,[.,[.,[.,.]]]],.]]] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 3

[1,3,5,6,7,2,8,4] => [.,[[.,[.,[.,[.,.]]]],[[.,.],.]]] => [1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[1,3,5,6,7,8,2,4] => [.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]] => [1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 3

[3,6,1,2,7,4,8,5] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4

[3,6,1,7,2,4,8,5] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[3,6,7,1,2,4,8,5] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[3,6,1,2,7,8,4,5] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4

[3,1,6,7,2,8,4,5] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[3,6,1,7,2,8,4,5] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[3,6,7,1,2,8,4,5] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[3,6,1,7,8,2,4,5] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[3,6,7,8,1,2,4,5] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[3,1,6,7,2,4,5,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[3,6,1,2,4,7,5,8] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 5

[1,3,6,2,7,4,5,8] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 5

[3,6,1,2,4,7,8,5] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 4

[3,1,2,6,7,4,8,5] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 4

[1,3,6,2,7,4,8,5] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 4

[1,3,6,7,2,4,8,5] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[3,1,2,6,7,8,4,5] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 4

[1,3,6,2,7,8,4,5] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 4

[1,3,6,7,8,2,4,5] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[3,6,1,2,8,4,5,7] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5

[3,1,6,8,2,4,5,7] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[3,6,1,8,2,4,5,7] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[3,6,8,1,2,4,5,7] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[3,6,1,2,4,8,5,7] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 5

[1,3,6,2,4,8,5,7] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 5

[3,1,2,6,8,4,5,7] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 5

[3,6,1,2,4,5,8,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 5

[1,3,6,2,4,5,8,7] => [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => [1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 5

[1,3,4,6,2,5,8,7] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[1,3,4,6,8,2,5,7] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[3,6,1,2,4,5,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6

[1,3,6,2,4,5,7,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 6

[1,3,4,6,2,5,7,8] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[3,1,2,4,6,7,5,8] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => 5

[1,3,4,6,2,7,5,8] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[1,3,4,6,7,2,5,8] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[3,1,2,4,6,7,8,5] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4

[1,3,4,6,7,2,8,5] => [.,[[.,[.,[.,[.,.]]]],[[.,.],.]]] => [1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[3,7,1,2,8,4,5,6] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5

[3,1,7,8,2,4,5,6] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[3,7,1,8,2,4,5,6] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[3,7,8,1,2,4,5,6] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[3,7,1,2,4,8,5,6] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 5

[1,3,7,2,4,8,5,6] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 5

[3,1,2,7,8,4,5,6] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 5

[1,3,7,2,8,4,5,6] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 5

[1,3,7,8,2,4,5,6] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[3,7,1,2,4,5,8,6] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 5

[1,3,7,2,4,5,8,6] => [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => [1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 5

[1,3,4,2,7,5,8,6] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 4

[1,3,4,7,2,5,8,6] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[3,1,2,4,7,8,5,6] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => 5

[1,3,4,2,7,8,5,6] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 4

[1,3,4,7,8,2,5,6] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[3,7,1,2,4,5,6,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6

[1,3,7,2,4,5,6,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 6

[1,3,4,7,2,5,6,8] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[1,3,4,5,7,2,6,8] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[3,1,2,4,5,7,8,6] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 5

[1,3,4,5,7,8,2,6] => [.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]] => [1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 3

[3,8,1,2,4,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6

[1,3,8,2,4,5,6,7] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 6

[1,3,4,2,8,5,6,7] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 5

[1,3,4,8,2,5,6,7] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[1,3,4,2,5,8,6,7] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 5

[1,3,4,5,2,8,6,7] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[1,3,4,5,8,2,6,7] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[1,3,4,5,6,8,2,7] => [.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]] => [1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 3

[4,5,1,2,6,3,8,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4

[4,1,5,6,2,3,8,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[4,5,1,6,2,3,8,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[4,5,6,1,2,3,8,7] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[4,5,1,2,6,8,3,7] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4

[4,1,5,6,2,8,3,7] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[4,5,6,1,2,8,3,7] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[4,1,5,6,8,2,3,7] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[4,5,1,6,8,2,3,7] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[4,5,6,1,8,2,3,7] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[4,5,6,8,1,2,3,7] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[4,1,5,6,2,3,7,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[4,5,1,6,2,3,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[4,5,1,2,6,7,3,8] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4

[4,5,1,6,2,7,3,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[4,5,6,1,2,7,3,8] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[4,5,6,1,7,2,3,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[4,5,1,2,6,7,8,3] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 3

[4,5,1,6,2,7,8,3] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[4,5,6,1,2,7,8,3] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[4,1,5,6,7,2,8,3] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[4,5,1,6,7,2,8,3] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[4,5,6,1,7,2,8,3] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[4,5,6,7,1,2,8,3] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[4,1,5,6,7,8,2,3] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 3

[4,5,1,6,7,8,2,3] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[4,5,6,1,7,8,2,3] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[4,5,6,7,1,8,2,3] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,5,1,2,7,3,8,6] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4

[4,5,1,7,2,3,8,6] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[4,5,1,2,7,8,3,6] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4

[4,1,5,7,2,8,3,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[4,5,1,7,2,8,3,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[4,5,7,1,2,8,3,6] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[4,5,1,7,8,2,3,6] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[4,5,7,8,1,2,3,6] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[4,5,1,2,7,3,6,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5

[4,5,1,2,3,7,6,8] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 5

[1,4,5,2,3,7,6,8] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 5

[4,1,2,5,7,3,6,8] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 5

[1,4,5,2,7,3,6,8] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 5

[1,4,5,7,2,3,6,8] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[1,4,5,2,3,7,8,6] => [.,[[.,[.,.]],[.,[[.,[.,.]],.]]]] => [1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 4

[4,1,2,5,7,3,8,6] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 4

[1,4,5,2,7,3,8,6] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 4

[1,4,5,7,2,3,8,6] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[4,1,2,5,7,8,3,6] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 4

[1,4,5,2,7,8,3,6] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 4

[1,4,5,7,8,2,3,6] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[4,5,1,2,8,3,6,7] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5

[4,5,1,8,2,3,6,7] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[4,5,8,1,2,3,6,7] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[4,5,1,2,3,8,6,7] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 5

[1,4,5,2,3,8,6,7] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 5

[4,1,2,5,8,3,6,7] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 5

[1,4,5,2,8,3,6,7] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 5

[4,1,2,5,6,3,8,7] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 4

[1,4,5,2,6,3,8,7] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 4

[4,1,2,5,6,8,3,7] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 4

[1,4,5,2,6,8,3,7] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 4

[1,4,5,6,8,2,3,7] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[1,4,5,2,3,6,7,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 6

[4,1,2,5,6,3,7,8] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 5

[1,4,5,2,6,3,7,8] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 5

[1,4,5,6,2,3,7,8] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[4,1,2,5,6,7,3,8] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 4

[1,4,5,2,6,7,3,8] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 4

[1,4,5,6,2,7,3,8] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[1,4,5,6,7,2,3,8] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[4,1,2,5,6,7,8,3] => [[.,.],[.,[[.,[.,[.,[.,.]]]],.]]] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 3

[1,4,2,5,6,7,8,3] => [.,[[.,.],[[.,[.,[.,[.,.]]]],.]]] => [1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 3

[1,4,5,2,6,7,8,3] => [.,[[.,[.,.]],[[.,[.,[.,.]]],.]]] => [1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 3

[1,4,5,6,2,7,8,3] => [.,[[.,[.,[.,.]]],[[.,[.,.]],.]]] => [1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3

[1,4,5,6,7,2,8,3] => [.,[[.,[.,[.,[.,.]]]],[[.,.],.]]] => [1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[1,4,5,6,7,8,2,3] => [.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]] => [1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 3

[4,1,6,7,2,3,8,5] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[4,6,7,1,2,3,8,5] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[4,6,1,2,7,8,3,5] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4

[4,6,1,7,2,8,3,5] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[4,6,7,1,2,8,3,5] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[4,1,6,7,8,2,3,5] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[4,6,1,7,8,2,3,5] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[4,6,7,1,8,2,3,5] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[4,6,7,8,1,2,3,5] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[4,1,6,7,2,3,5,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[4,6,1,7,2,3,5,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[4,6,7,1,2,3,5,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[4,6,1,2,3,7,5,8] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 5

[4,1,2,6,7,3,5,8] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 5

[1,4,6,2,7,3,5,8] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 5

[1,4,6,7,2,3,5,8] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[1,4,6,2,3,7,8,5] => [.,[[.,[.,.]],[.,[[.,[.,.]],.]]]] => [1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 4

[4,1,2,6,7,3,8,5] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 4

[1,4,6,2,7,3,8,5] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 4

[1,4,6,2,7,8,3,5] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 4

[1,4,6,7,2,8,3,5] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[1,4,6,7,8,2,3,5] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[4,6,1,2,8,3,5,7] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5

[4,1,6,8,2,3,5,7] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[4,6,1,8,2,3,5,7] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[4,6,8,1,2,3,5,7] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[4,6,1,2,3,8,5,7] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 5

[1,4,6,2,3,8,5,7] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 5

[1,4,6,2,8,3,5,7] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 5

[1,4,6,8,2,3,5,7] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[4,6,1,2,3,5,8,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 5

[1,4,6,2,3,5,8,7] => [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => [1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 5

[1,2,4,6,3,5,8,7] => [.,[.,[[.,[.,.]],[.,[[.,.],.]]]]] => [1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 5

[4,1,2,3,6,8,5,7] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => 5

[1,2,4,6,3,8,5,7] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => [1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 5

[1,2,4,6,8,3,5,7] => [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 5

[4,6,1,2,3,5,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6

[1,4,6,2,3,5,7,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 6

[1,2,4,6,3,5,7,8] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => [1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 6

[4,1,2,3,6,7,5,8] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => 5

[1,2,4,6,3,7,5,8] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => [1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 5

[4,1,2,3,6,7,8,5] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4

[4,7,1,2,8,3,5,6] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5

[4,1,7,8,2,3,5,6] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[4,7,1,8,2,3,5,6] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[4,7,8,1,2,3,5,6] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[4,7,1,2,3,8,5,6] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 5

[1,4,7,2,3,8,5,6] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 5

[4,1,2,7,8,3,5,6] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 5

[1,4,7,2,8,3,5,6] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 5

[1,4,7,8,2,3,5,6] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[4,7,1,2,3,5,8,6] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 5

[1,4,7,2,3,5,8,6] => [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => [1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 5

[1,2,4,7,3,5,8,6] => [.,[.,[[.,[.,.]],[.,[[.,.],.]]]]] => [1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 5

[4,1,2,3,7,8,5,6] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => 5

[1,2,4,7,3,8,5,6] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => [1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 5

[1,2,4,7,8,3,5,6] => [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 5

[4,7,1,2,3,5,6,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6

[1,4,7,2,3,5,6,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 6

[1,2,4,7,3,5,6,8] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => [1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 6

[1,2,4,5,7,3,6,8] => [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 5

[4,1,2,3,5,7,8,6] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 5

[1,2,4,5,7,3,8,6] => [.,[.,[[.,[.,[.,.]]],[[.,.],.]]]] => [1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 4

[1,2,4,5,7,8,3,6] => [.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]] => [1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 4

[4,8,1,2,3,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6

[1,4,8,2,3,5,6,7] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 6

[1,2,4,8,3,5,6,7] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => [1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 6

[1,2,4,5,3,8,6,7] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => [1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 5

[1,2,4,5,8,3,6,7] => [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 5

[1,2,4,5,6,8,3,7] => [.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]] => [1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 4

[1,4,2,3,5,6,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 7

[5,6,1,2,7,3,8,4] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4

[5,1,6,7,2,3,8,4] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[5,6,1,7,2,3,8,4] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[5,6,7,1,2,3,8,4] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[5,6,1,2,7,8,3,4] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4

[5,1,6,7,2,8,3,4] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[5,6,7,1,2,8,3,4] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[5,1,6,7,8,2,3,4] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[5,6,1,7,8,2,3,4] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[5,6,7,1,8,2,3,4] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[5,6,1,7,2,3,4,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[5,1,2,6,7,3,4,8] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 5

[1,5,6,7,2,3,4,8] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[5,6,1,2,3,7,8,4] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 4

[1,5,6,2,3,7,8,4] => [.,[[.,[.,.]],[.,[[.,[.,.]],.]]]] => [1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 4

[5,1,2,6,7,3,8,4] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 4

[1,5,6,7,2,3,8,4] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[5,1,2,6,7,8,3,4] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 4

[1,5,6,2,7,8,3,4] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 4

[1,5,6,7,2,8,3,4] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[1,5,6,7,8,2,3,4] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[5,6,1,2,8,3,4,7] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5

[5,6,1,8,2,3,4,7] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[5,6,8,1,2,3,4,7] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[5,6,1,2,3,8,4,7] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 5

[1,5,6,2,3,8,4,7] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 5

[5,1,2,6,8,3,4,7] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 5

[1,5,6,2,8,3,4,7] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 5

[1,5,6,8,2,3,4,7] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[5,6,1,2,3,4,8,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 5

[1,5,6,2,3,4,8,7] => [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => [1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 5

[1,2,5,6,3,4,8,7] => [.,[.,[[.,[.,.]],[.,[[.,.],.]]]]] => [1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 5

[5,1,2,3,6,8,4,7] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => 5

[1,2,5,6,3,8,4,7] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => [1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 5

[1,2,5,6,8,3,4,7] => [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 5

[1,5,6,2,3,4,7,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 6

[1,2,5,6,3,4,7,8] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => [1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 6

[5,1,2,3,6,7,4,8] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => 5

[1,2,5,6,3,7,4,8] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => [1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 5

[5,1,2,3,6,7,8,4] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4

[1,2,5,6,3,7,8,4] => [.,[.,[[.,[.,.]],[[.,[.,.]],.]]]] => [1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 4

[1,2,5,6,7,3,8,4] => [.,[.,[[.,[.,[.,.]]],[[.,.],.]]]] => [1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 4

[1,2,5,6,7,8,3,4] => [.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]] => [1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 4

[5,7,1,2,8,3,4,6] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5

[5,1,7,8,2,3,4,6] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[5,7,1,8,2,3,4,6] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[5,7,8,1,2,3,4,6] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[5,7,1,2,3,8,4,6] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 5

[1,5,7,2,3,8,4,6] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 5

[5,1,2,7,8,3,4,6] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 5

[1,5,7,2,8,3,4,6] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 5

[1,5,7,8,2,3,4,6] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[5,7,1,2,3,4,8,6] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 5

[1,5,7,2,3,4,8,6] => [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => [1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 5

[1,2,5,7,3,4,8,6] => [.,[.,[[.,[.,.]],[.,[[.,.],.]]]]] => [1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 5

[5,1,2,3,7,8,4,6] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => 5

[1,2,5,7,3,8,4,6] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => [1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 5

[1,2,5,7,8,3,4,6] => [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 5

[5,7,1,2,3,4,6,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6

[1,2,5,7,3,4,6,8] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => [1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 6

[1,2,3,5,7,4,6,8] => [.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 6

[5,1,2,3,4,7,8,6] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 5

[1,2,3,5,7,4,8,6] => [.,[.,[.,[[.,[.,.]],[[.,.],.]]]]] => [1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 5

[1,2,3,5,7,8,4,6] => [.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 5

[5,8,1,2,3,4,6,7] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6

[1,5,8,2,3,4,6,7] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 6

[1,2,5,8,3,4,6,7] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => [1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 6

[1,2,3,5,8,4,6,7] => [.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 6

[1,2,3,5,6,8,4,7] => [.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 5

[1,5,2,3,4,6,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 7

[6,7,1,2,8,3,4,5] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5

[6,1,7,8,2,3,4,5] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[6,7,1,8,2,3,4,5] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[6,7,1,2,3,8,4,5] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 5

[1,6,7,2,3,8,4,5] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 5

[6,1,2,7,8,3,4,5] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 5

[1,6,7,2,8,3,4,5] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 5

[1,6,7,8,2,3,4,5] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[6,7,1,2,3,4,8,5] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 5

[1,6,7,2,3,4,8,5] => [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => [1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 5

[1,2,6,7,3,4,8,5] => [.,[.,[[.,[.,.]],[.,[[.,.],.]]]]] => [1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 5

[6,1,2,3,7,8,4,5] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => 5

[1,2,6,7,3,8,4,5] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => [1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 5

[1,2,6,7,8,3,4,5] => [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 5

[1,6,7,2,3,4,5,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 6

[1,2,6,7,3,4,5,8] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => [1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 6

[1,2,3,6,7,4,5,8] => [.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 6

[6,1,2,3,4,7,8,5] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 5

[1,2,3,6,7,4,8,5] => [.,[.,[.,[[.,[.,.]],[[.,.],.]]]]] => [1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 5

[1,2,3,6,7,8,4,5] => [.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 5

[6,8,1,2,3,4,5,7] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6

[1,6,8,2,3,4,5,7] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 6

[1,2,6,8,3,4,5,7] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => [1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 6

[1,2,3,6,8,4,5,7] => [.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 6

[1,2,3,4,6,8,5,7] => [.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 6

[1,6,2,3,4,5,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 7

[1,7,8,2,3,4,5,6] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 6

[1,2,7,8,3,4,5,6] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => [1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 6

[1,2,3,7,8,4,5,6] => [.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 6

[1,2,3,4,7,8,5,6] => [.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 6

[1,7,2,3,4,5,6,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 7

[1,8,2,3,4,5,6,7] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 7

[8,4,5,2,3,7,6,1] => [[[[.,.],[.,.]],[.,[[.,.],.]]],.] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[7,4,5,2,3,8,1,6] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[6,4,5,2,3,1,8,7] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[5,4,6,2,1,3,8,7] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[3,6,1,5,4,2,8,7] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[5,6,4,3,1,2,8,7] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 3

[6,7,4,3,8,1,2,5] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[5,7,4,3,1,8,2,6] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[3,7,1,5,4,8,2,6] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[3,8,1,5,4,7,6,2] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2

[5,8,4,3,1,7,6,2] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2

[6,8,4,3,7,1,5,2] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[7,8,4,3,6,5,1,2] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[6,8,5,7,3,1,4,2] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[3,8,1,6,7,4,5,2] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2

[3,7,1,6,8,4,2,5] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[5,4,7,2,1,8,3,6] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[6,4,7,2,8,1,3,5] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[7,4,6,2,8,3,1,5] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[8,4,6,2,7,3,5,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[3,4,1,2,8,7,6,5] => [[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 3

[8,4,7,2,6,5,3,1] => [[[[.,.],[.,.]],[[[.,.],.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1

[7,4,8,2,6,5,1,3] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[6,4,8,2,7,1,5,3] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[5,4,8,2,1,7,6,3] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[4,5,8,1,2,7,6,3] => [[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[3,5,1,8,2,7,6,4] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[2,1,5,8,3,7,6,4] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3

[3,6,1,8,7,2,5,4] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[4,6,8,1,7,2,5,3] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[5,7,8,6,1,4,2,3] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[4,7,8,1,6,5,2,3] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[3,7,1,8,6,5,2,4] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[2,1,7,8,6,5,3,4] => [[.,.],[[[[.,[.,.]],.],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => 3

[3,8,1,7,6,5,4,2] => [[.,[.,.]],[[[[[.,.],.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2

[3,2,5,1,4,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[4,2,5,1,3,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[4,2,6,1,3,5,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[5,3,6,1,2,4,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[6,2,4,1,3,5,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[6,3,5,1,2,4,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[5,3,7,1,2,4,6,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[5,4,7,1,2,3,6,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[6,2,7,1,3,4,5,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[6,3,7,1,2,4,5,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[6,4,7,1,2,3,5,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[7,3,5,1,2,4,6,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[7,3,6,1,2,4,5,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[7,4,6,1,2,3,5,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[3,2,8,1,4,5,6,7] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[4,2,8,1,3,5,6,7] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[5,4,8,1,2,3,6,7] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[6,2,8,1,3,4,5,7] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[6,3,8,1,2,4,5,7] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[6,4,8,1,2,3,5,7] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[6,5,8,1,2,3,4,7] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[7,2,8,1,3,4,5,6] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[7,3,8,1,2,4,5,6] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[7,4,8,1,2,3,5,6] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[7,5,8,1,2,3,4,6] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[8,2,4,1,3,5,6,7] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[8,3,5,1,2,4,6,7] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[8,3,6,1,2,4,5,7] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[8,3,7,1,2,4,5,6] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[8,4,7,1,2,3,5,6] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[8,5,7,1,2,3,4,6] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[3,2,5,7,1,4,6,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[4,2,5,7,1,3,6,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[5,2,4,7,1,3,6,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[4,2,6,7,1,3,5,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[5,2,6,7,1,3,4,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[5,3,6,7,1,2,4,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[6,2,5,7,1,3,4,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[3,2,5,8,1,4,6,7] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[4,2,5,8,1,3,6,7] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[4,3,5,8,1,2,6,7] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[5,2,4,8,1,3,6,7] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[3,2,6,8,1,4,5,7] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[4,2,6,8,1,3,5,7] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[5,2,6,8,1,3,4,7] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[6,2,4,8,1,3,5,7] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[6,3,4,8,1,2,5,7] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[6,2,5,8,1,3,4,7] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[6,3,5,8,1,2,4,7] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[6,4,5,8,1,2,3,7] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[3,2,7,8,1,4,5,6] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[5,3,7,8,1,2,4,6] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[5,4,7,8,1,2,3,6] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[6,2,7,8,1,3,4,5] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[6,3,7,8,1,2,4,5] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[6,4,7,8,1,2,3,5] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[7,2,4,8,1,3,5,6] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[7,3,4,8,1,2,5,6] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[7,3,5,8,1,2,4,6] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[7,4,5,8,1,2,3,6] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[7,4,6,8,1,2,3,5] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[8,3,4,6,1,2,5,7] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[8,3,5,6,1,2,4,7] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[8,2,4,7,1,3,5,6] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[8,2,5,7,1,3,4,6] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[8,3,5,7,1,2,4,6] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[8,2,6,7,1,3,4,5] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[8,4,6,7,1,2,3,5] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[3,6,2,5,1,4,7,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[4,6,2,5,1,3,7,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[4,6,3,5,1,2,7,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[5,6,2,4,1,3,7,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[3,7,2,5,1,4,6,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[4,7,3,5,1,2,6,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[3,7,2,6,1,4,5,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[4,7,3,6,1,2,5,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[5,7,2,6,1,3,4,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[6,7,2,5,1,3,4,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[4,8,2,5,1,3,6,7] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[5,8,2,4,1,3,6,7] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[5,8,3,4,1,2,6,7] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[5,8,3,6,1,2,4,7] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[5,8,4,6,1,2,3,7] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[6,8,3,5,1,2,4,7] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[3,8,2,7,1,4,5,6] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[4,8,2,7,1,3,5,6] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[4,8,3,7,1,2,5,6] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[5,8,2,7,1,3,4,6] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[5,8,3,7,1,2,4,6] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[5,8,4,7,1,2,3,6] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[6,8,2,7,1,3,4,5] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[6,8,3,7,1,2,4,5] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[6,8,5,7,1,2,3,4] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[7,8,2,4,1,3,5,6] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[7,8,2,5,1,3,4,6] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[7,8,3,5,1,2,4,6] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[7,8,4,6,1,2,3,5] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[3,6,2,5,8,1,4,7] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[4,6,3,5,8,1,2,7] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[5,6,2,4,8,1,3,7] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[4,7,2,5,8,1,3,6] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[4,7,3,5,8,1,2,6] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[5,7,2,4,8,1,3,6] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[5,7,3,4,8,1,2,6] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[4,7,3,6,8,1,2,5] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[5,7,2,6,8,1,3,4] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[5,7,4,6,8,1,2,3] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[6,7,3,4,8,1,2,5] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[6,7,3,5,8,1,2,4] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[3,8,2,5,7,1,4,6] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[4,8,3,5,7,1,2,6] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[5,8,2,4,7,1,3,6] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[3,8,2,6,7,1,4,5] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[5,8,2,6,7,1,3,4] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[5,8,3,6,7,1,2,4] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[6,8,2,5,7,1,3,4] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[7,8,2,4,6,1,3,5] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[7,8,3,4,6,1,2,5] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[7,8,2,5,6,1,3,4] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[7,8,3,5,6,1,2,4] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[4,3,7,2,6,1,5,8] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[5,4,7,2,6,1,3,8] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[6,3,7,2,5,1,4,8] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[6,4,7,2,5,1,3,8] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[6,4,7,3,5,1,2,8] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[4,3,8,2,6,1,5,7] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[5,3,8,2,6,1,4,7] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[5,4,8,2,6,1,3,7] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[5,4,8,3,6,1,2,7] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[6,3,8,2,5,1,4,7] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[6,4,8,2,5,1,3,7] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[6,4,8,3,5,1,2,7] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[6,5,8,2,4,1,3,7] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[6,5,8,3,4,1,2,7] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[4,3,8,2,7,1,5,6] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[5,3,8,2,7,1,4,6] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[5,4,8,2,7,1,3,6] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[5,4,8,3,7,1,2,6] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[6,3,8,2,7,1,4,5] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[6,4,8,2,7,1,3,5] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[7,3,8,2,5,1,4,6] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[7,4,8,3,5,1,2,6] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[7,5,8,2,4,1,3,6] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[7,5,8,2,6,1,3,4] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[7,5,8,4,6,1,2,3] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[7,6,8,2,5,1,3,4] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[7,6,8,3,5,1,2,4] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[8,4,6,2,5,1,3,7] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[8,5,6,2,4,1,3,7] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[8,4,7,3,5,1,2,6] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[8,5,7,2,4,1,3,6] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[8,3,7,2,6,1,4,5] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[8,4,7,2,6,1,3,5] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[8,4,7,3,6,1,2,5] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[8,5,7,2,6,1,3,4] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[8,6,7,2,4,1,3,5] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[8,6,7,2,5,1,3,4] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[8,6,7,3,5,1,2,4] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[4,8,3,7,2,6,1,5] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,8,3,7,2,6,1,4] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,8,4,7,2,6,1,3] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,8,4,7,3,6,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,8,3,7,2,5,1,4] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,8,4,7,2,5,1,3] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,8,4,7,3,5,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,8,5,7,2,4,1,3] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,8,5,7,3,4,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[7,8,3,6,2,5,1,4] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[7,8,4,6,2,5,1,3] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[7,8,4,6,3,5,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[7,8,5,6,2,4,1,3] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[8,1,2,3,6,7,4,5] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => 5

[8,1,2,5,6,3,4,7] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 5

[8,1,2,5,7,3,4,6] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 5

[7,1,2,5,6,3,8,4] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 4

[8,1,2,5,6,7,3,4] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 4

[3,1,4,8,2,7,5,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[8,1,4,5,2,3,6,7] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[7,1,4,5,2,3,8,6] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[8,1,4,6,2,3,5,7] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[7,1,4,8,2,3,5,6] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[7,1,4,6,2,3,8,5] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[6,1,4,5,2,8,3,7] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[8,1,4,5,2,7,3,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[8,1,4,6,2,7,3,5] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[6,1,4,5,2,7,8,3] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3

[8,1,4,5,6,2,3,7] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[8,1,4,5,7,2,3,6] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[7,1,4,5,6,2,8,3] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[8,1,4,5,6,7,2,3] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 3

[2,8,1,3,4,7,5,6] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 5

[2,8,1,3,6,4,5,7] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5

[2,8,1,3,7,4,5,6] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5

[2,7,1,3,6,4,8,5] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4

[2,5,1,3,8,7,4,6] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 4

[2,8,1,3,6,7,4,5] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4

[2,4,1,8,3,7,5,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[2,8,1,5,3,4,6,7] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[2,7,1,5,3,4,8,6] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[2,8,1,6,3,4,5,7] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[2,7,1,6,3,4,8,5] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[2,6,1,5,3,8,4,7] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[2,8,1,5,3,7,4,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[2,6,1,5,3,7,8,4] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[2,4,1,8,6,3,5,7] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[2,4,1,8,7,3,5,6] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[2,4,1,7,6,3,8,5] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[2,8,1,5,6,3,4,7] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[2,8,1,5,7,3,4,6] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[2,8,1,7,6,3,4,5] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[2,7,1,5,6,3,8,4] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[2,4,1,5,8,7,3,6] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3

[2,4,1,8,6,7,3,5] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[2,8,1,5,6,7,3,4] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[5,8,1,2,3,7,4,6] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 5

[5,8,1,2,6,3,4,7] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5

[5,8,1,2,7,3,4,6] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5

[5,7,1,2,6,3,8,4] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4

[5,8,1,2,6,7,3,4] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4

[6,8,1,5,2,3,4,7] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[6,7,1,5,2,3,8,4] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[6,8,1,5,2,7,3,4] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[7,8,1,5,6,2,3,4] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[2,3,8,1,4,7,5,6] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[2,3,8,1,6,4,5,7] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[2,3,8,1,7,4,5,6] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[2,3,7,1,6,4,8,5] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[2,3,5,1,8,7,4,6] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[2,3,8,1,6,7,4,5] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[2,6,8,1,3,7,4,5] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[2,7,8,1,6,3,4,5] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[7,3,4,1,2,5,8,6] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[6,3,4,1,2,8,5,7] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[8,3,4,1,2,7,5,6] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[6,3,4,1,2,7,8,5] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[7,3,5,1,2,4,8,6] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[6,3,7,1,2,4,8,5] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[6,3,5,1,2,8,4,7] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[8,3,5,1,2,7,4,6] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[6,3,8,1,2,7,4,5] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[6,3,5,1,2,7,8,4] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[6,8,4,1,2,3,5,7] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 5

[6,7,4,1,2,3,8,5] => [[[.,[.,.]],.],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 4

[6,8,5,1,2,3,4,7] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 5

[6,7,5,1,2,3,8,4] => [[[.,[.,.]],.],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 4

[6,8,4,1,2,7,3,5] => [[[.,[.,.]],.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[6,8,5,1,2,7,3,4] => [[[.,[.,.]],.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[5,3,4,1,8,2,6,7] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[5,3,4,1,7,2,8,6] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[8,3,4,1,6,2,5,7] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[8,3,4,1,7,2,5,6] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[7,3,4,1,6,2,8,5] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[8,3,5,1,6,2,4,7] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[8,3,5,1,7,2,4,6] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[7,3,8,1,6,2,4,5] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[7,3,5,1,6,2,8,4] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[7,8,4,1,6,2,3,5] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[7,8,5,1,6,2,3,4] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[5,3,4,1,6,8,2,7] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[5,3,4,1,8,7,2,6] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[8,3,4,1,6,7,2,5] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[8,3,5,1,6,7,2,4] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[5,3,4,1,6,7,8,2] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[2,3,4,8,1,7,5,6] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,8,4,5,1,3,6,7] => [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[2,8,4,6,1,3,5,7] => [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[2,7,4,8,1,3,5,6] => [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[2,7,8,5,1,3,4,6] => [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4

[2,7,8,6,1,3,4,5] => [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4

[7,3,4,5,1,2,8,6] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[7,3,4,6,1,2,8,5] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[6,3,4,5,1,8,2,7] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[8,3,4,5,1,7,2,6] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[8,3,4,6,1,7,2,5] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,3,4,5,1,7,8,2] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[2,8,4,5,6,1,3,7] => [[.,[[.,.],[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[2,8,4,5,7,1,3,6] => [[.,[[.,.],[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[2,7,4,5,6,1,8,3] => [[.,[[.,.],[.,[.,.]]]],[[.,.],.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[8,3,4,5,7,1,2,6] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[7,3,4,5,6,1,8,2] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[2,8,4,5,6,7,1,3] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[3,5,2,6,1,4,8,7] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[3,5,2,6,4,1,8,7] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[3,5,2,7,4,8,1,6] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[3,5,2,7,4,8,6,1] => [[[.,[.,.]],[[.,.],[[.,.],.]]],.] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 1

[4,5,7,2,3,8,6,1] => [[[.,[.,[.,.]]],[.,[[.,.],.]]],.] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[4,5,7,2,3,8,1,6] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[4,5,6,2,3,1,8,7] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[4,5,6,2,1,3,8,7] => [[[.,[.,[.,.]]],.],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[3,5,1,6,4,2,8,7] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[4,5,6,1,3,2,8,7] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[4,5,6,3,1,2,8,7] => [[[.,[.,[.,.]]],.],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[4,5,7,3,2,8,1,6] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[4,5,7,3,2,8,6,1] => [[[[.,[.,[.,.]]],.],[[.,.],.]],.] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1

[4,6,7,3,8,2,5,1] => [[[[.,[.,[.,.]]],[.,.]],[.,.]],.] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[4,6,7,3,8,2,1,5] => [[[[.,[.,[.,.]]],[.,.]],.],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[4,6,7,3,8,1,2,5] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[4,5,7,3,1,8,2,6] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[4,5,7,1,3,8,2,6] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[3,5,1,7,4,8,2,6] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[2,1,5,7,4,8,3,6] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[2,1,5,7,4,8,6,3] => [[.,.],[[[.,[.,.]],[[.,.],.]],.]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2

[3,5,1,7,4,8,6,2] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2

[4,5,7,1,3,8,6,2] => [[.,[.,[.,.]]],[[.,[[.,.],.]],.]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[4,5,7,3,1,8,6,2] => [[[.,[.,[.,.]]],.],[[[.,.],.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[4,6,7,3,8,1,5,2] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[4,6,7,3,8,5,1,2] => [[[.,[.,[.,.]]],[[.,.],.]],[.,.]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[4,6,7,3,8,5,2,1] => [[[[.,[.,[.,.]]],[[.,.],.]],.],.] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

[5,6,7,8,3,1,4,2] => [[[.,[.,[.,[.,.]]]],.],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[5,6,7,8,1,3,4,2] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[4,6,7,1,8,3,5,2] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[3,6,1,7,8,4,5,2] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2

[2,1,6,7,8,4,5,3] => [[.,.],[[[.,[.,[.,.]]],[.,.]],.]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2

[2,1,6,7,8,4,3,5] => [[.,.],[[[.,[.,[.,.]]],.],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => 3

[3,6,1,7,8,4,2,5] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[4,6,7,1,8,3,2,5] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[5,6,7,8,1,3,2,4] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,5,7,2,1,8,3,6] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[4,6,7,2,8,1,3,5] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[4,6,7,2,8,3,1,5] => [[[.,[.,[.,.]]],[[.,.],.]],[.,.]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[4,6,7,2,8,3,5,1] => [[[.,[.,[.,.]]],[[.,.],[.,.]]],.] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[3,6,2,7,8,4,5,1] => [[[.,[.,.]],[[.,[.,.]],[.,.]]],.] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 1

[3,6,2,7,8,4,1,5] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[3,6,2,7,8,1,4,5] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[3,5,2,7,1,8,4,6] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,4,2,1,7,8,5,6] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[3,4,1,2,7,8,6,5] => [[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 3

[3,5,2,7,1,8,6,4] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[3,6,2,7,8,1,5,4] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[3,6,2,7,8,5,1,4] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[3,6,2,7,8,5,4,1] => [[[.,[.,.]],[[[.,[.,.]],.],.]],.] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 1

[4,6,7,2,8,5,3,1] => [[[.,[.,[.,.]]],[[[.,.],.],.]],.] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1

[4,6,7,2,8,5,1,3] => [[[.,[.,[.,.]]],[[.,.],.]],[.,.]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[4,6,7,2,8,1,5,3] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[4,5,7,2,1,8,6,3] => [[[.,[.,[.,.]]],.],[[[.,.],.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[4,5,7,1,2,8,6,3] => [[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[3,5,1,7,2,8,6,4] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[2,1,5,7,3,8,6,4] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3

[2,1,6,7,8,3,5,4] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[3,6,1,7,8,2,5,4] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[4,6,7,1,8,2,5,3] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[5,6,7,8,1,2,4,3] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[5,6,7,8,2,1,4,3] => [[[.,[.,[.,[.,.]]]],.],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[5,6,7,8,2,4,1,3] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,6,7,8,2,4,3,1] => [[[.,[.,[.,[.,.]]]],[[.,.],.]],.] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 1

[5,6,7,8,1,4,2,3] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,6,7,1,8,5,2,3] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[3,6,1,7,8,5,2,4] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[2,1,6,7,8,5,3,4] => [[.,.],[[[.,[.,[.,.]]],.],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => 3

[3,6,1,7,8,5,4,2] => [[.,[.,.]],[[[[.,[.,.]],.],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 2

[4,6,7,1,8,5,3,2] => [[.,[.,[.,.]]],[[[[.,.],.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[5,6,7,8,1,4,3,2] => [[.,[.,[.,[.,.]]]],[[[.,.],.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[5,6,7,8,4,1,3,2] => [[[.,[.,[.,[.,.]]]],.],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[3,6,7,4,5,8,1,2] => [[.,[[.,[.,.]],[.,[.,.]]]],[.,.]] => [1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2

[2,6,7,4,5,1,8,3] => [[.,[[.,[.,.]],[.,.]]],[[.,.],.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2

[1,6,7,4,5,2,3,8] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 4

[4,5,3,7,8,6,1,2] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[6,4,8,3,7,5,1,2] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[3,2,5,6,1,8,7,4] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[4,2,5,6,8,1,7,3] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[7,8,2,4,5,1,6,3] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[7,8,1,4,5,2,3,6] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[5,1,3,8,2,6,4,7] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[7,8,1,3,2,5,4,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[7,8,2,3,1,5,6,4] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[5,2,3,8,1,6,7,4] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[6,3,8,2,1,7,5,4] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[7,8,3,2,1,6,5,4] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2

[7,8,4,2,6,1,5,3] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[4,5,2,7,8,1,6,3] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[1,6,7,3,2,5,4,8] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 4

[2,6,7,3,1,5,8,4] => [[.,[[.,[.,.]],.]],[[.,[.,.]],.]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 2

[3,6,7,2,1,8,5,4] => [[[.,[.,[.,.]]],.],[[[.,.],.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[7,8,5,6,2,1,4,3] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[6,4,8,1,7,2,3,5] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[7,8,3,1,2,6,4,5] => [[[.,[.,.]],.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[6,2,8,1,3,4,7,5] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[7,8,2,1,3,4,6,5] => [[[.,[.,.]],.],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 4

[8,4,5,1,2,7,3,6] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[7,4,5,1,2,8,3,6] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[6,4,5,1,2,3,8,7] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[5,4,6,1,2,3,8,7] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[3,6,1,5,2,4,8,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[5,6,4,1,2,3,8,7] => [[[.,[.,.]],.],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 4

[6,7,4,1,8,2,3,5] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[5,7,4,1,2,8,3,6] => [[[.,[.,.]],.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[3,7,1,5,2,8,4,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[3,8,1,5,2,7,4,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[5,8,4,1,2,7,3,6] => [[[.,[.,.]],.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[6,8,4,1,7,2,3,5] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[5,8,6,7,1,2,3,4] => [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[3,8,1,6,7,2,4,5] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[3,7,1,6,8,2,4,5] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[5,7,6,8,1,2,3,4] => [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[5,4,7,1,2,8,3,6] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[6,4,7,1,8,2,3,5] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[7,4,6,1,8,2,3,5] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[8,4,6,1,7,2,3,5] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[3,4,1,2,8,7,5,6] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 4

[8,4,7,1,6,2,3,5] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[7,4,8,1,6,2,3,5] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[5,4,8,1,2,7,3,6] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[4,5,8,1,2,7,3,6] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[3,5,1,8,2,7,4,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[2,1,5,8,3,7,4,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[3,6,1,8,7,2,4,5] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[4,6,8,1,7,2,3,5] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[5,7,8,6,1,2,3,4] => [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4

[4,7,8,1,6,2,3,5] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[3,7,1,8,6,2,4,5] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[2,1,7,8,6,3,4,5] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[3,8,1,7,6,2,4,5] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[6,4,7,3,8,5,1,2] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[6,4,7,3,5,8,1,2] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[6,4,7,2,5,1,8,3] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[6,4,8,3,5,7,1,2] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[6,4,8,2,5,1,7,3] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[7,8,4,2,5,1,6,3] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[7,8,4,2,5,1,3,6] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[6,3,8,2,1,5,4,7] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[7,8,3,2,1,5,4,6] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[7,8,3,2,1,5,6,4] => [[[[.,[.,.]],.],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 2

[6,3,8,2,1,5,7,4] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[6,3,7,2,1,5,4,8] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[6,3,7,2,1,5,8,4] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[6,3,7,2,1,8,5,4] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[6,4,7,2,8,1,5,3] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[6,5,7,8,2,1,4,3] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[6,3,7,2,1,8,4,5] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[6,3,7,2,1,4,8,5] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[6,3,7,2,1,4,5,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[7,8,4,2,6,1,3,5] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[7,8,3,2,1,6,4,5] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[6,3,8,2,1,7,4,5] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[6,3,8,2,1,4,7,5] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[7,8,3,2,1,4,6,5] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 3

[6,3,8,2,1,4,5,7] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[7,8,5,6,1,2,4,3] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[7,8,4,1,6,2,5,3] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[7,8,1,4,6,2,5,3] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[1,6,8,4,7,2,5,3] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 3

[7,8,1,3,2,6,5,4] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[7,8,3,4,6,5,1,2] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[7,8,2,4,6,1,5,3] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[7,8,2,1,3,6,5,4] => [[[.,[.,.]],.],[.,[[[.,.],.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 3

[7,8,1,2,3,6,5,4] => [[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 4

[1,6,8,2,3,7,5,4] => [.,[[.,[.,.]],[.,[[[.,.],.],.]]]] => [1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 4

[6,2,8,1,3,7,5,4] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[3,6,8,4,7,5,1,2] => [[.,[[.,[.,.]],[[.,.],.]]],[.,.]] => [1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2

[2,6,8,4,7,1,5,3] => [[.,[[.,[.,.]],[.,.]]],[[.,.],.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2

[2,6,8,3,1,7,5,4] => [[.,[[.,[.,.]],.]],[[[.,.],.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2

[2,6,8,1,3,7,5,4] => [[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[1,2,5,8,3,7,6,4] => [.,[.,[[.,[.,.]],[[[.,.],.],.]]]] => [1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 4

[2,4,1,3,8,7,6,5] => [[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 3

[6,3,8,1,2,7,5,4] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[5,1,3,8,2,7,6,4] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3

[6,4,8,1,7,2,5,3] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[4,5,1,8,7,2,6,3] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[3,6,8,1,2,7,5,4] => [[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[4,6,8,2,7,1,5,3] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[4,6,8,3,7,5,1,2] => [[[.,[.,[.,.]]],[[.,.],.]],[.,.]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[4,5,3,8,7,6,1,2] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[4,5,2,8,7,1,6,3] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[3,5,2,8,1,7,6,4] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[6,2,5,1,4,3,8,7] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[5,2,6,1,4,3,8,7] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[5,2,7,1,4,3,8,6] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[5,2,8,1,4,3,7,6] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[6,2,8,1,4,3,7,5] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[6,2,7,1,4,3,8,5] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[7,2,6,1,4,3,8,5] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[7,2,5,1,4,3,8,6] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[8,2,5,1,4,3,7,6] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[8,2,6,1,4,3,7,5] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[8,2,6,1,5,3,7,4] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[7,2,6,1,5,3,8,4] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[6,2,7,1,5,3,8,4] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[6,2,8,1,5,3,7,4] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[8,4,7,1,3,2,6,5] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[7,4,8,1,3,2,6,5] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[7,3,8,1,4,2,6,5] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[8,3,7,1,4,2,6,5] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[8,3,7,1,5,2,6,4] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[7,3,8,1,5,2,6,4] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[8,3,7,2,6,1,5,4] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[7,3,8,2,6,1,5,4] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[3,4,2,6,8,1,5,7] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[5,3,6,2,8,1,4,7] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[5,3,6,2,4,8,1,7] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[5,7,3,8,2,4,1,6] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,7,3,8,2,4,6,1] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1

[4,5,2,6,3,8,1,7] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[4,5,2,1,6,8,3,7] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[5,6,2,8,1,3,4,7] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[3,5,6,1,4,8,2,7] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[4,1,5,6,3,8,2,7] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[4,5,1,6,3,8,2,7] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[4,5,6,3,2,8,1,7] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[7,4,5,3,8,2,1,6] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[7,4,5,3,8,2,6,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[6,7,4,8,3,2,5,1] => [[[[[.,[.,.]],[.,.]],.],[.,.]],.] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1

[6,7,4,8,3,2,1,5] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2

[6,7,4,1,8,3,2,5] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[7,4,5,3,1,8,2,6] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[4,7,1,5,8,3,2,6] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[5,3,7,8,1,4,2,6] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[7,5,8,2,4,6,1,3] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[7,3,5,8,1,4,6,2] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[4,5,1,7,8,3,6,2] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2

[6,7,4,3,8,1,5,2] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[6,7,4,8,3,1,5,2] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[6,7,4,8,3,5,2,1] => [[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1

[5,6,7,3,8,4,2,1] => [[[[.,[.,[.,.]]],[[.,.],.]],.],.] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

[5,6,7,3,1,8,4,2] => [[[.,[.,[.,.]]],.],[[[.,.],.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[5,6,1,7,3,8,4,2] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2

[5,1,6,7,3,8,4,2] => [[.,.],[[[.,[.,.]],[[.,.],.]],.]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2

[6,4,7,1,8,3,5,2] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[6,7,8,3,1,4,5,2] => [[[.,[.,[.,.]]],.],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[6,7,2,8,4,5,1,3] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[6,7,2,8,4,1,3,5] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[5,1,6,7,3,2,8,4] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3

[5,6,1,7,3,2,8,4] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[5,6,7,3,2,1,8,4] => [[[[.,[.,[.,.]]],.],.],[[.,.],.]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[5,6,7,3,2,8,4,1] => [[[[.,[.,[.,.]]],.],[[.,.],.]],.] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1

[5,6,2,7,3,8,4,1] => [[[.,[.,.]],[[.,.],[[.,.],.]]],.] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 1

[5,6,2,7,3,1,8,4] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[5,6,2,1,7,3,8,4] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[6,7,2,1,8,3,4,5] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[7,5,8,2,1,3,4,6] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[5,7,3,1,8,2,4,6] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[4,7,1,5,2,8,3,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[6,7,4,2,1,8,3,5] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[6,7,4,2,8,3,1,5] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[6,7,4,2,8,3,5,1] => [[[[.,[.,.]],.],[[.,.],[.,.]]],.] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 1

[3,6,7,2,8,4,5,1] => [[[.,[.,[.,.]]],[[.,.],[.,.]]],.] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[3,6,7,2,8,4,1,5] => [[[.,[.,[.,.]]],[[.,.],.]],[.,.]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[3,6,7,2,1,8,4,5] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[5,7,3,8,2,1,4,6] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3

[3,4,7,8,2,1,5,6] => [[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[3,7,8,1,4,6,2,5] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[3,4,7,8,2,6,1,5] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,7,3,8,2,6,1,4] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[3,6,7,2,8,5,1,4] => [[[.,[.,[.,.]]],[[.,.],.]],[.,.]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[3,6,7,8,5,2,1,4] => [[[.,[[.,[.,[.,.]]],.]],.],[.,.]] => [1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 2

[3,6,7,8,5,2,4,1] => [[[.,[[.,[.,[.,.]]],.]],[.,.]],.] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[6,4,7,8,2,5,3,1] => [[[[.,.],[.,[.,.]]],[[.,.],.]],.] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => 1

[6,4,7,8,2,1,5,3] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[4,1,5,7,8,2,6,3] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[5,3,7,8,1,6,2,4] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,7,2,8,5,1,3,4] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[5,6,2,1,7,8,4,3] => [[[.,[.,.]],.],[[[.,[.,.]],.],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 2

[5,6,2,7,1,8,4,3] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[5,6,2,7,8,4,3,1] => [[[.,[.,.]],[[[.,[.,.]],.],.]],.] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 1

[5,6,7,2,8,4,3,1] => [[[.,[.,[.,.]]],[[[.,.],.],.]],.] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1

[5,6,7,2,1,8,4,3] => [[[.,[.,[.,.]]],.],[[[.,.],.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[5,6,1,7,2,8,4,3] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[5,1,6,7,2,8,4,3] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3

[6,4,7,1,8,2,5,3] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[3,6,7,1,8,5,2,4] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[6,7,8,5,2,4,1,3] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[6,7,8,3,5,1,4,2] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[4,6,7,8,1,5,3,2] => [[.,[.,[.,[.,.]]]],[[[.,.],.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[5,1,6,7,8,4,3,2] => [[.,.],[[[[.,[.,[.,.]]],.],.],.]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => 2

[5,6,1,7,8,4,3,2] => [[.,[.,.]],[[[[.,[.,.]],.],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 2

[5,6,7,1,8,4,3,2] => [[.,[.,[.,.]]],[[[[.,.],.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[7,2,4,5,8,3,6,1] => [[[.,.],[[.,[.,[.,.]]],[.,.]]],.] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1

[2,4,5,3,7,1,8,6] => [[.,[[.,[.,.]],[.,.]]],[[.,.],.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2

[8,2,4,5,6,3,1,7] => [[[.,.],[[.,[.,[.,.]]],.]],[.,.]] => [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => 2

[8,2,4,5,6,1,3,7] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[8,1,2,4,5,6,3,7] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 4

[8,2,5,1,3,6,4,7] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[8,5,6,2,1,4,3,7] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[8,1,4,5,6,3,2,7] => [[.,.],[[[.,[.,[.,.]]],.],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => 3

[4,5,3,7,2,1,8,6] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[7,4,5,8,3,2,6,1] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1

[4,3,6,7,2,8,5,1] => [[[[.,.],[.,[.,.]]],[[.,.],.]],.] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => 1

[4,3,6,7,2,8,1,5] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[4,5,3,7,1,8,2,6] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,3,4,7,1,2,8,6] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[7,5,8,2,1,4,6,3] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[7,4,5,8,3,6,1,2] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[4,3,6,7,8,1,5,2] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[6,4,7,8,3,5,2,1] => [[[[[.,.],[.,[.,.]]],[.,.]],.],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1

[3,5,6,7,8,4,1,2] => [[.,[[.,[.,[.,[.,.]]]],.]],[.,.]] => [1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 2

[3,1,5,6,7,8,4,2] => [[.,.],[[[.,[.,[.,[.,.]]]],.],.]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => 2

[4,6,1,7,8,3,5,2] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2

[3,6,7,1,4,8,5,2] => [[.,[.,[.,.]]],[[.,[[.,.],.]],.]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[6,2,4,1,7,8,5,3] => [[[.,.],[.,.]],[[[.,[.,.]],.],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[2,6,7,1,4,8,3,5] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[4,3,6,7,8,1,2,5] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[1,5,3,6,7,8,2,4] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[3,5,6,7,8,2,1,4] => [[[.,[.,[.,[.,[.,.]]]]],.],[.,.]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 2

[3,5,6,7,8,2,4,1] => [[[.,[.,[.,[.,[.,.]]]]],[.,.]],.] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 1

[5,2,7,1,3,8,4,6] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[4,5,2,7,8,1,3,6] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[4,2,6,7,8,3,1,5] => [[[.,.],[[.,[.,[.,.]]],.]],[.,.]] => [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => 2

[4,2,6,7,8,3,5,1] => [[[.,.],[[.,[.,[.,.]]],[.,.]]],.] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1

[3,6,2,7,4,8,5,1] => [[[.,[.,.]],[[.,.],[[.,.],.]]],.] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 1

[3,6,2,7,4,8,1,5] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[4,7,2,1,3,5,8,6] => [[[.,[.,.]],.],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 4

[7,8,4,2,1,3,6,5] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 3

[7,8,1,3,4,2,6,5] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[7,8,3,4,2,1,6,5] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[3,6,2,7,1,8,5,4] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[6,7,3,8,2,5,4,1] => [[[[.,[.,.]],[.,.]],[[.,.],.]],.] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 1

[6,4,7,8,5,2,3,1] => [[[[.,.],[[.,[.,.]],.]],[.,.]],.] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[2,6,4,7,8,1,5,3] => [[.,[[.,.],[.,[.,.]]]],[[.,.],.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[4,6,2,7,8,1,5,3] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[7,5,8,2,1,6,3,4] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[6,2,7,1,3,8,5,4] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[4,6,1,7,8,5,2,3] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[5,1,2,6,7,8,4,3] => [[.,.],[.,[[[.,[.,[.,.]]],.],.]]] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => 3

[5,2,6,7,8,4,1,3] => [[[.,.],[[.,[.,[.,.]]],.]],[.,.]] => [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => 2

[5,2,6,7,8,4,3,1] => [[[.,.],[[[.,[.,[.,.]]],.],.]],.] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => 1

[2,5,6,7,8,4,1,3] => [[.,[[.,[.,[.,[.,.]]]],.]],[.,.]] => [1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 2

[2,6,7,1,3,8,5,4] => [[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[6,7,8,2,1,5,4,3] => [[[.,[.,[.,.]]],.],[[[.,.],.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[6,7,3,8,5,1,4,2] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[6,4,7,8,5,3,1,2] => [[[[.,.],[[.,[.,.]],.]],.],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => 2

[4,5,2,3,7,6,1,8] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[1,5,6,3,4,8,7,2] => [.,[[[.,[.,.]],[.,[[.,.],.]]],.]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 2

[4,6,2,7,3,5,1,8] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[3,2,6,7,4,5,1,8] => [[[.,.],[[.,[.,.]],[.,.]]],[.,.]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[4,7,2,6,5,3,1,8] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[6,8,5,4,2,1,3,7] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 3

[4,8,2,6,5,1,3,7] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[8,1,6,7,4,5,2,3] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[7,1,6,8,4,2,5,3] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3

[6,1,7,8,2,4,5,3] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3

[4,1,2,7,8,5,6,3] => [[.,.],[.,[[[.,[.,.]],[.,.]],.]]] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 3

[4,8,2,7,1,5,3,6] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[7,8,6,1,4,2,3,5] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[1,6,7,8,3,4,5,2] => [.,[[[.,[.,[.,.]]],[.,[.,.]]],.]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[8,6,7,1,3,4,2,5] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[7,6,8,1,3,2,4,5] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[5,7,8,2,1,3,4,6] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[4,7,2,8,1,3,5,6] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[3,2,6,8,4,1,5,7] => [[[.,.],[[.,[.,.]],.]],[.,[.,.]]] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[4,6,2,8,3,1,5,7] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[5,6,8,2,3,1,4,7] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[6,5,8,3,2,1,4,7] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3

[7,5,8,3,1,2,4,6] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[8,5,7,3,1,4,2,6] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[1,5,7,3,8,4,6,2] => [.,[[[.,[.,.]],[[.,.],[.,.]]],.]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 2

[4,5,2,3,8,1,6,7] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[4,5,2,3,1,8,7,6] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[1,5,8,3,7,6,4,2] => [.,[[[.,[.,.]],[[[.,.],.],.]],.]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 2

[5,6,1,2,3,8,7,4] => [[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 4

[4,6,2,1,3,8,7,5] => [[[.,[.,.]],.],[.,[[[.,.],.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 3

[3,2,6,1,4,8,7,5] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[3,2,7,1,8,4,6,5] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[4,7,2,1,8,3,6,5] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[5,7,1,2,8,3,6,4] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4

[6,7,1,8,2,3,5,4] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[1,7,8,6,5,3,4,2] => [.,[[[[[.,[.,.]],.],.],[.,.]],.]] => [1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 2

[7,8,1,6,5,2,3,4] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[6,8,1,7,2,5,3,4] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[5,8,1,2,7,6,3,4] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 4

[4,8,2,1,7,6,3,5] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[3,2,8,1,7,6,4,5] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[4,5,1,2,3,8,7,6] => [[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 4

[4,6,1,2,3,8,7,5] => [[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 4

[8,1,6,7,2,4,5,3] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3

[7,1,6,8,2,4,5,3] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3

[4,7,1,2,8,3,6,5] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4

[3,1,2,7,8,5,6,4] => [[.,.],[.,[[[.,[.,.]],[.,.]],.]]] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 3

[4,7,1,6,2,3,5,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[4,8,1,6,2,3,5,7] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[4,8,1,7,2,3,5,6] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[4,8,1,2,7,3,6,5] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4

[5,8,1,2,7,3,6,4] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4

[1,5,8,3,7,4,6,2] => [.,[[[.,[.,.]],[[.,.],[.,.]]],.]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 2

[6,8,1,7,2,3,5,4] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[7,8,1,6,2,3,5,4] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[1,7,8,6,3,4,5,2] => [.,[[[[.,[.,.]],.],[.,[.,.]]],.]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 2

[3,2,5,1,6,4,8,7] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[4,2,5,1,6,3,8,7] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[4,3,5,1,6,2,8,7] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[4,3,5,2,7,1,8,6] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[4,3,6,2,7,5,8,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[4,3,6,2,7,1,8,5] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[4,3,6,1,7,2,8,5] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[4,3,5,1,7,2,8,6] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[4,3,5,1,7,6,8,2] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[4,3,6,1,7,5,8,2] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[5,3,6,1,7,4,8,2] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[5,3,6,1,7,2,8,4] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[5,3,6,2,7,1,8,4] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[5,3,6,2,7,4,8,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[5,2,6,1,7,3,8,4] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[4,2,5,1,7,3,8,6] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[4,2,6,1,7,3,8,5] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[3,2,6,1,7,4,8,5] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[3,2,5,1,7,4,8,6] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[3,2,4,1,7,5,8,6] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[3,2,5,1,7,6,8,4] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[3,2,6,1,7,5,8,4] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[4,2,6,1,7,5,8,3] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[4,2,5,1,7,6,8,3] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[5,2,6,1,7,4,8,3] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[5,4,6,2,7,3,8,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[5,4,6,2,7,1,8,3] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[5,4,6,1,7,2,8,3] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[5,4,6,1,7,3,8,2] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[5,4,6,3,7,1,8,2] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[8,3,5,2,1,6,4,7] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[8,2,4,5,7,3,6,1] => [[[.,.],[[.,[.,[.,.]]],[.,.]]],.] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1

[2,4,5,7,3,1,8,6] => [[.,[[.,[.,[.,.]]],.]],[[.,.],.]] => [1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[8,1,5,6,4,3,2,7] => [[.,.],[[[[.,[.,.]],.],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => 3

[5,7,4,3,2,1,8,6] => [[[[[.,[.,.]],.],.],.],[[.,.],.]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2

[8,5,7,4,3,2,6,1] => [[[[[[.,.],[.,.]],.],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1

[4,6,8,3,2,7,5,1] => [[[[.,[.,[.,.]]],.],[[.,.],.]],.] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1

[1,4,6,7,3,2,8,5] => [.,[[[.,[.,[.,.]]],.],[[.,.],.]]] => [1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3

[5,4,7,3,1,8,2,6] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[5,7,4,2,1,3,8,6] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 3

[8,5,7,4,2,1,6,3] => [[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[4,6,3,8,7,1,5,2] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[4,8,1,6,7,3,5,2] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2

[8,2,6,1,4,7,5,3] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[3,7,1,6,4,8,2,5] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[1,7,3,5,6,8,2,4] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[1,3,6,7,5,8,2,4] => [.,[[.,[[.,[.,.]],[.,.]]],[.,.]]] => [1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 3

[3,6,8,5,7,2,4,1] => [[[.,[[.,[.,.]],[.,.]]],[.,.]],.] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[3,8,2,4,6,7,5,1] => [[[.,[.,.]],[.,[[.,[.,.]],.]]],.] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 1

[3,7,2,6,4,8,1,5] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[3,2,6,1,4,7,8,5] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[5,3,7,2,1,8,4,6] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[4,7,3,2,1,5,8,6] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 3

[8,5,7,3,2,1,6,4] => [[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[8,3,6,7,2,1,5,4] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[3,7,8,6,2,1,5,4] => [[[.,[[.,[.,.]],.]],.],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 2

[4,6,8,2,1,7,5,3] => [[[.,[.,[.,.]]],.],[[[.,.],.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[8,5,7,2,1,3,6,4] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[8,2,6,7,1,3,5,4] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[8,3,6,1,7,5,2,4] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[4,6,1,8,7,2,5,3] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[8,1,2,5,6,7,4,3] => [[.,.],[.,[[[.,[.,[.,.]]],.],.]]] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => 3

[2,1,7,8,5,6,4,3] => [[.,.],[[[[.,[.,.]],[.,.]],.],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[3,7,8,1,6,5,2,4] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[2,7,8,6,1,3,5,4] => [[.,[[.,[.,.]],.]],[.,[[.,.],.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 3

[8,1,6,7,5,4,3,2] => [[.,.],[[[[[.,[.,.]],.],.],.],.]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2

[4,6,3,5,1,2,8,7] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[6,8,1,4,5,7,3,2] => [[.,[.,.]],[[[.,[.,[.,.]]],.],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2

[3,6,2,4,5,1,8,7] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[2,6,1,4,5,3,8,7] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[6,1,2,4,5,3,8,7] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 4

[5,6,3,2,1,4,8,7] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 3

[3,7,8,4,5,1,2,6] => [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[2,1,6,8,5,7,3,4] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[5,6,3,8,1,7,2,4] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[8,5,7,4,1,6,3,2] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[2,5,8,4,7,6,1,3] => [[.,[[.,[.,.]],[[.,.],.]]],[.,.]] => [1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2

[2,4,8,3,5,6,7,1] => [[.,[[.,[.,.]],[.,[.,[.,.]]]]],.] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1

[7,5,8,4,3,6,1,2] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[2,1,5,8,4,6,7,3] => [[.,.],[[[.,[.,.]],[.,[.,.]]],.]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[2,1,4,8,3,6,7,5] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3

[2,3,8,1,5,6,7,4] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[4,3,8,2,5,6,7,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1

[4,8,2,3,5,6,7,1] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1

[3,8,2,1,5,6,7,4] => [[[.,[.,.]],.],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 2

[2,8,1,3,5,6,7,4] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 3

[8,1,2,3,5,6,7,4] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4

[7,8,2,4,3,6,1,5] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[6,8,3,2,4,1,7,5] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[2,1,7,8,5,4,3,6] => [[.,.],[[[[.,[.,.]],.],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => 3

[5,7,3,8,1,4,2,6] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,7,8,4,5,3,1,6] => [[.,[[[.,[.,.]],[.,.]],.]],[.,.]] => [1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2

[5,7,8,4,3,6,2,1] => [[[[[.,[.,[.,.]]],.],[.,.]],.],.] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1

[5,6,3,8,4,2,7,1] => [[[[.,[.,.]],[[.,.],.]],[.,.]],.] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 1

[4,8,3,6,2,1,7,5] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[5,8,3,2,6,1,7,4] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[4,5,3,8,6,2,7,1] => [[[[.,[.,.]],[[.,.],.]],[.,.]],.] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 1

[3,5,8,4,7,6,2,1] => [[[.,[[.,[.,.]],[[.,.],.]]],.],.] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 1

[5,8,2,4,7,6,1,3] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[5,7,3,6,1,8,2,4] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,8,3,5,2,1,7,4] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[7,8,5,4,2,6,1,3] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2

[4,8,1,2,5,6,7,3] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 3

[3,4,8,1,5,6,7,2] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[3,4,2,8,5,6,7,1] => [[[.,[.,.]],[[.,.],[.,[.,.]]]],.] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 1

[2,4,1,8,5,6,7,3] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 2

[8,3,4,1,5,6,7,2] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[6,7,2,4,5,8,3,1] => [[[.,[.,.]],[[.,[.,[.,.]]],.]],.] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[2,5,7,4,8,6,3,1] => [[.,[[[.,[.,.]],[[.,.],.]],.]],.] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 1

[5,6,3,7,1,8,4,2] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[5,7,1,4,8,6,2,3] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3

[5,6,3,1,8,2,7,4] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[4,6,3,5,8,2,7,1] => [[[[.,[.,.]],[.,[.,.]]],[.,.]],.] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[4,6,3,8,1,2,7,5] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[3,7,8,4,1,6,2,5] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[3,2,5,1,6,8,4,7] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[3,6,2,5,4,8,1,7] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[3,5,2,4,7,1,8,6] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[3,5,8,2,4,7,6,1] => [[[.,[.,[.,.]]],[.,[[.,.],.]]],.] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[4,2,5,8,3,7,6,1] => [[[.,.],[[.,[.,.]],[[.,.],.]]],.] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1

[6,3,5,1,4,8,2,7] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[4,6,1,5,3,8,2,7] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[4,3,6,2,8,7,5,1] => [[[[.,.],[.,.]],[[[.,.],.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1

[7,1,3,5,8,4,2,6] => [[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3

[7,2,5,8,4,1,3,6] => [[[.,.],[[.,[.,.]],.]],[.,[.,.]]] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[4,3,7,1,8,6,5,2] => [[[.,.],[.,.]],[[[[.,.],.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[4,8,3,7,6,5,2,1] => [[[[.,[.,.]],[[[.,.],.],.]],.],.] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 1

[4,6,1,8,7,3,5,2] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2

[5,7,1,6,3,2,8,4] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[4,7,2,6,3,1,8,5] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[7,3,6,2,4,1,8,5] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[3,6,7,2,1,4,8,5] => [[[.,[.,[.,.]]],.],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[4,3,7,8,2,1,5,6] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[8,3,7,1,4,6,2,5] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[3,8,2,5,7,1,6,4] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[8,3,6,2,7,1,5,4] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[7,8,3,6,2,1,5,4] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[4,7,8,2,1,6,5,3] => [[[.,[.,[.,.]]],.],[[[.,.],.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[4,2,6,8,1,7,5,3] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[5,4,8,2,7,1,6,3] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[4,8,1,5,7,2,6,3] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[5,8,3,7,1,6,2,4] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,6,8,1,7,5,2,4] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[5,1,6,8,2,7,4,3] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3

[5,2,7,1,8,6,4,3] => [[[.,.],[.,.]],[[[[.,.],.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[5,8,2,7,6,4,3,1] => [[[.,[.,.]],[[[[.,.],.],.],.]],.] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1

[4,7,1,8,6,2,5,3] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[7,8,3,1,6,5,2,4] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[8,5,7,1,6,4,3,2] => [[[.,.],[.,.]],[[[[.,.],.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[6,8,1,7,5,4,3,2] => [[.,[.,.]],[[[[[.,.],.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2

[4,7,2,6,3,5,1,8] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[6,8,5,2,3,1,4,7] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[4,8,2,6,3,1,5,7] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[8,1,6,7,2,3,4,5] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[7,1,6,8,2,3,4,5] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[6,5,8,2,3,1,4,7] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[8,5,7,2,1,3,4,6] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[4,5,2,3,1,8,6,7] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[1,5,8,2,7,3,4,6] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 5

[4,6,2,1,3,8,5,7] => [[[.,[.,.]],.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[3,2,6,1,4,8,5,7] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[3,2,7,1,8,4,5,6] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[4,7,2,1,8,3,5,6] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[1,7,8,6,2,3,4,5] => [.,[[[.,[.,.]],.],[.,[.,[.,.]]]]] => [1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 5

[7,8,1,6,2,3,4,5] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[6,8,1,7,2,3,4,5] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[4,8,2,1,7,3,5,6] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[3,2,8,1,7,4,5,6] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[6,3,5,1,2,4,8,7] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[4,3,5,6,1,2,8,7] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[2,6,1,5,4,3,8,7] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[5,7,4,6,2,8,3,1] => [[[[.,[.,.]],[.,.]],[[.,.],.]],.] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 1

[8,1,4,7,2,6,3,5] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[3,4,7,8,5,2,1,6] => [[[.,[.,[[.,[.,.]],.]]],.],[.,.]] => [1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 2

[5,8,2,4,6,7,3,1] => [[[.,[.,.]],[[.,[.,[.,.]]],.]],.] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[5,1,4,6,8,2,7,3] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[2,5,4,6,7,1,8,3] => [[.,[[.,.],[.,[.,.]]]],[[.,.],.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[2,4,6,3,7,5,8,1] => [[.,[[.,[.,.]],[[.,.],[.,.]]]],.] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 1

[6,5,8,4,1,7,3,2] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[2,1,4,8,3,7,6,5] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3

[2,3,8,1,6,7,5,4] => [[.,[.,[.,.]]],[[[.,[.,.]],.],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[4,3,7,2,6,8,5,1] => [[[[.,.],[.,.]],[[.,[.,.]],.]],.] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[4,7,2,3,8,5,6,1] => [[[.,[.,.]],[.,[[.,.],[.,.]]]],.] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 1

[3,8,2,1,7,5,6,4] => [[[.,[.,.]],.],[[[.,.],[.,.]],.]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[2,8,1,3,6,5,7,4] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 3

[2,7,8,5,4,3,1,6] => [[.,[[[[.,[.,.]],.],.],.]],[.,.]] => [1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 2

[8,3,6,1,4,2,7,5] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[7,3,5,8,2,4,1,6] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[2,3,4,1,8,5,7,6] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[8,3,5,6,2,7,1,4] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,3,6,1,8,7,2,4] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[5,6,2,8,7,4,1,3] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[7,8,5,6,1,4,2,3] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,8,3,6,1,7,2,4] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,7,3,5,2,1,8,4] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[4,6,1,2,8,7,3,5] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 4

[2,4,1,5,8,7,6,3] => [[.,[.,.]],[[.,[[[.,.],.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 2

[6,3,4,1,5,7,8,2] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[4,5,2,6,3,1,8,7] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[5,6,3,2,4,1,8,7] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[3,6,2,4,1,5,8,7] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[2,6,1,3,5,4,8,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4

[6,7,2,3,4,8,5,1] => [[[.,[.,.]],[.,[.,[[.,.],.]]]],.] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 1

[2,5,7,3,8,6,4,1] => [[.,[[.,[.,.]],[[[.,.],.],.]]],.] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 1

[3,6,7,4,1,8,5,2] => [[.,[[.,[.,.]],.]],[[[.,.],.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2

[5,6,3,7,4,8,1,2] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[2,1,6,7,4,8,5,3] => [[.,.],[[[.,[.,.]],[[.,.],.]],.]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2

[5,8,3,7,4,2,6,1] => [[[[.,[.,.]],[[.,.],.]],[.,.]],.] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 1

[7,8,1,3,5,2,6,4] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[4,8,1,2,7,6,3,5] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 4

[6,8,3,5,2,7,4,1] => [[[[.,[.,.]],[.,.]],[[.,.],.]],.] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 1

[3,4,2,8,5,7,6,1] => [[[.,[.,.]],[[.,.],[[.,.],.]]],.] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 1

[2,4,1,8,7,6,5,3] => [[.,[.,.]],[[[[[.,.],.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2

[5,7,1,6,8,2,4,3] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[5,6,2,1,8,7,3,4] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[4,6,2,5,8,3,7,1] => [[[.,[.,.]],[[.,[.,.]],[.,.]]],.] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 1

[5,6,2,8,4,3,1,7] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[4,7,2,8,1,5,3,6] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,7,8,6,3,4,1,2] => [[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => [1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[2,7,8,4,5,3,6,1] => [[.,[[[.,[.,.]],[.,.]],[.,.]]],.] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1

[5,7,3,8,1,4,6,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[2,1,7,8,5,4,6,3] => [[.,.],[[[[.,[.,.]],.],[.,.]],.]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 2

[2,1,5,8,4,6,3,7] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[7,5,8,4,3,6,2,1] => [[[[[[.,.],[.,.]],.],[.,.]],.],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1

[2,4,8,3,5,6,1,7] => [[.,[[.,[.,.]],[.,[.,.]]]],[.,.]] => [1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2

[3,4,8,1,7,2,5,6] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[2,3,8,1,4,6,7,5] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[4,3,8,2,5,1,7,6] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[2,1,4,8,3,5,7,6] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[6,8,2,4,3,5,1,7] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[4,8,2,3,5,1,6,7] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[3,8,2,1,4,6,5,7] => [[[.,[.,.]],.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[2,8,1,3,4,5,7,6] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 5

[3,5,7,2,4,1,6,8] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[7,5,8,2,4,1,6,3] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[3,5,7,2,4,6,1,8] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[7,5,8,2,4,6,3,1] => [[[[.,.],[.,.]],[[.,[.,.]],.]],.] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[6,5,8,2,1,3,7,4] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[3,5,6,2,1,8,7,4] => [[[.,[.,[.,.]]],.],[[[.,.],.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[3,5,7,2,4,1,8,6] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[3,5,7,2,4,6,8,1] => [[[.,[.,[.,.]]],[.,[.,[.,.]]]],.] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1

[4,5,2,6,3,1,7,8] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[5,1,6,7,4,3,8,2] => [[.,.],[[[[.,[.,.]],.],[.,.]],.]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 2

[7,1,6,8,4,3,5,2] => [[.,.],[[[[.,[.,.]],.],[.,.]],.]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 2

[5,6,8,2,3,1,7,4] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[6,5,8,2,4,3,1,7] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[6,5,8,2,4,3,7,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[5,1,6,7,4,3,2,8] => [[.,.],[[[[.,[.,.]],.],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => 3

[7,1,6,8,4,3,2,5] => [[.,.],[[[[.,[.,.]],.],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => 3

[5,7,8,6,3,4,2,1] => [[[[.,[[.,[.,.]],.]],[.,.]],.],.] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[4,1,6,7,8,3,2,5] => [[.,.],[[[.,[.,[.,.]]],.],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => 3

[4,5,2,6,3,7,1,8] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[4,5,2,7,3,8,1,6] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[3,5,6,2,4,8,7,1] => [[[.,[.,[.,.]]],[.,[[.,.],.]]],.] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[3,5,6,2,4,8,1,7] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[6,1,2,5,8,4,7,3] => [[.,.],[.,[[[.,[.,.]],[.,.]],.]]] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 3

[4,1,2,3,7,8,6,5] => [[.,.],[.,[.,[[[.,[.,.]],.],.]]]] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => 4

[4,5,2,7,3,8,6,1] => [[[.,[.,.]],[[.,.],[[.,.],.]]],.] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 1

[4,1,6,7,8,3,5,2] => [[.,.],[[[.,[.,[.,.]]],[.,.]],.]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2

[4,1,2,6,8,5,7,3] => [[.,.],[.,[[[.,[.,.]],[.,.]],.]]] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 3

[4,5,2,6,3,7,8,1] => [[[.,[.,.]],[[.,.],[.,[.,.]]]],.] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 1

[7,8,5,6,1,4,3,2] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[7,8,4,2,1,5,3,6] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[7,8,2,1,6,5,3,4] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[2,4,8,1,5,7,3,6] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[4,3,8,1,7,2,5,6] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[7,8,3,4,5,1,6,2] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[7,8,3,5,4,2,1,6] => [[[[.,[.,.]],[[.,.],.]],.],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2

[7,8,3,6,5,4,1,2] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[7,8,2,6,4,1,3,5] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[7,8,1,6,5,4,3,2] => [[.,[.,.]],[[[[[.,.],.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2

[1,3,8,2,6,4,7,5] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 4

[5,3,7,1,6,4,8,2] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[5,3,6,2,7,4,1,8] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[2,4,7,1,5,3,6,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[3,7,2,8,6,4,1,5] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[3,8,1,7,6,4,5,2] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2

[1,5,6,8,2,4,7,3] => [.,[[.,[.,[.,.]]],[[.,[.,.]],.]]] => [1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3

[2,6,1,4,7,3,5,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[5,6,7,3,8,4,1,2] => [[[.,[.,[.,.]]],[[.,.],.]],[.,.]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[4,5,6,7,2,8,1,3] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,7,1,4,2,3,8,6] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[6,2,4,1,8,3,7,5] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[5,7,2,4,1,6,3,8] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,7,5,8,1,4,3,2] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[4,8,2,1,5,6,3,7] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[4,2,7,8,1,6,3,5] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,3,7,8,2,1,6,4] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[3,6,7,8,5,1,4,2] => [[.,[[.,[.,[.,.]]],.]],[[.,.],.]] => [1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[3,7,8,5,1,2,4,6] => [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4

[2,7,8,6,5,4,1,3] => [[.,[[[[.,[.,.]],.],.],.]],[.,.]] => [1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 2

[7,3,6,2,4,8,1,5] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[4,3,7,1,2,5,8,6] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[3,6,2,7,1,4,8,5] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[5,3,6,7,1,2,8,4] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[4,7,1,5,2,3,8,6] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[5,7,4,2,3,8,1,6] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[5,8,2,6,3,7,1,4] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[2,6,5,8,1,3,4,7] => [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[2,5,7,4,8,1,3,6] => [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[5,4,6,7,2,8,1,3] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[3,5,7,1,4,8,2,6] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[5,3,7,2,4,8,1,6] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[5,4,7,3,8,1,2,6] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[7,4,6,3,8,1,2,5] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[8,4,6,3,7,1,2,5] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[4,7,1,5,8,6,2,3] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3

[5,7,2,8,1,6,3,4] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,3,7,8,5,1,2,4] => [[[.,.],[[.,[.,.]],.]],[.,[.,.]]] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[3,6,8,2,7,1,4,5] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[6,8,4,7,5,1,2,3] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[5,6,3,1,4,2,8,7] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[2,1,7,8,5,3,6,4] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3

[5,7,3,8,1,2,6,4] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[2,7,8,4,1,6,5,3] => [[.,[[.,[.,.]],.]],[[[.,.],.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2

[3,6,4,5,7,2,8,1] => [[[.,[[.,.],[.,[.,.]]]],[.,.]],.] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[6,7,3,5,2,4,8,1] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1

[5,6,2,3,1,8,4,7] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,8,3,5,2,7,1,4] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[7,8,5,2,3,6,1,4] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[6,8,2,1,7,3,4,5] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[2,8,1,7,3,4,5,6] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[4,8,1,5,7,2,3,6] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[3,6,2,7,1,8,4,5] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,3,7,1,2,8,4,5] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[7,2,6,1,8,3,4,5] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[4,3,5,1,6,8,2,7] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[5,4,6,3,8,7,1,2] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[6,3,8,1,7,2,4,5] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[7,6,8,2,3,5,1,4] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[3,7,8,2,4,6,1,5] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[6,7,3,8,2,5,1,4] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,4,7,8,2,6,1,3] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[1,7,8,3,6,2,4,5] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 4

[6,8,3,7,5,1,2,4] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[7,8,6,2,5,1,3,4] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[8,1,6,7,3,2,5,4] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3

[8,1,6,7,3,2,4,5] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[7,5,8,3,6,2,4,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[7,4,8,3,2,6,5,1] => [[[[[.,.],[.,.]],.],[[.,.],.]],.] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1

[7,4,8,3,2,5,6,1] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1

[7,5,8,3,6,2,1,4] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[7,4,8,3,2,6,1,5] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[7,4,8,3,2,5,1,6] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[7,6,8,1,4,5,2,3] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[7,6,8,1,3,2,5,4] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[7,4,8,3,2,1,5,6] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3

[7,4,8,3,2,1,6,5] => [[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[7,5,8,3,1,2,6,4] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[7,5,8,4,1,6,2,3] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[5,6,2,1,3,4,8,7] => [[[.,[.,.]],.],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 4

[2,1,7,8,4,3,5,6] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[7,8,1,2,5,4,6,3] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 3

[4,7,2,8,1,3,6,5] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[3,4,7,1,8,2,6,5] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[4,6,3,7,2,5,1,8] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[4,6,3,7,5,2,1,8] => [[[[.,[.,.]],[[.,.],.]],.],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2

[4,6,3,8,5,1,7,2] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[4,6,3,8,5,1,2,7] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[5,6,8,3,4,1,2,7] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[5,6,8,3,4,1,7,2] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[4,6,2,7,5,3,1,8] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[5,6,7,2,4,3,1,8] => [[[.,[.,[.,.]]],[[.,.],.]],[.,.]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[5,6,8,4,3,1,7,2] => [[[[.,[.,[.,.]]],.],.],[[.,.],.]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[5,6,8,4,3,1,2,7] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3

[5,7,8,4,1,6,2,3] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[5,7,8,4,1,6,3,2] => [[[.,[.,[.,.]]],.],[[[.,.],.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[5,7,8,4,1,3,6,2] => [[[.,[.,[.,.]]],.],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[5,6,8,4,2,1,7,3] => [[[[.,[.,[.,.]]],.],.],[[.,.],.]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[5,6,8,2,4,1,7,3] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[4,6,2,8,5,1,7,3] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[3,2,6,8,5,1,7,4] => [[[.,.],[[.,[.,.]],.]],[[.,.],.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[3,2,6,8,5,1,4,7] => [[[.,.],[[.,[.,.]],.]],[.,[.,.]]] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[4,6,2,8,5,1,3,7] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[5,6,8,2,4,1,3,7] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[5,6,8,4,2,1,3,7] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3

[5,7,8,4,1,3,2,6] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[5,7,8,4,1,2,6,3] => [[[.,[.,[.,.]]],.],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[5,7,8,4,1,2,3,6] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[6,7,8,1,5,2,3,4] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[6,7,8,1,5,2,4,3] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[6,7,8,1,5,3,2,4] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[6,7,8,1,3,5,2,4] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[5,7,8,2,1,6,3,4] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[4,7,2,8,1,6,3,5] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,2,7,8,1,6,4,5] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,2,7,8,1,6,5,4] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[4,7,2,8,1,6,5,3] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[5,7,8,2,1,6,4,3] => [[[.,[.,[.,.]]],.],[[[.,.],.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[6,7,8,1,3,5,4,2] => [[.,[.,[.,.]]],[[.,[[.,.],.]],.]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[6,7,8,1,5,3,4,2] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[6,7,8,1,5,4,3,2] => [[.,[.,[.,.]]],[[[[.,.],.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[6,7,8,1,5,4,2,3] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[6,7,8,1,4,5,2,3] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[6,7,8,1,4,5,3,2] => [[.,[.,[.,.]]],[[[.,[.,.]],.],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[6,7,8,1,4,3,5,2] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[6,7,8,1,3,4,5,2] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[5,7,8,2,1,4,6,3] => [[[.,[.,[.,.]]],.],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[4,7,2,8,1,5,6,3] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[3,2,7,8,1,5,6,4] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[3,2,6,8,4,1,7,5] => [[[.,.],[[.,[.,.]],.]],[[.,.],.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[4,6,2,8,3,1,7,5] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[5,6,8,3,2,1,7,4] => [[[[.,[.,[.,.]]],.],.],[[.,.],.]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[5,7,8,3,1,4,6,2] => [[[.,[.,[.,.]]],.],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[5,7,8,3,1,6,4,2] => [[[.,[.,[.,.]]],.],[[[.,.],.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[5,7,8,3,1,6,2,4] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[4,7,3,8,1,6,2,5] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,7,3,8,1,6,5,2] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[4,7,3,8,1,5,6,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[4,6,3,8,2,1,7,5] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[4,5,3,2,8,1,7,6] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[4,5,2,3,8,1,7,6] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[4,5,3,2,8,1,6,7] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[4,6,3,8,2,1,5,7] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3

[4,7,3,8,1,5,2,6] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,7,3,8,1,2,6,5] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[4,7,3,8,1,2,5,6] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[5,7,8,3,1,2,4,6] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[5,7,8,3,1,2,6,4] => [[[.,[.,[.,.]]],.],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[5,7,8,3,1,4,2,6] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[5,6,8,3,2,1,4,7] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3

[3,2,7,8,1,5,4,6] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,7,8,2,1,4,3,6] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[6,7,8,1,3,4,2,5] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[6,7,8,1,4,3,2,5] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[6,7,8,1,4,2,5,3] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[6,7,8,1,4,2,3,5] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[6,7,8,1,2,5,3,4] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[6,7,8,1,2,5,4,3] => [[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[6,7,8,1,2,4,5,3] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[6,7,8,1,3,2,5,4] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[5,7,8,2,1,3,6,4] => [[[.,[.,[.,.]]],.],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[3,2,7,8,1,4,6,5] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[6,7,8,1,3,2,4,5] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[6,7,8,1,2,4,3,5] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[6,7,8,1,2,3,5,4] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[2,8,4,5,6,1,7,3] => [[.,[[.,.],[.,[.,.]]]],[[.,.],.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[7,4,8,2,5,6,3,1] => [[[[.,.],[.,.]],[[.,[.,.]],.]],.] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[4,3,7,1,5,6,8,2] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[3,6,1,7,5,2,8,4] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[3,4,1,2,7,6,8,5] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 3

[3,4,2,1,7,5,8,6] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[3,5,2,6,4,8,7,1] => [[[.,[.,.]],[[.,.],[[.,.],.]]],.] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 1

[5,6,1,8,7,2,4,3] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[6,3,5,8,2,7,4,1] => [[[[.,.],[.,[.,.]]],[[.,.],.]],.] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => 1

[6,5,8,4,2,3,7,1] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1

[6,2,5,8,3,7,1,4] => [[[.,.],[[.,[.,.]],[.,.]]],[.,.]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[3,2,4,7,8,6,1,5] => [[[.,.],[.,[[.,[.,.]],.]]],[.,.]] => [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => 2

[5,2,4,7,1,8,3,6] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,3,6,1,4,8,2,7] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[7,3,5,6,8,4,2,1] => [[[[.,.],[[.,[.,[.,.]]],.]],.],.] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => 1

[6,3,5,1,8,2,7,4] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[2,6,1,5,8,4,7,3] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2

[5,7,1,6,3,8,4,2] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2

[3,2,4,1,7,8,5,6] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[5,1,4,7,2,8,6,3] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3

[3,6,4,7,8,2,5,1] => [[[.,[[.,.],[.,[.,.]]]],[.,.]],.] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[3,1,4,6,8,5,7,2] => [[.,.],[[.,[[.,[.,.]],[.,.]]],.]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 2

[6,3,4,5,7,1,8,2] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[7,3,4,1,2,6,5,8] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[6,7,3,2,5,4,8,1] => [[[[.,[.,.]],.],[[.,.],[.,.]]],.] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 1

[7,3,5,1,6,2,4,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[7,3,6,1,5,4,2,8] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[6,5,7,4,3,1,8,2] => [[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[6,3,7,1,5,4,8,2] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[2,3,8,1,5,4,7,6] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[2,5,8,4,3,1,7,6] => [[.,[[[.,[.,.]],.],.]],[[.,.],.]] => [1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 2

[2,6,8,4,3,7,1,5] => [[.,[[[.,[.,.]],.],[.,.]]],[.,.]] => [1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 2

[2,7,8,4,3,6,5,1] => [[.,[[[.,[.,.]],.],[[.,.],.]]],.] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 1

[2,7,8,5,6,3,4,1] => [[.,[[[.,[.,.]],[.,.]],[.,.]]],.] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1

[2,6,8,5,7,3,1,4] => [[.,[[[.,[.,.]],[.,.]],.]],[.,.]] => [1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2

[5,3,7,1,6,8,4,2] => [[[.,.],[.,.]],[[[.,[.,.]],.],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[4,6,7,5,8,3,1,2] => [[[.,[[.,[.,.]],[.,.]]],.],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 2

[4,7,5,6,8,2,3,1] => [[[.,[[.,.],[.,[.,.]]]],[.,.]],.] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[4,6,5,7,8,2,1,3] => [[[.,[[.,.],[.,[.,.]]]],.],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2

[5,4,6,7,1,8,2,3] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,3,6,1,7,8,2,4] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[6,3,5,1,7,2,8,4] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[6,4,5,7,1,2,8,3] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[5,6,4,7,2,8,1,3] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,7,3,2,6,8,4,1] => [[[[.,[.,.]],.],[[.,[.,.]],.]],.] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 1

[5,6,3,2,7,8,1,4] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[5,3,4,1,2,8,7,6] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[4,6,3,2,8,7,1,5] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[4,7,3,2,8,6,5,1] => [[[[.,[.,.]],.],[[[.,.],.],.]],.] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 1

[3,4,5,8,1,2,7,6] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[4,3,5,1,8,2,7,6] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[4,3,6,1,8,7,2,5] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[3,4,6,8,1,7,2,5] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,6,7,8,5,4,1,2] => [[.,[[[.,[.,[.,.]]],.],.]],[.,.]] => [1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 2

[3,5,7,8,6,1,4,2] => [[.,[.,[[.,[.,.]],.]]],[[.,.],.]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 2

[3,4,7,8,1,6,5,2] => [[.,[.,[.,[.,.]]]],[[[.,.],.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[2,3,8,1,7,6,5,4] => [[.,[.,[.,.]]],[[[[.,.],.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[7,4,6,1,8,3,5,2] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[8,3,5,1,7,4,6,2] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[8,3,4,1,7,5,6,2] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[4,8,3,1,7,5,6,2] => [[[.,[.,.]],.],[[[.,.],[.,.]],.]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[4,6,2,1,7,5,8,3] => [[[.,[.,.]],.],[[[.,.],[.,.]],.]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[1,4,6,2,7,5,8,3] => [.,[[.,[.,.]],[[[.,.],[.,.]],.]]] => [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 3

[6,8,4,3,1,7,5,2] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2

[3,6,8,4,1,7,5,2] => [[.,[[.,[.,.]],.]],[[[.,.],.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2

[3,6,7,5,1,8,4,2] => [[.,[[.,[.,.]],.]],[[[.,.],.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2

[7,5,6,1,8,3,4,2] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[6,7,5,1,8,4,3,2] => [[[.,[.,.]],.],[[[[.,.],.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2

[6,8,4,1,7,5,3,2] => [[[.,[.,.]],.],[[[[.,.],.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2

[6,7,5,3,1,8,4,2] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2

[2,4,6,1,7,5,8,3] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[4,7,1,6,5,8,2,3] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[4,8,2,6,5,7,1,3] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[4,6,1,2,7,5,8,3] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 3

[3,5,1,2,7,6,8,4] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 3

[6,7,1,5,8,2,3,4] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[2,3,5,1,7,6,8,4] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[3,6,7,1,5,8,2,4] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[5,2,3,1,7,6,8,4] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[3,5,2,1,7,6,8,4] => [[[.,[.,.]],.],[[[.,.],[.,.]],.]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[1,3,5,2,7,6,8,4] => [.,[[.,[.,.]],[[[.,.],[.,.]],.]]] => [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 3

[6,2,4,1,7,5,8,3] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[6,2,5,1,7,4,8,3] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[3,6,8,2,5,7,1,4] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[2,4,1,3,7,6,8,5] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 3

[2,5,1,3,7,6,8,4] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 3

[6,8,2,3,5,7,1,4] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[6,7,1,3,5,8,2,4] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[8,1,3,5,6,2,7,4] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[8,1,3,4,2,6,7,5] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3

[2,7,8,3,4,5,6,1] => [[.,[[.,[.,.]],[.,[.,[.,.]]]]],.] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1

[4,7,8,5,6,1,2,3] => [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[3,7,8,5,6,2,1,4] => [[[.,[[.,[.,.]],[.,.]]],.],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 2

[3,7,8,4,2,6,1,5] => [[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => [1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[3,7,8,2,4,5,1,6] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[3,6,2,8,4,5,1,7] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[2,3,6,7,4,5,8,1] => [[.,[.,[[.,[.,.]],[.,[.,.]]]]],.] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1

[3,5,2,4,8,6,1,7] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[6,4,5,1,7,8,2,3] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[6,2,4,1,3,7,5,8] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[6,2,5,1,7,3,4,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[2,5,6,7,8,3,4,1] => [[.,[[.,[.,[.,[.,.]]]],[.,.]]],.] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1

[2,4,6,7,3,8,5,1] => [[.,[[.,[.,[.,.]]],[[.,.],.]]],.] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1

[4,2,6,7,3,1,5,8] => [[[.,.],[[.,[.,.]],.]],[.,[.,.]]] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[4,7,8,2,3,1,5,6] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[4,7,8,3,2,1,6,5] => [[[[.,[.,[.,.]]],.],.],[[.,.],.]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[5,6,4,8,1,7,2,3] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,6,3,8,1,2,7,4] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[4,3,6,7,2,1,8,5] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[3,4,6,7,2,8,1,5] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[3,4,5,2,7,8,1,6] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[3,4,2,5,6,8,1,7] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[5,2,7,8,6,4,1,3] => [[[.,.],[[[.,[.,.]],.],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => 2

[5,1,2,7,8,6,4,3] => [[.,.],[.,[[[[.,[.,.]],.],.],.]]] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 3

[4,7,1,8,6,5,2,3] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[4,7,1,2,8,6,5,3] => [[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 3

[4,6,8,1,2,7,5,3] => [[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[7,8,1,6,3,5,2,4] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[7,8,1,3,6,5,2,4] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3

[7,8,3,6,5,2,1,4] => [[[[.,[.,.]],[[.,.],.]],.],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2

[4,7,2,8,6,1,5,3] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[4,2,7,1,8,6,5,3] => [[[.,.],[.,.]],[[[[.,.],.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[7,8,2,3,6,5,1,4] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[8,5,7,1,6,2,3,4] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[8,5,7,1,2,6,3,4] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[6,8,2,7,1,3,5,4] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[1,6,8,3,7,4,5,2] => [.,[[[.,[.,.]],[[.,.],[.,.]]],.]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 2

[1,6,8,3,4,7,5,2] => [.,[[[.,[.,.]],[.,[[.,.],.]]],.]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 2

[6,2,4,8,1,7,5,3] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[6,8,2,1,7,3,5,4] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[8,5,7,2,1,6,3,4] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[8,5,7,1,2,3,6,4] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[8,5,7,2,3,1,6,4] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[5,8,4,2,7,1,6,3] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[5,8,4,7,2,1,6,3] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[1,6,8,4,3,7,5,2] => [.,[[[[.,[.,.]],.],[[.,.],.]],.]] => [1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 2

[6,8,1,7,3,2,5,4] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[8,5,7,3,1,6,2,4] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[8,5,7,1,3,2,6,4] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[8,5,7,3,1,2,6,4] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[5,8,4,7,1,2,6,3] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[5,8,4,1,7,2,6,3] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[5,8,4,7,1,6,2,3] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[8,2,5,6,7,4,1,3] => [[[.,.],[[.,[.,[.,.]]],.]],[.,.]] => [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => 2

[6,8,1,3,7,2,5,4] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[4,6,2,8,1,7,5,3] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[8,2,4,5,7,1,6,3] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[7,3,5,1,8,4,6,2] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[7,3,4,1,8,5,6,2] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[4,5,6,2,1,8,7,3] => [[[.,[.,[.,.]]],.],[[[.,.],.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[4,5,7,1,6,8,2,3] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[6,1,2,5,8,3,4,7] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 5

[7,1,3,4,8,2,5,6] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[7,1,5,6,8,2,3,4] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[2,6,1,5,7,8,3,4] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[5,2,3,1,8,6,7,4] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[3,5,2,1,6,8,7,4] => [[[.,[.,.]],.],[[.,[[.,.],.]],.]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 2

[6,2,4,1,8,5,7,3] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[6,2,5,1,8,4,7,3] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[3,6,7,1,4,8,2,5] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[2,6,1,4,7,8,3,5] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[7,1,4,6,8,2,3,5] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[7,1,3,5,8,2,4,6] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[6,1,2,4,8,3,5,7] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 5

[5,2,3,1,6,4,8,7] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[7,4,5,2,3,1,8,6] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[8,6,7,3,5,2,4,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[7,3,5,2,4,1,8,6] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[6,3,5,2,4,1,8,7] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[5,2,4,1,6,3,8,7] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[6,3,4,1,5,2,8,7] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[7,3,4,1,5,2,8,6] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[8,6,7,3,4,1,5,2] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[8,5,7,3,4,1,6,2] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[8,5,6,2,7,3,4,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[8,4,7,3,5,1,6,2] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[8,4,7,3,6,2,5,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[7,3,6,2,5,1,8,4] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[6,2,5,1,7,3,8,4] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[5,2,4,1,7,3,8,6] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[6,2,4,1,7,3,8,5] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[8,5,7,3,6,2,4,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[8,5,7,4,6,2,3,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[7,4,6,2,3,1,8,5] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[6,2,3,1,7,4,8,5] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[5,2,3,1,7,4,8,6] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[4,2,3,1,7,5,8,6] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[6,2,3,1,8,5,7,4] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[8,5,6,2,3,1,7,4] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[8,5,6,2,4,1,7,3] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[5,2,4,1,8,6,7,3] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[8,4,6,2,5,1,7,3] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[8,4,5,1,6,2,7,3] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[8,4,5,1,7,3,6,2] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[7,3,6,2,8,4,5,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[7,8,5,6,1,3,4,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[3,6,1,4,7,2,5,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[4,6,1,2,5,7,3,8] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4

[1,4,8,2,5,7,3,6] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 4

[7,8,2,4,5,6,1,3] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[7,8,1,5,4,6,3,2] => [[.,[.,.]],[[[[.,.],[.,.]],.],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 2

[7,8,2,1,6,3,4,5] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[7,8,4,5,3,1,6,2] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[1,5,8,4,3,2,7,6] => [.,[[[[.,[.,.]],.],.],[[.,.],.]]] => [1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 3

[5,6,1,4,3,2,7,8] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[1,4,6,8,3,7,5,2] => [.,[[[.,[.,[.,.]]],[[.,.],.]],.]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2

[2,5,8,1,4,7,6,3] => [[.,[.,[.,.]]],[[.,[[.,.],.]],.]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[3,5,8,4,7,6,1,2] => [[.,[[.,[.,.]],[[.,.],.]]],[.,.]] => [1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2

[5,6,2,1,4,7,8,3] => [[[.,[.,.]],.],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 2

[4,6,2,5,3,1,8,7] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[5,7,3,6,1,4,8,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[5,3,6,7,2,1,8,4] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[1,4,7,2,5,3,8,6] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 4

[1,6,7,5,8,2,4,3] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 3

[3,5,6,7,8,1,4,2] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[3,6,5,7,8,2,1,4] => [[[.,[[.,.],[.,[.,.]]]],.],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2

[2,1,6,8,4,5,3,7] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[2,7,1,8,5,3,4,6] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[4,3,7,8,1,2,6,5] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[5,7,8,6,3,2,1,4] => [[[[.,[[.,[.,.]],.]],.],.],[.,.]] => [1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 2

[5,7,8,6,1,3,4,2] => [[.,[[.,[.,.]],.]],[[.,[.,.]],.]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 2

[7,1,3,4,8,2,6,5] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[2,6,3,4,5,8,1,7] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[5,6,2,7,3,1,4,8] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[6,7,1,5,2,8,3,4] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[6,7,5,3,8,4,1,2] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[7,4,6,1,2,5,3,8] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[6,8,1,3,7,5,4,2] => [[.,[.,.]],[[.,[[[.,.],.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 2

[7,4,6,3,1,5,2,8] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[6,8,1,2,3,4,7,5] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 5

[5,8,2,3,7,6,4,1] => [[[.,[.,.]],[.,[[[.,.],.],.]]],.] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 1

[2,1,4,7,8,5,6,3] => [[.,.],[[.,[[.,[.,.]],[.,.]]],.]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 2

[2,5,7,8,1,4,6,3] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[3,5,7,4,1,6,2,8] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[5,8,4,7,6,2,1,3] => [[[[.,[.,.]],[[.,.],.]],.],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2

[6,4,8,3,1,7,2,5] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[5,8,3,7,1,6,4,2] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[6,4,8,1,2,7,3,5] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[6,8,5,1,2,3,7,4] => [[[.,[.,.]],.],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 4

[6,8,5,2,4,3,7,1] => [[[[.,[.,.]],.],[[.,.],[.,.]]],.] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 1

[6,8,5,3,1,2,7,4] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 3

[4,5,1,2,7,6,3,8] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 4

[4,5,1,2,6,8,7,3] => [[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 3

[3,5,6,1,8,4,7,2] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[3,5,7,1,2,8,6,4] => [[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[3,6,2,7,5,1,4,8] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[4,2,6,1,7,3,5,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[4,5,3,1,7,6,2,8] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[3,5,2,7,8,1,6,4] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[3,4,6,8,5,2,7,1] => [[[.,[.,[[.,[.,.]],.]]],[.,.]],.] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[4,2,5,6,1,8,7,3] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[4,5,3,1,6,8,7,2] => [[[.,[.,.]],.],[[.,[[.,.],.]],.]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 2

[3,1,2,6,8,5,4,7] => [[.,.],[.,[[[.,[.,.]],.],[.,.]]]] => [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => 4

[3,7,1,2,5,4,8,6] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4

[1,3,7,2,4,8,6,5] => [.,[[.,[.,.]],[.,[[[.,.],.],.]]]] => [1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 4

[2,4,1,7,8,6,5,3] => [[.,[.,.]],[[[[.,[.,.]],.],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 2

[2,3,7,1,5,8,6,4] => [[.,[.,[.,.]]],[[.,[[.,.],.]],.]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[5,2,8,1,3,7,4,6] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[2,1,6,8,3,4,7,5] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[2,6,8,3,1,5,7,4] => [[.,[[.,[.,.]],.]],[[.,[.,.]],.]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 2

[4,7,2,3,6,8,1,5] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[5,7,4,6,2,8,1,3] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,7,3,4,6,1,8,2] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[8,2,3,5,1,6,7,4] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[2,4,8,1,7,3,5,6] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[4,8,3,1,7,2,5,6] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[5,8,4,7,3,1,6,2] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[4,6,8,3,1,7,5,2] => [[[.,[.,[.,.]]],.],[[[.,.],.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[6,3,8,2,7,1,5,4] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[5,3,8,1,2,6,4,7] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[5,7,4,1,6,2,3,8] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[6,8,5,3,1,7,4,2] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2

[8,4,5,1,2,6,3,7] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[5,6,3,7,1,2,4,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[4,5,7,8,3,1,6,2] => [[[.,[.,[.,[.,.]]]],.],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[4,7,2,5,8,1,6,3] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[8,1,3,4,6,2,5,7] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[3,8,2,4,6,7,1,5] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[3,5,6,8,2,7,1,4] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[2,4,5,6,8,1,7,3] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[4,8,3,5,6,1,7,2] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[5,6,2,3,7,8,1,4] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[6,8,4,7,1,5,3,2] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[6,8,4,7,2,5,3,1] => [[[[.,[.,.]],[.,.]],[[.,.],.]],.] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 1

[4,8,3,7,5,1,2,6] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[3,5,8,2,7,6,4,1] => [[[.,[.,[.,.]]],[[[.,.],.],.]],.] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1

[3,5,8,1,7,6,4,2] => [[.,[.,[.,.]]],[[[[.,.],.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[2,5,8,1,7,6,4,3] => [[.,[.,[.,.]]],[[[[.,.],.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[8,2,4,6,1,5,3,7] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[8,1,4,6,2,5,3,7] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[1,5,8,2,7,6,4,3] => [.,[[.,[.,.]],[[[[.,.],.],.],.]]] => [1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 3

[2,5,8,3,7,6,4,1] => [[.,[[.,[.,.]],[[[.,.],.],.]]],.] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 1

[1,3,8,2,7,6,4,5] => [.,[[.,[.,.]],[[[.,.],.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 4

[8,2,3,1,6,5,4,7] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[2,3,8,1,7,6,4,5] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[3,4,1,8,7,6,5,2] => [[.,[.,.]],[[[[[.,.],.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2

[3,8,2,1,7,5,4,6] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[5,2,8,1,7,6,4,3] => [[[.,.],[.,.]],[[[[.,.],.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[5,3,8,1,7,6,4,2] => [[[.,.],[.,.]],[[[[.,.],.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[5,3,8,2,7,6,4,1] => [[[[.,.],[.,.]],[[[.,.],.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1

[6,8,3,2,7,5,4,1] => [[[[.,[.,.]],.],[[[.,.],.],.]],.] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 1

[6,8,3,1,7,5,4,2] => [[[.,[.,.]],.],[[[[.,.],.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2

[6,8,2,1,7,5,4,3] => [[[.,[.,.]],.],[[[[.,.],.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2

[6,8,2,7,1,5,3,4] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[8,5,6,1,2,4,3,7] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[6,8,1,2,7,5,4,3] => [[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 3

[6,8,2,3,7,5,4,1] => [[[.,[.,.]],[.,[[[.,.],.],.]]],.] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 1

[4,8,1,7,2,5,3,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[3,8,1,2,7,5,4,6] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 4

[2,8,1,3,7,5,4,6] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 4

[3,5,1,8,2,4,7,6] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[1,4,5,2,8,3,7,6] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 4

[7,1,3,5,2,8,4,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[7,2,5,1,8,3,4,6] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[1,4,5,2,8,7,3,6] => [.,[[.,[.,.]],[[[.,.],.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 4

[1,5,7,4,2,8,3,6] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 4

[4,3,7,1,8,2,5,6] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[5,7,8,6,2,4,1,3] => [[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => [1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[5,7,1,6,2,4,3,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[8,1,4,5,3,7,6,2] => [[.,.],[[[.,[.,.]],[[.,.],.]],.]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2

[6,1,4,5,3,8,7,2] => [[.,.],[[[.,[.,.]],[[.,.],.]],.]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2

[6,1,4,5,3,7,8,2] => [[.,.],[[[.,[.,.]],[.,[.,.]]],.]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[5,1,7,8,6,2,4,3] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3

[6,1,4,8,3,5,7,2] => [[.,.],[[[.,[.,.]],[.,[.,.]]],.]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[7,1,4,5,3,8,6,2] => [[.,.],[[[.,[.,.]],[[.,.],.]],.]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2

[7,1,4,5,3,6,8,2] => [[.,.],[[[.,[.,.]],[.,[.,.]]],.]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[8,1,4,5,3,6,7,2] => [[.,.],[[[.,[.,.]],[.,[.,.]]],.]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[6,3,5,7,2,1,4,8] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[6,3,5,8,2,1,7,4] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[6,3,5,7,2,1,8,4] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[8,4,5,7,3,6,1,2] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,4,5,8,3,7,2,1] => [[[[[.,.],[.,[.,.]]],[.,.]],.],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1

[5,8,1,6,2,4,3,7] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[6,3,5,8,2,1,4,7] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[2,3,4,1,8,6,5,7] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[8,3,5,6,2,1,4,7] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[8,3,5,7,2,1,6,4] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[7,4,5,6,3,1,8,2] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[8,4,5,6,3,1,7,2] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[7,3,5,6,2,8,1,4] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[7,3,5,8,2,1,6,4] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[7,3,5,6,2,1,4,8] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[2,6,1,3,8,5,7,4] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 3

[2,7,1,3,6,5,8,4] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 3

[7,3,5,1,2,8,4,6] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[7,8,1,6,3,4,2,5] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[8,3,5,7,2,4,1,6] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[2,3,4,1,8,7,5,6] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[2,3,8,1,6,4,7,5] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[2,3,8,1,4,5,7,6] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[8,5,6,3,4,1,7,2] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[7,8,5,4,1,3,6,2] => [[[[.,[.,.]],.],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 2

[6,8,5,4,2,1,7,3] => [[[[[.,[.,.]],.],.],.],[[.,.],.]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2

[4,8,2,6,5,1,7,3] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[4,1,3,8,2,7,5,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[4,8,2,7,1,6,5,3] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[7,8,6,1,5,3,4,2] => [[[.,[.,.]],.],[[[.,.],[.,.]],.]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[1,7,8,2,5,6,3,4] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 4

[8,6,7,1,4,5,3,2] => [[[.,.],[.,.]],[[[.,[.,.]],.],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[7,6,8,1,4,3,5,2] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[6,5,8,3,2,1,7,4] => [[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[7,5,8,3,1,4,6,2] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[8,5,7,3,1,6,4,2] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[1,6,8,4,2,7,3,5] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 4

[5,6,1,3,4,2,7,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[4,6,2,1,5,3,7,8] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[3,2,6,1,5,4,7,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[3,2,7,1,4,6,5,8] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[4,7,2,1,3,6,5,8] => [[[.,[.,.]],.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[5,7,1,3,2,6,4,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[6,7,1,2,4,5,3,8] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4

[7,8,1,2,3,5,6,4] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 4

[6,8,1,2,4,3,7,5] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4

[5,8,1,3,2,4,7,6] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[4,8,2,1,3,5,7,6] => [[[.,[.,.]],.],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 4

[3,2,8,1,4,5,7,6] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[6,7,3,8,5,1,2,4] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[6,7,4,5,1,8,3,2] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[5,3,7,8,6,1,2,4] => [[[.,.],[[.,[.,.]],.]],[.,[.,.]]] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[3,8,4,5,7,1,2,6] => [[.,[[.,.],[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[4,5,6,7,1,8,3,2] => [[.,[.,[.,[.,.]]]],[[[.,.],.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[3,5,6,2,7,4,8,1] => [[[.,[.,[.,.]]],[[.,.],[.,.]]],.] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[3,5,6,1,7,8,4,2] => [[.,[.,[.,.]]],[[[.,[.,.]],.],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[2,5,6,1,8,7,4,3] => [[.,[.,[.,.]]],[[[[.,.],.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[2,5,6,8,1,7,3,4] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[8,2,4,5,1,6,3,7] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[1,5,6,8,2,3,7,4] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[1,5,6,2,8,4,7,3] => [.,[[.,[.,.]],[[[.,.],[.,.]],.]]] => [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 3

[2,5,6,3,4,7,8,1] => [[.,[[.,[.,.]],[.,[.,[.,.]]]]],.] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1

[8,2,3,1,5,6,4,7] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[2,4,1,6,8,7,5,3] => [[.,[.,.]],[[[.,[[.,.],.]],.],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 2

[3,4,1,6,7,8,5,2] => [[.,[.,.]],[[[.,[.,[.,.]]],.],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2

[5,2,7,8,1,6,3,4] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,3,7,2,6,4,8,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[6,7,3,1,5,8,4,2] => [[[.,[.,.]],.],[[[.,[.,.]],.],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 2

[6,7,2,1,8,5,4,3] => [[[.,[.,.]],.],[[[[.,.],.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2

[6,7,2,8,1,5,3,4] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,7,8,2,1,4,3,5] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[6,7,1,2,8,4,5,3] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 3

[6,7,1,3,4,8,5,2] => [[.,[.,.]],[[.,[.,[[.,.],.]]],.]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 2

[5,1,7,8,2,3,6,4] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[3,8,1,2,7,4,5,6] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5

[3,1,4,5,7,8,6,2] => [[.,.],[[.,[.,[[.,[.,.]],.]]],.]] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[5,2,6,1,4,8,7,3] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[5,7,2,3,8,6,1,4] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[5,7,2,3,8,1,6,4] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[5,6,2,3,1,8,7,4] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[5,6,2,1,3,8,7,4] => [[[.,[.,.]],.],[.,[[[.,.],.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 3

[5,6,1,3,2,8,7,4] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[5,6,3,1,2,8,7,4] => [[[.,[.,.]],.],[.,[[[.,.],.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 3

[5,6,3,2,1,8,7,4] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2

[5,7,3,2,8,1,6,4] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[5,7,3,2,8,6,1,4] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[6,7,3,8,2,1,5,4] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[6,7,3,8,1,2,5,4] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[5,7,3,1,8,2,6,4] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[5,7,1,3,8,2,6,4] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[1,5,7,4,8,3,6,2] => [.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 2

[1,5,7,4,8,6,3,2] => [.,[[[[.,[.,.]],[[.,.],.]],.],.]] => [1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 2

[5,7,1,3,8,6,2,4] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3

[5,7,3,1,8,6,2,4] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[6,7,3,8,1,5,2,4] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,7,3,8,5,2,1,4] => [[[[.,[.,.]],[[.,.],.]],.],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2

[6,7,8,3,1,4,2,5] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[6,7,1,8,3,5,2,4] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[6,1,7,8,4,5,2,3] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[1,6,7,8,4,5,3,2] => [.,[[[[.,[.,[.,.]]],[.,.]],.],.]] => [1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[1,6,7,8,4,3,5,2] => [.,[[[[.,[.,[.,.]]],.],[.,.]],.]] => [1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 2

[6,1,7,8,4,2,5,3] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3

[6,7,1,8,3,2,5,4] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[5,7,2,1,8,3,6,4] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[6,7,2,8,1,3,5,4] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[6,7,2,8,3,1,5,4] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[6,7,2,8,3,5,1,4] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[6,2,7,8,4,5,1,3] => [[[.,.],[[.,[.,.]],[.,.]]],[.,.]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[6,2,7,8,4,1,5,3] => [[[.,.],[[.,[.,.]],.]],[[.,.],.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[6,2,7,8,1,4,5,3] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[5,2,7,1,8,4,6,3] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[4,1,2,7,8,6,5,3] => [[.,.],[.,[[[[.,[.,.]],.],.],.]]] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 3

[6,2,7,8,1,5,4,3] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[6,2,7,8,5,1,4,3] => [[[.,.],[[.,[.,.]],.]],[[.,.],.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[6,2,7,8,5,4,1,3] => [[[.,.],[[[.,[.,.]],.],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => 2

[6,7,2,8,5,3,1,4] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[5,7,2,1,8,6,3,4] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[5,7,1,2,8,6,3,4] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 4

[1,5,7,3,8,6,4,2] => [.,[[[.,[.,.]],[[[.,.],.],.]],.]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 2

[1,6,7,8,3,5,4,2] => [.,[[[.,[.,[.,.]]],[[.,.],.]],.]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2

[6,1,7,8,2,5,4,3] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3

[6,7,1,8,2,5,3,4] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[6,7,8,2,4,1,3,5] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[6,7,8,2,4,3,1,5] => [[[.,[.,[.,.]]],[[.,.],.]],[.,.]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[6,7,1,8,5,2,3,4] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[6,1,7,8,5,2,4,3] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3

[1,6,7,8,5,3,4,2] => [.,[[[[.,[.,[.,.]]],.],[.,.]],.]] => [1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 2

[6,1,7,8,5,4,2,3] => [[.,.],[[[[.,[.,.]],.],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => 3

[6,7,1,8,5,3,2,4] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[6,7,8,4,1,3,2,5] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[5,6,1,4,8,7,3,2] => [[.,[.,.]],[[[.,[[.,.],.]],.],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 2

[3,4,7,1,8,6,5,2] => [[.,[.,[.,.]]],[[[[.,.],.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[5,3,7,1,6,8,2,4] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[4,6,1,2,7,8,5,3] => [[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 3

[5,7,1,4,8,3,2,6] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[7,8,3,5,1,4,6,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[5,8,1,4,6,7,2,3] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[6,5,8,4,3,7,2,1] => [[[[[[.,.],[.,.]],.],[.,.]],.],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1

[8,3,6,1,2,5,7,4] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[5,6,1,8,7,3,2,4] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[6,5,8,4,2,7,3,1] => [[[[[.,.],[.,.]],.],[[.,.],.]],.] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1

[5,8,2,6,4,7,3,1] => [[[.,[.,.]],[[[.,.],[.,.]],.]],.] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 1

[7,8,5,3,2,6,4,1] => [[[[[.,[.,.]],.],.],[[.,.],.]],.] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 1

[6,8,3,1,7,2,5,4] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[7,8,1,6,3,2,5,4] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[2,8,1,7,3,5,6,4] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[4,8,1,3,7,2,6,5] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[6,7,3,1,8,4,2,5] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[8,2,6,1,7,3,5,4] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[4,7,5,6,8,3,2,1] => [[[[.,[[.,.],[.,[.,.]]]],.],.],.] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1

[5,4,8,1,7,2,6,3] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[3,6,8,2,4,7,5,1] => [[[.,[.,[.,.]]],[.,[[.,.],.]]],.] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[5,7,3,8,2,6,4,1] => [[[[.,[.,.]],[.,.]],[[.,.],.]],.] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 1

[4,7,2,8,6,3,5,1] => [[[.,[.,.]],[[[.,.],.],[.,.]]],.] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 1

[7,8,3,6,4,5,1,2] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[6,8,3,7,4,5,1,2] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[5,8,3,7,4,6,1,2] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[4,7,3,8,5,6,1,2] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[4,7,2,8,5,6,1,3] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[4,7,1,8,5,6,2,3] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[3,7,1,8,5,6,2,4] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[3,7,2,8,5,6,1,4] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[5,8,2,7,4,6,1,3] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[6,8,2,7,4,5,1,3] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[7,8,2,6,4,5,1,3] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[7,8,1,6,4,5,2,3] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[6,8,1,7,4,5,2,3] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[5,8,1,7,4,6,2,3] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[4,8,1,7,3,6,2,5] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[5,8,1,7,3,6,2,4] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[6,8,1,7,3,5,2,4] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[7,8,2,6,3,5,1,4] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[6,8,2,7,3,5,1,4] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[5,8,2,7,3,6,1,4] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[4,8,2,7,3,6,1,5] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[3,7,2,8,4,6,1,5] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[3,7,1,8,4,6,2,5] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[6,8,5,7,1,4,2,3] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,5,1,8,6,7,3,4] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[2,6,1,8,5,7,3,4] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[6,8,4,7,1,5,2,3] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[7,8,4,6,1,5,2,3] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[7,8,3,6,1,5,2,4] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,8,3,7,1,5,2,4] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,8,3,7,1,6,2,5] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,6,1,8,4,7,3,5] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[3,7,2,6,1,8,4,5] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,7,1,6,2,8,4,5] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[4,8,1,6,2,7,3,5] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[5,8,1,6,2,7,3,4] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[7,8,1,5,2,6,3,4] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[7,8,2,5,1,6,3,4] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,8,2,5,1,7,3,4] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,8,2,6,1,7,3,4] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,8,2,6,1,7,3,5] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,7,4,8,3,5,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,7,4,5,2,8,1,3] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,7,4,6,2,3,1,8] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,7,4,6,3,8,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,7,4,8,3,6,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,8,4,5,3,7,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,8,4,6,3,7,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,6,4,8,3,7,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,6,3,7,2,4,1,8] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,6,3,7,2,8,1,4] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,6,3,8,2,7,1,4] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,6,4,8,2,7,1,3] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,8,4,6,2,7,1,3] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,8,4,5,2,7,1,3] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[7,8,4,5,2,6,1,3] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,8,4,5,2,3,1,7] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,8,4,6,2,3,1,7] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,6,4,8,2,3,1,7] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,6,3,8,2,4,1,7] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,6,3,4,2,8,1,7] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[4,6,3,5,2,7,1,8] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[4,6,3,5,2,8,1,7] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[4,6,3,8,2,5,1,7] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[4,8,3,6,2,5,1,7] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,8,3,6,2,4,1,7] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,8,3,5,2,4,1,7] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[7,8,3,5,2,4,1,6] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[7,8,3,5,2,6,1,4] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,8,3,6,2,7,1,4] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[4,8,3,6,2,7,1,5] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[4,6,3,8,2,7,1,5] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[4,6,3,7,2,8,1,5] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[4,7,3,6,2,5,1,8] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[4,7,3,6,2,8,1,5] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[4,7,3,8,2,6,1,5] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,7,4,8,2,6,1,3] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,7,3,6,2,8,1,4] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,7,3,6,2,4,1,8] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,7,3,5,2,4,1,8] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,7,3,5,2,8,1,4] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,7,4,8,2,5,1,3] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,7,5,8,2,4,1,3] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,8,5,7,2,3,1,4] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,7,4,8,2,3,1,5] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,7,3,8,2,4,1,5] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,7,3,4,2,8,1,5] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,7,3,4,2,6,1,8] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,7,3,4,2,8,1,6] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,7,4,8,2,3,1,6] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,8,4,7,2,3,1,6] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,8,4,7,2,3,1,5] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[7,8,4,6,2,3,1,5] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[7,8,3,6,2,4,1,5] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,8,3,7,2,4,1,5] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,8,3,7,2,4,1,6] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[4,8,3,7,2,5,1,6] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[4,7,3,8,2,5,1,6] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[4,7,3,5,2,8,1,6] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[4,7,3,5,2,6,1,8] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[4,5,3,7,2,6,1,8] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[4,5,3,7,2,8,1,6] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[4,5,3,8,2,7,1,6] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[4,8,3,5,2,7,1,6] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,8,3,4,2,7,1,6] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,8,3,4,2,7,1,5] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[7,8,3,4,2,6,1,5] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,8,3,4,2,5,1,7] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,8,3,4,2,6,1,7] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[4,8,3,5,2,6,1,7] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[4,5,3,8,2,6,1,7] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[4,5,3,6,2,8,1,7] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,6,4,2,3,1,8,7] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[6,4,5,3,1,2,8,7] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[5,4,6,1,3,2,8,7] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[4,6,8,1,7,3,2,5] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[4,7,8,1,6,3,5,2] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[7,4,8,1,6,5,3,2] => [[[.,.],[.,.]],[[[[.,.],.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[5,4,8,1,3,7,6,2] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[8,4,5,3,1,7,6,2] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[5,4,7,1,3,8,2,6] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[6,4,8,1,7,5,2,3] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[8,4,6,3,7,2,1,5] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[2,1,7,8,6,4,5,3] => [[.,.],[[[[.,[.,.]],.],[.,.]],.]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 2

[7,6,8,5,2,4,3,1] => [[[[[.,.],[.,.]],.],[[.,.],.]],.] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1

[5,7,8,6,2,3,1,4] => [[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => [1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[5,8,4,2,3,7,6,1] => [[[[.,[.,.]],.],[.,[[.,.],.]]],.] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 1

[7,8,4,2,6,5,3,1] => [[[[.,[.,.]],.],[[[.,.],.],.]],.] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 1

[3,6,1,8,7,4,2,5] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[3,7,1,8,6,4,5,2] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2

[3,8,1,6,7,5,2,4] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[3,7,1,6,8,2,5,4] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[6,7,4,2,8,1,5,3] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[6,8,4,2,7,5,1,3] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[6,7,5,8,1,3,4,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[7,5,6,8,1,4,2,3] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,5,7,8,1,2,4,3] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[8,1,3,4,5,6,7,2] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2

[8,4,7,2,5,6,1,3] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[6,5,8,2,4,7,3,1] => [[[[.,.],[.,.]],[[.,[.,.]],.]],.] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[5,6,2,1,4,8,3,7] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[3,6,1,8,5,2,4,7] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[3,4,1,2,8,6,5,7] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 4

[5,8,1,6,3,2,4,7] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[3,8,2,6,1,5,7,4] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[8,5,6,4,2,1,7,3] => [[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[7,2,5,8,3,1,6,4] => [[[.,.],[[.,[.,.]],.]],[[.,.],.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[1,5,7,3,2,4,6,8] => [.,[[[.,[.,.]],.],[.,[.,[.,.]]]]] => [1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 5

[5,8,2,4,1,3,7,6] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[4,8,1,6,3,2,7,5] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[8,1,6,7,4,3,2,5] => [[.,.],[[[[.,[.,.]],.],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => 3

[2,4,1,3,8,7,5,6] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 4

[2,5,8,3,1,7,4,6] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[2,8,1,3,6,4,7,5] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4

[6,8,2,3,4,1,5,7] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[4,2,5,7,8,6,1,3] => [[[.,.],[.,[[.,[.,.]],.]]],[.,.]] => [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => 2

[7,2,3,1,8,5,6,4] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[8,2,5,1,7,3,4,6] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[7,8,2,1,4,3,5,6] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[5,7,2,3,1,6,8,4] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[6,8,4,1,3,2,5,7] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[5,3,8,1,2,7,4,6] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[5,7,3,1,2,6,4,8] => [[[.,[.,.]],.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[1,5,8,2,4,6,3,7] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 4

[1,5,8,4,2,7,3,6] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 4

[1,4,6,2,8,3,7,5] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 4

[5,3,6,1,2,8,4,7] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[6,3,4,1,2,5,8,7] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[4,5,2,6,8,1,7,3] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[4,2,5,6,7,8,1,3] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2

[5,2,3,6,7,1,8,4] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[6,2,3,4,1,7,8,5] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[7,2,3,1,4,5,8,6] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[8,1,2,5,6,4,3,7] => [[.,.],[.,[[[.,[.,.]],.],[.,.]]]] => [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => 4

[5,1,4,8,2,7,3,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[1,4,6,8,2,7,3,5] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[5,1,4,7,2,8,3,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[5,7,2,8,1,3,4,6] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[4,1,5,8,2,7,3,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[1,4,6,2,8,7,3,5] => [.,[[.,[.,.]],[[[.,.],.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 4

[1,4,7,2,6,8,3,5] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 4

[1,2,3,6,8,5,7,4] => [.,[.,[.,[[[.,[.,.]],[.,.]],.]]]] => [1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 4

[5,3,7,1,8,2,4,6] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[3,1,7,8,2,6,4,5] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[5,2,8,1,3,4,7,6] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[1,2,3,7,8,5,6,4] => [.,[.,[.,[[[.,[.,.]],[.,.]],.]]]] => [1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 4

[2,1,7,8,3,4,6,5] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[4,7,8,5,6,2,1,3] => [[[.,[[.,[.,.]],[.,.]]],.],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 2

[5,7,8,4,2,6,1,3] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[6,7,8,3,2,1,5,4] => [[[[.,[.,[.,.]]],.],.],[[.,.],.]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[4,7,8,3,2,1,5,6] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3

[5,7,8,3,2,1,4,6] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3

[5,6,3,4,1,2,8,7] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[8,5,7,4,2,6,3,1] => [[[[[.,.],[.,.]],.],[[.,.],.]],.] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1

[7,5,8,4,2,6,1,3] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[2,1,7,8,5,6,3,4] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[6,8,3,7,5,1,4,2] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[5,7,3,8,1,6,2,4] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,2,5,8,4,6,1,7] => [[[.,.],[[.,[.,.]],[.,.]]],[.,.]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[3,5,2,4,1,7,6,8] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,5,2,3,7,1,6,8] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[4,2,5,8,3,1,6,7] => [[[.,.],[[.,[.,.]],.]],[.,[.,.]]] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[4,1,5,8,3,2,6,7] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[4,7,3,5,2,1,6,8] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3

[4,3,6,2,5,1,7,8] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[4,6,3,2,5,1,7,8] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[4,6,7,1,3,2,5,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[4,5,1,7,3,2,6,8] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[4,5,1,3,7,2,6,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[3,5,1,4,2,7,6,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[2,5,1,4,3,7,8,6] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[4,3,6,1,5,2,7,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[4,6,3,1,5,2,7,8] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[4,3,6,1,7,2,5,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[6,3,4,1,2,7,5,8] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[6,2,4,1,3,7,8,5] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[4,6,3,1,7,2,5,8] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[5,3,6,2,1,4,7,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[5,6,2,7,1,3,4,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[4,5,2,7,3,1,6,8] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[4,6,7,2,3,1,5,8] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[4,6,2,1,7,3,5,8] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[3,2,6,1,4,7,5,8] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[3,6,2,1,4,7,5,8] => [[[.,[.,.]],.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[3,6,7,2,4,5,1,8] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[3,5,2,7,4,6,1,8] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[3,7,2,4,8,5,1,6] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[3,2,6,1,5,7,4,8] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[3,6,2,1,5,7,4,8] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[4,2,6,1,5,3,7,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[6,2,5,1,3,7,8,4] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[6,3,5,1,2,7,4,8] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[6,4,5,1,7,2,3,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[2,3,1,8,5,4,7,6] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[2,4,1,5,8,3,7,6] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[3,4,5,1,2,8,7,6] => [[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[3,4,5,1,8,2,7,6] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[3,4,5,8,2,1,7,6] => [[[.,[.,[.,[.,.]]]],.],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[3,4,5,2,8,1,7,6] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[3,4,6,2,1,7,8,5] => [[[.,[.,[.,.]]],.],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[3,4,6,2,1,7,5,8] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[3,5,6,2,7,1,4,8] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[3,5,6,2,7,1,8,4] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[3,5,6,2,7,8,1,4] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[3,4,6,8,2,7,5,1] => [[[.,[.,[.,[.,.]]]],[[.,.],.]],.] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 1

[3,4,6,2,8,7,5,1] => [[[.,[.,[.,.]]],[[[.,.],.],.]],.] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1

[3,5,6,2,7,8,4,1] => [[[.,[.,[.,.]]],[[.,[.,.]],.]],.] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[3,5,6,2,7,4,1,8] => [[[.,[.,[.,.]]],[[.,.],.]],[.,.]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[4,5,6,7,2,8,3,1] => [[[.,[.,[.,[.,.]]]],[[.,.],.]],.] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 1

[4,5,6,7,2,1,8,3] => [[[.,[.,[.,[.,.]]]],.],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[2,3,1,8,6,7,4,5] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[2,5,1,6,7,8,4,3] => [[.,[.,.]],[[[.,[.,[.,.]]],.],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2

[2,5,1,6,7,4,8,3] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2

[2,5,1,6,7,4,3,8] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[3,5,6,1,7,4,2,8] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[3,5,6,1,7,4,8,2] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[3,4,6,1,8,7,5,2] => [[.,[.,[.,.]]],[[[[.,.],.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[3,4,6,8,1,7,5,2] => [[.,[.,[.,[.,.]]]],[[[.,.],.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[4,5,6,7,8,1,3,2] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[4,5,6,7,1,3,8,2] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[4,5,6,7,1,3,2,8] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,5,6,7,3,1,8,2] => [[[.,[.,[.,[.,.]]]],.],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[5,8,2,4,3,7,1,6] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[4,2,5,6,1,8,3,7] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,2,5,6,1,7,3,8] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,1,5,7,3,2,4,8] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[6,1,5,8,3,2,4,7] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[3,8,2,4,7,1,5,6] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[3,6,8,2,4,7,1,5] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[4,3,5,6,7,1,8,2] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[3,7,1,5,6,8,2,4] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[3,7,1,5,8,2,4,6] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[3,2,5,1,7,4,6,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[3,2,5,1,8,4,6,7] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[3,2,5,1,7,8,4,6] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[7,8,3,2,4,6,1,5] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[6,1,5,7,8,3,2,4] => [[.,.],[[[.,[.,[.,.]]],.],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => 3

[4,2,5,6,1,7,8,3] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[3,2,5,1,8,7,4,6] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[3,2,5,1,6,4,7,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[3,2,4,1,8,7,5,6] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[3,2,5,1,6,8,7,4] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[3,2,5,1,6,7,8,4] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[3,2,4,1,8,5,6,7] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[3,2,4,1,7,5,6,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[3,2,4,1,6,8,5,7] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[3,2,4,1,8,5,7,6] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[3,2,5,1,8,4,7,6] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[3,2,5,1,6,7,4,8] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[4,2,6,1,8,3,7,5] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[5,2,6,1,8,3,7,4] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[8,4,6,1,7,3,5,2] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[5,2,6,1,8,4,7,3] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[3,2,5,1,7,6,4,8] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[3,2,5,1,8,6,4,7] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[4,2,6,1,8,5,7,3] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[8,5,6,1,7,3,4,2] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[3,6,8,5,1,7,4,2] => [[.,[[.,[.,.]],.]],[[[.,.],.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2

[3,2,5,1,8,6,7,4] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[3,2,4,1,8,6,5,7] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[3,2,4,1,5,8,6,7] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[3,2,5,1,7,8,6,4] => [[[.,.],[.,.]],[[[.,[.,.]],.],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[7,8,5,1,6,4,2,3] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[3,2,5,1,8,7,6,4] => [[[.,.],[.,.]],[[[[.,.],.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[6,5,7,3,1,8,4,2] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[4,6,3,7,1,8,5,2] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[4,6,3,7,5,1,8,2] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[4,2,6,1,7,5,3,8] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[2,5,7,4,1,6,3,8] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[2,5,7,4,1,6,8,3] => [[.,[[.,[.,.]],.]],[[.,[.,.]],.]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 2

[5,4,7,3,6,1,8,2] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[5,4,7,8,3,1,6,2] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[5,8,4,3,6,1,7,2] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[5,4,8,3,6,1,7,2] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[3,2,5,8,1,6,7,4] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[2,5,4,6,8,1,7,3] => [[.,[[.,.],[.,[.,.]]]],[[.,.],.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[4,6,2,1,8,5,7,3] => [[[.,[.,.]],.],[[[.,.],[.,.]],.]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[2,4,1,7,5,8,6,3] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2

[2,4,1,7,5,3,8,6] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[5,4,8,2,1,6,3,7] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[2,5,8,4,1,6,3,7] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[3,2,5,6,1,8,4,7] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,8,3,2,6,1,5,7] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[3,5,2,8,1,6,4,7] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,2,7,1,5,4,8,6] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[3,2,7,1,5,8,6,4] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[3,8,2,5,1,6,7,4] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[4,8,3,2,6,7,1,5] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[4,3,8,2,6,7,1,5] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[4,3,7,2,6,8,1,5] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[4,3,7,8,2,6,1,5] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[2,5,7,4,8,1,6,3] => [[.,[[.,[.,.]],[.,.]]],[[.,.],.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2

[3,2,5,7,8,1,6,4] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[3,2,5,7,1,6,8,4] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[3,2,5,7,1,6,4,8] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,2,6,1,7,8,5,3] => [[[.,.],[.,.]],[[[.,[.,.]],.],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[3,5,2,1,7,4,6,8] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[3,5,2,1,7,8,4,6] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[5,8,4,2,1,7,3,6] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[4,6,2,1,8,3,7,5] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[2,4,1,7,3,8,6,5] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[3,2,7,1,4,8,6,5] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[3,5,8,2,1,7,4,6] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[4,8,3,7,2,1,5,6] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3

[4,3,7,2,8,1,5,6] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[4,3,7,2,1,5,6,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[4,8,3,2,7,1,5,6] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[3,5,2,8,1,7,4,6] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,8,3,2,1,5,6,7] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4

[4,3,8,2,1,5,6,7] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[6,2,3,1,5,4,8,7] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[8,4,5,2,3,1,7,6] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[8,6,7,2,5,3,4,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[6,4,5,1,3,2,8,7] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[6,3,5,1,4,2,8,7] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[8,3,5,2,4,1,7,6] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[8,3,7,2,4,1,6,5] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[8,3,5,1,4,2,7,6] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[8,4,5,1,3,2,7,6] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[8,6,7,4,5,1,3,2] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[8,6,7,1,5,3,4,2] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[8,6,7,3,5,1,4,2] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[8,5,7,3,6,1,4,2] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[8,3,7,1,6,4,5,2] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[8,3,7,1,6,2,5,4] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[8,3,7,2,6,4,5,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[8,2,7,1,6,3,5,4] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[8,2,7,1,4,3,6,5] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[8,4,7,2,3,1,6,5] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[8,2,3,1,7,4,6,5] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[8,2,3,1,5,4,7,6] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[4,2,3,1,8,5,7,6] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[8,6,7,2,3,1,5,4] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[8,2,3,1,7,5,6,4] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[8,5,7,2,6,3,4,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[8,5,7,2,6,1,4,3] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[8,6,7,2,5,1,4,3] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[8,6,7,1,5,2,4,3] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[8,6,7,1,3,2,5,4] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[8,2,7,1,6,4,5,3] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[8,4,7,2,6,3,5,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[8,4,7,2,6,1,5,3] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[8,4,7,1,6,2,5,3] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[8,5,7,1,6,2,4,3] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[8,5,7,4,6,1,3,2] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[8,5,7,1,6,3,4,2] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[8,4,7,1,6,3,5,2] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[8,4,7,3,6,1,5,2] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[2,4,8,3,6,1,7,5] => [[.,[[.,[.,.]],[.,.]]],[[.,.],.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2

[6,5,8,1,3,2,7,4] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[6,7,2,8,4,1,5,3] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[3,6,2,8,4,5,7,1] => [[[.,[.,.]],[[.,.],[.,[.,.]]]],.] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 1

[2,6,1,8,4,5,7,3] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 2

[3,1,6,8,4,5,7,2] => [[.,.],[[[.,[.,.]],[.,[.,.]]],.]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[2,3,6,8,4,5,7,1] => [[.,[.,[[.,[.,.]],[.,[.,.]]]]],.] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1

[6,3,7,8,4,1,5,2] => [[[.,.],[[.,[.,.]],.]],[[.,.],.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[1,3,7,8,4,6,5,2] => [.,[[.,[[.,[.,.]],[[.,.],.]]],.]] => [1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 2

[1,5,7,8,2,4,6,3] => [.,[[.,[.,[.,.]]],[[.,[.,.]],.]]] => [1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3

[5,1,7,8,2,4,6,3] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3

[3,6,7,8,4,2,5,1] => [[[.,[[.,[.,[.,.]]],.]],[.,.]],.] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[3,2,7,8,4,6,5,1] => [[[.,.],[[.,[.,.]],[[.,.],.]]],.] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1

[5,2,7,8,1,4,6,3] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[1,2,7,8,5,4,6,3] => [.,[.,[[[[.,[.,.]],.],[.,.]],.]]] => [1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 3

[7,2,5,8,3,4,6,1] => [[[.,.],[[.,[.,.]],[.,[.,.]]]],.] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1

[7,3,5,8,2,4,6,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1

[3,4,2,1,8,5,6,7] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[5,7,1,8,3,4,6,2] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 2

[1,6,8,5,4,3,2,7] => [.,[[[[[.,[.,.]],.],.],.],[.,.]]] => [1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 3

[4,6,8,5,1,3,2,7] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[5,6,8,1,4,3,2,7] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[2,4,8,3,6,5,1,7] => [[.,[[.,[.,.]],[[.,.],.]]],[.,.]] => [1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2

[5,6,8,4,1,3,2,7] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[4,6,8,1,5,3,2,7] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[1,6,8,4,5,3,2,7] => [.,[[[[.,[.,.]],[.,.]],.],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 3

[3,7,1,8,5,4,6,2] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2

[5,7,8,4,3,6,1,2] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[6,5,8,4,2,3,1,7] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[6,4,8,2,5,3,1,7] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[2,8,3,4,5,1,6,7] => [[.,[[.,.],[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[4,2,3,1,8,5,6,7] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[2,8,1,5,3,4,7,6] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[3,8,1,5,2,4,6,7] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[3,5,1,4,8,2,6,7] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[8,3,5,1,4,7,2,6] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[2,8,1,5,4,7,3,6] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[2,8,1,4,3,7,6,5] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[1,6,7,2,8,4,3,5] => [.,[[.,[.,.]],[[[.,.],.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 4

[6,7,1,4,2,8,3,5] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[6,3,7,1,4,8,2,5] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[3,7,8,1,5,2,4,6] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[6,7,1,3,2,4,8,5] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[5,8,1,3,7,2,4,6] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[1,2,5,8,3,7,4,6] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => [1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 5

[2,8,1,7,3,5,4,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[4,2,8,1,7,3,6,5] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[2,8,1,7,4,3,6,5] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[2,8,1,7,5,3,4,6] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[8,3,7,1,5,2,4,6] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[4,2,8,1,7,6,3,5] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[2,8,1,7,6,4,3,5] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[7,8,3,4,1,6,2,5] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,7,3,4,1,8,2,5] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,8,3,4,1,7,2,6] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,7,3,4,1,5,2,8] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,7,3,4,1,6,2,8] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,6,2,7,3,4,1,8] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[4,6,2,8,3,5,1,7] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[4,8,3,5,1,6,2,7] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,6,2,4,1,7,3,8] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,5,1,7,3,8,2,6] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[4,6,2,7,3,8,1,5] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[5,6,2,7,3,8,1,4] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[5,6,2,7,4,8,1,3] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[5,6,3,8,4,7,1,2] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[4,6,2,8,3,7,1,5] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[4,5,1,7,3,6,2,8] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[4,6,3,5,2,1,8,7] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[6,8,2,4,5,7,3,1] => [[[.,[.,.]],[[.,[.,[.,.]]],.]],.] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[3,6,1,4,5,2,8,7] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[2,1,6,8,5,7,4,3] => [[.,.],[[[[.,[.,.]],[.,.]],.],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[6,8,3,5,1,7,4,2] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[2,5,8,4,7,6,3,1] => [[.,[[[.,[.,.]],[[.,.],.]],.]],.] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 1

[4,3,8,1,5,6,7,2] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[4,8,1,3,5,6,7,2] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2

[5,8,3,6,1,4,7,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[4,8,3,6,1,2,7,5] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[3,8,1,2,5,6,7,4] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 3

[5,8,3,6,2,4,7,1] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1

[5,8,3,6,2,1,7,4] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[2,6,8,4,5,7,1,3] => [[.,[[.,[.,.]],[.,[.,.]]]],[.,.]] => [1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2

[6,8,3,5,1,7,2,4] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,1,5,8,3,6,7,4] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3

[5,8,3,6,1,2,7,4] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[2,4,8,1,5,6,7,3] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[4,8,2,1,5,6,7,3] => [[[.,[.,.]],.],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 2

[3,4,8,2,5,6,7,1] => [[[.,[.,[.,.]]],[.,[.,[.,.]]]],.] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1

[5,8,1,4,7,6,2,3] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3

[5,8,3,1,6,2,7,4] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[4,5,3,8,6,1,7,2] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[3,4,1,8,5,6,7,2] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 2

[3,5,7,2,6,4,8,1] => [[[.,[.,[.,.]]],[[.,.],[.,.]]],.] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[2,5,7,3,6,4,8,1] => [[.,[[.,[.,.]],[[.,.],[.,.]]]],.] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 1

[1,5,7,3,6,8,4,2] => [.,[[[.,[.,.]],[[.,[.,.]],.]],.]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 2

[6,7,2,3,5,4,8,1] => [[[.,[.,.]],[.,[[.,.],[.,.]]]],.] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 1

[8,2,4,7,1,6,5,3] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[6,7,1,3,5,8,4,2] => [[.,[.,.]],[[.,[[.,[.,.]],.]],.]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 2

[4,8,3,7,6,1,5,2] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[8,1,4,7,2,6,5,3] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3

[3,8,2,1,7,6,5,4] => [[[.,[.,.]],.],[[[[.,.],.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2

[6,7,1,2,8,5,4,3] => [[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 3

[8,2,3,1,7,6,5,4] => [[[.,.],[.,.]],[[[[.,.],.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[3,4,1,7,6,8,5,2] => [[.,[.,.]],[[[[.,.],[.,.]],.],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 2

[8,5,7,2,1,6,4,3] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[1,5,7,2,8,6,4,3] => [.,[[.,[.,.]],[[[[.,.],.],.],.]]] => [1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 3

[2,5,7,1,8,6,4,3] => [[.,[.,[.,.]]],[[[[.,.],.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[3,5,7,1,6,8,4,2] => [[.,[.,[.,.]]],[[[.,[.,.]],.],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[6,7,4,5,8,1,3,2] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[2,5,7,8,1,6,4,3] => [[.,[.,[.,[.,.]]]],[[[.,.],.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[1,5,7,8,2,6,4,3] => [.,[[.,[.,[.,.]]],[[[.,.],.],.]]] => [1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3

[8,5,7,1,2,6,4,3] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[5,3,7,8,6,1,4,2] => [[[.,.],[[.,[.,.]],.]],[[.,.],.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[6,7,2,8,1,5,4,3] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[5,2,7,8,1,6,4,3] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[3,2,8,1,7,6,5,4] => [[[.,.],[.,.]],[[[[.,.],.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[1,3,8,2,7,6,5,4] => [.,[[.,[.,.]],[[[[.,.],.],.],.]]] => [1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 3

[5,1,7,8,2,6,4,3] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3

[6,7,1,8,2,5,4,3] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[4,8,1,7,2,6,5,3] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[3,8,1,2,7,6,5,4] => [[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 3

[2,8,1,3,7,6,5,4] => [[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 3

[6,7,1,8,4,5,2,3] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[3,7,1,5,8,2,6,4] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[2,7,1,5,8,3,6,4] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[5,6,4,1,8,7,2,3] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[6,4,5,1,8,7,2,3] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[5,4,6,1,8,7,2,3] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[4,5,6,1,8,7,2,3] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[3,5,6,1,8,2,7,4] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[2,5,6,1,8,3,7,4] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[2,4,6,1,3,8,7,5] => [[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[3,4,6,1,2,8,7,5] => [[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[4,3,6,1,2,8,7,5] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[5,3,6,1,8,2,7,4] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[8,1,3,5,7,2,6,4] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[8,1,2,5,7,3,6,4] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 4

[6,2,5,1,8,3,7,4] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[4,2,6,1,3,8,7,5] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[2,3,6,1,4,8,7,5] => [[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[6,2,4,1,3,8,7,5] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[8,1,3,4,2,7,6,5] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3

[6,3,4,1,2,8,7,5] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[4,6,3,1,2,8,7,5] => [[[.,[.,.]],.],[.,[[[.,.],.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 3

[2,7,1,4,3,8,6,5] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[3,7,1,4,2,8,6,5] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[4,7,1,3,2,8,6,5] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[8,1,6,7,2,3,5,4] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[4,7,1,2,3,8,6,5] => [[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 4

[3,7,1,2,4,8,6,5] => [[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 4

[2,7,1,3,4,8,6,5] => [[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 4

[3,6,2,1,4,8,7,5] => [[[.,[.,.]],.],[.,[[[.,.],.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 3

[5,6,2,1,8,3,7,4] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[3,5,2,4,1,8,7,6] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[6,2,3,1,4,8,7,5] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[2,4,6,3,5,8,7,1] => [[.,[[.,[.,.]],[.,[[.,.],.]]]],.] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 1

[2,4,6,3,5,8,1,7] => [[.,[[.,[.,.]],[.,[.,.]]]],[.,.]] => [1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2

[2,4,6,1,5,3,8,7] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[2,4,6,1,5,8,3,7] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[2,4,1,6,5,8,3,7] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[2,4,1,6,5,8,7,3] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2

[2,4,6,1,5,8,7,3] => [[.,[.,[.,.]]],[[.,[[.,.],.]],.]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[2,4,6,8,1,5,7,3] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[2,4,6,1,8,5,7,3] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[2,4,1,6,8,5,7,3] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2

[2,1,4,6,8,5,7,3] => [[.,.],[[.,[[.,[.,.]],[.,.]]],.]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 2

[2,1,4,6,8,5,3,7] => [[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3

[2,4,1,6,8,5,3,7] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[2,4,6,1,8,5,3,7] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[2,4,6,8,1,5,3,7] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,4,6,8,3,5,7,1] => [[.,[[.,[.,[.,.]]],[.,[.,.]]]],.] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1

[2,4,6,8,3,5,1,7] => [[.,[[.,[.,[.,.]]],[.,.]]],[.,.]] => [1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[2,4,6,8,3,1,5,7] => [[.,[[.,[.,[.,.]]],.]],[.,[.,.]]] => [1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[2,4,6,3,1,8,5,7] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[2,4,6,3,8,1,5,7] => [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[2,4,6,3,8,5,1,7] => [[.,[[.,[.,.]],[[.,.],.]]],[.,.]] => [1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2

[2,4,6,3,8,5,7,1] => [[.,[[.,[.,.]],[[.,.],[.,.]]]],.] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 1

[2,4,3,6,8,1,5,7] => [[.,[[.,.],[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[2,4,1,3,6,8,7,5] => [[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 3

[2,4,3,6,8,1,7,5] => [[.,[[.,.],[.,[.,.]]]],[[.,.],.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[2,4,6,3,8,1,7,5] => [[.,[[.,[.,.]],[.,.]]],[[.,.],.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2

[2,1,4,6,8,3,7,5] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[2,4,1,6,8,3,7,5] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[2,4,6,1,8,3,7,5] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[2,4,6,8,1,3,7,5] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[2,4,6,8,3,1,7,5] => [[.,[[.,[.,[.,.]]],.]],[[.,.],.]] => [1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[4,6,2,8,5,7,1,3] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[2,6,1,4,8,7,5,3] => [[.,[.,.]],[[.,[[[.,.],.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 2

[2,6,1,4,8,7,3,5] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3

[5,2,4,7,3,6,8,1] => [[[.,.],[[.,[.,.]],[.,[.,.]]]],.] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1

[5,1,4,7,3,8,2,6] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[6,8,1,3,7,2,4,5] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[5,8,2,1,7,3,4,6] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[5,7,2,1,8,3,4,6] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[6,7,1,3,8,2,4,5] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[5,1,2,4,8,3,6,7] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 5

[4,3,6,1,5,8,2,7] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[2,6,1,4,5,8,3,7] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[4,3,5,2,1,8,6,7] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[2,7,8,3,6,1,4,5] => [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[4,8,2,5,1,3,7,6] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[4,7,2,5,1,3,8,6] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[3,7,2,1,5,4,8,6] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[3,8,2,1,5,4,7,6] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[3,8,2,1,4,5,7,6] => [[[.,[.,.]],.],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 4

[3,7,2,1,4,5,8,6] => [[[.,[.,.]],.],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 4

[3,2,7,1,4,6,8,5] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[3,2,8,1,4,6,7,5] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[3,2,8,1,4,7,6,5] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[3,8,2,1,4,7,5,6] => [[[.,[.,.]],.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[3,8,2,1,5,7,4,6] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[4,8,2,5,1,7,3,6] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,7,2,5,1,8,3,6] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,7,2,1,5,8,4,6] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[3,7,2,1,4,8,5,6] => [[[.,[.,.]],.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[3,2,7,1,6,8,4,5] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[3,2,8,1,6,7,4,5] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[3,8,2,1,7,4,5,6] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[3,2,8,1,7,4,6,5] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[3,2,8,1,6,4,7,5] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[3,2,7,1,6,4,8,5] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[5,7,8,3,4,1,2,6] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[4,2,7,8,1,3,6,5] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[4,2,6,8,1,3,7,5] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[4,2,6,7,1,3,8,5] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[3,2,6,1,8,4,7,5] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[3,7,2,1,8,4,5,6] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[3,7,2,1,8,5,4,6] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[4,7,3,8,5,1,2,6] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[4,3,7,8,6,1,2,5] => [[[.,.],[[.,[.,.]],.]],[.,[.,.]]] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[3,2,7,1,8,6,4,5] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[3,2,6,1,8,7,4,5] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[4,2,6,8,1,7,3,5] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,2,6,7,1,8,3,5] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,2,6,1,7,8,4,5] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[1,4,6,2,7,8,5,3] => [.,[[.,[.,.]],[[[.,[.,.]],.],.]]] => [1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 3

[4,3,6,7,8,5,1,2] => [[[.,.],[[.,[.,[.,.]]],.]],[.,.]] => [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => 2

[4,5,6,3,8,7,1,2] => [[[.,[.,[.,.]]],[[.,.],.]],[.,.]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[3,6,8,5,4,7,1,2] => [[.,[[[.,[.,.]],.],[.,.]]],[.,.]] => [1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 2

[6,8,3,5,4,7,1,2] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[7,1,2,5,8,3,6,4] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 4

[7,8,1,2,4,6,5,3] => [[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 3

[7,8,3,1,4,2,6,5] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[4,3,6,1,8,2,7,5] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[4,8,1,5,2,3,7,6] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[5,8,1,6,4,3,2,7] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[6,1,5,7,4,3,2,8] => [[.,.],[[[[.,[.,.]],.],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => 3

[3,4,6,1,5,8,2,7] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[7,8,4,1,5,3,2,6] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[7,8,5,1,6,3,2,4] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[2,6,1,5,7,3,8,4] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[6,8,1,7,4,3,2,5] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[5,6,1,7,4,3,2,8] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[6,1,7,8,4,3,2,5] => [[.,.],[[[[.,[.,.]],.],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => 3

[3,1,6,7,5,8,2,4] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[7,8,1,6,5,3,2,4] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[7,8,2,1,4,5,6,3] => [[[.,[.,.]],.],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 2

[2,8,1,5,4,6,7,3] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 2

[6,1,2,5,7,3,8,4] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 4

[4,3,6,1,5,7,2,8] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[1,3,6,8,5,7,2,4] => [.,[[.,[[.,[.,.]],[.,.]]],[.,.]]] => [1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 3

[2,4,6,3,7,1,8,5] => [[.,[[.,[.,.]],[.,.]]],[[.,.],.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2

[4,1,6,7,3,8,2,5] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[5,4,6,1,3,7,2,8] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[1,2,4,5,8,3,7,6] => [.,[.,[[.,[.,[.,.]]],[[.,.],.]]]] => [1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 4

[7,8,2,3,4,1,6,5] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[7,8,1,4,6,3,2,5] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[7,1,5,8,4,3,2,6] => [[.,.],[[[[.,[.,.]],.],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => 3

[6,5,7,1,4,3,2,8] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[7,5,8,1,4,3,2,6] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[1,5,7,8,4,3,2,6] => [.,[[[[.,[.,[.,.]]],.],.],[.,.]]] => [1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 3

[7,8,4,6,1,3,2,5] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[7,8,5,4,1,3,2,6] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[3,5,6,4,1,8,2,7] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[6,8,5,1,4,3,2,7] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[3,4,6,2,7,1,5,8] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[3,6,2,5,4,1,7,8] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[4,3,6,2,8,1,5,7] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[6,2,4,5,1,3,7,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[4,3,6,8,1,7,2,5] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[1,6,7,4,8,3,5,2] => [.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 2

[1,4,6,3,7,5,8,2] => [.,[[[.,[.,.]],[[.,.],[.,.]]],.]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 2

[4,6,7,2,5,8,1,3] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[2,4,6,1,7,5,3,8] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[1,4,6,3,5,8,7,2] => [.,[[[.,[.,.]],[.,[[.,.],.]]],.]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 2

[1,5,8,4,3,6,7,2] => [.,[[[[.,[.,.]],.],[.,[.,.]]],.]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 2

[5,4,6,2,7,8,1,3] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[5,6,3,2,7,1,4,8] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[5,6,3,2,7,1,8,4] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[8,5,6,3,2,7,1,4] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[5,4,6,2,8,1,7,3] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[2,4,1,7,8,5,3,6] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[5,6,3,2,1,8,4,7] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[3,5,2,1,6,4,7,8] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[6,8,4,3,2,1,5,7] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 3

[5,3,8,2,1,6,4,7] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[8,4,6,3,2,1,7,5] => [[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[7,8,4,3,2,1,6,5] => [[[[[.,[.,.]],.],.],.],[[.,.],.]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2

[5,4,7,2,1,8,6,3] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[7,5,8,3,2,6,1,4] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[5,7,3,2,1,6,8,4] => [[[[.,[.,.]],.],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 2

[5,7,3,2,1,6,4,8] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[6,3,7,2,5,1,8,4] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[6,7,8,3,5,2,1,4] => [[[[.,[.,[.,.]]],[.,.]],.],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[6,2,5,7,8,4,1,3] => [[[.,.],[[.,[.,[.,.]]],.]],[.,.]] => [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => 2

[2,1,5,7,8,6,3,4] => [[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3

[3,6,7,2,8,1,4,5] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[6,3,7,2,8,1,4,5] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[3,2,6,1,7,4,5,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[3,5,2,1,4,7,6,8] => [[[.,[.,.]],.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[7,3,5,2,1,8,4,6] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[2,5,8,4,1,3,7,6] => [[.,[[.,[.,.]],.]],[.,[[.,.],.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 3

[2,4,1,7,8,3,6,5] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[3,7,2,8,6,1,4,5] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[3,6,8,2,1,7,4,5] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[5,3,8,2,1,4,7,6] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[4,7,3,2,1,5,6,8] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4

[8,4,7,3,2,1,5,6] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3

[8,3,5,2,1,4,7,6] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[3,5,2,1,4,6,8,7] => [[[.,[.,.]],.],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 4

[7,8,3,5,4,6,1,2] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[5,7,1,6,2,8,3,4] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[5,7,1,6,2,8,4,3] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[2,3,6,1,5,4,8,7] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[7,3,5,1,8,4,2,6] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[7,3,5,1,8,6,4,2] => [[[.,.],[.,.]],[[[[.,.],.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[5,7,3,6,2,8,4,1] => [[[[.,[.,.]],[.,.]],[[.,.],.]],.] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 1

[7,3,5,1,8,6,2,4] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[6,3,5,1,8,2,4,7] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[7,3,5,6,8,4,1,2] => [[[.,.],[[.,[.,[.,.]]],.]],[.,.]] => [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => 2

[7,3,5,6,8,1,4,2] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[7,3,5,6,8,1,2,4] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[5,7,1,6,3,8,2,4] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[6,3,5,7,8,2,1,4] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 2

[6,3,5,7,8,2,4,1] => [[[[.,.],[.,[.,[.,.]]]],[.,.]],.] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 1

[5,7,3,6,1,8,4,2] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[2,3,4,8,1,7,6,5] => [[.,[.,[.,[.,.]]]],[[[.,.],.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[2,3,4,8,1,6,7,5] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[2,1,4,5,8,3,7,6] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[2,3,4,8,1,6,5,7] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,3,4,8,1,5,7,6] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[7,8,2,6,1,5,3,4] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[7,8,1,6,2,5,3,4] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[5,8,1,7,2,6,3,4] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[5,8,2,7,1,6,3,4] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,8,1,7,5,6,3,4] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[2,8,1,7,4,6,3,5] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[4,8,2,7,1,6,3,5] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,8,1,7,2,6,3,5] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[4,8,1,7,5,6,2,3] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[3,8,1,7,5,6,2,4] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[3,8,1,7,4,6,2,5] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[3,8,1,7,2,6,4,5] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[3,8,2,7,1,6,4,5] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,8,2,7,4,6,1,5] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[3,8,2,7,5,6,1,4] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[4,8,2,7,5,6,1,3] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[4,8,3,7,5,6,1,2] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[2,8,1,7,3,6,4,5] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[1,6,7,4,2,8,5,3] => [.,[[[.,[.,.]],.],[[[.,.],.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 3

[1,6,7,3,8,5,2,4] => [.,[[[.,[.,.]],[[.,.],.]],[.,.]]] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 3

[1,5,7,8,2,6,3,4] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[2,5,3,7,8,1,6,4] => [[.,[[.,.],[.,[.,.]]]],[[.,.],.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[4,8,1,3,6,7,2,5] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[6,3,8,1,4,7,2,5] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[5,8,1,3,6,2,7,4] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[1,5,7,4,2,6,8,3] => [.,[[[.,[.,.]],.],[[.,[.,.]],.]]] => [1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3

[5,8,1,4,2,6,3,7] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[3,5,6,1,2,8,7,4] => [[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[3,5,7,1,8,6,2,4] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[3,6,2,7,5,1,8,4] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[3,4,5,8,2,7,1,6] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[3,4,6,2,8,1,5,7] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[3,5,2,6,8,1,7,4] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[4,2,5,6,1,3,8,7] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[5,3,6,8,4,7,2,1] => [[[[.,.],[[.,[.,.]],[.,.]]],.],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1

[3,7,2,5,4,8,6,1] => [[[.,[.,.]],[[.,.],[[.,.],.]]],.] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 1

[4,7,2,5,8,3,6,1] => [[[.,[.,.]],[[.,[.,.]],[.,.]]],.] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 1

[5,2,6,8,4,3,7,1] => [[[.,.],[[[.,[.,.]],.],[.,.]]],.] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1

[5,1,6,8,4,3,2,7] => [[.,.],[[[[.,[.,.]],.],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => 3

[5,7,1,8,4,3,2,6] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[2,7,1,5,4,3,8,6] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[8,5,6,7,1,3,2,4] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[8,4,6,1,7,3,2,5] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[8,3,6,1,4,7,2,5] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[6,7,8,5,1,3,2,4] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[5,7,2,8,4,3,6,1] => [[[.,[.,.]],[[[.,.],.],[.,.]]],.] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 1

[6,7,8,2,4,3,5,1] => [[[.,[.,[.,.]]],[[.,.],[.,.]]],.] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[8,3,6,2,4,7,5,1] => [[[[.,.],[.,.]],[.,[[.,.],.]]],.] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[5,7,3,8,4,6,2,1] => [[[[.,[.,.]],[[.,.],[.,.]]],.],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 1

[4,7,3,5,8,6,2,1] => [[[[.,[.,.]],[.,[[.,.],.]]],.],.] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 1

[5,6,4,3,8,7,1,2] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[3,6,2,4,8,1,5,7] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[3,4,7,2,8,1,6,5] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[1,4,7,2,5,8,6,3] => [.,[[.,[.,.]],[[.,[[.,.],.]],.]]] => [1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 3

[3,5,6,4,8,7,1,2] => [[.,[[.,[.,.]],[[.,.],.]]],[.,.]] => [1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2

[4,6,8,5,3,7,1,2] => [[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => [1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[6,8,5,3,4,7,1,2] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[7,8,1,4,2,6,5,3] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[7,4,5,3,2,8,1,6] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[5,8,3,6,1,4,2,7] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[1,4,6,2,5,8,3,7] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 4

[3,6,2,5,8,1,7,4] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[6,1,7,8,2,4,3,5] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[7,1,3,4,5,2,8,6] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[7,8,2,4,6,3,1,5] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[7,2,5,8,3,4,1,6] => [[[.,.],[[.,[.,.]],[.,.]]],[.,.]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[7,5,8,4,1,2,3,6] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[3,5,7,8,4,1,2,6] => [[.,[[.,[.,[.,.]]],.]],[.,[.,.]]] => [1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[2,4,6,7,3,1,8,5] => [[.,[[.,[.,[.,.]]],.]],[[.,.],.]] => [1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[7,8,4,6,3,1,2,5] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3

[5,6,8,4,2,3,1,7] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[6,8,5,4,3,1,2,7] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 3

[6,7,5,8,2,1,4,3] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[6,8,5,2,1,4,7,3] => [[[[.,[.,.]],.],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 2

[3,8,2,5,6,1,7,4] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[2,8,1,5,6,3,7,4] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[8,1,2,5,6,3,7,4] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 4

[5,1,3,7,8,6,2,4] => [[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3

[7,2,5,8,1,6,4,3] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[8,2,5,6,3,7,1,4] => [[[.,.],[[.,[.,.]],[.,.]]],[.,.]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[7,5,6,2,4,1,8,3] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[5,8,1,6,3,7,2,4] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[3,8,1,6,5,7,2,4] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[7,8,5,4,1,6,2,3] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[7,5,6,4,2,1,8,3] => [[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[7,4,6,2,5,1,8,3] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[6,1,3,4,5,7,8,2] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2

[5,4,7,3,6,8,1,2] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[3,4,7,8,5,6,1,2] => [[.,[.,[[.,[.,.]],[.,.]]]],[.,.]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 2

[3,4,7,2,5,1,6,8] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[1,4,7,2,5,8,3,6] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 4

[3,6,2,4,7,1,5,8] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[6,8,3,4,5,7,1,2] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[4,3,6,7,5,8,1,2] => [[[.,.],[[.,[.,.]],[.,.]]],[.,.]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[4,8,2,6,1,5,3,7] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,3,6,2,5,1,8,7] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[7,8,3,2,5,1,4,6] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[7,8,1,2,5,6,3,4] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4

[7,1,3,6,8,4,2,5] => [[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3

[7,1,5,8,3,6,2,4] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[6,1,5,7,4,2,8,3] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3

[6,5,7,1,4,2,3,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[5,6,8,1,3,2,4,7] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[6,8,5,1,3,4,2,7] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[2,8,3,4,5,1,7,6] => [[.,[[.,.],[.,[.,.]]]],[[.,.],.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[2,4,7,3,6,1,8,5] => [[.,[[.,[.,.]],[.,.]]],[[.,.],.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2

[7,5,6,8,1,4,3,2] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[2,4,7,1,6,5,3,8] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[1,2,7,8,5,4,3,6] => [.,[.,[[[[.,[.,.]],.],.],[.,.]]]] => [1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 4

[2,8,1,4,5,6,3,7] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[4,2,6,1,8,5,3,7] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[7,8,2,1,4,5,3,6] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[7,8,4,1,5,3,6,2] => [[[.,[.,.]],.],[[[.,.],[.,.]],.]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[3,4,6,1,5,8,7,2] => [[.,[.,[.,.]]],[[.,[[.,.],.]],.]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[5,8,1,6,3,4,7,2] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 2

[6,8,1,7,5,2,3,4] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[5,6,1,7,4,8,2,3] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[3,6,1,5,7,4,2,8] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[2,5,6,1,7,4,8,3] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[6,1,7,8,5,3,4,2] => [[.,.],[[[[.,[.,.]],.],[.,.]],.]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 2

[7,8,5,2,4,6,3,1] => [[[[.,[.,.]],.],[[.,[.,.]],.]],.] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 1

[7,8,1,6,2,4,5,3] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[6,8,1,4,7,2,5,3] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[5,4,7,1,8,3,2,6] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[6,7,1,4,8,3,2,5] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[2,7,1,8,4,5,3,6] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[6,3,5,8,4,7,2,1] => [[[[.,.],[[.,[.,.]],[.,.]]],.],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1

[6,2,4,1,3,5,8,7] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[2,6,1,4,3,5,8,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[4,6,2,1,3,5,8,7] => [[[.,[.,.]],.],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 4

[2,6,1,4,3,8,5,7] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[2,8,1,4,3,6,5,7] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[4,8,2,1,3,6,5,7] => [[[.,[.,.]],.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[6,8,2,1,4,3,5,7] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[2,8,1,4,6,3,5,7] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[2,6,1,4,8,3,5,7] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[2,6,4,8,1,3,5,7] => [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[4,6,2,8,1,3,5,7] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[4,2,6,1,8,3,5,7] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[6,2,4,1,8,3,5,7] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[2,4,1,3,8,6,5,7] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 4

[8,2,6,1,4,3,5,7] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[4,2,8,1,3,6,5,7] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[2,4,8,1,3,6,5,7] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[2,4,1,8,3,6,5,7] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[2,1,4,8,3,6,5,7] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[2,4,8,1,6,3,5,7] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[8,4,6,2,1,3,5,7] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[4,6,8,2,1,3,5,7] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[2,6,8,4,1,3,5,7] => [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4

[2,6,8,1,4,3,5,7] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[2,6,1,8,4,3,5,7] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[2,1,6,8,4,3,5,7] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[6,8,4,2,1,3,5,7] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4

[3,2,6,1,5,4,8,7] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[6,2,4,1,5,3,8,7] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[4,3,6,1,5,2,8,7] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[4,3,5,2,8,1,7,6] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[4,3,7,2,6,5,8,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[4,3,8,2,6,1,7,5] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[4,3,8,1,7,2,6,5] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[4,3,8,1,5,2,7,6] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[5,4,8,1,3,2,7,6] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[4,3,7,1,8,5,6,2] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[8,4,6,1,3,2,7,5] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[8,3,5,1,7,2,6,4] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[8,3,5,2,6,1,7,4] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[7,3,5,2,6,4,8,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[8,2,7,1,5,3,6,4] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[8,2,4,1,5,3,7,6] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[8,2,4,1,7,3,6,5] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[3,2,8,1,5,4,7,6] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[3,2,7,1,8,5,6,4] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[6,5,7,2,4,3,8,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[6,5,8,2,4,1,7,3] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[7,2,4,1,8,5,6,3] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[7,6,8,2,4,1,5,3] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[7,6,8,1,5,2,4,3] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[7,2,8,1,5,4,6,3] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[5,4,7,2,6,3,8,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[5,4,8,2,6,1,7,3] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[6,5,8,1,7,2,4,3] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[6,5,7,4,8,1,3,2] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[6,5,7,1,8,3,4,2] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[5,4,7,1,8,3,6,2] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[5,4,6,3,8,1,7,2] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[2,5,3,4,7,1,8,6] => [[.,[[.,.],[.,[.,.]]]],[[.,.],.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[2,4,8,3,5,7,6,1] => [[.,[[.,[.,.]],[.,[[.,.],.]]]],.] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 1

[5,1,4,8,3,2,6,7] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[1,5,8,4,3,2,6,7] => [.,[[[[.,[.,.]],.],.],[.,[.,.]]]] => [1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 4

[1,5,7,3,8,4,2,6] => [.,[[[.,[.,.]],[[.,.],.]],[.,.]]] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 3

[5,1,4,7,8,3,2,6] => [[.,.],[[[.,[.,[.,.]]],.],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => 3

[4,8,1,5,7,3,6,2] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2

[1,6,8,5,3,7,4,2] => [.,[[[[.,[.,.]],.],[[.,.],.]],.]] => [1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 2

[6,8,1,7,4,3,5,2] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2

[6,4,8,1,7,3,5,2] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[2,6,8,4,3,7,5,1] => [[.,[[[.,[.,.]],.],[[.,.],.]]],.] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 1

[6,2,4,8,3,7,5,1] => [[[.,.],[[.,[.,.]],[[.,.],.]]],.] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1

[2,6,7,3,1,4,8,5] => [[.,[[.,[.,.]],.]],[.,[[.,.],.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 3

[2,7,1,8,3,5,4,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[7,8,2,6,3,1,5,4] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[8,3,7,1,5,6,2,4] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[1,7,8,5,2,6,4,3] => [.,[[[.,[.,.]],.],[[[.,.],.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 3

[7,8,1,6,4,2,5,3] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[7,8,6,1,5,3,2,4] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[6,3,5,2,1,4,8,7] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[6,3,5,7,2,8,4,1] => [[[[.,.],[.,[.,.]]],[[.,.],.]],.] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => 1

[4,5,3,6,1,2,8,7] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[3,5,1,4,6,2,8,7] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[8,3,4,5,7,2,1,6] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 2

[5,7,4,6,3,8,2,1] => [[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1

[8,1,4,7,3,6,2,5] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[5,1,4,6,8,3,7,2] => [[.,.],[[[.,[.,[.,.]]],[.,.]],.]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2

[4,7,1,3,5,8,6,2] => [[.,[.,.]],[[.,[.,[[.,.],.]]],.]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 2

[4,8,3,7,1,2,6,5] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[3,8,1,2,5,7,6,4] => [[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 3

[5,3,7,8,2,4,6,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1

[8,3,6,2,1,4,7,5] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[5,3,6,2,8,7,1,4] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[5,7,8,6,4,2,1,3] => [[[[.,[[.,[.,.]],.]],.],.],[.,.]] => [1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 2

[2,6,7,5,4,8,1,3] => [[.,[[[.,[.,.]],.],[.,.]]],[.,.]] => [1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 2

[6,7,3,5,1,8,2,4] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,1,6,7,5,8,3,4] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[2,1,5,7,3,6,8,4] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3

[5,7,3,6,1,2,8,4] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[2,4,7,1,6,5,8,3] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[4,6,2,1,8,7,5,3] => [[[.,[.,.]],.],[[[[.,.],.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2

[3,4,6,2,7,8,5,1] => [[[.,[.,[.,.]]],[[.,[.,.]],.]],.] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[4,6,1,2,5,8,7,3] => [[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 3

[5,6,1,4,8,2,7,3] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[5,6,3,1,8,7,2,4] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[3,5,6,4,7,1,8,2] => [[.,[[.,[.,.]],[.,.]]],[[.,.],.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2

[3,4,6,1,5,7,8,2] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[3,4,1,5,7,6,8,2] => [[.,[.,.]],[[.,[[.,.],[.,.]]],.]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 2

[3,8,2,7,1,6,5,4] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[3,8,2,7,6,1,5,4] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[3,8,2,7,6,5,1,4] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[3,8,2,7,6,5,4,1] => [[[.,[.,.]],[[[[.,.],.],.],.]],.] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1

[7,3,4,2,1,6,5,8] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[7,3,5,2,6,4,1,8] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[1,4,6,7,3,8,2,5] => [.,[[[.,[.,[.,.]]],[.,.]],[.,.]]] => [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[6,4,5,7,1,3,8,2] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[6,3,5,1,7,4,8,2] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[2,4,6,7,3,8,1,5] => [[.,[[.,[.,[.,.]]],[.,.]]],[.,.]] => [1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[1,4,6,7,3,8,5,2] => [.,[[[.,[.,[.,.]]],[[.,.],.]],.]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2

[1,5,6,7,8,3,4,2] => [.,[[[.,[.,[.,[.,.]]]],[.,.]],.]] => [1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2

[2,5,6,7,8,3,1,4] => [[.,[[.,[.,[.,[.,.]]]],.]],[.,.]] => [1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 2

[5,3,6,1,7,8,4,2] => [[[.,.],[.,.]],[[[.,[.,.]],.],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[5,4,6,7,1,8,3,2] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[1,5,6,7,8,3,2,4] => [.,[[[.,[.,[.,[.,.]]]],.],[.,.]]] => [1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 3

[6,4,5,7,2,1,8,3] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[5,4,6,7,2,8,3,1] => [[[[.,.],[.,[.,.]]],[[.,.],.]],.] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => 1

[6,3,5,2,7,1,8,4] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[6,3,4,2,1,7,8,5] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[4,3,6,2,7,8,5,1] => [[[[.,.],[.,.]],[[.,[.,.]],.]],.] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[3,4,6,7,2,8,5,1] => [[[.,[.,[.,[.,.]]]],[[.,.],.]],.] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 1

[1,5,6,7,8,2,4,3] => [.,[[.,[.,[.,[.,.]]]],[[.,.],.]]] => [1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[1,5,6,7,8,4,2,3] => [.,[[[.,[.,[.,[.,.]]]],.],[.,.]]] => [1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 3

[3,4,6,7,1,8,5,2] => [[.,[.,[.,[.,.]]]],[[[.,.],.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[4,3,6,1,7,8,5,2] => [[[.,.],[.,.]],[[[.,[.,.]],.],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[6,8,2,4,5,7,1,3] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[3,7,8,4,5,2,6,1] => [[[.,[[.,[.,.]],[.,.]]],[.,.]],.] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[7,8,1,4,5,3,6,2] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2

[4,8,3,6,1,5,7,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[5,8,3,1,6,4,7,2] => [[[.,[.,.]],.],[[[.,.],[.,.]],.]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[5,8,1,4,7,6,3,2] => [[.,[.,.]],[[[.,[[.,.],.]],.],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 2

[6,2,8,1,3,5,4,7] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[2,5,1,3,8,4,7,6] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4

[1,2,4,8,3,7,6,5] => [.,[.,[[.,[.,.]],[[[.,.],.],.]]]] => [1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 4

[2,4,8,1,3,7,6,5] => [[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[2,4,8,3,7,6,1,5] => [[.,[[.,[.,.]],[[.,.],.]]],[.,.]] => [1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2

[1,4,8,2,3,7,6,5] => [.,[[.,[.,.]],[.,[[[.,.],.],.]]]] => [1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 4

[6,3,8,1,5,2,4,7] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[5,3,8,1,2,4,7,6] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[5,1,3,8,2,4,7,6] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[3,6,2,8,7,5,1,4] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[4,2,6,1,8,7,3,5] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[3,4,8,1,7,2,6,5] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[7,8,3,5,4,1,6,2] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[7,8,2,5,4,6,1,3] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[4,2,7,1,8,3,6,5] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[2,7,1,4,8,3,5,6] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[4,7,1,6,2,3,8,5] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[1,2,6,7,4,8,5,3] => [.,[.,[[[.,[.,.]],[[.,.],.]],.]]] => [1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 3

[3,1,6,7,4,2,8,5] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3

[4,7,1,2,5,3,8,6] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4

[8,2,5,1,3,7,6,4] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[4,7,2,5,3,1,8,6] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[5,7,4,3,2,8,1,6] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2

[5,8,3,2,7,1,6,4] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[5,8,4,6,7,1,3,2] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[3,7,2,6,8,4,1,5] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[6,3,5,1,8,4,2,7] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[4,7,2,5,8,6,3,1] => [[[.,[.,.]],[[.,[[.,.],.]],.]],.] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 1

[5,4,8,1,7,6,2,3] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[5,2,8,1,7,3,6,4] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[6,4,7,8,1,5,3,2] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[6,3,7,8,5,2,4,1] => [[[[.,.],[[.,[.,.]],.]],[.,.]],.] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[4,7,3,8,6,5,1,2] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[5,1,7,8,4,3,2,6] => [[.,.],[[[[.,[.,.]],.],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => 3

[5,1,2,4,6,3,8,7] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 4

[4,1,5,7,8,3,2,6] => [[.,.],[[[.,[.,[.,.]]],.],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => 3

[4,7,1,8,3,6,2,5] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[4,1,7,8,5,2,3,6] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[4,7,1,6,3,2,8,5] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[6,8,1,4,3,7,2,5] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[7,8,3,2,4,1,6,5] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[6,7,1,4,3,8,2,5] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[8,1,2,3,6,7,5,4] => [[.,.],[.,[.,[[[.,[.,.]],.],.]]]] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => 4

[7,1,2,3,6,8,5,4] => [[.,.],[.,[.,[[[.,[.,.]],.],.]]]] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => 4

[7,8,2,6,3,4,1,5] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[6,8,2,7,3,4,1,5] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[6,7,2,8,3,4,1,5] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[3,7,8,1,4,2,6,5] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[3,6,8,1,4,2,7,5] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[3,5,7,8,2,4,1,6] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[3,6,7,1,4,2,8,5] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[5,8,3,7,1,4,2,6] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,7,3,2,4,1,8,5] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[7,1,2,3,5,6,8,4] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4

[5,1,2,3,7,8,6,4] => [[.,.],[.,[.,[[[.,[.,.]],.],.]]]] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => 4

[6,1,2,3,5,7,8,4] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4

[2,4,8,1,7,3,6,5] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[6,8,1,4,7,2,3,5] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[6,8,1,7,3,5,4,2] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2

[6,8,1,2,7,3,5,4] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4

[1,5,8,2,7,6,3,4] => [.,[[.,[.,.]],[[[.,.],.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 4

[5,8,2,7,6,3,4,1] => [[[.,[.,.]],[[[.,.],.],[.,.]]],.] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 1

[6,2,8,1,7,3,5,4] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[6,8,2,1,7,4,3,5] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[2,5,8,4,1,7,6,3] => [[.,[[.,[.,.]],.]],[[[.,.],.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2

[1,5,8,4,7,2,6,3] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 3

[5,6,3,1,2,4,8,7] => [[[.,[.,.]],.],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 4

[5,6,2,4,3,1,8,7] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[5,6,1,2,4,3,8,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4

[4,5,8,1,7,2,3,6] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[3,5,1,8,7,4,6,2] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2

[3,5,1,8,7,2,6,4] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[4,5,8,3,1,7,2,6] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[7,1,4,8,2,6,5,3] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3

[6,8,1,3,7,5,2,4] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3

[3,7,8,1,2,6,5,4] => [[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[1,3,7,8,2,6,5,4] => [.,[[.,[.,[.,.]]],[[[.,.],.],.]]] => [1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3

[2,3,7,8,1,6,5,4] => [[.,[.,[.,[.,.]]]],[[[.,.],.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[2,7,8,1,3,6,5,4] => [[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[8,1,2,6,7,3,5,4] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 4

[8,1,2,6,7,5,3,4] => [[.,.],[.,[[[.,[.,.]],.],[.,.]]]] => [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => 4

[8,2,5,7,1,3,6,4] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[2,8,1,6,7,3,5,4] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[2,6,8,3,7,1,5,4] => [[.,[[.,[.,.]],[.,.]]],[[.,.],.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2

[6,8,3,4,1,7,5,2] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[6,8,3,7,4,1,5,2] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[2,6,8,3,7,5,1,4] => [[.,[[.,[.,.]],[[.,.],.]]],[.,.]] => [1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2

[2,8,1,6,7,5,3,4] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[8,2,5,7,1,6,3,4] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[8,4,7,2,3,6,1,5] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[8,5,7,4,2,6,1,3] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[8,3,5,7,4,1,6,2] => [[[.,.],[[.,[.,.]],.]],[[.,.],.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[8,2,3,5,7,1,6,4] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[8,2,4,7,3,6,1,5] => [[[.,.],[[.,[.,.]],[.,.]]],[.,.]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[8,2,7,1,4,6,3,5] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[8,4,7,1,3,6,2,5] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[1,6,8,3,7,2,5,4] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 3

[8,3,5,7,1,2,6,4] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[1,4,6,8,2,7,5,3] => [.,[[.,[.,[.,.]]],[[[.,.],.],.]]] => [1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3

[8,5,6,3,1,7,4,2] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[5,6,2,8,1,7,4,3] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[8,3,5,7,1,6,2,4] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[1,6,8,3,7,5,2,4] => [.,[[[.,[.,.]],[[.,.],.]],[.,.]]] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 3

[6,3,8,2,7,5,1,4] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[6,8,4,2,7,1,5,3] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[8,4,5,7,3,1,6,2] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[8,3,4,7,2,6,1,5] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[8,3,7,2,4,6,1,5] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[2,8,4,5,7,1,6,3] => [[.,[[.,.],[.,[.,.]]]],[[.,.],.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[7,3,4,8,2,1,6,5] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[6,3,4,8,2,7,5,1] => [[[[.,.],[.,[.,.]]],[[.,.],.]],.] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => 1

[5,3,4,1,8,2,7,6] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[8,1,4,5,2,3,7,6] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[4,5,3,2,8,7,1,6] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[5,6,3,2,7,8,4,1] => [[[[.,[.,.]],.],[[.,[.,.]],.]],.] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 1

[5,7,3,2,6,4,8,1] => [[[[.,[.,.]],.],[[.,.],[.,.]]],.] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 1

[6,7,3,2,5,4,1,8] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[2,7,5,6,1,3,4,8] => [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[5,6,4,7,2,8,3,1] => [[[[.,[.,.]],[.,.]],[[.,.],.]],.] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 1

[6,4,5,7,1,8,2,3] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,4,6,1,7,8,2,3] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[8,1,5,6,7,2,3,4] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[6,3,5,1,8,7,2,4] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[7,3,6,1,8,5,4,2] => [[[.,.],[.,.]],[[[[.,.],.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[6,3,7,8,5,4,2,1] => [[[[.,.],[[[.,[.,.]],.],.]],.],.] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 1

[5,3,7,8,6,4,1,2] => [[[.,.],[[[.,[.,.]],.],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => 2

[3,4,7,8,6,1,5,2] => [[.,[.,[[.,[.,.]],.]]],[[.,.],.]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 2

[7,5,6,4,3,1,8,2] => [[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[4,6,7,5,3,8,1,2] => [[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => [1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[3,6,7,5,1,4,8,2] => [[.,[[.,[.,.]],.]],[[.,[.,.]],.]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 2

[8,1,6,7,5,4,2,3] => [[.,.],[[[[.,[.,.]],.],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => 3

[7,1,5,8,2,6,3,4] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[5,7,8,1,2,4,6,3] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[5,7,8,1,3,4,6,2] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[5,8,1,7,3,4,6,2] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 2

[8,1,5,7,2,4,6,3] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3

[7,1,2,4,6,8,5,3] => [[.,.],[.,[[.,[[.,[.,.]],.]],.]]] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 3

[7,1,2,6,8,5,3,4] => [[.,.],[.,[[[.,[.,.]],.],[.,.]]]] => [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => 4

[6,1,2,7,8,5,3,4] => [[.,.],[.,[[[.,[.,.]],.],[.,.]]]] => [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => 4

[5,7,1,3,8,4,6,2] => [[.,[.,.]],[[.,[[.,.],[.,.]]],.]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 2

[5,7,1,8,4,2,6,3] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[7,1,4,5,2,8,6,3] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3

[4,7,3,1,5,8,6,2] => [[[.,[.,.]],.],[[.,[[.,.],.]],.]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 2

[8,3,7,1,2,6,4,5] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[5,8,1,7,2,4,6,3] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[5,8,1,3,4,7,6,2] => [[.,[.,.]],[[.,[.,[[.,.],.]]],.]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 2

[8,1,2,6,7,4,5,3] => [[.,.],[.,[[[.,[.,.]],[.,.]],.]]] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 3

[1,2,3,5,8,4,7,6] => [.,[.,[.,[[.,[.,.]],[[.,.],.]]]]] => [1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 5

[3,1,7,8,4,6,5,2] => [[.,.],[[[.,[.,.]],[[.,.],.]],.]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2

[1,2,3,6,8,5,4,7] => [.,[.,[.,[[[.,[.,.]],.],[.,.]]]]] => [1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 5

[7,8,5,6,3,1,4,2] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[7,5,6,3,1,4,2,8] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[7,5,8,3,1,4,2,6] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[7,8,5,3,1,4,2,6] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[7,8,5,3,1,6,2,4] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[7,8,5,3,1,6,4,2] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2

[7,8,5,3,6,4,1,2] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[7,5,8,3,4,1,6,2] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[7,5,6,3,4,1,8,2] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[7,5,6,3,1,2,8,4] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[7,5,8,3,6,4,1,2] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[7,5,8,3,6,1,4,2] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[7,5,8,3,1,6,4,2] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[7,5,6,8,3,1,4,2] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[7,5,6,3,1,8,2,4] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[7,5,6,3,1,8,4,2] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[7,5,6,3,8,1,4,2] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[7,5,6,3,8,4,1,2] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[3,6,2,5,4,1,8,7] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[3,5,2,8,4,7,6,1] => [[[.,[.,.]],[[.,.],[[.,.],.]]],.] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 1

[5,4,7,3,2,8,6,1] => [[[[[.,.],[.,.]],.],[[.,.],.]],.] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1

[5,4,8,3,2,7,6,1] => [[[[[.,.],[.,.]],.],[[.,.],.]],.] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1

[6,4,5,3,2,1,8,7] => [[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[4,5,8,3,2,7,6,1] => [[[[.,[.,[.,.]]],.],[[.,.],.]],.] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1

[5,8,4,3,2,7,6,1] => [[[[[.,[.,.]],.],.],[[.,.],.]],.] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 1

[2,1,5,8,4,7,6,3] => [[.,.],[[[.,[.,.]],[[.,.],.]],.]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2

[5,7,4,3,2,8,6,1] => [[[[[.,[.,.]],.],.],[[.,.],.]],.] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 1

[4,7,8,3,6,5,2,1] => [[[[.,[.,[.,.]]],[[.,.],.]],.],.] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

[4,6,8,3,7,5,2,1] => [[[[.,[.,[.,.]]],[[.,.],.]],.],.] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

[8,4,5,3,2,7,6,1] => [[[[[.,.],[.,.]],.],[[.,.],.]],.] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1

[8,4,7,3,6,5,2,1] => [[[[[.,.],[.,.]],[[.,.],.]],.],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

[8,4,6,3,7,5,2,1] => [[[[[.,.],[.,.]],[[.,.],.]],.],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

[7,4,6,3,8,5,2,1] => [[[[[.,.],[.,.]],[[.,.],.]],.],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

[3,7,2,6,8,5,4,1] => [[[.,[.,.]],[[[.,[.,.]],.],.]],.] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 1

[3,8,2,6,7,5,4,1] => [[[.,[.,.]],[[[.,[.,.]],.],.]],.] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 1

[3,8,2,5,4,7,6,1] => [[[.,[.,.]],[[.,.],[[.,.],.]]],.] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 1

[3,7,2,8,6,5,4,1] => [[[.,[.,.]],[[[[.,.],.],.],.]],.] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1

[3,6,2,8,7,5,4,1] => [[[.,[.,.]],[[[[.,.],.],.],.]],.] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1

[6,4,7,3,8,5,2,1] => [[[[[.,.],[.,.]],[[.,.],.]],.],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

[6,4,8,3,7,5,2,1] => [[[[[.,.],[.,.]],[[.,.],.]],.],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

[7,4,8,3,6,5,2,1] => [[[[[.,.],[.,.]],[[.,.],.]],.],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

[7,4,5,3,2,8,6,1] => [[[[[.,.],[.,.]],.],[[.,.],.]],.] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1

[7,8,4,3,6,5,2,1] => [[[[[.,[.,.]],.],[[.,.],.]],.],.] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 1

[6,8,5,7,4,3,2,1] => [[[[[[.,[.,.]],[.,.]],.],.],.],.] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1

[6,8,4,3,7,5,2,1] => [[[[[.,[.,.]],.],[[.,.],.]],.],.] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 1

[6,7,4,3,8,5,2,1] => [[[[[.,[.,.]],.],[[.,.],.]],.],.] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 1

[4,6,8,3,5,7,1,2] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[6,8,1,2,4,5,7,3] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 3

[3,5,8,2,4,7,1,6] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[8,3,5,2,4,1,6,7] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[4,2,5,7,3,6,1,8] => [[[.,.],[[.,[.,.]],[.,.]]],[.,.]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[4,5,2,8,3,1,6,7] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[4,2,5,8,3,7,1,6] => [[[.,.],[[.,[.,.]],[.,.]]],[.,.]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[2,1,6,8,4,7,3,5] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[1,2,5,8,3,6,7,4] => [.,[.,[[.,[.,.]],[[.,[.,.]],.]]]] => [1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 4

[5,3,6,8,4,7,1,2] => [[[.,.],[[.,[.,.]],[.,.]]],[.,.]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[3,1,2,6,8,5,7,4] => [[.,.],[.,[[[.,[.,.]],[.,.]],.]]] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 3

[5,4,8,3,2,1,6,7] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3

[4,3,6,2,7,5,1,8] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[4,6,3,2,1,8,5,7] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[3,5,1,2,7,8,6,4] => [[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 3

[5,4,7,3,8,6,1,2] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[5,8,4,7,6,3,1,2] => [[[[.,[.,.]],[[.,.],.]],.],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2

[8,3,5,1,2,7,6,4] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[4,8,3,1,7,2,6,5] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[4,6,3,1,5,2,8,7] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[4,7,3,6,5,2,1,8] => [[[[.,[.,.]],[[.,.],.]],.],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2

[1,6,7,2,8,4,5,3] => [.,[[.,[.,.]],[[[.,.],[.,.]],.]]] => [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 3

[5,7,1,8,2,4,6,3] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[5,1,2,7,8,3,6,4] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 4

[2,4,1,7,8,6,3,5] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[7,8,3,2,5,6,1,4] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[7,4,6,2,5,3,1,8] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[8,2,4,1,6,5,3,7] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[4,2,8,1,7,5,3,6] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[8,2,4,1,7,6,3,5] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[8,5,7,3,6,4,1,2] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[6,8,3,7,5,4,1,2] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[8,1,6,7,5,2,4,3] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3

[2,8,1,7,5,4,3,6] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[2,5,1,8,6,4,3,7] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[5,7,2,6,4,3,1,8] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[1,7,8,6,5,2,4,3] => [.,[[[[.,[.,.]],.],.],[[.,.],.]]] => [1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 3

[4,6,3,2,7,5,1,8] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[7,4,8,3,1,6,2,5] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[7,1,5,8,3,2,6,4] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3

[5,7,4,1,8,2,6,3] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[5,7,4,3,1,8,6,2] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2

[7,4,6,3,5,2,1,8] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[1,3,5,6,8,4,2,7] => [.,[[.,[[.,[.,[.,.]]],.]],[.,.]]] => [1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3

[7,3,6,8,5,1,2,4] => [[[.,.],[[.,[.,.]],.]],[.,[.,.]]] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[1,3,7,2,6,8,4,5] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 4

[4,2,6,7,3,5,1,8] => [[[.,.],[[.,[.,.]],[.,.]]],[.,.]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[3,6,2,4,7,5,1,8] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[3,6,2,4,1,8,5,7] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[7,3,8,2,1,6,4,5] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[7,3,5,2,1,8,6,4] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[3,8,2,7,1,5,4,6] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,6,8,2,1,5,4,7] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[2,4,8,1,6,5,3,7] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[4,2,8,1,5,7,3,6] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[7,2,5,6,4,3,1,8] => [[[.,.],[[[.,[.,.]],.],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => 2

[1,2,5,7,8,4,3,6] => [.,[.,[[[.,[.,[.,.]]],.],[.,.]]]] => [1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 4

[1,2,7,8,3,6,5,4] => [.,[.,[[.,[.,.]],[[[.,.],.],.]]]] => [1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 4

[7,1,5,8,3,4,6,2] => [[.,.],[[[.,[.,.]],[.,[.,.]]],.]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[2,7,1,4,5,8,3,6] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[7,1,4,5,6,8,2,3] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 3

[7,1,3,4,2,6,8,5] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3

[7,1,5,6,4,3,8,2] => [[.,.],[[[[.,[.,.]],.],[.,.]],.]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 2

[2,5,1,7,4,3,6,8] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[2,5,1,4,7,8,6,3] => [[.,[.,.]],[[.,[[.,[.,.]],.]],.]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 2

[3,5,1,4,8,6,2,7] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3

[3,6,2,4,7,8,1,5] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[5,6,2,4,8,7,1,3] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[6,3,8,2,4,7,1,5] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[6,5,7,8,2,4,1,3] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,3,4,2,8,5,1,7] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[3,4,7,2,5,8,1,6] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[4,6,8,1,3,5,2,7] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[4,3,8,1,2,7,5,6] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[3,4,1,7,5,6,8,2] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 2

[3,4,1,5,7,6,2,8] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3

[8,4,7,2,5,3,6,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[4,7,8,1,2,3,6,5] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[6,7,5,2,1,3,8,4] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 3

[8,4,5,3,7,2,6,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[7,2,3,4,1,6,5,8] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,8,5,7,2,1,3,4] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3

[6,3,5,2,1,7,4,8] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[6,8,5,3,1,4,2,7] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[1,6,8,2,4,3,7,5] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 4

[1,5,6,2,4,7,3,8] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 4

[1,5,6,2,4,7,8,3] => [.,[[.,[.,.]],[[.,[.,[.,.]]],.]]] => [1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 3

[1,5,8,2,4,7,3,6] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 4

[1,5,7,2,4,8,3,6] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 4

[1,6,7,2,4,3,8,5] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 4

[1,5,6,7,2,4,8,3] => [.,[[.,[.,[.,.]]],[[.,[.,.]],.]]] => [1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3

[1,5,8,2,4,6,7,3] => [.,[[.,[.,.]],[[.,[.,[.,.]]],.]]] => [1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 3

[1,5,7,2,4,6,8,3] => [.,[[.,[.,.]],[[.,[.,[.,.]]],.]]] => [1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 3

[1,5,7,8,3,2,4,6] => [.,[[[.,[.,[.,.]]],.],[.,[.,.]]]] => [1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[1,5,8,3,2,4,6,7] => [.,[[[.,[.,.]],.],[.,[.,[.,.]]]]] => [1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 5

[1,5,6,2,4,8,3,7] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 4

[1,5,6,2,4,8,7,3] => [.,[[.,[.,.]],[[.,[[.,.],.]],.]]] => [1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 3

[1,6,7,5,2,3,8,4] => [.,[[[.,[.,.]],.],[.,[[.,.],.]]]] => [1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 4

[1,5,8,3,2,4,7,6] => [.,[[[.,[.,.]],.],[.,[[.,.],.]]]] => [1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 4

[1,6,8,4,2,3,7,5] => [.,[[[.,[.,.]],.],[.,[[.,.],.]]]] => [1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 4

[1,6,8,5,2,3,7,4] => [.,[[[.,[.,.]],.],[.,[[.,.],.]]]] => [1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 4

[1,5,7,3,2,4,8,6] => [.,[[[.,[.,.]],.],[.,[[.,.],.]]]] => [1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 4

[1,6,7,4,2,3,8,5] => [.,[[[.,[.,.]],.],[.,[[.,.],.]]]] => [1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 4

[4,7,1,3,8,2,5,6] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[4,7,8,1,2,6,5,3] => [[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[6,8,5,7,3,2,1,4] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2

[1,4,8,3,6,2,5,7] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 4

[7,8,1,5,4,6,2,3] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[7,8,1,5,2,4,3,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[7,8,5,6,1,3,2,4] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[7,8,1,3,2,6,4,5] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[7,8,1,6,2,4,3,5] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[7,8,1,4,2,6,3,5] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[7,8,1,4,2,5,3,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[7,8,2,1,4,3,6,5] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[1,4,7,3,2,5,8,6] => [.,[[[.,[.,.]],.],[.,[[.,.],.]]]] => [1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 4

[6,8,5,4,3,2,1,7] => [[[[[[.,[.,.]],.],.],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 2

[6,8,1,4,3,2,7,5] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[6,8,5,1,3,2,7,4] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[1,4,5,8,3,7,6,2] => [.,[[[.,[.,[.,.]]],[[.,.],.]],.]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2

[6,8,5,4,1,2,7,3] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 3

[6,8,2,4,3,7,1,5] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[7,5,8,4,3,2,1,6] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2

[5,4,6,8,2,1,7,3] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[6,1,4,5,3,2,8,7] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3

[5,7,1,2,4,3,8,6] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4

[5,3,6,8,1,7,2,4] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,2,6,8,5,7,1,4] => [[[.,.],[[.,[.,.]],[.,.]]],[.,.]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[6,3,7,2,4,8,5,1] => [[[[.,.],[.,.]],[.,[[.,.],.]]],.] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[8,4,7,1,2,5,6,3] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[8,3,5,6,7,4,1,2] => [[[.,.],[[.,[.,[.,.]]],.]],[.,.]] => [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => 2

[4,2,7,1,8,5,6,3] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[4,7,8,3,1,5,6,2] => [[[.,[.,[.,.]]],.],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[3,4,7,2,8,5,6,1] => [[[.,[.,[.,.]]],[[.,.],[.,.]]],.] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[3,7,1,4,8,5,6,2] => [[.,[.,.]],[[.,[[.,.],[.,.]]],.]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 2

[7,8,2,6,4,1,5,3] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[4,5,2,7,6,1,8,3] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[5,1,6,8,4,7,2,3] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[7,3,5,8,4,2,1,6] => [[[[.,.],[[.,[.,.]],.]],.],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => 2

[3,2,5,8,4,1,7,6] => [[[.,.],[[.,[.,.]],.]],[[.,.],.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[8,4,7,1,5,2,3,6] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[4,7,8,1,3,5,6,2] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[4,8,2,7,3,5,6,1] => [[[.,[.,.]],[[.,.],[.,[.,.]]]],.] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 1

[3,8,1,7,2,5,6,4] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[8,2,3,7,1,5,6,4] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[4,3,8,2,7,6,1,5] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[6,8,4,2,1,3,7,5] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 3

[7,8,2,4,3,5,6,1] => [[[.,[.,.]],[[.,.],[.,[.,.]]]],.] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 1

[6,8,5,2,7,4,3,1] => [[[[.,[.,.]],.],[[[.,.],.],.]],.] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 1

[3,6,8,1,4,5,2,7] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[6,8,1,2,4,5,3,7] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4

[5,8,1,6,2,3,4,7] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[8,3,6,1,4,5,2,7] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[2,3,6,8,4,5,1,7] => [[.,[.,[[.,[.,.]],[.,.]]]],[.,.]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 2

[5,8,4,3,7,6,1,2] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[6,5,8,4,3,1,7,2] => [[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[7,2,8,1,3,6,4,5] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[4,8,3,2,5,6,7,1] => [[[[.,[.,.]],.],[.,[.,[.,.]]]],.] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1

[8,2,3,1,5,6,7,4] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[1,4,8,2,3,6,7,5] => [.,[[.,[.,.]],[.,[[.,[.,.]],.]]]] => [1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 4

[3,1,2,7,8,6,4,5] => [[.,.],[.,[[[.,[.,.]],.],[.,.]]]] => [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => 4

[3,5,8,1,2,4,7,6] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[4,5,8,1,2,3,7,6] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[4,2,7,1,8,6,3,5] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[5,4,8,2,3,6,7,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1

[5,8,3,6,7,4,1,2] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[2,3,1,6,8,4,7,5] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[1,4,7,3,2,8,5,6] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 4

[2,7,1,4,3,8,5,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[2,4,1,8,6,3,7,5] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[6,8,5,1,7,2,3,4] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[3,5,2,8,6,1,7,4] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[8,2,5,6,1,4,7,3] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[2,6,1,8,3,7,5,4] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[4,7,1,6,2,8,5,3] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[3,6,8,5,1,2,7,4] => [[.,[[.,[.,.]],.]],[.,[[.,.],.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 3

[5,1,4,8,2,6,7,3] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3

[4,8,2,5,1,6,7,3] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[5,4,8,3,7,6,1,2] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[5,3,4,8,1,6,7,2] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[7,5,8,4,1,2,6,3] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[7,5,8,4,6,1,3,2] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[7,6,8,1,4,3,2,5] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[6,7,3,8,4,5,1,2] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[6,7,4,5,1,8,2,3] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,5,3,8,6,7,1,2] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[4,8,3,6,5,7,1,2] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[5,6,4,7,1,8,2,3] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,6,1,7,3,8,2,4] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[5,6,1,8,2,7,3,4] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[5,6,1,8,4,7,2,3] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[4,8,1,6,5,7,2,3] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[4,5,1,8,6,7,2,3] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[7,8,4,5,1,6,2,3] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,8,2,3,1,6,5,7] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,6,2,8,1,4,3,7] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,6,3,4,1,8,2,7] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[7,8,2,5,3,4,1,6] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[7,8,1,5,3,6,2,4] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[6,7,2,5,3,4,1,8] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[6,7,1,5,3,8,2,4] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[6,7,5,8,1,4,2,3] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,7,2,3,1,8,4,5] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,7,2,8,1,4,3,5] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,4,2,7,5,6,1,8] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[3,4,1,7,5,8,2,6] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[2,3,1,7,5,8,4,6] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[2,3,1,8,4,7,5,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[7,8,2,3,1,6,4,5] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[7,8,2,6,1,4,3,5] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,8,1,4,3,7,5,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[3,7,2,5,4,6,1,8] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[4,5,2,7,3,6,1,8] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[4,5,1,8,2,7,3,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[3,4,1,8,2,7,5,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[3,4,1,8,6,7,2,5] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[3,4,2,5,1,8,6,7] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,4,2,8,1,6,5,7] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,8,2,5,1,6,4,7] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,5,2,8,1,6,3,7] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,5,3,6,1,8,2,7] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[7,1,5,8,4,6,2,3] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[8,6,7,1,4,2,5,3] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[7,6,8,2,4,5,1,3] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[8,6,7,2,4,1,5,3] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[8,5,7,2,1,4,3,6] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[8,5,7,2,1,4,6,3] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[8,5,7,4,1,6,2,3] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[8,5,7,4,1,2,6,3] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[6,1,5,8,4,2,7,3] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3

[5,8,3,6,4,1,2,7] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[8,4,7,2,1,5,3,6] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[8,4,7,2,1,5,6,3] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[2,5,7,8,6,3,4,1] => [[.,[[.,[[.,[.,.]],.]],[.,.]]],.] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[4,6,3,2,1,5,8,7] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 3

[5,8,1,3,7,6,4,2] => [[.,[.,.]],[[.,[[[.,.],.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 2

[4,7,2,3,6,1,8,5] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[4,2,6,8,5,7,3,1] => [[[.,.],[[[.,[.,.]],[.,.]],.]],.] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1

[8,1,6,7,5,3,4,2] => [[.,.],[[[[.,[.,.]],.],[.,.]],.]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 2

[6,4,7,8,5,3,2,1] => [[[[[.,.],[[.,[.,.]],.]],.],.],.] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 1

[6,3,7,1,5,2,8,4] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[3,2,6,8,4,7,5,1] => [[[.,.],[[.,[.,.]],[[.,.],.]]],.] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1

[8,4,6,1,3,2,5,7] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[4,2,5,1,6,7,8,3] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[3,7,1,4,6,8,5,2] => [[.,[.,.]],[[.,[[.,[.,.]],.]],.]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 2

[7,8,2,5,6,1,4,3] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[2,6,7,3,5,1,8,4] => [[.,[[.,[.,.]],[.,.]]],[[.,.],.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2

[7,6,8,4,2,5,3,1] => [[[[[.,.],[.,.]],.],[[.,.],.]],.] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1

[8,5,7,1,6,3,2,4] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[6,5,7,2,8,4,3,1] => [[[[.,.],[.,.]],[[[.,.],.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1

[6,5,8,2,1,7,3,4] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[6,2,5,8,4,3,7,1] => [[[.,.],[[[.,[.,.]],.],[.,.]]],.] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1

[8,6,7,1,5,4,3,2] => [[[.,.],[.,.]],[[[[.,.],.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[2,1,6,8,5,4,3,7] => [[.,.],[[[[.,[.,.]],.],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => 3

[4,8,2,7,6,1,3,5] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[3,8,1,2,6,7,4,5] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4

[5,8,4,3,2,7,1,6] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2

[5,8,4,7,2,1,3,6] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3

[6,3,8,2,4,5,7,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1

[5,8,4,2,3,6,1,7] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[5,8,2,4,3,1,6,7] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[1,4,8,2,6,3,5,7] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 5

[1,3,8,2,6,4,5,7] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 5

[1,5,7,2,3,6,4,8] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 5

[1,3,8,2,4,5,7,6] => [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => [1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 5

[1,7,8,2,3,6,4,5] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 5

[1,6,7,8,2,3,5,4] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[1,7,8,2,5,3,6,4] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 4

[1,7,8,2,4,5,3,6] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 4

[1,2,7,8,3,6,4,5] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => [1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 5

[1,7,8,2,4,3,6,5] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 4

[6,7,3,1,5,2,8,4] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[6,8,3,1,5,2,7,4] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[6,7,4,5,1,2,8,3] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[6,7,5,4,1,2,8,3] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 3

[6,3,8,1,5,2,7,4] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[5,6,8,4,1,7,2,3] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[4,6,8,5,7,1,2,3] => [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[5,3,8,1,6,7,2,4] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[4,6,7,5,8,1,2,3] => [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[4,7,5,6,8,1,2,3] => [[.,[[.,.],[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[4,6,5,7,8,1,2,3] => [[.,[[.,.],[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[5,7,4,6,1,8,2,3] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,8,4,6,1,7,2,3] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,8,3,1,6,7,2,4] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[5,7,3,1,6,8,2,4] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[5,6,3,1,7,8,2,4] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[5,8,3,1,7,6,2,4] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[5,7,4,8,1,6,2,3] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,4,6,8,1,7,2,3] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,3,8,1,7,6,2,4] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[4,7,8,6,5,1,2,3] => [[.,[[[.,[.,.]],.],.]],[.,[.,.]]] => [1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 3

[2,4,6,3,7,5,1,8] => [[.,[[.,[.,.]],[[.,.],.]]],[.,.]] => [1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2

[2,3,1,8,6,5,4,7] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[3,6,8,2,1,4,5,7] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[3,5,8,2,4,1,6,7] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[2,5,7,1,4,8,6,3] => [[.,[.,[.,.]]],[[.,[[.,.],.]],.]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[2,4,8,1,5,7,6,3] => [[.,[.,[.,.]]],[[.,[[.,.],.]],.]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[2,4,8,1,3,5,7,6] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[4,8,6,7,1,2,3,5] => [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[4,1,2,6,7,5,3,8] => [[.,.],[.,[[[.,[.,.]],.],[.,.]]]] => [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => 4

[3,4,1,7,5,6,2,8] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[4,1,6,7,5,3,8,2] => [[.,.],[[[[.,[.,.]],.],[.,.]],.]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 2

[7,3,5,8,1,4,2,6] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[1,4,7,8,5,6,2,3] => [.,[[.,[[.,[.,.]],[.,.]]],[.,.]]] => [1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 3

[3,4,7,1,5,8,6,2] => [[.,[.,[.,.]]],[[.,[[.,.],.]],.]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[3,6,1,4,7,8,5,2] => [[.,[.,.]],[[.,[[.,[.,.]],.]],.]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 2

[1,6,8,4,7,5,2,3] => [.,[[[.,[.,.]],[[.,.],.]],[.,.]]] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 3

[6,8,1,3,5,7,2,4] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[3,8,1,6,5,4,2,7] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[4,8,1,6,7,5,3,2] => [[.,[.,.]],[[[[.,[.,.]],.],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 2

[4,7,2,6,8,1,5,3] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[5,7,8,6,2,1,4,3] => [[[.,[[.,[.,.]],.]],.],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 2

[3,7,2,4,5,1,6,8] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[3,4,1,7,5,2,6,8] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[4,8,2,1,3,7,5,6] => [[[.,[.,.]],.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[4,3,7,8,5,1,6,2] => [[[.,.],[[.,[.,.]],.]],[[.,.],.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[5,4,8,2,7,6,1,3] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[5,8,2,6,3,4,1,7] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[5,1,7,8,4,3,6,2] => [[.,.],[[[[.,[.,.]],.],[.,.]],.]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 2

[6,3,8,1,4,7,5,2] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[3,8,4,5,6,1,2,7] => [[.,[[.,.],[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[1,4,3,5,7,8,2,6] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[3,6,7,2,4,8,1,5] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[4,6,1,8,5,7,2,3] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[4,7,1,2,8,5,6,3] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 3

[1,4,7,2,8,5,6,3] => [.,[[.,[.,.]],[[[.,.],[.,.]],.]]] => [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 3

[3,6,8,1,5,7,2,4] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[6,8,1,5,7,2,3,4] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[7,6,8,1,2,3,5,4] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[2,7,1,5,8,6,3,4] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3

[2,4,7,1,8,5,6,3] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[4,7,2,1,8,5,6,3] => [[[.,[.,.]],.],[[[.,.],[.,.]],.]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[7,6,8,2,1,3,5,4] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[6,7,4,1,8,5,3,2] => [[[.,[.,.]],.],[[[[.,.],.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2

[6,7,4,3,1,8,5,2] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2

[7,2,8,1,6,4,5,3] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[7,1,6,8,5,4,2,3] => [[.,.],[[[[.,[.,.]],.],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => 3

[7,1,2,6,8,5,4,3] => [[.,.],[.,[[[[.,[.,.]],.],.],.]]] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 3

[7,6,8,3,1,2,5,4] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[3,6,7,1,8,5,4,2] => [[.,[.,[.,.]]],[[[[.,.],.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[7,2,6,8,5,4,1,3] => [[[.,.],[[[.,[.,.]],.],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => 2

[7,6,8,2,3,1,5,4] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[2,7,1,6,8,5,4,3] => [[.,[.,.]],[[[[.,[.,.]],.],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 2

[6,7,3,1,8,5,4,2] => [[[.,[.,.]],.],[[[[.,.],.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2

[6,7,1,8,5,4,3,2] => [[.,[.,.]],[[[[[.,.],.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2

[7,6,8,3,2,1,5,4] => [[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[4,7,8,5,6,1,3,2] => [[.,[[.,[.,.]],[.,.]]],[[.,.],.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2

[5,6,4,8,1,2,7,3] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[8,1,5,6,7,2,4,3] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[6,4,5,1,8,2,7,3] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[5,4,6,7,1,2,8,3] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[4,3,6,7,2,1,5,8] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[5,3,6,7,1,4,2,8] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[8,1,4,6,7,3,2,5] => [[.,.],[[[.,[.,[.,.]]],.],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => 3

[8,1,3,6,7,4,5,2] => [[.,.],[[.,[[.,[.,.]],[.,.]]],.]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 2

[5,2,6,7,1,4,8,3] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[4,2,6,7,3,1,8,5] => [[[.,.],[[.,[.,.]],.]],[[.,.],.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[6,2,4,1,5,8,7,3] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[8,1,4,5,3,7,2,6] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[6,3,4,1,5,8,2,7] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[5,3,4,2,1,8,6,7] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[4,3,5,2,7,1,6,8] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[5,6,3,8,1,4,2,7] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,7,8,2,3,1,6,5] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[5,6,2,8,1,4,7,3] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[6,2,3,1,5,7,8,4] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[7,8,4,2,1,6,5,3] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2

[7,8,4,2,1,5,6,3] => [[[[.,[.,.]],.],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 2

[6,2,3,4,7,8,1,5] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2

[7,8,3,4,6,2,1,5] => [[[[.,[.,.]],[.,[.,.]]],.],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2

[6,2,3,7,8,5,1,4] => [[[.,.],[.,[[.,[.,.]],.]]],[.,.]] => [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => 2

[6,2,4,1,7,3,5,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[4,5,6,8,3,2,1,7] => [[[[.,[.,[.,[.,.]]]],.],.],[.,.]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2

[5,6,1,4,2,3,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[5,6,8,4,3,7,1,2] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[5,6,1,4,2,3,8,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[6,2,3,4,5,8,1,7] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2

[5,6,2,4,1,7,8,3] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[5,7,2,4,1,8,6,3] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[5,4,7,8,3,2,1,6] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2

[5,7,1,3,4,2,6,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[5,8,1,3,4,2,6,7] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[4,8,2,6,3,7,5,1] => [[[.,[.,.]],[[.,.],[[.,.],.]]],.] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 1

[4,3,8,1,6,2,5,7] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[5,8,4,3,7,1,6,2] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[6,8,1,2,4,3,5,7] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5

[4,3,8,2,7,5,6,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[4,1,3,8,2,6,5,7] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[3,7,8,1,5,4,2,6] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[7,3,8,1,5,4,6,2] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[3,4,8,1,6,2,5,7] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[3,4,2,1,8,6,5,7] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[3,6,7,8,4,1,2,5] => [[.,[[.,[.,[.,.]]],.]],[.,[.,.]]] => [1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[4,1,7,8,5,3,2,6] => [[.,.],[[[[.,[.,.]],.],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => 3

[3,7,8,2,6,4,5,1] => [[[.,[.,[.,.]]],[[.,.],[.,.]]],.] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[4,2,3,8,1,6,5,7] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,3,7,8,5,2,1,6] => [[[[.,.],[[.,[.,.]],.]],.],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => 2

[2,6,8,4,7,3,1,5] => [[.,[[[.,[.,.]],[.,.]],.]],[.,.]] => [1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2

[3,2,4,8,1,6,5,7] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,4,8,3,6,1,5,7] => [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[3,1,4,8,2,6,5,7] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[6,7,2,8,3,5,4,1] => [[[.,[.,.]],[[.,.],[[.,.],.]]],.] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 1

[4,8,3,6,2,1,5,7] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3

[3,5,8,2,6,1,4,7] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[2,4,5,7,3,8,1,6] => [[.,[[.,[.,[.,.]]],[.,.]]],[.,.]] => [1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[6,2,4,5,8,3,1,7] => [[[.,.],[[.,[.,[.,.]]],.]],[.,.]] => [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => 2

[4,8,1,2,5,6,3,7] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4

[8,1,3,5,2,6,4,7] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[6,2,5,1,8,4,3,7] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[3,6,1,5,8,4,2,7] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[6,1,4,5,8,3,2,7] => [[.,.],[[[.,[.,[.,.]]],.],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => 3

[5,6,4,8,1,3,2,7] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,8,4,3,7,2,6,1] => [[[[[.,[.,.]],.],[.,.]],[.,.]],.] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1

[4,6,8,3,7,2,5,1] => [[[[.,[.,[.,.]]],[.,.]],[.,.]],.] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[7,4,6,3,2,8,1,5] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[4,7,8,5,3,1,2,6] => [[[.,[[.,[.,.]],.]],.],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 3

[5,7,3,4,1,2,8,6] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[8,5,7,4,3,6,1,2] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[4,3,8,1,6,7,5,2] => [[[.,.],[.,.]],[[[.,[.,.]],.],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[4,7,8,3,6,1,5,2] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[1,5,7,3,2,6,8,4] => [.,[[[.,[.,.]],.],[[.,[.,.]],.]]] => [1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3

[1,6,7,3,2,5,8,4] => [.,[[[.,[.,.]],.],[[.,[.,.]],.]]] => [1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3

[3,2,6,8,5,7,4,1] => [[[.,.],[[[.,[.,.]],[.,.]],.]],.] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1

[5,8,2,3,6,7,4,1] => [[[.,[.,.]],[.,[[.,[.,.]],.]]],.] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 1

[2,5,7,4,1,8,3,6] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[4,2,6,1,7,8,3,5] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[3,7,1,8,4,2,5,6] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[8,3,5,2,7,6,1,4] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[3,6,2,8,7,1,5,4] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[4,2,7,8,6,1,5,3] => [[[.,.],[[.,[.,.]],.]],[[.,.],.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[6,8,2,4,7,1,5,3] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[6,8,3,1,7,5,2,4] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[5,8,1,6,7,2,4,3] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[6,2,8,1,5,7,4,3] => [[[.,.],[.,.]],[[[.,[.,.]],.],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[5,7,8,2,6,1,4,3] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[8,6,7,5,2,4,3,1] => [[[[[.,.],[.,.]],.],[[.,.],.]],.] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1

[7,2,6,8,1,5,4,3] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[1,2,7,8,5,6,4,3] => [.,[.,[[[[.,[.,.]],[.,.]],.],.]]] => [1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 3

[7,4,8,1,6,2,5,3] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[3,7,1,8,2,6,5,4] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[8,6,7,5,1,4,3,2] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[7,8,6,5,4,1,3,2] => [[[[[.,[.,.]],.],.],.],[[.,.],.]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2

[5,8,4,3,2,1,6,7] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 3

[6,4,7,3,2,1,8,5] => [[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[5,8,3,6,2,1,4,7] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3

[5,8,4,2,6,1,3,7] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[4,8,3,2,5,1,7,6] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[4,3,7,2,5,1,8,6] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[6,2,7,8,5,1,3,4] => [[[.,.],[[.,[.,.]],.]],[.,[.,.]]] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[6,4,7,3,1,5,8,2] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[5,4,7,3,1,8,6,2] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[5,8,3,2,1,4,7,6] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 3

[5,8,2,6,1,4,3,7] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,8,4,1,6,7,3,2] => [[[.,[.,.]],.],[[[.,[.,.]],.],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 2

[6,4,7,1,5,8,3,2] => [[[.,.],[.,.]],[[[.,[.,.]],.],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[4,8,3,1,5,6,7,2] => [[[.,[.,.]],.],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 2

[5,8,2,1,6,4,3,7] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[3,8,2,1,5,4,6,7] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[6,2,7,1,5,4,3,8] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[5,2,7,1,6,4,3,8] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[4,2,7,1,5,6,3,8] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[3,2,7,1,5,4,6,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[2,8,1,6,5,4,3,7] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[6,1,7,8,5,4,3,2] => [[.,.],[[[[[.,[.,.]],.],.],.],.]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2

[4,5,8,1,2,6,3,7] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[1,4,5,7,2,6,3,8] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[8,1,3,5,7,2,4,6] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[3,6,8,1,7,2,4,5] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[3,4,5,6,8,1,7,2] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[4,5,8,2,6,7,1,3] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[8,2,3,5,6,7,1,4] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2

[2,7,8,1,3,5,4,6] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[2,7,8,3,5,6,1,4] => [[.,[[.,[.,.]],[.,[.,.]]]],[.,.]] => [1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2

[2,4,5,7,8,1,6,3] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[4,5,8,1,7,6,3,2] => [[.,[.,[.,.]]],[[[[.,.],.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[2,3,6,7,8,1,5,4] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[3,6,8,1,2,5,4,7] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[1,3,6,7,2,5,4,8] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[3,6,8,1,7,5,4,2] => [[.,[.,[.,.]]],[[[[.,.],.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[8,2,6,7,5,4,1,3] => [[[.,.],[[[.,[.,.]],.],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => 2

[2,7,8,6,3,1,5,4] => [[.,[[[.,[.,.]],.],.]],[[.,.],.]] => [1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 2

[2,7,8,1,6,5,4,3] => [[.,[.,[.,.]]],[[[[.,.],.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[2,1,7,8,3,6,5,4] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3

[5,8,3,7,6,2,1,4] => [[[[.,[.,.]],[[.,.],.]],.],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2

[4,6,3,2,7,8,1,5] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[3,8,2,4,7,5,1,6] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[5,8,2,1,7,6,4,3] => [[[.,[.,.]],.],[[[[.,.],.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2

[6,3,8,1,5,7,4,2] => [[[.,.],[.,.]],[[[.,[.,.]],.],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[7,8,3,1,5,4,6,2] => [[[.,[.,.]],.],[[[.,.],[.,.]],.]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[7,2,8,1,4,6,5,3] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[6,2,3,1,4,5,8,7] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[5,6,1,4,3,2,8,7] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[5,7,1,8,3,6,2,4] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[6,8,1,4,5,3,2,7] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[6,7,1,5,4,3,8,2] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2

[6,5,7,1,3,8,2,4] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[8,2,6,1,4,7,3,5] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[5,8,1,6,3,7,4,2] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2

[8,3,5,6,1,7,4,2] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[7,3,5,8,1,6,2,4] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,7,8,5,1,6,4,3] => [[.,[[.,[.,.]],.]],[[[.,.],.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2

[2,8,3,4,6,1,5,7] => [[.,[[.,.],[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[3,4,7,2,8,1,5,6] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[4,2,3,5,8,1,6,7] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[3,2,4,6,1,5,8,7] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[3,2,4,5,6,8,1,7] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2

[5,6,8,1,4,2,7,3] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[1,5,7,8,4,6,2,3] => [.,[[[.,[.,[.,.]]],[.,.]],[.,.]]] => [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[1,3,5,7,8,6,2,4] => [.,[[.,[.,[[.,[.,.]],.]]],[.,.]]] => [1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 3

[3,5,7,8,6,1,2,4] => [[.,[.,[[.,[.,.]],.]]],[.,[.,.]]] => [1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 3

[3,5,1,6,8,2,7,4] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[3,1,5,6,8,2,7,4] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[2,3,5,6,8,1,7,4] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[5,6,4,8,2,1,7,3] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[2,5,1,6,8,3,7,4] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[5,1,2,6,8,3,7,4] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 4

[5,7,1,8,6,2,3,4] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[1,6,7,5,2,8,3,4] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 4

[2,6,7,5,1,8,3,4] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[5,7,2,8,6,1,3,4] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[3,5,7,8,6,2,1,4] => [[[.,[.,[[.,[.,.]],.]]],.],[.,.]] => [1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 2

[5,1,7,8,6,3,4,2] => [[.,.],[[[[.,[.,.]],.],[.,.]],.]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 2

[5,1,3,7,8,6,4,2] => [[.,.],[[.,[[[.,[.,.]],.],.]],.]] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2

[5,2,7,8,4,6,1,3] => [[[.,.],[[.,[.,.]],[.,.]]],[.,.]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[3,2,5,7,8,6,1,4] => [[[.,.],[.,[[.,[.,.]],.]]],[.,.]] => [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => 2

[1,2,6,7,5,8,3,4] => [.,[.,[[[.,[.,.]],[.,.]],[.,.]]]] => [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 4

[6,7,5,2,4,1,8,3] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[6,7,2,5,3,8,1,4] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[6,7,4,5,2,1,8,3] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[5,1,7,8,6,4,3,2] => [[.,.],[[[[[.,[.,.]],.],.],.],.]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2

[2,5,7,8,6,3,1,4] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => [1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 2

[5,1,7,8,6,3,2,4] => [[.,.],[[[[.,[.,.]],.],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => 3

[1,6,7,5,3,8,2,4] => [.,[[[[.,[.,.]],.],[.,.]],[.,.]]] => [1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 3

[1,6,7,5,4,2,8,3] => [.,[[[[.,[.,.]],.],.],[[.,.],.]]] => [1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 3

[6,7,5,1,4,2,8,3] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[5,7,8,6,4,1,2,3] => [[[.,[[.,[.,.]],.]],.],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 3

[2,4,7,1,5,6,8,3] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[6,7,4,1,5,2,8,3] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[1,6,7,4,5,2,8,3] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 3

[6,7,5,4,2,1,8,3] => [[[[[.,[.,.]],.],.],.],[[.,.],.]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2

[6,7,4,2,5,1,8,3] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[7,3,5,1,8,2,6,4] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[7,3,5,1,8,2,4,6] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[2,6,7,4,1,8,3,5] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[2,1,6,7,3,8,5,4] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3

[4,6,1,5,8,7,3,2] => [[.,[.,.]],[[[.,[[.,.],.]],.],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 2

[4,6,1,5,8,2,3,7] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[2,3,4,7,8,1,6,5] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[6,8,5,4,3,2,7,1] => [[[[[[.,[.,.]],.],.],.],[.,.]],.] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1

[6,8,5,4,3,7,2,1] => [[[[[[.,[.,.]],.],.],[.,.]],.],.] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1

[5,8,4,3,2,1,7,6] => [[[[[.,[.,.]],.],.],.],[[.,.],.]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2

[8,3,4,6,2,1,5,7] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[3,5,6,2,1,8,4,7] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[3,5,2,6,8,4,1,7] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[2,4,5,7,3,8,6,1] => [[.,[[.,[.,[.,.]]],[[.,.],.]]],.] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1

[4,2,5,6,8,3,1,7] => [[[.,.],[[.,[.,[.,.]]],.]],[.,.]] => [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => 2

[4,2,8,1,5,6,3,7] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[2,5,6,1,8,4,3,7] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[5,3,6,8,1,4,2,7] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,5,6,8,1,3,2,7] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[1,4,5,6,8,3,2,7] => [.,[[[.,[.,[.,[.,.]]]],.],[.,.]]] => [1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 3

[4,5,6,3,8,2,1,7] => [[[[.,[.,[.,.]]],[.,.]],.],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[4,5,3,7,2,8,6,1] => [[[[.,[.,.]],[.,.]],[[.,.],.]],.] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 1

[6,4,7,3,2,8,5,1] => [[[[[.,.],[.,.]],.],[[.,.],.]],.] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1

[6,1,4,7,3,2,8,5] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3

[1,7,8,4,5,3,2,6] => [.,[[[[.,[.,.]],[.,.]],.],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 3

[2,5,1,7,4,3,8,6] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[2,5,7,4,1,8,6,3] => [[.,[[.,[.,.]],.]],[[[.,.],.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2

[5,3,7,1,4,8,6,2] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[5,6,3,7,8,4,2,1] => [[[[.,[.,.]],[[.,[.,.]],.]],.],.] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 1

[5,6,1,3,7,8,4,2] => [[.,[.,.]],[[.,[[.,[.,.]],.]],.]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 2

[5,6,1,7,8,3,4,2] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2

[6,7,2,4,1,8,5,3] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[6,7,2,1,4,3,8,5] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[6,4,7,3,1,2,8,5] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[5,6,3,1,2,7,8,4] => [[[.,[.,.]],.],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 3

[5,6,1,3,2,7,8,4] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[5,6,3,2,1,7,8,4] => [[[[.,[.,.]],.],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 2

[2,5,6,3,7,8,4,1] => [[.,[[.,[.,.]],[[.,[.,.]],.]]],.] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 1

[2,5,6,3,1,7,8,4] => [[.,[[.,[.,.]],.]],[[.,[.,.]],.]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 2

[6,3,7,2,8,4,5,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[6,3,7,2,8,4,1,5] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[4,7,2,1,3,8,6,5] => [[[.,[.,.]],.],[.,[[[.,.],.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 3

[1,3,7,8,6,4,2,5] => [.,[[.,[[[.,[.,.]],.],.]],[.,.]]] => [1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 3

[5,7,3,8,2,1,6,4] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[6,3,7,8,5,2,1,4] => [[[[.,.],[[.,[.,.]],.]],.],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => 2

[4,6,2,7,8,5,3,1] => [[[.,[.,.]],[[[.,[.,.]],.],.]],.] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 1

[4,6,2,1,7,8,5,3] => [[[.,[.,.]],.],[[[.,[.,.]],.],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 2

[7,4,5,8,1,2,6,3] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[2,5,1,7,3,8,6,4] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[6,7,2,1,3,8,5,4] => [[[.,[.,.]],.],[.,[[[.,.],.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 3

[5,1,6,7,8,2,4,3] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[6,3,7,1,8,5,2,4] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[6,2,7,1,8,5,4,3] => [[[.,.],[.,.]],[[[[.,.],.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[4,1,3,6,8,2,5,7] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[4,2,3,6,8,1,5,7] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[4,5,2,1,3,8,7,6] => [[[.,[.,.]],.],[.,[[[.,.],.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 3

[6,2,4,5,8,1,3,7] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[1,6,3,4,5,8,2,7] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[3,4,1,8,5,2,7,6] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[3,4,2,5,8,6,7,1] => [[[.,[.,.]],[.,[[.,.],[.,.]]]],.] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 1

[4,3,6,2,8,1,7,5] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[4,2,3,7,1,8,6,5] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[2,7,8,5,4,1,3,6] => [[.,[[[.,[.,.]],.],.]],[.,[.,.]]] => [1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 3

[4,8,3,1,2,7,6,5] => [[[.,[.,.]],.],[.,[[[.,.],.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 3

[3,5,2,7,4,1,8,6] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[2,8,4,7,1,3,5,6] => [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[8,2,4,6,7,1,3,5] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[4,8,2,3,6,7,1,5] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[3,5,2,7,6,1,8,4] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[5,8,3,2,1,6,7,4] => [[[[.,[.,.]],.],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 2

[5,8,2,7,4,1,6,3] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[5,3,7,1,6,2,8,4] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[5,2,4,7,1,8,6,3] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[5,3,4,7,1,8,6,2] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[5,8,4,7,6,2,3,1] => [[[[.,[.,.]],[[.,.],.]],[.,.]],.] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 1

[1,3,5,2,4,8,7,6] => [.,[[.,[.,.]],[.,[[[.,.],.],.]]]] => [1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 4

[4,7,1,6,5,8,3,2] => [[.,[.,.]],[[[[.,.],[.,.]],.],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 2

[6,8,4,3,2,7,1,5] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2

[3,4,7,8,2,1,6,5] => [[[.,[.,[.,[.,.]]]],.],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[5,2,3,1,6,8,7,4] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[2,4,7,3,8,1,6,5] => [[.,[[.,[.,.]],[.,.]]],[[.,.],.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2

[6,3,8,2,7,4,1,5] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[3,5,1,7,8,4,2,6] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[5,4,7,8,3,6,2,1] => [[[[[.,.],[.,[.,.]]],[.,.]],.],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1

[3,5,7,2,4,8,1,6] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[8,4,7,2,3,1,5,6] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[8,4,7,1,3,2,5,6] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[8,4,7,2,1,3,5,6] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[3,5,7,2,6,1,8,4] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[5,8,3,2,6,7,1,4] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[2,8,1,5,4,7,6,3] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2

[3,5,1,7,6,8,2,4] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[5,8,2,6,1,3,7,4] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[2,5,7,8,4,1,6,3] => [[.,[[.,[.,[.,.]]],.]],[[.,.],.]] => [1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[4,2,8,1,5,6,7,3] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[3,4,5,1,6,8,7,2] => [[.,[.,[.,.]]],[[.,[[.,.],.]],.]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[2,7,1,8,5,4,6,3] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2

[8,2,4,1,5,6,7,3] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[4,6,3,5,8,1,7,2] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[1,7,8,3,5,4,6,2] => [.,[[[.,[.,.]],[[.,.],[.,.]]],.]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 2

[3,4,5,1,8,6,7,2] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[3,8,1,4,5,6,7,2] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2

[3,4,5,7,8,2,6,1] => [[[.,[.,[.,[.,[.,.]]]]],[.,.]],.] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 1

[3,4,6,2,8,5,1,7] => [[[.,[.,[.,.]]],[[.,.],.]],[.,.]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[3,4,6,8,1,5,2,7] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,4,7,2,1,8,6,5] => [[[.,[.,[.,.]]],.],[[[.,.],.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[3,4,8,2,1,5,6,7] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[3,5,2,7,8,4,6,1] => [[[.,[.,.]],[[.,[.,.]],[.,.]]],.] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 1

[3,5,6,2,8,4,1,7] => [[[.,[.,[.,.]]],[[.,.],.]],[.,.]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[3,5,6,8,4,1,2,7] => [[.,[[.,[.,[.,.]]],.]],[.,[.,.]]] => [1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[3,5,7,2,4,8,6,1] => [[[.,[.,[.,.]]],[.,[[.,.],.]]],.] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[3,5,7,2,8,4,6,1] => [[[.,[.,[.,.]]],[[.,.],[.,.]]],.] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[3,5,7,8,4,1,6,2] => [[.,[[.,[.,[.,.]]],.]],[[.,.],.]] => [1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[3,6,2,1,8,5,4,7] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[3,6,7,2,8,5,4,1] => [[[.,[.,[.,.]]],[[[.,.],.],.]],.] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1

[3,6,8,2,4,5,1,7] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[3,7,2,1,4,8,6,5] => [[[.,[.,.]],.],[.,[[[.,.],.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 3

[3,7,2,8,4,5,6,1] => [[[.,[.,.]],[[.,.],[.,[.,.]]]],.] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 1

[3,7,8,2,4,5,6,1] => [[[.,[.,[.,.]]],[.,[.,[.,.]]]],.] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1

[3,8,2,1,4,5,6,7] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 5

[4,1,5,6,7,8,3,2] => [[.,.],[[[.,[.,[.,[.,.]]]],.],.]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => 2

[4,1,6,7,3,8,5,2] => [[.,.],[[[.,[.,.]],[[.,.],.]],.]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2

[4,1,6,8,3,5,2,7] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[4,5,2,6,8,1,3,7] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[4,5,7,3,8,1,6,2] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[4,5,8,3,2,1,6,7] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3

[4,6,2,7,8,5,1,3] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[4,6,7,3,2,8,5,1] => [[[[.,[.,[.,.]]],.],[[.,.],.]],.] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1

[4,7,2,8,3,5,6,1] => [[[.,[.,.]],[[.,.],[.,[.,.]]]],.] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 1

[4,7,8,3,2,5,6,1] => [[[[.,[.,[.,.]]],.],[.,[.,.]]],.] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1

[4,8,2,3,1,5,6,7] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[5,1,2,6,8,4,3,7] => [[.,.],[.,[[[.,[.,.]],.],[.,.]]]] => [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => 4

[5,6,2,3,8,4,1,7] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[5,6,2,7,8,4,1,3] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[5,6,8,3,4,2,1,7] => [[[[.,[.,[.,.]]],[.,.]],.],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[5,7,2,3,4,8,6,1] => [[[.,[.,.]],[.,[.,[[.,.],.]]]],.] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 1

[5,7,8,3,4,2,6,1] => [[[[.,[.,[.,.]]],[.,.]],[.,.]],.] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[5,8,2,3,4,1,6,7] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[6,1,2,3,7,8,5,4] => [[.,.],[.,[.,[[[.,[.,.]],.],.]]]] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => 4

[6,1,2,7,8,5,4,3] => [[.,.],[.,[[[[.,[.,.]],.],.],.]]] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 3

[6,1,7,8,4,5,3,2] => [[.,.],[[[[.,[.,.]],[.,.]],.],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[6,7,2,3,8,5,4,1] => [[[.,[.,.]],[.,[[[.,.],.],.]]],.] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 1

[6,7,2,8,4,5,3,1] => [[[.,[.,.]],[[[.,.],[.,.]],.]],.] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 1

[5,8,1,2,4,3,7,6] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4

[1,3,5,7,2,6,4,8] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[3,1,6,8,2,4,7,5] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[3,6,2,8,1,5,7,4] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[2,6,1,3,8,4,7,5] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4

[8,2,5,7,4,6,1,3] => [[[.,.],[[.,[.,.]],[.,.]]],[.,.]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[8,2,5,1,3,7,4,6] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[7,8,2,5,3,1,6,4] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[6,8,1,5,3,2,4,7] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[1,6,7,5,3,2,4,8] => [.,[[[[.,[.,.]],.],.],[.,[.,.]]]] => [1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 4

[7,8,1,6,4,2,3,5] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[8,1,3,7,2,6,4,5] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[7,8,4,2,5,6,1,3] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[8,4,7,2,5,6,3,1] => [[[[.,.],[.,.]],[[.,[.,.]],.]],.] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[6,8,5,4,3,1,7,2] => [[[[[.,[.,.]],.],.],.],[[.,.],.]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2

[3,6,1,8,5,2,7,4] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[3,4,1,2,8,6,7,5] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 3

[6,8,3,5,4,1,7,2] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[7,2,5,8,3,6,1,4] => [[[.,.],[[.,[.,.]],[.,.]]],[.,.]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[7,2,6,8,5,3,1,4] => [[[.,.],[[[.,[.,.]],.],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => 2

[1,5,7,4,2,6,3,8] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 4

[4,2,3,1,7,8,5,6] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[6,8,3,4,5,1,7,2] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[6,3,7,1,5,8,4,2] => [[[.,.],[.,.]],[[[.,[.,.]],.],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[2,5,1,8,4,3,7,6] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[6,1,3,4,5,8,2,7] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 3

[8,3,4,1,5,2,7,6] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[7,2,5,1,8,4,3,6] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[3,6,1,5,8,7,4,2] => [[.,[.,.]],[[[.,[[.,.],.]],.],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 2

[5,4,6,8,1,2,7,3] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[6,4,7,2,3,5,8,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1

[6,8,4,1,3,5,7,2] => [[[.,[.,.]],.],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 2

[3,4,7,8,6,2,5,1] => [[[.,[.,[[.,[.,.]],.]]],[.,.]],.] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[4,1,3,5,7,8,6,2] => [[.,.],[[.,[.,[[.,[.,.]],.]]],.]] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[4,7,3,2,8,1,6,5] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[2,4,7,3,8,5,6,1] => [[.,[[.,[.,.]],[[.,.],[.,.]]]],.] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 1

[7,8,2,5,4,3,1,6] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[5,7,3,2,4,1,8,6] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[2,8,3,4,7,1,5,6] => [[.,[[.,.],[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[4,1,3,6,7,8,2,5] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 3

[3,8,1,5,6,2,7,4] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[8,2,5,6,1,7,4,3] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[3,6,2,1,7,5,8,4] => [[[.,[.,.]],.],[[[.,.],[.,.]],.]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[4,7,2,6,5,8,1,3] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[6,8,1,4,2,7,3,5] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[6,3,4,7,1,8,2,5] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,4,7,8,2,5,6,1] => [[[.,[.,[.,[.,.]]]],[.,[.,.]]],.] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1

[1,8,2,4,5,6,7,3] => [.,[[.,.],[[.,[.,[.,[.,.]]]],.]]] => [1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 3

[5,2,4,1,6,8,7,3] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[4,3,5,6,1,8,7,2] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[5,3,4,1,7,6,8,2] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[1,4,7,3,5,6,8,2] => [.,[[[.,[.,.]],[.,[.,[.,.]]]],.]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2

[5,1,2,6,8,4,7,3] => [[.,.],[.,[[[.,[.,.]],[.,.]],.]]] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 3

[4,1,2,6,8,5,3,7] => [[.,.],[.,[[[.,[.,.]],.],[.,.]]]] => [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => 4

[2,3,1,7,5,4,8,6] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[1,2,7,8,5,6,3,4] => [.,[.,[[[.,[.,.]],[.,.]],[.,.]]]] => [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 4

[1,2,6,8,5,7,3,4] => [.,[.,[[[.,[.,.]],[.,.]],[.,.]]]] => [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 4

[1,5,6,8,2,7,3,4] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[1,3,8,2,6,7,4,5] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 4

[1,4,7,2,8,6,3,5] => [.,[[.,[.,.]],[[[.,.],.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 4

[1,6,7,8,2,5,3,4] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[1,2,6,8,3,7,5,4] => [.,[.,[[.,[.,.]],[[[.,.],.],.]]]] => [1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 4

[1,5,7,8,2,3,6,4] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[1,4,7,2,8,3,6,5] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 4

[1,3,6,2,4,8,7,5] => [.,[[.,[.,.]],[.,[[[.,.],.],.]]]] => [1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 4

[1,6,7,3,4,8,5,2] => [.,[[[.,[.,.]],[.,[[.,.],.]]],.]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 2

[1,2,6,8,5,3,7,4] => [.,[.,[[[.,[.,.]],.],[[.,.],.]]]] => [1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 4

[1,2,7,8,5,3,6,4] => [.,[.,[[[.,[.,.]],.],[[.,.],.]]]] => [1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 4

[1,2,7,8,6,3,5,4] => [.,[.,[[[.,[.,.]],.],[[.,.],.]]]] => [1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 4

[1,6,7,8,5,2,3,4] => [.,[[[.,[.,[.,.]]],.],[.,[.,.]]]] => [1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[1,5,7,8,6,2,3,4] => [.,[[.,[[.,[.,.]],.]],[.,[.,.]]]] => [1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 4

[1,2,7,8,6,5,3,4] => [.,[.,[[[[.,[.,.]],.],.],[.,.]]]] => [1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 4

[5,2,6,7,3,4,8,1] => [[[.,.],[[.,[.,.]],[.,[.,.]]]],.] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1

[5,6,2,1,7,8,3,4] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[5,6,2,1,4,8,7,3] => [[[.,[.,.]],.],[[.,[[.,.],.]],.]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 2

[2,6,1,4,5,8,7,3] => [[.,[.,.]],[[.,[.,[[.,.],.]]],.]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 2

[2,6,1,7,5,8,3,4] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[2,6,1,7,4,8,5,3] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2

[5,1,2,7,8,4,3,6] => [[.,.],[.,[[[.,[.,.]],.],[.,.]]]] => [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => 4

[2,6,1,7,4,8,3,5] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[5,4,6,1,3,8,7,2] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[2,6,1,5,4,8,7,3] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2

[2,6,1,4,7,8,5,3] => [[.,[.,.]],[[.,[[.,[.,.]],.]],.]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 2

[2,6,1,5,4,8,3,7] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[5,1,2,4,8,3,7,6] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 4

[5,6,3,1,4,8,2,7] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[5,4,6,3,1,8,7,2] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[5,2,6,1,7,8,4,3] => [[[.,.],[.,.]],[[[.,[.,.]],.],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[2,1,3,7,8,6,4,5] => [[.,.],[.,[[[.,[.,.]],.],[.,.]]]] => [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => 4

[2,1,3,7,8,5,6,4] => [[.,.],[.,[[[.,[.,.]],[.,.]],.]]] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 3

[5,2,4,1,7,8,6,3] => [[[.,.],[.,.]],[[[.,[.,.]],.],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[2,1,3,6,8,5,7,4] => [[.,.],[.,[[[.,[.,.]],[.,.]],.]]] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 3

[8,5,7,4,6,3,2,1] => [[[[[[.,.],[.,.]],[.,.]],.],.],.] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1

[8,6,7,3,5,4,2,1] => [[[[[.,.],[.,.]],[[.,.],.]],.],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

[8,5,7,3,6,4,2,1] => [[[[[.,.],[.,.]],[[.,.],.]],.],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

[8,3,7,2,6,5,4,1] => [[[[.,.],[.,.]],[[[.,.],.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1

[8,5,7,2,6,4,3,1] => [[[[.,.],[.,.]],[[[.,.],.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1

[8,6,7,2,5,4,3,1] => [[[[.,.],[.,.]],[[[.,.],.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1

[8,4,7,1,6,5,3,2] => [[[.,.],[.,.]],[[[[.,.],.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[8,3,7,1,6,5,4,2] => [[[.,.],[.,.]],[[[[.,.],.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[8,2,7,1,6,5,4,3] => [[[.,.],[.,.]],[[[[.,.],.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[8,6,7,5,4,1,3,2] => [[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[6,8,1,3,2,5,4,7] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[6,8,1,4,2,5,3,7] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[7,8,3,6,1,4,2,5] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[7,8,2,5,3,6,1,4] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[7,8,2,5,1,4,3,6] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[7,8,1,4,3,6,2,5] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[5,8,1,4,3,7,2,6] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[6,8,2,5,1,4,3,7] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,8,2,5,3,7,1,4] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[6,8,2,5,4,7,1,3] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[2,5,1,4,3,7,6,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[2,6,1,4,3,7,5,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[2,6,1,5,3,7,4,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[5,8,3,6,4,7,1,2] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[5,8,2,6,4,7,1,3] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[4,8,2,6,3,7,1,5] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[4,8,1,5,3,7,2,6] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[4,8,1,5,2,6,3,7] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[4,8,3,7,1,5,2,6] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,8,3,7,1,4,2,5] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,8,1,3,2,6,4,7] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[5,8,4,7,1,3,2,6] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,8,4,7,1,3,2,5] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,8,5,7,1,3,2,4] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,7,1,3,2,6,5,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[3,7,1,4,2,6,5,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[3,7,1,5,2,6,4,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[3,7,2,6,1,5,4,8] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,7,2,6,5,8,1,4] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[4,7,3,6,5,8,1,2] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[6,8,4,3,7,2,1,5] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[6,7,4,3,5,1,8,2] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[6,7,3,5,4,8,2,1] => [[[[.,[.,.]],[[.,.],[.,.]]],.],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 1

[7,6,8,3,5,2,4,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[6,3,5,7,8,4,2,1] => [[[[.,.],[[.,[.,[.,.]]],.]],.],.] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => 1

[5,6,8,3,7,2,1,4] => [[[[.,[.,[.,.]]],[.,.]],.],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[4,6,8,3,5,7,2,1] => [[[[.,[.,[.,.]]],[.,[.,.]]],.],.] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1

[5,3,8,2,4,1,6,7] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[4,8,3,6,2,5,7,1] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1

[4,7,8,3,5,6,2,1] => [[[[.,[.,[.,.]]],[.,[.,.]]],.],.] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1

[5,3,4,8,2,7,6,1] => [[[[.,.],[.,[.,.]]],[[.,.],.]],.] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => 1

[5,8,3,7,2,6,4,1] => [[[[.,[.,.]],[.,.]],[[.,.],.]],.] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 1

[5,8,4,2,3,1,6,7] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[5,8,4,2,3,1,7,6] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[6,4,5,3,8,2,1,7] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[6,4,5,3,7,1,8,2] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[5,6,3,4,8,2,1,7] => [[[[.,[.,.]],[.,[.,.]]],.],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2

[5,3,7,2,4,1,6,8] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[4,7,3,6,2,5,8,1] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1

[4,5,8,3,6,7,2,1] => [[[[.,[.,[.,.]]],[.,[.,.]]],.],.] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1

[4,5,8,3,7,2,6,1] => [[[[.,[.,[.,.]]],[.,.]],[.,.]],.] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[5,3,6,8,2,1,4,7] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[5,3,6,7,1,8,2,4] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,6,3,5,7,8,2,1] => [[[[.,[.,.]],[.,[.,[.,.]]]],.],.] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1

[4,5,7,3,6,8,2,1] => [[[[.,[.,[.,.]]],[.,[.,.]]],.],.] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1

[5,7,4,8,6,3,2,1] => [[[[[.,[.,.]],[[.,.],.]],.],.],.] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 1

[3,5,6,7,2,8,4,1] => [[[.,[.,[.,[.,.]]]],[[.,.],.]],.] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 1

[1,3,8,2,4,6,5,7] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 5

[1,6,8,2,5,3,7,4] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 4

[1,3,5,2,8,4,7,6] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 4

[1,5,8,2,3,7,4,6] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 5

[1,6,8,2,3,5,4,7] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 5

[5,3,6,1,2,4,8,7] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[7,1,5,8,4,2,3,6] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[8,1,5,7,4,2,3,6] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[7,1,4,5,8,2,3,6] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[7,8,3,1,2,4,6,5] => [[[.,[.,.]],.],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 4

[7,3,8,1,2,4,6,5] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[8,3,7,1,2,4,6,5] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[8,3,6,1,2,4,7,5] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[7,3,6,1,2,4,8,5] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[6,7,1,8,4,2,3,5] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[6,8,1,7,4,2,3,5] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[2,1,7,8,5,3,4,6] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[6,8,1,4,2,3,7,5] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[6,8,3,1,2,7,4,5] => [[[.,[.,.]],.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[6,7,3,1,2,8,4,5] => [[[.,[.,.]],.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[6,7,1,4,2,3,8,5] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[4,3,6,8,5,7,1,2] => [[[.,.],[[.,[.,.]],[.,.]]],[.,.]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[2,6,1,5,8,3,4,7] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[5,7,1,6,8,4,3,2] => [[.,[.,.]],[[[[.,[.,.]],.],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 2

[4,8,1,2,5,7,3,6] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4

[1,7,8,4,6,2,5,3] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 3

[2,7,4,6,8,1,3,5] => [[.,[[.,.],[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[8,2,6,7,5,4,3,1] => [[[.,.],[[[[.,[.,.]],.],.],.]],.] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 1

[3,4,2,7,8,1,6,5] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[3,6,1,4,5,8,2,7] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[1,6,7,4,5,3,8,2] => [.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 2

[1,4,7,2,8,5,3,6] => [.,[[.,[.,.]],[[[.,.],.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 4

[6,8,5,7,1,2,4,3] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[6,8,2,1,5,7,3,4] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[2,7,8,1,4,6,3,5] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[4,8,2,5,7,1,6,3] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[4,1,6,8,5,3,7,2] => [[.,.],[[[[.,[.,.]],.],[.,.]],.]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 2

[6,7,1,3,4,5,8,2] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2

[6,3,4,2,8,7,5,1] => [[[[.,.],[.,.]],[[[.,.],.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1

[2,5,6,3,4,8,7,1] => [[.,[[.,[.,.]],[.,[[.,.],.]]]],.] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 1

[4,5,2,8,3,7,6,1] => [[[.,[.,.]],[[.,.],[[.,.],.]]],.] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 1

[5,8,2,4,7,6,3,1] => [[[.,[.,.]],[[.,[[.,.],.]],.]],.] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 1

[6,8,2,5,3,4,7,1] => [[[.,[.,.]],[[.,.],[.,[.,.]]]],.] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 1

[7,2,5,6,4,8,1,3] => [[[.,.],[[.,[.,.]],[.,.]]],[.,.]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[1,6,7,4,8,2,3,5] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 4

[7,1,3,5,8,2,6,4] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[4,1,3,8,2,6,7,5] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3

[3,6,1,4,7,2,8,5] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[1,5,8,4,7,2,3,6] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 4

[7,1,3,6,2,8,4,5] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[2,7,1,4,6,3,8,5] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[4,7,5,6,8,1,3,2] => [[.,[[.,.],[.,[.,.]]]],[[.,.],.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[5,7,4,3,6,2,8,1] => [[[[[.,[.,.]],.],[.,.]],[.,.]],.] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1

[6,7,5,1,2,8,3,4] => [[[.,[.,.]],.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[5,2,6,8,3,4,7,1] => [[[.,.],[[.,[.,.]],[.,[.,.]]]],.] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1

[3,6,8,4,7,2,5,1] => [[[.,[[.,[.,.]],[.,.]]],[.,.]],.] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[2,1,5,6,8,3,7,4] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[5,8,1,2,6,4,7,3] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 3

[1,6,8,3,2,7,4,5] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 4

[6,5,7,2,8,4,1,3] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[5,4,8,3,6,2,7,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[5,8,2,7,4,3,6,1] => [[[.,[.,.]],[[[.,.],.],[.,.]]],.] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 1

[6,4,5,8,2,7,3,1] => [[[[.,.],[.,[.,.]]],[[.,.],.]],.] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => 1

[5,7,3,6,4,8,2,1] => [[[[.,[.,.]],[[.,.],[.,.]]],.],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 1

[1,5,6,4,8,2,7,3] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 3

[3,1,5,6,4,8,7,2] => [[.,.],[[[.,[.,.]],[[.,.],.]],.]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2

[3,5,1,6,4,7,8,2] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 2

[2,3,5,1,8,4,7,6] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[2,3,6,1,8,5,4,7] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[2,3,6,1,8,5,7,4] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[1,2,5,8,4,7,3,6] => [.,[.,[[[.,[.,.]],[.,.]],[.,.]]]] => [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 4

[1,3,6,8,5,2,7,4] => [.,[[.,[[.,[.,.]],.]],[[.,.],.]]] => [1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 3

[1,2,6,8,5,4,3,7] => [.,[.,[[[[.,[.,.]],.],.],[.,.]]]] => [1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 4

[1,3,5,8,2,4,7,6] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[1,4,6,8,3,2,5,7] => [.,[[[.,[.,[.,.]]],.],[.,[.,.]]]] => [1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[3,5,7,4,8,1,2,6] => [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[4,6,1,7,5,8,2,3] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[1,2,6,7,3,8,5,4] => [.,[.,[[.,[.,.]],[[[.,.],.],.]]]] => [1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 4

[1,2,5,7,3,8,6,4] => [.,[.,[[.,[.,.]],[[[.,.],.],.]]]] => [1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 4

[3,5,4,6,8,2,7,1] => [[[.,[[.,.],[.,[.,.]]]],[.,.]],.] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[3,1,6,7,5,8,4,2] => [[.,.],[[[[.,[.,.]],[.,.]],.],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[4,6,2,7,5,8,3,1] => [[[.,[.,.]],[[[.,.],[.,.]],.]],.] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 1

[3,5,7,4,8,2,6,1] => [[[.,[[.,[.,.]],[.,.]]],[.,.]],.] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[1,4,6,8,3,5,7,2] => [.,[[[.,[.,[.,.]]],[.,[.,.]]],.]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[1,3,5,8,2,7,4,6] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[1,2,5,8,4,7,6,3] => [.,[.,[[[.,[.,.]],[[.,.],.]],.]]] => [1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 3

[5,7,1,2,8,6,4,3] => [[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 3

[6,4,5,7,2,8,1,3] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,3,4,7,2,8,1,6] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,3,6,2,7,1,4,8] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[2,6,3,4,7,1,5,8] => [[.,[[.,.],[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[2,7,3,4,5,8,1,6] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[3,7,4,5,6,8,1,2] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[2,5,7,3,6,8,1,4] => [[.,[[.,[.,.]],[.,[.,.]]]],[.,.]] => [1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2

[7,3,5,2,4,8,1,6] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[6,2,3,1,8,4,7,5] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[8,3,5,2,7,1,4,6] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[8,1,5,7,2,3,6,4] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[7,3,8,2,4,5,6,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1

[1,7,8,3,4,5,6,2] => [.,[[[.,[.,.]],[.,[.,[.,.]]]],.]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2

[1,4,5,8,3,6,7,2] => [.,[[[.,[.,[.,.]]],[.,[.,.]]],.]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[2,5,7,1,8,3,6,4] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[6,2,7,1,8,4,5,3] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[4,7,1,3,8,5,6,2] => [[.,[.,.]],[[.,[[.,.],[.,.]]],.]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 2

[4,1,3,6,8,2,7,5] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[5,3,4,6,8,2,7,1] => [[[[.,.],[.,[.,[.,.]]]],[.,.]],.] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 1

[4,6,3,8,7,1,2,5] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[3,8,1,7,2,4,5,6] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[6,8,2,3,5,1,4,7] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[4,7,8,2,6,1,3,5] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[7,8,3,6,2,4,5,1] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1

[3,6,2,4,7,1,8,5] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[3,4,7,2,5,1,8,6] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[3,6,2,5,7,1,4,8] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[5,6,1,2,8,4,3,7] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 4

[4,3,8,1,2,6,7,5] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[6,5,7,2,4,8,1,3] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[3,4,1,6,5,8,7,2] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2

[3,5,1,2,4,8,7,6] => [[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 4

[4,3,5,1,2,8,7,6] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[3,1,4,6,2,8,7,5] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3

[3,4,5,6,1,8,7,2] => [[.,[.,[.,[.,.]]]],[[[.,.],.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[1,4,7,2,6,3,5,8] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 5

[8,1,4,7,2,3,6,5] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[6,3,5,1,7,4,2,8] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[5,4,8,1,6,3,2,7] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[4,6,3,7,5,8,1,2] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[5,7,4,3,8,1,2,6] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[1,4,8,3,7,6,5,2] => [.,[[[.,[.,.]],[[[.,.],.],.]],.]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 2

[4,3,8,2,1,6,5,7] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[3,8,1,6,7,5,4,2] => [[.,[.,.]],[[[[.,[.,.]],.],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 2

[3,7,2,6,8,5,1,4] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[1,7,8,5,4,3,6,2] => [.,[[[[[.,[.,.]],.],.],[.,.]],.]] => [1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 2

[7,8,5,4,3,1,6,2] => [[[[[.,[.,.]],.],.],.],[[.,.],.]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2

[3,6,1,4,2,7,5,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[3,4,1,8,5,7,6,2] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2

[3,8,5,6,7,2,1,4] => [[[.,[[.,.],[.,[.,.]]]],.],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2

[8,5,6,1,4,2,3,7] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[8,3,6,1,7,2,4,5] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[5,2,4,6,1,7,3,8] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[1,4,6,3,7,2,8,5] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 3

[3,7,2,6,5,4,1,8] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[3,8,2,6,5,1,7,4] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[7,8,2,5,4,1,6,3] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[4,5,1,3,7,2,8,6] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[7,1,3,6,2,8,5,4] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3

[8,1,3,6,2,7,5,4] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3

[1,2,4,7,3,8,6,5] => [.,[.,[[.,[.,.]],[[[.,.],.],.]]]] => [1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 4

[4,1,7,8,2,6,5,3] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3

[5,6,1,8,2,7,4,3] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[4,2,7,8,1,6,5,3] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[7,2,8,1,6,5,4,3] => [[[.,.],[.,.]],[[[[.,.],.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[6,7,8,5,1,4,3,2] => [[[.,[.,[.,.]]],.],[[[.,.],.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[5,6,3,8,4,1,7,2] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[8,4,6,7,1,5,3,2] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[5,6,4,7,8,1,3,2] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[7,3,5,1,2,8,6,4] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[1,4,6,2,3,8,7,5] => [.,[[.,[.,.]],[.,[[[.,.],.],.]]]] => [1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 4

[2,3,1,7,6,4,8,5] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[4,5,2,1,7,3,8,6] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[5,6,7,1,2,8,4,3] => [[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[3,7,1,6,2,8,5,4] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[2,7,1,3,8,6,5,4] => [[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 3

[7,8,1,2,6,5,4,3] => [[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 3

[3,8,1,6,2,7,5,4] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[5,6,8,1,2,7,4,3] => [[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[4,6,3,1,8,2,7,5] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[5,8,4,2,7,3,1,6] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[8,1,3,7,2,6,5,4] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3

[7,1,5,8,4,2,6,3] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3

[1,7,8,4,3,5,6,2] => [.,[[[[.,[.,.]],.],[.,[.,.]]],.]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 2

[2,6,1,7,3,5,4,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[3,1,5,8,4,2,6,7] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[5,7,4,8,3,2,1,6] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2

[5,4,8,2,7,3,1,6] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[5,8,3,2,6,4,1,7] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[6,8,2,4,7,5,1,3] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[7,3,8,2,6,4,1,5] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[4,6,8,2,7,3,1,5] => [[[.,[.,[.,.]]],[[.,.],.]],[.,.]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[6,8,1,7,2,5,4,3] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[5,8,3,7,6,2,4,1] => [[[[.,[.,.]],[[.,.],.]],[.,.]],.] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 1

[6,8,3,2,5,4,7,1] => [[[[.,[.,.]],.],[[.,.],[.,.]]],.] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 1

[1,5,7,8,4,3,6,2] => [.,[[[[.,[.,[.,.]]],.],[.,.]],.]] => [1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 2

[6,3,8,1,5,4,7,2] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[5,8,4,7,2,6,3,1] => [[[[.,[.,.]],[.,.]],[[.,.],.]],.] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 1

[5,8,3,2,7,6,4,1] => [[[[.,[.,.]],.],[[[.,.],.],.]],.] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 1

[3,5,7,4,2,6,1,8] => [[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => [1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[4,3,5,1,6,8,7,2] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[7,4,8,1,5,2,3,6] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[7,5,8,3,2,4,1,6] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[7,4,8,2,1,3,5,6] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[5,4,8,2,1,7,3,6] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[2,1,7,8,3,6,4,5] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[6,3,8,1,2,5,7,4] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[3,6,7,1,2,5,8,4] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[7,8,3,1,2,5,6,4] => [[[.,[.,.]],.],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 3

[7,8,1,3,2,4,6,5] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[7,8,2,1,3,5,4,6] => [[[.,[.,.]],.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[5,2,3,7,1,8,6,4] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[2,6,7,3,1,8,4,5] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[2,6,7,1,3,5,4,8] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[3,2,5,7,1,8,4,6] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,1,4,7,8,2,3,6] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[5,3,4,7,8,6,1,2] => [[[.,.],[.,[[.,[.,.]],.]]],[.,.]] => [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => 2

[1,6,7,3,2,4,8,5] => [.,[[[.,[.,.]],.],[.,[[.,.],.]]]] => [1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 4

[5,1,3,7,2,6,8,4] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3

[5,2,4,7,8,1,6,3] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[4,5,2,8,6,1,7,3] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[4,5,1,8,6,2,3,7] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[3,4,2,1,8,7,5,6] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[7,6,8,5,2,1,4,3] => [[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[7,8,6,3,2,1,5,4] => [[[[[.,[.,.]],.],.],.],[[.,.],.]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2

[7,8,1,3,2,4,5,6] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[7,8,4,1,5,2,3,6] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[4,6,7,1,5,2,3,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[3,2,5,6,1,4,7,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[3,5,2,6,1,4,7,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[3,5,4,6,7,8,1,2] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[2,5,4,6,7,1,3,8] => [[.,[[.,.],[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[2,6,7,4,5,1,3,8] => [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[4,2,5,6,7,1,3,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[7,3,5,2,4,1,6,8] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[1,3,6,7,5,2,8,4] => [.,[[.,[[.,[.,.]],.]],[[.,.],.]]] => [1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 3

[7,3,4,1,6,2,5,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[7,3,4,1,6,5,2,8] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[7,3,4,1,5,6,2,8] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[7,3,4,1,5,2,6,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[1,3,6,7,2,5,8,4] => [.,[[.,[.,[.,.]]],[[.,[.,.]],.]]] => [1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3

[5,6,1,4,7,3,8,2] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2

[6,3,4,5,8,1,7,2] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[2,4,5,1,6,8,7,3] => [[.,[.,[.,.]]],[[.,[[.,.],.]],.]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[2,3,4,5,8,1,7,6] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[5,6,1,4,7,2,8,3] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[3,1,4,6,7,8,5,2] => [[.,.],[[.,[[.,[.,[.,.]]],.]],.]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => 2

[1,4,5,2,6,8,7,3] => [.,[[.,[.,.]],[[.,[[.,.],.]],.]]] => [1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 3

[5,6,1,2,7,4,8,3] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 3

[6,3,5,2,4,7,8,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1

[2,3,6,7,1,5,8,4] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[2,3,6,7,5,1,8,4] => [[.,[.,[[.,[.,.]],.]]],[[.,.],.]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 2

[7,3,4,5,8,1,6,2] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[7,3,4,5,8,1,2,6] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[1,3,4,5,8,2,7,6] => [.,[[.,[.,[.,[.,.]]]],[[.,.],.]]] => [1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[6,3,4,5,8,2,1,7] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 2

[6,3,4,5,8,2,7,1] => [[[[.,.],[.,[.,[.,.]]]],[.,.]],.] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 1

[5,7,4,6,1,8,3,2] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[6,3,4,5,8,1,2,7] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[7,3,4,5,8,2,1,6] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 2

[7,3,4,5,8,2,6,1] => [[[[.,.],[.,[.,[.,.]]]],[.,.]],.] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 1

[4,7,8,2,6,1,5,3] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[8,4,7,3,6,5,1,2] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[8,4,6,1,7,5,3,2] => [[[.,.],[.,.]],[[[[.,.],.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[6,4,7,1,8,3,2,5] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[7,4,8,3,6,1,5,2] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[4,3,6,8,5,1,7,2] => [[[.,.],[[.,[.,.]],.]],[[.,.],.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[2,6,1,8,3,5,7,4] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[2,1,6,8,3,7,4,5] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[8,2,4,1,7,5,6,3] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[2,6,1,8,3,5,4,7] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[8,2,4,1,7,5,3,6] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[2,4,7,1,8,5,3,6] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[2,7,1,8,3,5,6,4] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[1,6,8,3,7,2,4,5] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 4

[3,8,1,5,7,2,4,6] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[1,2,6,8,4,7,3,5] => [.,[.,[[[.,[.,.]],[.,.]],[.,.]]]] => [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 4

[6,1,5,8,2,4,7,3] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3

[1,2,4,8,3,6,7,5] => [.,[.,[[.,[.,.]],[[.,[.,.]],.]]]] => [1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 4

[4,1,2,7,8,3,6,5] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 4

[3,5,7,4,8,6,1,2] => [[.,[[.,[.,.]],[[.,.],.]]],[.,.]] => [1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2

[5,8,1,2,3,7,6,4] => [[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 4

[4,1,2,7,8,6,3,5] => [[.,.],[.,[[[.,[.,.]],.],[.,.]]]] => [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => 4

[3,1,7,8,6,2,4,5] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[3,6,2,1,4,8,5,7] => [[[.,[.,.]],.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[3,4,7,1,5,2,8,6] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[3,6,7,4,1,5,8,2] => [[.,[[.,[.,.]],.]],[[.,[.,.]],.]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 2

[6,5,8,2,3,7,1,4] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[5,7,8,6,1,3,2,4] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[2,4,8,1,6,3,7,5] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[2,4,5,3,8,6,1,7] => [[.,[[.,[.,.]],[[.,.],.]]],[.,.]] => [1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2

[2,4,1,6,7,8,5,3] => [[.,[.,.]],[[[.,[.,[.,.]]],.],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2

[5,6,7,3,2,8,1,4] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[2,5,7,3,6,8,4,1] => [[.,[[.,[.,.]],[[.,[.,.]],.]]],.] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 1

[3,4,7,8,1,2,6,5] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[3,6,7,8,1,4,5,2] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[3,6,2,8,1,5,4,7] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,3,6,8,5,1,4,7] => [[.,[.,[[.,[.,.]],.]]],[.,[.,.]]] => [1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 3

[7,3,5,8,4,6,1,2] => [[[.,.],[[.,[.,.]],[.,.]]],[.,.]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[7,4,5,8,2,1,3,6] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[6,3,4,8,2,5,7,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1

[8,4,6,3,7,2,5,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[7,4,6,3,8,5,1,2] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[2,5,6,8,3,4,1,7] => [[.,[[.,[.,[.,.]]],[.,.]]],[.,.]] => [1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[8,4,6,2,7,5,3,1] => [[[[.,.],[.,.]],[[[.,.],.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1

[8,5,6,7,2,4,3,1] => [[[[.,.],[.,[.,.]]],[[.,.],.]],.] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => 1

[2,5,6,8,4,3,1,7] => [[.,[[[.,[.,[.,.]]],.],.]],[.,.]] => [1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 2

[2,5,7,8,4,1,3,6] => [[.,[[.,[.,[.,.]]],.]],[.,[.,.]]] => [1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[6,5,7,8,4,1,3,2] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[7,5,6,8,2,4,1,3] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[7,4,6,2,8,5,1,3] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[3,5,6,8,2,4,1,7] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[3,5,6,8,4,2,1,7] => [[[.,[[.,[.,[.,.]]],.]],.],[.,.]] => [1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 2

[2,6,7,8,1,4,5,3] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[3,6,7,8,1,4,2,5] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,5,7,8,2,1,4,6] => [[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[2,6,7,8,1,4,3,5] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,5,7,8,3,1,4,2] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[2,5,7,8,3,1,4,6] => [[.,[[.,[.,[.,.]]],.]],[.,[.,.]]] => [1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[2,4,7,3,8,1,5,6] => [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[6,4,7,3,8,1,5,2] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[6,4,7,3,8,1,2,5] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[7,4,6,3,8,2,1,5] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[6,4,5,2,3,8,1,7] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[6,4,5,3,2,8,1,7] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[5,4,6,3,8,2,1,7] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[5,4,7,3,8,1,6,2] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[2,5,7,8,3,1,6,4] => [[.,[[.,[.,[.,.]]],.]],[[.,.],.]] => [1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[4,5,7,8,3,1,2,6] => [[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[4,5,6,8,2,3,1,7] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,4,6,2,8,3,1,7] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[5,4,7,2,8,1,3,6] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[4,5,7,8,2,1,3,6] => [[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[4,6,7,8,1,3,2,5] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,6,7,8,1,3,5,2] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[2,6,7,8,1,3,5,4] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[2,6,7,8,1,5,3,4] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,6,7,8,1,5,2,3] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,6,7,8,1,2,5,3] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[4,5,7,8,2,1,6,3] => [[[.,[.,[.,[.,.]]]],.],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[5,4,7,2,8,1,6,3] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[3,5,7,8,2,1,6,4] => [[[.,[.,[.,[.,.]]]],.],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[3,6,7,8,1,2,5,4] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[3,6,7,8,1,5,2,4] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,6,7,8,1,5,4,2] => [[.,[.,[.,[.,.]]]],[[[.,.],.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[2,6,7,8,1,5,4,3] => [[.,[.,[.,[.,.]]]],[[[.,.],.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[4,2,7,1,5,3,8,6] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[3,2,6,7,5,1,4,8] => [[[.,.],[[.,[.,.]],.]],[.,[.,.]]] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[2,7,1,3,5,4,8,6] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4

[4,7,2,1,5,8,6,3] => [[[.,[.,.]],.],[[.,[[.,.],.]],.]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 2

[1,3,4,8,2,7,5,6] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[3,1,4,8,2,6,7,5] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3

[4,8,3,6,5,1,7,2] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[6,4,7,3,5,1,8,2] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[3,6,1,7,5,8,2,4] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[7,3,5,1,6,8,2,4] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[4,7,3,5,6,1,8,2] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[3,4,6,8,5,1,7,2] => [[.,[.,[[.,[.,.]],.]]],[[.,.],.]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 2

[4,6,8,2,1,5,7,3] => [[[.,[.,[.,.]]],.],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[6,8,2,1,3,5,7,4] => [[[.,[.,.]],.],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 3

[2,7,3,6,1,4,5,8] => [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[2,6,1,3,5,8,4,7] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4

[4,6,2,8,1,5,3,7] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,5,6,2,7,1,3,8] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[6,7,3,8,4,1,5,2] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[2,7,8,4,1,5,6,3] => [[.,[[.,[.,.]],.]],[[.,[.,.]],.]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 2

[2,7,1,8,5,6,3,4] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[8,2,5,1,6,7,3,4] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[8,2,4,5,1,6,7,3] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[3,8,4,5,6,1,7,2] => [[.,[[.,.],[.,[.,.]]]],[[.,.],.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[4,5,8,3,6,7,1,2] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[4,5,8,3,7,6,1,2] => [[[.,[.,[.,.]]],[[.,.],.]],[.,.]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[7,2,3,4,8,1,6,5] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[7,2,3,4,8,1,5,6] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[7,2,3,5,8,1,4,6] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[7,8,2,3,6,1,4,5] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[7,8,2,3,6,1,5,4] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[7,2,3,5,8,1,6,4] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[3,5,6,4,1,2,7,8] => [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4

[7,8,5,4,1,2,6,3] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 3

[3,5,6,4,1,2,8,7] => [[.,[[.,[.,.]],.]],[.,[[.,.],.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 3

[7,2,3,4,5,1,8,6] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[3,5,8,4,1,2,7,6] => [[.,[[.,[.,.]],.]],[.,[[.,.],.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 3

[3,5,8,4,1,2,6,7] => [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4

[3,5,8,4,1,6,2,7] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[3,5,8,4,1,6,7,2] => [[.,[[.,[.,.]],.]],[[.,[.,.]],.]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 2

[2,5,8,4,1,7,3,6] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[3,5,6,4,1,8,7,2] => [[.,[[.,[.,.]],.]],[[[.,.],.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2

[2,6,4,5,1,3,7,8] => [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[2,5,6,4,1,7,8,3] => [[.,[[.,[.,.]],.]],[[.,[.,.]],.]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 2

[7,8,5,4,1,6,3,2] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2

[2,5,6,4,1,7,3,8] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[7,8,6,2,1,3,5,4] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 3

[4,6,1,5,3,2,8,7] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[3,6,1,4,2,5,8,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[2,6,4,5,7,8,1,3] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[7,2,5,6,8,1,3,4] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[6,1,3,4,2,8,7,5] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3

[2,4,5,6,1,8,7,3] => [[.,[.,[.,[.,.]]]],[[[.,.],.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[6,8,2,7,4,3,5,1] => [[[.,[.,.]],[[[.,.],.],[.,.]]],.] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 1

[4,7,8,5,1,6,3,2] => [[.,[[.,[.,.]],.]],[[[.,.],.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2

[2,5,1,8,7,4,6,3] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2

[3,7,1,8,4,5,6,2] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 2

[4,6,7,2,5,8,3,1] => [[[.,[.,[.,.]]],[[.,[.,.]],.]],.] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[6,4,5,1,7,8,3,2] => [[[.,.],[.,.]],[[[.,[.,.]],.],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[4,2,3,1,7,8,6,5] => [[[.,.],[.,.]],[[[.,[.,.]],.],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[3,4,2,1,8,6,7,5] => [[[.,[.,.]],.],[[[.,.],[.,.]],.]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[6,4,5,8,3,1,2,7] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[3,6,8,1,5,2,4,7] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[7,4,6,8,5,1,2,3] => [[[.,.],[[.,[.,.]],.]],[.,[.,.]]] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[2,1,6,8,3,7,5,4] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3

[3,6,8,2,4,1,5,7] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[6,2,8,1,7,5,4,3] => [[[.,.],[.,.]],[[[[.,.],.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[4,2,8,1,5,3,6,7] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[4,6,2,8,3,7,5,1] => [[[.,[.,.]],[[.,.],[[.,.],.]]],.] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 1

[2,1,5,8,3,6,4,7] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[7,8,5,6,4,1,3,2] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[5,8,4,1,6,3,7,2] => [[[.,[.,.]],.],[[[.,.],[.,.]],.]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[4,8,1,3,5,7,6,2] => [[.,[.,.]],[[.,[.,[[.,.],.]]],.]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 2

[3,8,1,4,5,6,2,7] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[7,6,8,3,5,1,4,2] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[6,5,8,4,7,1,3,2] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[6,7,4,2,5,3,1,8] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[4,7,3,5,6,2,1,8] => [[[[.,[.,.]],[.,[.,.]]],.],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2

[3,7,2,5,6,4,1,8] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[7,8,3,5,6,1,4,2] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[1,6,8,5,2,7,4,3] => [.,[[[.,[.,.]],.],[[[.,.],.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 3

[6,7,4,8,2,1,5,3] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[3,2,7,8,6,1,5,4] => [[[.,.],[[.,[.,.]],.]],[[.,.],.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[6,8,4,1,2,3,7,5] => [[[.,[.,.]],.],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 4

[3,8,1,5,2,7,6,4] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[1,5,2,4,6,7,8,3] => [.,[[.,.],[[.,[.,[.,[.,.]]]],.]]] => [1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 3

[7,1,4,6,3,2,8,5] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3

[4,5,3,1,6,7,8,2] => [[[.,[.,.]],.],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 2

[3,5,2,1,6,7,8,4] => [[[.,[.,.]],.],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 2

[5,2,3,1,6,7,8,4] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[3,2,5,6,1,7,8,4] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[6,8,4,7,2,1,3,5] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3

[5,7,4,6,1,3,8,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[6,7,4,1,5,3,8,2] => [[[.,[.,.]],.],[[[.,.],[.,.]],.]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[6,8,1,5,4,7,3,2] => [[.,[.,.]],[[[[.,.],[.,.]],.],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 2

[3,8,1,5,6,4,2,7] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[6,8,4,1,2,5,3,7] => [[[.,[.,.]],.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[3,2,8,1,6,5,4,7] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[3,2,6,1,5,7,8,4] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[3,5,1,4,6,7,8,2] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2

[3,2,5,1,4,7,8,6] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[5,1,3,4,6,7,8,2] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2

[2,6,1,3,8,7,5,4] => [[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 3

[2,6,8,1,5,7,4,3] => [[.,[.,[.,.]]],[[[.,[.,.]],.],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[2,7,1,6,4,8,3,5] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[2,7,1,6,5,3,8,4] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[2,8,1,7,6,5,4,3] => [[.,[.,.]],[[[[[.,.],.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2

[3,7,1,8,6,5,4,2] => [[.,[.,.]],[[[[[.,.],.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2

[3,6,8,5,1,4,7,2] => [[.,[[.,[.,.]],.]],[[.,[.,.]],.]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 2

[7,3,5,8,2,1,4,6] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[7,3,6,2,1,4,5,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[6,8,4,5,2,1,7,3] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[4,6,8,5,1,7,3,2] => [[.,[[.,[.,.]],.]],[[[.,.],.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2

[5,4,8,2,7,3,6,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[6,3,7,2,4,8,1,5] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[5,6,8,4,2,7,3,1] => [[[[.,[.,[.,.]]],.],[[.,.],.]],.] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1

[5,7,4,2,8,1,3,6] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[6,4,7,3,1,8,2,5] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[7,5,8,4,6,3,2,1] => [[[[[[.,.],[.,.]],[.,.]],.],.],.] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1

[5,6,3,7,4,2,1,8] => [[[[.,[.,.]],[[.,.],.]],.],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2

[6,4,8,1,3,2,5,7] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[3,7,2,4,6,5,1,8] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[8,1,3,4,5,2,6,7] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[1,6,8,4,2,5,3,7] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 4

[6,7,4,8,5,1,2,3] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[3,2,7,8,5,1,6,4] => [[[.,.],[[.,[.,.]],.]],[[.,.],.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[3,2,8,1,5,4,6,7] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[3,7,1,4,2,5,8,6] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[7,1,4,6,3,8,5,2] => [[.,.],[[[.,[.,.]],[[.,.],.]],.]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2

[3,5,2,1,8,7,6,4] => [[[.,[.,.]],.],[[[[.,.],.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2

[5,2,3,4,7,1,8,6] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[6,7,3,1,5,4,2,8] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[5,8,3,1,2,4,7,6] => [[[.,[.,.]],.],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 4

[3,8,1,5,6,4,7,2] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2

[6,8,4,1,2,5,7,3] => [[[.,[.,.]],.],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 3

[3,2,8,1,6,5,7,4] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[3,5,1,4,6,7,2,8] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[4,5,8,2,1,3,7,6] => [[[.,[.,[.,.]]],.],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[5,8,2,3,1,4,6,7] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[3,2,5,1,4,6,8,7] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[5,1,3,4,6,2,7,8] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[6,8,2,4,5,1,3,7] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[4,6,7,3,1,5,2,8] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[6,8,1,3,5,2,7,4] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[6,8,3,1,4,5,7,2] => [[[.,[.,.]],.],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 2

[4,5,7,2,3,6,8,1] => [[[.,[.,[.,.]]],[.,[.,[.,.]]]],.] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1

[4,5,2,7,1,6,8,3] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[7,2,4,8,1,5,3,6] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,6,3,1,7,8,5,2] => [[[.,[.,.]],.],[[[.,[.,.]],.],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 2

[4,8,3,7,6,5,1,2] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[7,8,2,6,5,1,4,3] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[7,8,2,6,1,5,4,3] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[4,2,8,1,7,6,5,3] => [[[.,.],[.,.]],[[[[.,.],.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[4,8,2,7,6,1,5,3] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[4,8,1,7,6,5,3,2] => [[.,[.,.]],[[[[[.,.],.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2

[6,4,8,1,7,5,3,2] => [[[.,.],[.,.]],[[[[.,.],.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[7,8,4,1,6,5,3,2] => [[[.,[.,.]],.],[[[[.,.],.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2

[7,8,3,1,6,5,4,2] => [[[.,[.,.]],.],[[[[.,.],.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2

[6,3,8,1,7,5,4,2] => [[[.,.],[.,.]],[[[[.,.],.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[7,8,2,1,6,5,4,3] => [[[.,[.,.]],.],[[[[.,.],.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2

[6,8,1,4,2,3,5,7] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[8,2,3,6,1,4,5,7] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[6,2,3,8,1,4,5,7] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[4,6,2,3,8,1,5,7] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[4,8,2,3,6,1,5,7] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[2,6,3,8,1,4,5,7] => [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[2,8,3,6,1,4,5,7] => [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[8,3,6,2,4,1,5,7] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[8,3,6,2,1,4,5,7] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[6,3,8,2,4,1,5,7] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[1,4,7,2,5,6,8,3] => [.,[[.,[.,.]],[[.,[.,[.,.]]],.]]] => [1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 3

[1,4,6,2,8,5,7,3] => [.,[[.,[.,.]],[[[.,.],[.,.]],.]]] => [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 3

[7,8,1,4,2,5,6,3] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[6,1,3,5,8,2,7,4] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[4,6,2,1,7,5,3,8] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[4,6,2,3,7,8,1,5] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[4,6,3,7,1,2,8,5] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[3,8,2,5,4,1,7,6] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[7,8,4,2,6,3,1,5] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[5,8,2,7,4,3,1,6] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[4,3,6,8,1,2,7,5] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[3,8,1,7,5,6,4,2] => [[.,[.,.]],[[[[.,.],[.,.]],.],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 2

[8,2,5,7,3,6,4,1] => [[[.,.],[[.,[.,.]],[[.,.],.]]],.] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1

[8,2,6,7,5,3,4,1] => [[[.,.],[[[.,[.,.]],.],[.,.]]],.] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1

[2,4,1,3,8,5,7,6] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4

[2,4,1,3,5,8,7,6] => [[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 4

[2,6,1,3,5,8,7,4] => [[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 3

[4,6,1,3,5,8,7,2] => [[.,[.,.]],[[.,[.,[[.,.],.]]],.]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 2

[8,2,4,1,3,5,7,6] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[8,2,6,1,3,5,7,4] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[8,4,6,1,3,5,7,2] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[8,1,4,6,3,5,7,2] => [[.,.],[[[.,[.,.]],[.,[.,.]]],.]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[6,4,8,1,3,5,7,2] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[6,2,8,1,3,5,7,4] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[4,2,8,1,3,5,7,6] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[2,6,8,1,3,5,7,4] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[4,6,8,1,3,5,7,2] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[4,6,1,8,3,5,7,2] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 2

[4,1,6,8,3,5,7,2] => [[.,.],[[[.,[.,.]],[.,[.,.]]],.]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[1,4,6,3,8,5,7,2] => [.,[[[.,[.,.]],[[.,.],[.,.]]],.]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 2

[4,6,1,3,8,5,7,2] => [[.,[.,.]],[[.,[[.,.],[.,.]]],.]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 2

[2,4,1,8,3,5,7,6] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[2,1,6,8,3,5,7,4] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3

[4,1,3,6,8,5,7,2] => [[.,.],[[.,[[.,[.,.]],[.,.]]],.]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 2

[2,6,1,4,3,5,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[2,8,1,4,3,5,7,6] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[2,8,1,6,3,5,7,4] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[4,8,1,3,6,5,7,2] => [[.,[.,.]],[[.,[[.,.],[.,.]]],.]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 2

[1,4,8,3,6,5,7,2] => [.,[[[.,[.,.]],[[.,.],[.,.]]],.]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 2

[4,8,1,6,3,5,7,2] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 2

[4,6,2,1,3,5,7,8] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 5

[6,8,1,4,3,5,7,2] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 2

[1,6,8,4,3,5,7,2] => [.,[[[[.,[.,.]],.],[.,[.,.]]],.]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 2

[7,8,6,5,2,1,4,3] => [[[[[.,[.,.]],.],.],.],[[.,.],.]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2

[5,7,4,1,8,6,3,2] => [[[.,[.,.]],.],[[[[.,.],.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2

[5,6,4,2,8,3,7,1] => [[[[.,[.,.]],.],[[.,.],[.,.]]],.] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 1

[5,6,4,2,7,3,1,8] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[5,7,1,4,6,3,2,8] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[5,8,1,4,6,3,7,2] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2

[3,6,7,4,5,8,2,1] => [[[.,[[.,[.,.]],[.,[.,.]]]],.],.] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 1

[3,5,7,4,6,8,2,1] => [[[.,[[.,[.,.]],[.,[.,.]]]],.],.] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 1

[6,8,4,1,7,2,5,3] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[5,4,6,1,7,8,3,2] => [[[.,.],[.,.]],[[[.,[.,.]],.],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[5,6,4,1,8,7,3,2] => [[[.,[.,.]],.],[[[[.,.],.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2

[3,5,8,4,6,7,2,1] => [[[.,[[.,[.,.]],[.,[.,.]]]],.],.] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 1

[3,6,8,4,5,7,2,1] => [[[.,[[.,[.,.]],[.,[.,.]]]],.],.] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 1

[3,7,8,4,5,6,2,1] => [[[.,[[.,[.,.]],[.,[.,.]]]],.],.] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 1

[6,8,1,4,5,3,7,2] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2

[6,7,1,4,5,3,2,8] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[3,7,1,5,4,6,2,8] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[3,8,1,5,4,6,7,2] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 2

[3,7,1,5,4,6,8,2] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 2

[6,7,1,4,5,3,8,2] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2

[5,7,1,4,6,3,8,2] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2

[5,6,4,2,7,3,8,1] => [[[[.,[.,.]],.],[[.,.],[.,.]]],.] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 1

[5,4,7,2,8,3,1,6] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[5,4,7,2,8,3,6,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[5,6,4,2,8,3,1,7] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[5,8,1,4,6,3,2,7] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[3,8,1,5,4,6,2,7] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[3,6,1,5,4,2,7,8] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[3,6,1,5,4,8,2,7] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[6,8,3,1,4,2,5,7] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[7,3,8,1,4,2,5,6] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[6,7,3,1,4,2,8,5] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[3,6,1,5,4,7,8,2] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 2

[3,4,1,2,7,6,5,8] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 4

[3,4,1,2,6,8,7,5] => [[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 3

[6,8,3,1,4,7,2,5] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[6,4,7,2,8,5,1,3] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[5,8,1,4,7,3,2,6] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[7,8,1,4,5,3,2,6] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[3,8,1,5,4,7,2,6] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[3,6,1,5,4,8,7,2] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2

[3,6,1,5,4,7,2,8] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[6,7,3,1,4,2,5,8] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[6,8,3,1,4,2,7,5] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[7,8,3,1,4,6,2,5] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[7,8,4,2,6,5,1,3] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[7,8,3,1,4,6,5,2] => [[[.,[.,.]],.],[[.,[[.,.],.]],.]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 2

[6,7,3,1,4,5,2,8] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[3,7,1,5,4,2,6,8] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[3,8,1,5,4,2,7,6] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[5,8,1,4,7,3,6,2] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2

[6,8,4,2,7,5,3,1] => [[[[.,[.,.]],.],[[[.,.],.],.]],.] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 1

[6,4,7,2,8,5,3,1] => [[[[.,.],[.,.]],[[[.,.],.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1

[6,3,7,1,4,8,5,2] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[6,8,3,1,4,7,5,2] => [[[.,[.,.]],.],[[.,[[.,.],.]],.]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 2

[3,7,1,5,4,8,6,2] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2

[3,4,1,2,8,5,7,6] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4

[3,4,1,2,5,8,7,6] => [[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 4

[3,7,1,5,4,2,8,6] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[6,7,3,1,4,5,8,2] => [[[.,[.,.]],.],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 2

[7,3,8,1,4,5,2,6] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[7,3,8,1,4,5,6,2] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[6,8,3,1,4,5,2,7] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[3,8,1,5,4,2,6,7] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[8,5,7,4,3,2,1,6] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2

[6,5,8,4,3,2,1,7] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2

[4,5,2,7,3,1,8,6] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[4,8,2,6,3,5,7,1] => [[[.,[.,.]],[[.,.],[.,[.,.]]]],.] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 1

[7,8,2,1,5,6,4,3] => [[[.,[.,.]],.],[[[.,[.,.]],.],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 2

[5,2,7,1,8,6,3,4] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[3,7,8,4,1,2,6,5] => [[.,[[.,[.,.]],.]],[.,[[.,.],.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 3

[3,7,8,5,1,2,6,4] => [[.,[[.,[.,.]],.]],[.,[[.,.],.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 3

[4,7,8,6,1,2,5,3] => [[.,[[.,[.,.]],.]],[.,[[.,.],.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 3

[5,7,8,6,1,2,4,3] => [[.,[[.,[.,.]],.]],[.,[[.,.],.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 3

[6,4,7,8,3,1,2,5] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[7,3,4,8,2,1,5,6] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[2,4,8,3,1,5,7,6] => [[.,[[.,[.,.]],.]],[.,[[.,.],.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 3

[8,3,4,7,2,5,6,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1

[8,3,5,7,2,4,6,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1

[8,4,6,7,2,3,5,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1

[2,6,8,5,1,3,7,4] => [[.,[[.,[.,.]],.]],[.,[[.,.],.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 3

[2,6,8,4,1,3,7,5] => [[.,[[.,[.,.]],.]],[.,[[.,.],.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 3

[2,5,8,3,1,4,7,6] => [[.,[[.,[.,.]],.]],[.,[[.,.],.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 3

[7,4,6,8,2,1,3,5] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[2,3,6,8,1,5,4,7] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,5,6,1,4,7,8,3] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[2,5,6,1,4,7,3,8] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[7,3,5,1,6,8,4,2] => [[[.,.],[.,.]],[[[.,[.,.]],.],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[5,7,8,6,2,3,4,1] => [[[.,[[.,[.,.]],.]],[.,[.,.]]],.] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 1

[6,3,5,1,7,2,4,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[7,3,5,8,4,1,2,6] => [[[.,.],[[.,[.,.]],.]],[.,[.,.]]] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[7,3,5,8,4,1,6,2] => [[[.,.],[[.,[.,.]],.]],[[.,.],.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[3,4,1,5,6,8,7,2] => [[.,[.,.]],[[.,[.,[[.,.],.]]],.]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 2

[3,7,1,6,8,5,2,4] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[2,3,1,8,6,4,7,5] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[2,3,1,8,6,4,5,7] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[3,7,1,6,8,5,4,2] => [[.,[.,.]],[[[[.,[.,.]],.],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 2

[7,3,5,8,4,6,2,1] => [[[[.,.],[[.,[.,.]],[.,.]]],.],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1

[2,3,4,7,1,6,5,8] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,3,4,7,1,6,8,5] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[2,3,4,6,1,8,7,5] => [[.,[.,[.,[.,.]]]],[[[.,.],.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[6,3,5,8,4,2,7,1] => [[[[.,.],[[.,[.,.]],.]],[.,.]],.] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[6,3,5,8,4,2,1,7] => [[[[.,.],[[.,[.,.]],.]],.],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => 2

[5,2,4,6,8,3,7,1] => [[[.,.],[[.,[.,[.,.]]],[.,.]]],.] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1

[1,5,7,4,6,3,2,8] => [.,[[[[.,[.,.]],[.,.]],.],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 3

[6,8,3,4,5,7,2,1] => [[[[.,[.,.]],[.,[.,[.,.]]]],.],.] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1

[2,5,7,4,6,3,8,1] => [[.,[[[.,[.,.]],[.,.]],[.,.]]],.] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1

[5,1,4,6,8,3,2,7] => [[.,.],[[[.,[.,[.,.]]],.],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => 3

[5,8,2,4,7,3,6,1] => [[[.,[.,.]],[[.,[.,.]],[.,.]]],.] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 1

[6,8,3,2,4,7,5,1] => [[[[.,[.,.]],.],[.,[[.,.],.]]],.] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 1

[5,3,6,2,4,8,7,1] => [[[[.,.],[.,.]],[.,[[.,.],.]]],.] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[3,5,2,8,6,1,4,7] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[3,7,2,5,1,4,8,6] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[8,2,3,6,1,4,7,5] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[7,2,3,6,1,4,8,5] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[1,3,7,2,5,8,4,6] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 4

[7,4,8,1,3,6,2,5] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[8,1,2,3,5,7,4,6] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => 5

[7,1,2,3,5,8,4,6] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => 5

[2,3,1,8,5,4,6,7] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[3,5,2,6,7,1,8,4] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[3,8,1,6,5,2,7,4] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[6,8,3,1,7,2,4,5] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[3,7,2,5,6,1,8,4] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[6,8,4,2,5,1,7,3] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[7,3,8,1,6,5,2,4] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[8,3,7,1,6,5,2,4] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[4,2,3,7,8,5,1,6] => [[[.,.],[.,[[.,[.,.]],.]]],[.,.]] => [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => 2

[6,4,7,8,1,5,2,3] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,7,4,8,1,5,2,3] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[8,4,6,7,1,5,2,3] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[7,4,6,8,1,5,2,3] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[8,5,6,7,1,4,2,3] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[8,6,7,5,1,4,2,3] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[2,4,6,7,1,5,8,3] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[6,7,8,5,1,4,2,3] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[7,8,6,5,1,4,2,3] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[8,2,7,1,5,3,4,6] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[3,2,7,1,5,8,4,6] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[6,3,7,1,5,4,2,8] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[7,3,8,1,5,4,2,6] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[4,5,1,3,6,8,2,7] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[3,6,8,1,5,4,2,7] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[6,8,3,1,5,4,2,7] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[3,6,2,1,5,8,4,7] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[4,8,2,1,7,5,3,6] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[2,3,8,1,5,7,4,6] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[4,7,1,2,6,3,8,5] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4

[2,7,8,1,5,3,4,6] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[6,7,2,1,5,3,4,8] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[4,7,2,1,8,5,3,6] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[5,7,8,6,1,4,3,2] => [[.,[[.,[.,.]],.]],[[[.,.],.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2

[3,7,1,4,5,6,8,2] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2

[3,5,1,4,7,6,8,2] => [[.,[.,.]],[[.,[[.,.],[.,.]]],.]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 2

[6,8,5,7,1,4,3,2] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[6,5,7,8,1,4,3,2] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[7,2,3,1,5,6,4,8] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[4,2,8,1,6,5,3,7] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[6,2,4,1,8,5,3,7] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[7,1,5,8,4,3,6,2] => [[.,.],[[[[.,[.,.]],.],[.,.]],.]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 2

[5,8,1,6,4,3,7,2] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2

[8,2,6,1,4,5,3,7] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[6,2,8,1,4,5,3,7] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[7,2,6,1,5,3,4,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[7,1,2,5,8,3,4,6] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 5

[7,1,4,5,6,8,3,2] => [[.,.],[[[.,[.,[.,[.,.]]]],.],.]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => 2

[8,5,6,7,1,4,3,2] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[7,6,8,5,1,4,3,2] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[2,6,7,1,4,5,3,8] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[3,5,1,7,4,6,8,2] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 2

[7,1,5,6,4,8,3,2] => [[.,.],[[[[.,[.,.]],[.,.]],.],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[7,8,6,5,1,4,3,2] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2

[5,3,6,2,1,8,7,4] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[5,3,7,2,1,4,6,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[5,3,7,2,8,4,1,6] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[7,2,4,5,8,3,1,6] => [[[.,.],[[.,[.,[.,.]]],.]],[.,.]] => [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => 2

[7,2,4,5,1,3,6,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[6,2,4,5,1,8,7,3] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[3,1,4,5,2,8,7,6] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3

[3,7,4,5,1,2,6,8] => [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[3,7,4,5,8,2,1,6] => [[[.,[[.,.],[.,[.,.]]]],.],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2

[6,3,7,1,8,4,2,5] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[5,7,4,1,6,3,2,8] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[5,7,4,8,6,3,1,2] => [[[[.,[.,.]],[[.,.],.]],.],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2

[4,8,3,5,6,7,1,2] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[1,8,3,5,6,7,2,4] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[4,8,1,5,6,7,2,3] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[4,1,3,5,6,7,2,8] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 3

[5,8,4,3,6,1,2,7] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[1,5,8,4,6,7,3,2] => [.,[[[[.,[.,.]],[.,[.,.]]],.],.]] => [1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 2

[1,4,8,3,6,7,5,2] => [.,[[[.,[.,.]],[[.,[.,.]],.]],.]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 2

[4,3,8,2,1,7,5,6] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[3,8,1,5,6,7,4,2] => [[.,[.,.]],[[[.,[.,[.,.]]],.],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2

[3,8,2,5,6,7,1,4] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[8,1,3,5,6,7,4,2] => [[.,.],[[.,[[.,[.,[.,.]]],.]],.]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => 2

[7,8,4,3,6,2,1,5] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[6,3,5,8,2,7,1,4] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[7,3,6,1,8,2,4,5] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[8,3,5,2,1,7,4,6] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[4,3,5,8,1,7,2,6] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,3,7,2,5,6,8,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1

[3,7,1,5,6,2,8,4] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[4,7,1,5,6,8,2,3] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[5,3,4,6,2,8,1,7] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,4,7,2,3,8,1,5] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[6,5,7,2,8,3,1,4] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[5,3,7,2,4,8,6,1] => [[[[.,.],[.,.]],[.,[[.,.],.]]],.] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[8,5,6,4,1,7,2,3] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[8,4,6,2,3,1,7,5] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[5,8,1,7,4,3,2,6] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[7,3,4,2,6,8,1,5] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[3,6,7,5,2,4,8,1] => [[[.,[[.,[.,.]],.]],[.,[.,.]]],.] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 1

[3,6,7,5,2,4,1,8] => [[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => [1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[5,8,1,7,4,2,6,3] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[3,7,8,6,2,4,5,1] => [[[.,[[.,[.,.]],.]],[.,[.,.]]],.] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 1

[4,8,1,7,3,6,5,2] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2

[2,6,1,5,4,7,8,3] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 2

[4,6,3,5,8,7,1,2] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[3,5,6,2,4,1,7,8] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[2,5,6,1,4,8,3,7] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[6,7,8,4,1,5,3,2] => [[[.,[.,[.,.]]],.],[[[.,.],.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[7,1,6,8,4,5,3,2] => [[.,.],[[[[.,[.,.]],[.,.]],.],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[7,1,5,6,4,2,3,8] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[5,7,4,6,8,1,3,2] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[5,7,8,1,4,6,3,2] => [[.,[.,[.,.]]],[[[.,[.,.]],.],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[8,1,5,7,4,6,3,2] => [[.,.],[[[[.,[.,.]],[.,.]],.],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[8,1,4,5,6,7,3,2] => [[.,.],[[[.,[.,[.,[.,.]]]],.],.]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => 2

[5,6,7,1,4,2,3,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[3,5,1,8,2,6,4,7] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[3,5,1,2,8,4,7,6] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4

[3,6,2,8,5,1,7,4] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[8,2,7,1,5,4,6,3] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[1,7,8,2,6,4,3,5] => [.,[[.,[.,.]],[[[.,.],.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 4

[7,1,5,8,3,2,4,6] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[8,1,4,7,3,2,5,6] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[4,7,8,1,3,2,5,6] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[8,3,5,7,1,6,4,2] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[8,3,6,1,4,5,7,2] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[2,6,8,3,4,5,7,1] => [[.,[[.,[.,.]],[.,[.,[.,.]]]]],.] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1

[2,5,7,3,4,8,6,1] => [[.,[[.,[.,.]],[.,[[.,.],.]]]],.] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 1

[2,7,8,5,3,6,4,1] => [[.,[[[.,[.,.]],.],[[.,.],.]]],.] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 1

[4,8,1,7,2,3,6,5] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[3,7,1,8,2,6,4,5] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[3,1,7,8,2,5,6,4] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3

[7,3,6,1,4,8,5,2] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[7,8,3,6,1,4,5,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[7,4,8,1,2,3,6,5] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[7,4,6,1,2,8,3,5] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[5,7,1,2,3,6,4,8] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 5

[3,6,8,1,2,7,4,5] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[8,4,6,1,2,3,7,5] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[4,8,1,5,2,7,3,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[8,6,7,4,1,2,5,3] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[6,4,8,1,2,5,3,7] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[6,7,3,1,4,8,5,2] => [[[.,[.,.]],.],[[.,[[.,.],.]],.]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 2

[5,6,3,8,7,1,4,2] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[5,4,7,1,2,8,6,3] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[6,7,4,1,2,8,3,5] => [[[.,[.,.]],.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[6,7,4,1,2,5,3,8] => [[[.,[.,.]],.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[7,8,6,4,1,2,5,3] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 3

[2,4,6,3,5,7,1,8] => [[.,[[.,[.,.]],[.,[.,.]]]],[.,.]] => [1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2

[1,4,6,3,7,2,5,8] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 4

[8,2,3,4,5,1,7,6] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[3,8,2,4,6,1,7,5] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[7,8,2,4,3,1,6,5] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[4,5,8,2,3,1,7,6] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[6,1,3,5,7,2,4,8] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[7,1,3,6,2,5,4,8] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[8,1,3,6,2,4,7,5] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[6,1,5,8,2,7,3,4] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[4,5,2,8,1,6,7,3] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[6,2,5,8,1,4,7,3] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[8,2,7,1,4,6,5,3] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[1,3,8,2,5,7,4,6] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 4

[8,4,5,7,1,6,3,2] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[3,5,6,8,4,1,7,2] => [[.,[[.,[.,[.,.]]],.]],[[.,.],.]] => [1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[6,2,3,1,5,4,7,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[7,2,3,1,4,6,5,8] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[8,2,3,1,4,5,7,6] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[2,6,1,4,5,3,7,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[4,5,6,1,3,2,7,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[4,5,7,1,2,6,3,8] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[6,7,1,4,2,5,3,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[2,7,1,3,5,6,4,8] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4

[2,8,1,3,4,6,7,5] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 4

[7,8,1,2,5,3,6,4] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4

[1,2,6,7,5,3,8,4] => [.,[.,[[[.,[.,.]],.],[[.,.],.]]]] => [1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 4

[1,6,7,5,3,8,4,2] => [.,[[[[.,[.,.]],.],[[.,.],.]],.]] => [1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 2

[1,3,8,2,6,5,7,4] => [.,[[.,[.,.]],[[[.,.],[.,.]],.]]] => [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 3

[1,3,4,8,2,5,7,6] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[1,4,8,3,2,5,7,6] => [.,[[[.,[.,.]],.],[.,[[.,.],.]]]] => [1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 4

[1,4,8,3,5,7,6,2] => [.,[[[.,[.,.]],[.,[[.,.],.]]],.]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 2

[1,2,4,8,3,5,7,6] => [.,[.,[[.,[.,.]],[.,[[.,.],.]]]]] => [1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 5

[1,4,8,2,3,5,7,6] => [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => [1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 5

[6,5,7,3,8,2,4,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[4,2,6,7,5,8,3,1] => [[[.,.],[[[.,[.,.]],[.,.]],.]],.] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1

[6,7,5,2,1,8,4,3] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2

[5,6,8,3,1,7,2,4] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[6,1,4,8,3,2,7,5] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3

[3,4,7,1,8,6,2,5] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[3,4,6,8,2,1,5,7] => [[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[3,8,2,5,6,1,4,7] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[3,5,2,8,6,4,1,7] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[4,2,5,7,3,8,6,1] => [[[.,.],[[.,[.,.]],[[.,.],.]]],.] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1

[5,2,6,8,4,1,3,7] => [[[.,.],[[.,[.,.]],.]],[.,[.,.]]] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[1,5,6,8,3,4,2,7] => [.,[[[.,[.,[.,.]]],[.,.]],[.,.]]] => [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[4,5,8,1,6,3,2,7] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[4,5,1,6,8,3,2,7] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[4,5,7,3,8,2,6,1] => [[[[.,[.,[.,.]]],[.,.]],[.,.]],.] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[4,5,3,1,7,8,2,6] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[5,7,3,8,4,6,1,2] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[1,4,5,7,3,8,6,2] => [.,[[[.,[.,[.,.]]],[[.,.],.]],.]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2

[4,6,3,7,8,5,2,1] => [[[[.,[.,.]],[[.,[.,.]],.]],.],.] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 1

[5,3,6,7,8,4,2,1] => [[[[.,.],[[.,[.,[.,.]]],.]],.],.] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => 1

[4,6,1,7,3,8,5,2] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2

[6,3,7,1,8,4,5,2] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[6,7,2,4,8,1,5,3] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[2,6,1,4,7,3,8,5] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[3,2,5,6,7,8,1,4] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2

[5,2,3,6,7,8,4,1] => [[[.,.],[.,[[.,[.,[.,.]]],.]]],.] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => 1

[6,7,1,3,2,8,4,5] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[6,2,7,1,3,4,8,5] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[6,7,3,8,2,4,5,1] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1

[3,6,2,7,4,1,8,5] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[6,7,3,2,1,4,8,5] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 3

[7,2,4,1,8,3,5,6] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[3,5,7,2,1,8,6,4] => [[[.,[.,[.,.]]],.],[[[.,.],.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[6,7,8,3,2,5,1,4] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[6,3,7,8,2,5,4,1] => [[[[.,.],[.,[.,.]]],[[.,.],.]],.] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => 1

[2,6,7,4,8,5,3,1] => [[.,[[[.,[.,.]],[[.,.],.]],.]],.] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 1

[6,2,4,7,1,8,5,3] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[4,6,2,7,1,8,5,3] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[1,3,7,8,5,2,6,4] => [.,[[.,[[.,[.,.]],.]],[[.,.],.]]] => [1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 3

[2,5,7,8,1,6,3,4] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,3,7,1,8,2,5,4] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[2,5,6,1,7,8,4,3] => [[.,[.,[.,.]]],[[[.,[.,.]],.],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[5,6,1,2,7,8,4,3] => [[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 3

[6,7,2,1,8,5,3,4] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[6,7,2,8,5,4,1,3] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[1,6,7,4,8,5,3,2] => [.,[[[[.,[.,.]],[[.,.],.]],.],.]] => [1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 2

[3,6,2,7,1,4,5,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[5,2,4,8,1,3,7,6] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[5,2,3,4,8,1,6,7] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[3,5,2,4,7,1,6,8] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[5,3,4,8,1,6,2,7] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,5,3,7,1,6,2,8] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,2,6,7,3,8,1,5] => [[[.,.],[[.,[.,.]],[.,.]]],[.,.]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[1,5,7,4,2,8,6,3] => [.,[[[.,[.,.]],.],[[[.,.],.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 3

[1,3,7,2,8,6,4,5] => [.,[[.,[.,.]],[[[.,.],.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 4

[4,2,3,5,6,8,1,7] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2

[4,2,6,7,3,8,5,1] => [[[.,.],[[.,[.,.]],[[.,.],.]]],.] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1

[3,2,5,6,8,1,7,4] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[6,4,5,2,3,8,7,1] => [[[[.,.],[.,.]],[.,[[.,.],.]]],.] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[4,6,2,5,3,8,7,1] => [[[.,[.,.]],[[.,.],[[.,.],.]]],.] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 1

[6,8,2,7,4,5,3,1] => [[[.,[.,.]],[[[.,.],[.,.]],.]],.] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 1

[8,2,4,6,7,5,3,1] => [[[.,.],[[.,[[.,[.,.]],.]],.]],.] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1

[4,6,8,2,7,5,3,1] => [[[.,[.,[.,.]]],[[[.,.],.],.]],.] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1

[4,2,5,6,3,8,1,7] => [[[.,.],[[.,[.,.]],[.,.]]],[.,.]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[6,2,5,7,4,8,3,1] => [[[.,.],[[[.,[.,.]],[.,.]],.]],.] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1

[6,7,3,2,5,8,4,1] => [[[[.,[.,.]],.],[[.,[.,.]],.]],.] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 1

[5,7,8,2,6,3,4,1] => [[[.,[.,[.,.]]],[[.,.],[.,.]]],.] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[5,3,6,7,4,1,8,2] => [[[.,.],[[.,[.,.]],.]],[[.,.],.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[3,4,8,2,7,5,1,6] => [[[.,[.,[.,.]]],[[.,.],.]],[.,.]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[2,4,8,1,5,3,7,6] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[3,4,8,1,6,2,7,5] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[2,8,1,6,5,7,4,3] => [[.,[.,.]],[[[[.,.],[.,.]],.],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 2

[4,6,8,2,5,3,7,1] => [[[.,[.,[.,.]]],[[.,.],[.,.]]],.] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[8,1,2,4,6,7,3,5] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 4

[5,2,6,8,4,3,1,7] => [[[.,.],[[[.,[.,.]],.],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => 2

[7,8,1,5,4,3,6,2] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2

[2,7,8,5,4,6,1,3] => [[.,[[[.,[.,.]],.],[.,.]]],[.,.]] => [1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 2

[5,7,4,3,8,6,2,1] => [[[[[.,[.,.]],.],[[.,.],.]],.],.] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 1

[4,8,1,6,3,5,2,7] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[4,7,3,2,5,1,8,6] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[3,2,8,1,4,6,5,7] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[4,7,8,3,1,2,6,5] => [[[.,[.,[.,.]]],.],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[4,7,8,2,1,3,6,5] => [[[.,[.,[.,.]]],.],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[4,1,6,8,2,3,7,5] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[4,5,1,2,8,3,7,6] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4

[4,6,2,8,1,3,7,5] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[3,6,2,8,4,7,1,5] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[4,2,6,8,3,1,7,5] => [[[.,.],[[.,[.,.]],.]],[[.,.],.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[4,1,2,5,8,3,7,6] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 4

[5,2,4,1,3,8,7,6] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[3,5,1,4,8,7,2,6] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3

[3,4,5,1,8,7,2,6] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[4,3,6,8,2,1,7,5] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[2,4,6,8,3,7,5,1] => [[.,[[.,[.,[.,.]]],[[.,.],.]]],.] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1

[3,4,5,2,8,7,1,6] => [[[.,[.,[.,.]]],[[.,.],.]],[.,.]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[6,5,7,4,2,8,3,1] => [[[[[.,.],[.,.]],.],[[.,.],.]],.] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1

[6,7,5,3,8,2,4,1] => [[[[[.,[.,.]],.],[.,.]],[.,.]],.] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1

[8,3,5,6,2,4,1,7] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,2,3,7,8,4,5,1] => [[[.,.],[.,[[.,[.,.]],[.,.]]]],.] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1

[7,5,8,2,6,3,4,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[1,5,6,7,3,4,8,2] => [.,[[[.,[.,[.,.]]],[.,[.,.]]],.]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[6,7,8,2,1,4,5,3] => [[[.,[.,[.,.]]],.],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[3,5,8,2,7,1,6,4] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[3,4,2,8,5,1,7,6] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[3,4,1,8,2,6,7,5] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[8,4,6,3,7,1,5,2] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[6,8,3,4,1,5,7,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[6,8,2,5,7,4,1,3] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[2,8,5,6,7,1,3,4] => [[.,[[.,.],[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[2,5,7,3,8,4,6,1] => [[.,[[.,[.,.]],[[.,.],[.,.]]]],.] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 1

[4,2,7,1,8,5,3,6] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[8,3,6,7,1,5,4,2] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[5,7,8,4,3,1,6,2] => [[[[.,[.,[.,.]]],.],.],[[.,.],.]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[3,5,7,1,4,8,6,2] => [[.,[.,[.,.]]],[[.,[[.,.],.]],.]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[5,7,4,8,3,6,2,1] => [[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1

[4,3,7,2,5,8,1,6] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[3,2,4,7,8,5,6,1] => [[[.,.],[.,[[.,[.,.]],[.,.]]]],.] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1

[3,8,2,1,6,4,5,7] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[4,6,8,3,2,1,5,7] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3

[3,2,6,8,5,4,1,7] => [[[.,.],[[[.,[.,.]],.],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => 2

[7,3,8,2,5,4,1,6] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[4,8,2,6,5,3,1,7] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[2,6,8,5,4,1,3,7] => [[.,[[[.,[.,.]],.],.]],[.,[.,.]]] => [1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 3

[6,4,8,3,7,2,5,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[4,7,3,6,2,1,8,5] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[3,8,1,5,7,4,6,2] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2

[4,8,3,6,7,1,5,2] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[4,7,8,3,1,6,5,2] => [[[.,[.,[.,.]]],.],[[[.,.],.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[4,6,1,3,8,7,5,2] => [[.,[.,.]],[[.,[[[.,.],.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 2

[6,8,2,1,7,4,5,3] => [[[.,[.,.]],.],[[[.,.],[.,.]],.]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[3,7,1,6,4,2,8,5] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[3,6,1,2,7,5,8,4] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 3

[3,6,2,5,8,7,4,1] => [[[.,[.,.]],[[.,[[.,.],.]],.]],.] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 1

[4,7,2,6,3,8,1,5] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[3,7,2,4,6,1,8,5] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[5,3,7,2,8,1,4,6] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[7,3,8,2,6,5,1,4] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[5,2,8,1,7,6,3,4] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[3,6,1,8,7,5,2,4] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[5,6,1,2,8,7,4,3] => [[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 3

[7,8,5,1,6,2,4,3] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[5,7,2,4,6,8,1,3] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[6,4,7,1,3,8,5,2] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[4,5,1,2,7,6,8,3] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 3

[5,4,6,8,3,1,2,7] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[2,6,7,4,5,3,1,8] => [[.,[[[.,[.,.]],[.,.]],.]],[.,.]] => [1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2

[2,8,1,3,6,5,4,7] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 4

[3,4,2,6,8,7,1,5] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[6,8,3,2,7,1,5,4] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[3,7,1,2,4,6,5,8] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 5

[7,5,6,8,2,1,4,3] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[3,4,6,2,8,5,7,1] => [[[.,[.,[.,.]]],[[.,.],[.,.]]],.] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[4,7,1,6,5,2,8,3] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[4,7,3,6,5,1,8,2] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[3,4,6,1,8,5,2,7] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[4,3,7,1,6,8,2,5] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[3,8,1,4,2,6,5,7] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[3,8,2,4,5,6,7,1] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1

[3,8,2,4,1,6,7,5] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[3,8,2,5,4,6,7,1] => [[[.,[.,.]],[[.,.],[.,[.,.]]]],.] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 1

[4,2,6,7,5,3,1,8] => [[[.,.],[[[.,[.,.]],.],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => 2

[3,2,6,1,4,5,8,7] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[3,8,1,2,4,6,5,7] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 5

[8,4,7,2,5,1,6,3] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[7,4,6,2,3,5,8,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1

[4,5,7,1,2,6,8,3] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[6,7,1,3,8,4,2,5] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3

[4,8,3,6,5,2,1,7] => [[[[.,[.,.]],[[.,.],.]],.],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2

[3,6,8,5,1,2,4,7] => [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4

[6,1,7,8,2,5,3,4] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[6,7,5,2,8,1,4,3] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[7,5,6,1,2,8,4,3] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[4,1,3,7,8,6,2,5] => [[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3

[5,1,6,8,4,2,7,3] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3

[7,4,8,2,3,6,5,1] => [[[[.,.],[.,.]],[.,[[.,.],.]]],.] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[5,6,8,4,7,3,2,1] => [[[[[.,[.,[.,.]]],[.,.]],.],.],.] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1

[6,4,7,8,5,2,1,3] => [[[[.,.],[[.,[.,.]],.]],.],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => 2

[3,7,4,8,1,2,5,6] => [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[7,6,8,3,2,5,4,1] => [[[[[.,.],[.,.]],.],[[.,.],.]],.] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1

[7,6,8,3,1,4,5,2] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[3,1,4,8,2,5,7,6] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[5,8,2,6,3,1,4,7] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[6,8,2,3,7,4,1,5] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[7,8,2,3,4,6,5,1] => [[[.,[.,.]],[.,[.,[[.,.],.]]]],.] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 1

[8,1,3,6,2,5,4,7] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[2,7,1,6,3,5,4,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[2,7,1,5,4,3,6,8] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[8,1,5,6,2,3,7,4] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[8,1,4,5,3,2,6,7] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[2,7,1,4,5,3,6,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[3,7,1,6,2,5,4,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[3,7,1,4,5,2,6,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[3,6,2,1,5,4,7,8] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[2,3,6,1,5,4,7,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[3,5,2,4,1,6,7,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[6,3,4,1,5,2,7,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[6,2,4,1,5,3,7,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[6,2,5,1,3,7,4,8] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[6,7,1,2,8,3,5,4] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4

[6,7,1,2,5,4,3,8] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 4

[5,6,2,1,3,7,4,8] => [[[.,[.,.]],.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[5,2,6,1,3,7,4,8] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[2,4,6,1,5,3,7,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[4,7,1,3,5,2,6,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[4,7,1,5,3,2,6,8] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[5,7,1,4,2,6,3,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[5,7,1,6,2,3,8,4] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[5,6,3,1,2,7,4,8] => [[[.,[.,.]],.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[5,3,6,1,2,7,4,8] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[3,4,6,1,5,2,7,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[6,8,5,2,3,4,1,7] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[8,5,6,2,7,1,4,3] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[8,6,7,5,3,1,4,2] => [[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[5,6,2,4,7,8,1,3] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[3,4,6,1,7,8,5,2] => [[.,[.,[.,.]]],[[[.,[.,.]],.],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[4,8,5,6,7,2,3,1] => [[[.,[[.,.],[.,[.,.]]]],[.,.]],.] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[5,8,1,7,2,6,4,3] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[8,1,5,7,2,6,4,3] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3

[4,8,1,5,2,6,7,3] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[3,7,8,5,1,6,2,4] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[8,6,7,1,5,2,3,4] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[6,1,7,8,5,2,3,4] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[7,5,6,2,1,8,4,3] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[4,5,3,6,8,2,7,1] => [[[[.,[.,.]],[.,[.,.]]],[.,.]],.] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[5,6,3,4,8,1,7,2] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[4,6,7,8,5,1,3,2] => [[.,[[.,[.,[.,.]]],.]],[[.,.],.]] => [1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[4,6,8,1,5,3,7,2] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[6,4,5,8,3,2,7,1] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1

[6,5,8,1,3,4,7,2] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[5,6,8,3,1,2,7,4] => [[[.,[.,[.,.]]],.],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[7,6,8,3,5,2,1,4] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[6,7,8,3,5,1,2,4] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[3,4,8,1,2,6,7,5] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[5,8,2,4,3,6,7,1] => [[[.,[.,.]],[[.,.],[.,[.,.]]]],.] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 1

[5,8,2,3,1,6,7,4] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[6,8,2,3,5,1,7,4] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[7,8,2,3,5,6,1,4] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[2,7,8,4,1,6,3,5] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[4,8,2,5,7,6,3,1] => [[[.,[.,.]],[[.,[[.,.],.]],.]],.] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 1

[4,6,1,5,2,3,8,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[6,2,3,5,1,4,8,7] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[2,6,7,5,1,8,4,3] => [[.,[[.,[.,.]],.]],[[[.,.],.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2

[6,2,5,1,8,3,4,7] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[7,4,6,8,5,3,2,1] => [[[[[.,.],[[.,[.,.]],.]],.],.],.] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 1

[8,1,3,5,7,4,6,2] => [[.,.],[[.,[[.,[.,.]],[.,.]]],.]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 2

[7,8,6,1,3,5,2,4] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[5,6,7,2,8,1,3,4] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[2,5,1,8,6,7,4,3] => [[.,[.,.]],[[[[.,.],[.,.]],.],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 2

[3,5,1,8,6,7,4,2] => [[.,[.,.]],[[[[.,.],[.,.]],.],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 2

[5,6,3,2,8,1,4,7] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[2,7,5,8,1,3,4,6] => [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[6,3,8,1,4,2,5,7] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[7,4,6,8,5,1,3,2] => [[[.,.],[[.,[.,.]],.]],[[.,.],.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[7,1,5,8,2,6,4,3] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3

[3,6,8,2,4,1,7,5] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[4,5,8,2,6,7,3,1] => [[[.,[.,[.,.]]],[[.,[.,.]],.]],.] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[5,2,8,1,6,7,3,4] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[2,5,8,4,6,7,3,1] => [[.,[[[.,[.,.]],[.,[.,.]]],.]],.] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[5,8,3,4,6,7,2,1] => [[[[.,[.,.]],[.,[.,[.,.]]]],.],.] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1

[4,2,8,1,6,7,3,5] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[2,4,8,1,6,7,3,5] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[7,8,5,3,6,4,2,1] => [[[[[.,[.,.]],.],[[.,.],.]],.],.] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 1

[5,8,4,1,6,7,2,3] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[3,8,1,4,6,7,2,5] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[8,2,3,4,6,7,1,5] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2

[8,3,6,2,5,4,1,7] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[5,4,8,3,2,6,1,7] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[3,5,8,2,4,6,1,7] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[6,4,7,8,2,3,1,5] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,8,3,6,4,2,1,7] => [[[[.,[.,.]],[[.,.],.]],.],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2

[5,7,4,3,1,2,6,8] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4

[5,1,4,8,3,7,2,6] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[2,1,6,8,5,4,7,3] => [[.,.],[[[[.,[.,.]],.],[.,.]],.]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 2

[6,1,5,7,8,2,4,3] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[7,3,6,1,2,5,4,8] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[5,4,7,1,3,2,6,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[5,7,4,8,2,1,3,6] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3

[4,6,8,2,5,1,3,7] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[7,4,6,2,1,5,3,8] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[5,7,2,3,8,1,4,6] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[5,8,3,6,1,7,4,2] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[4,7,1,2,5,8,6,3] => [[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 3

[6,8,4,1,2,7,5,3] => [[[.,[.,.]],.],[.,[[[.,.],.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 3

[7,5,8,1,2,6,4,3] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[7,4,8,1,6,3,5,2] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[5,8,2,1,7,3,6,4] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[3,6,1,8,2,4,7,5] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[3,5,1,8,7,2,4,6] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[4,6,1,8,3,7,2,5] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[4,7,1,2,8,6,3,5] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 4

[5,8,4,1,7,6,2,3] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[7,6,8,1,5,4,2,3] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[8,1,2,4,5,3,6,7] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 5

[1,4,7,3,5,8,2,6] => [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 3

[8,4,6,2,3,5,1,7] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[5,4,8,2,3,6,1,7] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[6,8,5,3,4,1,2,7] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[6,8,3,7,2,1,4,5] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3

[6,1,5,8,2,3,4,7] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[6,1,5,7,8,2,3,4] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[6,5,8,4,1,2,3,7] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[8,5,7,4,1,2,3,6] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[1,5,7,4,8,2,3,6] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 4

[7,5,8,1,3,6,2,4] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[5,7,1,3,8,2,4,6] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[7,6,8,1,5,2,3,4] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[7,1,5,8,3,4,2,6] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[2,4,1,7,5,8,3,6] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[7,1,4,6,3,8,2,5] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[3,4,7,2,6,8,5,1] => [[[.,[.,[.,.]]],[[.,[.,.]],.]],.] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[3,4,7,1,6,8,2,5] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[3,4,7,1,6,8,5,2] => [[.,[.,[.,.]]],[[[.,[.,.]],.],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[2,4,1,7,5,3,6,8] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[3,4,1,7,8,6,2,5] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[3,4,7,2,6,8,1,5] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[5,4,7,3,6,8,2,1] => [[[[[.,.],[.,.]],[.,[.,.]]],.],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1

[3,4,7,2,6,5,1,8] => [[[.,[.,[.,.]]],[[.,.],.]],[.,.]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[4,8,3,2,5,6,1,7] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[4,8,3,1,2,6,5,7] => [[[.,[.,.]],.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[3,4,7,1,6,2,5,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[3,4,7,1,6,2,8,5] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[3,4,7,2,6,5,8,1] => [[[.,[.,[.,.]]],[[.,.],[.,.]]],.] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[4,8,3,1,2,6,7,5] => [[[.,[.,.]],.],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 3

[5,8,1,6,3,4,2,7] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[6,8,5,1,3,7,2,4] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[6,8,5,1,3,4,7,2] => [[[.,[.,.]],.],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 2

[5,8,3,4,2,6,7,1] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1

[5,4,7,3,6,2,8,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[5,4,7,2,6,1,8,3] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[2,4,7,3,6,1,5,8] => [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[5,8,3,2,1,6,4,7] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[5,4,7,3,6,2,1,8] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[4,3,7,8,5,1,2,6] => [[[.,.],[[.,[.,.]],.]],[.,[.,.]]] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[5,3,7,8,4,1,2,6] => [[[.,.],[[.,[.,.]],.]],[.,[.,.]]] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[6,4,5,3,8,2,7,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[7,4,6,3,8,2,5,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[7,5,6,3,8,2,4,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[8,5,6,3,7,2,4,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[7,4,6,3,5,2,8,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[8,4,6,3,5,2,7,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[8,4,7,3,5,2,6,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[8,5,7,3,4,2,6,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[6,5,8,3,4,2,7,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[7,5,8,3,4,2,6,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[7,5,8,4,6,2,3,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[7,4,8,3,6,2,5,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[7,4,8,3,5,2,6,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[6,4,8,3,5,2,7,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[6,4,7,3,5,2,8,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[5,4,8,3,7,2,6,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[6,5,8,3,7,2,4,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[6,5,8,4,7,2,3,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[6,4,7,3,8,2,5,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[5,4,7,3,8,2,6,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[5,4,6,3,8,2,7,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[5,3,6,2,4,7,8,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1

[5,3,6,1,4,8,7,2] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[5,3,7,2,4,6,8,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1

[6,7,3,1,4,8,2,5] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[5,3,7,1,4,8,2,6] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[5,2,7,1,8,4,3,6] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[6,7,2,1,8,4,3,5] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[6,7,2,1,8,4,5,3] => [[[.,[.,.]],.],[[[.,.],[.,.]],.]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[5,2,6,1,8,4,3,7] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[5,2,6,1,8,7,4,3] => [[[.,.],[.,.]],[[[[.,.],.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[5,2,6,1,8,7,3,4] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[5,2,6,1,8,3,4,7] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[6,7,3,1,5,8,2,4] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[5,2,7,1,8,3,6,4] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[6,7,2,1,8,3,5,4] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[5,2,7,1,8,3,4,6] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[6,3,8,2,4,5,1,7] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[6,3,7,8,2,4,1,5] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,6,7,3,8,2,4,1] => [[[[.,[.,[.,.]]],[.,.]],[.,.]],.] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[5,4,7,2,6,8,1,3] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[5,3,8,2,4,6,7,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1

[6,4,8,2,7,5,1,3] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[5,6,3,7,8,2,4,1] => [[[[.,[.,.]],[.,[.,.]]],[.,.]],.] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[6,3,7,2,5,8,4,1] => [[[[.,.],[.,.]],[[.,[.,.]],.]],.] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[5,3,6,8,2,4,7,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1

[5,3,6,7,8,2,4,1] => [[[[.,.],[.,[.,[.,.]]]],[.,.]],.] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 1

[5,6,3,4,2,1,8,7] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[6,3,4,2,1,5,8,7] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[5,6,4,2,1,3,8,7] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 3

[2,7,8,5,4,1,6,3] => [[.,[[[.,[.,.]],.],.]],[[.,.],.]] => [1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 2

[2,7,8,6,3,5,4,1] => [[.,[[[.,[.,.]],.],[[.,.],.]]],.] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 1

[2,5,6,3,8,4,1,7] => [[.,[[.,[.,.]],[[.,.],.]]],[.,.]] => [1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2

[6,3,4,2,1,8,5,7] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[3,7,8,5,6,4,2,1] => [[[.,[[[.,[.,.]],[.,.]],.]],.],.] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[3,7,8,6,4,2,1,5] => [[[.,[[[.,[.,.]],.],.]],.],[.,.]] => [1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 2

[2,1,7,8,6,4,3,5] => [[.,.],[[[[.,[.,.]],.],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => 3

[6,3,7,8,4,2,1,5] => [[[[.,.],[[.,[.,.]],.]],.],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => 2

[7,8,4,2,1,6,3,5] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[2,6,1,8,4,3,7,5] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[2,6,1,7,5,8,4,3] => [[.,[.,.]],[[[[.,.],[.,.]],.],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 2

[7,5,6,1,8,4,2,3] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[6,4,7,8,3,2,1,5] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2

[6,3,7,2,5,4,1,8] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[1,6,7,3,4,2,8,5] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 3

[7,8,5,2,1,4,6,3] => [[[[.,[.,.]],.],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 2

[6,8,5,2,3,1,7,4] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[4,8,2,6,3,1,7,5] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[4,8,2,7,1,5,6,3] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[7,8,6,1,3,4,5,2] => [[[.,[.,.]],.],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 2

[1,7,8,2,4,5,6,3] => [.,[[.,[.,.]],[[.,[.,[.,.]]],.]]] => [1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 3

[8,6,7,1,3,4,5,2] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[7,6,8,1,3,4,5,2] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[6,5,8,2,3,1,7,4] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[1,6,8,3,2,5,7,4] => [.,[[[.,[.,.]],.],[[.,[.,.]],.]]] => [1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3

[4,5,2,3,1,6,8,7] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[5,6,1,3,4,2,8,7] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[4,6,2,1,5,3,8,7] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[4,7,2,1,3,6,8,5] => [[[.,[.,.]],.],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 3

[5,7,1,3,2,6,8,4] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[6,7,1,2,4,5,8,3] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 3

[7,8,1,2,4,5,6,3] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 3

[5,8,1,3,2,6,7,4] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[4,8,2,1,3,6,7,5] => [[[.,[.,.]],.],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 3

[5,4,8,1,2,3,7,6] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[4,8,3,2,7,6,1,5] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[4,3,8,2,7,1,6,5] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[4,7,8,1,2,5,3,6] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[3,4,2,7,1,6,8,5] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[2,6,3,4,7,8,1,5] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[3,1,7,8,4,2,5,6] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[3,7,8,2,6,4,1,5] => [[[.,[.,[.,.]]],[[.,.],.]],[.,.]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[3,7,2,4,8,6,1,5] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[4,7,1,5,8,2,3,6] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[2,6,7,3,8,4,1,5] => [[.,[[.,[.,.]],[[.,.],.]]],[.,.]] => [1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2

[3,4,6,7,8,5,1,2] => [[.,[.,[[.,[.,[.,.]]],.]]],[.,.]] => [1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 2

[7,8,3,1,4,2,5,6] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[4,8,1,5,2,3,6,7] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[5,6,1,8,4,3,2,7] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[6,1,2,5,8,3,7,4] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 4

[1,3,6,7,8,5,2,4] => [.,[[.,[[.,[.,[.,.]]],.]],[.,.]]] => [1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3

[7,8,4,1,6,3,2,5] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[4,1,6,8,3,7,2,5] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[5,4,6,1,3,8,2,7] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[6,5,8,1,4,3,2,7] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[1,3,5,7,4,6,8,2] => [.,[[.,[[.,[.,.]],[.,[.,.]]]],.]] => [1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 2

[1,3,5,7,4,8,2,6] => [.,[[.,[[.,[.,.]],[.,.]]],[.,.]]] => [1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 3

[1,3,5,7,4,8,6,2] => [.,[[.,[[.,[.,.]],[[.,.],.]]],.]] => [1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 2

[1,3,5,7,8,4,2,6] => [.,[[.,[[.,[.,[.,.]]],.]],[.,.]]] => [1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3

[3,5,1,6,2,8,7,4] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[1,3,7,2,5,4,8,6] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 4

[2,5,7,4,3,8,1,6] => [[.,[[[.,[.,.]],.],[.,.]]],[.,.]] => [1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 2

[3,2,6,7,8,1,5,4] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[3,5,2,7,8,4,1,6] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[1,5,7,4,8,3,2,6] => [.,[[[[.,[.,.]],[.,.]],.],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 3

[4,6,2,1,7,8,3,5] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[3,5,2,6,8,4,7,1] => [[[.,[.,.]],[[.,[.,.]],[.,.]]],.] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 1

[1,5,7,2,4,8,6,3] => [.,[[.,[.,.]],[[.,[[.,.],.]],.]]] => [1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 3

[4,6,3,7,2,8,5,1] => [[[[.,[.,.]],[.,.]],[[.,.],.]],.] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 1

[1,4,7,3,8,6,2,5] => [.,[[[.,[.,.]],[[.,.],.]],[.,.]]] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 3

[5,1,6,8,2,4,3,7] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[5,3,7,8,2,4,1,6] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[8,2,4,7,3,1,5,6] => [[[.,.],[[.,[.,.]],.]],[.,[.,.]]] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[2,4,7,8,3,1,5,6] => [[.,[[.,[.,[.,.]]],.]],[.,[.,.]]] => [1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[3,2,4,8,1,5,6,7] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[3,2,4,6,8,1,5,7] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[8,1,5,7,3,2,4,6] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[8,4,6,7,2,3,1,5] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[4,6,7,8,2,3,1,5] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[7,4,6,8,2,3,1,5] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[7,2,4,8,3,1,5,6] => [[[.,.],[[.,[.,.]],.]],[.,[.,.]]] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[2,3,7,8,4,1,6,5] => [[.,[.,[[.,[.,.]],.]]],[[.,.],.]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 2

[4,7,8,6,2,3,1,5] => [[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => [1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[2,4,7,3,1,5,8,6] => [[.,[[.,[.,.]],.]],[.,[[.,.],.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 3

[4,3,6,1,5,8,7,2] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[4,6,3,5,1,8,7,2] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[4,6,3,1,5,8,7,2] => [[[.,[.,.]],.],[[.,[[.,.],.]],.]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 2

[4,6,1,5,3,8,7,2] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2

[4,6,1,5,8,3,7,2] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2

[6,4,8,3,7,1,5,2] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[2,6,8,5,3,7,1,4] => [[.,[[[.,[.,.]],.],[.,.]]],[.,.]] => [1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 2

[4,6,8,1,5,7,3,2] => [[.,[.,[.,.]]],[[[.,[.,.]],.],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[4,6,1,8,5,7,3,2] => [[.,[.,.]],[[[[.,.],[.,.]],.],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 2

[4,1,6,8,5,7,3,2] => [[.,.],[[[[.,[.,.]],[.,.]],.],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[1,4,6,8,5,7,3,2] => [.,[[[.,[[.,[.,.]],[.,.]]],.],.]] => [1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 2

[1,4,6,8,5,3,7,2] => [.,[[[.,[[.,[.,.]],.]],[.,.]],.]] => [1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 2

[4,6,1,8,5,3,7,2] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2

[2,6,8,5,3,1,7,4] => [[.,[[[.,[.,.]],.],.]],[[.,.],.]] => [1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 2

[2,6,8,5,1,7,3,4] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[4,6,8,3,5,1,7,2] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[4,6,8,3,1,5,7,2] => [[[.,[.,[.,.]]],.],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[4,6,3,1,8,5,7,2] => [[[.,[.,.]],.],[[[.,.],[.,.]],.]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[4,6,3,8,1,5,7,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[4,6,3,8,5,7,1,2] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[4,3,6,8,1,5,7,2] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[4,3,6,1,8,5,7,2] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[4,3,6,1,8,7,5,2] => [[[.,.],[.,.]],[[[[.,.],.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[4,3,6,8,1,7,5,2] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[4,6,3,8,1,7,5,2] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[4,6,3,1,8,7,5,2] => [[[.,[.,.]],.],[[[[.,.],.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2

[1,4,6,3,8,7,5,2] => [.,[[[.,[.,.]],[[[.,.],.],.]],.]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 2

[4,1,6,8,3,7,5,2] => [[.,.],[[[.,[.,.]],[[.,.],.]],.]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2

[4,6,1,8,3,7,5,2] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2

[4,6,8,1,3,7,5,2] => [[.,[.,[.,.]]],[[.,[[.,.],.]],.]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[2,3,4,7,8,5,6,1] => [[.,[.,[.,[[.,[.,.]],[.,.]]]]],.] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1

[2,3,7,1,4,8,6,5] => [[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[2,6,1,3,7,8,5,4] => [[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 3

[4,6,2,3,7,5,1,8] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[4,7,2,3,6,5,1,8] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[4,7,2,3,5,6,1,8] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[4,6,2,3,5,7,1,8] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[3,5,2,1,6,8,4,7] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[1,5,7,2,8,4,3,6] => [.,[[.,[.,.]],[[[.,.],.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 4

[3,5,2,1,8,6,4,7] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[3,6,8,4,2,1,5,7] => [[[.,[[.,[.,.]],.]],.],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 3

[1,5,8,2,7,4,3,6] => [.,[[.,[.,.]],[[[.,.],.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 4

[6,8,2,3,4,1,7,5] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[2,3,1,8,4,5,7,6] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[7,8,1,4,3,5,2,6] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[7,1,2,3,4,6,8,5] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 5

[8,1,2,3,4,6,7,5] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 5

[2,8,1,3,5,4,7,6] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4

[3,8,2,1,5,6,4,7] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[3,8,2,1,6,5,4,7] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[1,7,8,3,5,4,2,6] => [.,[[[.,[.,.]],[[.,.],.]],[.,.]]] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 3

[3,5,2,4,1,8,6,7] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,4,7,8,1,5,3,6] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,7,8,4,3,5,1,6] => [[.,[[[.,[.,.]],.],[.,.]]],[.,.]] => [1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 2

[7,8,2,3,4,6,1,5] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[6,7,1,3,4,8,2,5] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[6,8,1,3,4,7,2,5] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[6,7,2,3,4,1,8,5] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[5,8,4,2,1,6,7,3] => [[[[.,[.,.]],.],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 2

[5,8,4,1,2,6,7,3] => [[[.,[.,.]],.],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 3

[5,3,7,2,6,1,8,4] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[5,2,8,1,6,3,7,4] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[5,8,2,1,4,7,6,3] => [[[.,[.,.]],.],[[.,[[.,.],.]],.]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 2

[4,8,2,5,1,7,6,3] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[7,8,4,1,2,6,5,3] => [[[.,[.,.]],.],[.,[[[.,.],.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 3

[4,8,1,5,2,7,6,3] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[5,8,1,2,4,7,6,3] => [[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 3

[7,8,2,6,5,1,3,4] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[2,8,1,4,5,6,7,3] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2

[3,2,7,1,6,5,8,4] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[2,3,7,1,6,8,5,4] => [[.,[.,[.,.]]],[[[.,[.,.]],.],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[1,3,7,2,6,8,5,4] => [.,[[.,[.,.]],[[[.,[.,.]],.],.]]] => [1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 3

[7,8,2,6,5,3,1,4] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[3,2,6,7,5,8,1,4] => [[[.,.],[[.,[.,.]],[.,.]]],[.,.]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[7,8,3,6,5,1,2,4] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[5,1,4,6,8,2,3,7] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[4,3,7,2,6,5,1,8] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[3,4,6,1,5,7,2,8] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[1,6,8,5,7,3,4,2] => [.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 2

[2,4,1,5,8,6,3,7] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3

[4,6,1,2,5,8,3,7] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4

[5,6,7,2,1,4,8,3] => [[[.,[.,[.,.]]],.],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[7,8,6,5,1,2,4,3] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 3

[6,8,5,2,4,1,7,3] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[2,3,1,6,8,5,7,4] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2

[1,5,8,3,4,6,7,2] => [.,[[[.,[.,.]],[.,[.,[.,.]]]],.]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2

[2,3,8,1,6,5,4,7] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[8,1,4,7,2,5,3,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[3,5,2,4,1,7,8,6] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[3,4,7,8,6,2,1,5] => [[[.,[.,[[.,[.,.]],.]]],.],[.,.]] => [1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 2

[5,8,2,1,6,7,3,4] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[5,7,2,8,6,4,3,1] => [[[.,[.,.]],[[[[.,.],.],.],.]],.] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1

[2,7,8,4,6,3,1,5] => [[.,[[[.,[.,.]],[.,.]],.]],[.,.]] => [1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2

[1,4,5,7,2,6,8,3] => [.,[[.,[.,[.,.]]],[[.,[.,.]],.]]] => [1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3

[7,3,5,2,6,1,8,4] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[2,6,8,1,7,5,4,3] => [[.,[.,[.,.]]],[[[[.,.],.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[3,6,8,4,7,2,1,5] => [[[.,[[.,[.,.]],[.,.]]],.],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 2

[2,5,8,3,7,6,1,4] => [[.,[[.,[.,.]],[[.,.],.]]],[.,.]] => [1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2

[1,5,8,3,7,2,6,4] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 3

[3,5,8,4,7,2,1,6] => [[[.,[[.,[.,.]],[.,.]]],.],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 2

[5,6,8,2,3,7,1,4] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[1,6,8,4,2,7,5,3] => [.,[[[.,[.,.]],.],[[[.,.],.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 3

[1,5,8,4,2,7,6,3] => [.,[[[.,[.,.]],.],[[[.,.],.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 3

[1,5,8,2,3,7,6,4] => [.,[[.,[.,.]],[.,[[[.,.],.],.]]]] => [1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 4

[2,5,8,4,3,7,1,6] => [[.,[[[.,[.,.]],.],[.,.]]],[.,.]] => [1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 2

[5,6,8,4,1,2,7,3] => [[[.,[.,[.,.]]],.],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[5,6,8,1,3,2,7,4] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[1,6,8,4,3,2,7,5] => [.,[[[[.,[.,.]],.],.],[[.,.],.]]] => [1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 3

[5,6,8,4,3,2,1,7] => [[[[[.,[.,[.,.]]],.],.],.],[.,.]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2

[7,2,4,8,3,6,1,5] => [[[.,.],[[.,[.,.]],[.,.]]],[.,.]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[7,1,4,8,3,2,6,5] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3

[7,4,5,8,3,2,1,6] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2

[1,4,5,8,2,7,6,3] => [.,[[.,[.,[.,.]]],[[[.,.],.],.]]] => [1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3

[2,4,5,8,3,7,1,6] => [[.,[[.,[.,[.,.]]],[.,.]]],[.,.]] => [1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[1,4,5,8,3,2,7,6] => [.,[[[.,[.,[.,.]]],.],[[.,.],.]]] => [1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3

[7,2,5,1,8,6,4,3] => [[[.,.],[.,.]],[[[[.,.],.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[2,7,8,3,5,4,1,6] => [[.,[[.,[.,.]],[[.,.],.]]],[.,.]] => [1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2

[4,7,1,2,8,5,3,6] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 4

[4,8,1,2,7,5,3,6] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 4

[2,7,1,3,6,8,4,5] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4

[6,7,3,2,8,1,4,5] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[7,3,4,2,6,1,8,5] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[2,7,1,3,6,5,4,8] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 4

[6,4,8,2,1,5,3,7] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[6,8,3,2,5,1,4,7] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[7,8,6,1,5,4,3,2] => [[[.,[.,.]],.],[[[[.,.],.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2

[8,5,6,1,3,2,4,7] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[7,8,1,5,3,2,4,6] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[8,4,6,1,5,2,3,7] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[7,8,2,1,5,4,3,6] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[7,8,3,1,5,2,4,6] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[8,2,7,1,5,4,3,6] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[8,2,6,1,7,4,3,5] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[8,1,5,7,3,2,6,4] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3

[5,7,8,1,3,2,6,4] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[8,2,6,1,5,7,3,4] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[5,8,1,6,7,2,3,4] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[6,7,2,5,1,8,3,4] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,5,7,1,8,2,3,4] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[6,7,3,8,1,2,4,5] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[7,5,8,1,3,2,4,6] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[7,8,4,1,3,2,5,6] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[6,8,1,7,3,2,4,5] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[8,4,5,1,7,2,3,6] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[5,6,8,1,7,2,3,4] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[6,5,8,1,2,7,3,4] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[6,2,7,8,3,1,5,4] => [[[.,.],[[.,[.,.]],.]],[[.,.],.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[5,8,1,7,3,2,6,4] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[8,3,4,7,1,2,6,5] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[7,4,8,2,1,3,6,5] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[8,2,3,6,7,1,5,4] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[7,8,5,2,3,6,4,1] => [[[[.,[.,.]],.],[.,[[.,.],.]]],.] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 1

[6,8,5,2,3,4,7,1] => [[[[.,[.,.]],.],[.,[.,[.,.]]]],.] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1

[3,5,2,6,8,1,4,7] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[3,5,2,4,6,8,1,7] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[2,4,5,7,3,6,8,1] => [[.,[[.,[.,[.,.]]],[.,[.,.]]]],.] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1

[2,4,5,3,6,8,1,7] => [[.,[[.,[.,.]],[.,[.,.]]]],[.,.]] => [1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2

[5,2,4,6,8,1,3,7] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[5,1,3,4,6,8,2,7] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 3

[4,3,5,2,6,8,1,7] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[4,3,5,7,2,8,1,6] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[4,3,5,7,2,6,8,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1

[4,6,3,7,2,5,8,1] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1

[4,6,3,1,7,8,2,5] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[4,3,5,1,7,8,2,6] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[5,7,1,3,4,8,2,6] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[5,7,1,3,4,6,8,2] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2

[4,5,7,1,3,6,8,2] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[4,3,6,7,1,5,8,2] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[4,6,3,5,1,7,8,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[4,6,3,5,7,2,8,1] => [[[[.,[.,.]],[.,[.,.]]],[.,.]],.] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[3,5,6,4,1,7,8,2] => [[.,[[.,[.,.]],.]],[[.,[.,.]],.]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 2

[3,1,5,6,7,4,8,2] => [[.,.],[[[.,[.,[.,.]]],[.,.]],.]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2

[5,1,6,7,3,4,8,2] => [[.,.],[[[.,[.,.]],[.,[.,.]]],.]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[6,4,7,1,3,5,8,2] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[1,6,7,3,4,5,8,2] => [.,[[[.,[.,.]],[.,[.,[.,.]]]],.]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2

[2,6,7,4,5,8,1,3] => [[.,[[.,[.,.]],[.,[.,.]]]],[.,.]] => [1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2

[2,6,7,4,8,1,3,5] => [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[5,3,6,1,2,7,8,4] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[3,5,2,6,1,7,8,4] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[3,5,2,6,7,4,8,1] => [[[.,[.,.]],[[.,[.,.]],[.,.]]],.] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 1

[5,2,3,6,7,4,8,1] => [[[.,.],[.,[[.,[.,.]],[.,.]]]],.] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1

[5,2,3,6,1,7,8,4] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[5,2,6,1,3,7,8,4] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[4,2,6,7,3,5,8,1] => [[[.,.],[[.,[.,.]],[.,[.,.]]]],.] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1

[6,3,7,2,4,5,8,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1

[3,5,7,2,8,1,4,6] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[3,7,2,4,8,1,5,6] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[7,2,4,6,8,1,3,5] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[7,1,3,4,6,8,2,5] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 3

[3,7,2,4,6,8,1,5] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[3,5,7,2,6,8,1,4] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[6,3,7,2,5,8,1,4] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[6,3,5,7,2,8,1,4] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,3,5,7,2,4,8,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1

[6,2,4,5,7,3,8,1] => [[[.,.],[[.,[.,[.,.]]],[.,.]]],.] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1

[6,2,4,5,1,7,8,3] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[4,7,1,2,5,6,8,3] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 3

[2,6,7,5,8,1,3,4] => [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[4,6,7,1,2,5,8,3] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[5,6,2,4,7,3,8,1] => [[[.,[.,.]],[[.,[.,.]],[.,.]]],.] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 1

[5,6,4,1,2,7,8,3] => [[[.,[.,.]],.],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 3

[6,4,5,1,2,7,8,3] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[6,3,5,1,7,8,2,4] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[6,5,7,2,8,1,3,4] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[6,5,7,1,3,4,8,2] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[5,6,4,7,1,3,8,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[5,4,6,3,1,7,8,2] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[8,4,5,2,6,1,3,7] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[8,4,5,3,1,6,2,7] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[7,4,5,3,1,6,8,2] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[5,6,3,7,4,1,8,2] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[5,6,7,3,1,4,8,2] => [[[.,[.,[.,.]]],.],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[6,7,3,4,1,5,8,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[6,7,4,2,1,5,8,3] => [[[[.,[.,.]],.],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 2

[5,6,7,3,1,8,2,4] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[5,6,3,7,8,1,2,4] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[5,6,3,7,2,4,8,1] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1

[5,6,7,2,3,8,1,4] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[7,4,5,2,8,1,3,6] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[6,7,3,2,4,8,1,5] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[6,7,3,2,5,1,8,4] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[6,4,5,2,7,3,8,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[6,4,5,2,7,8,1,3] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[7,4,5,2,6,1,8,3] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[7,4,5,6,1,2,8,3] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[7,5,6,2,1,3,8,4] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[6,7,3,5,1,2,8,4] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[5,6,7,4,1,2,8,3] => [[[.,[.,[.,.]]],.],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[5,6,7,2,4,1,8,3] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[5,6,4,2,7,8,1,3] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[6,5,7,2,1,8,3,4] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[6,5,7,2,1,4,8,3] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[5,4,6,7,3,1,8,2] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[3,7,8,5,6,1,4,2] => [[.,[[.,[.,.]],[.,.]]],[[.,.],.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2

[1,7,8,5,6,3,4,2] => [.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 2

[5,7,3,8,6,4,1,2] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[1,5,7,8,6,3,4,2] => [.,[[[.,[[.,[.,.]],.]],[.,.]],.]] => [1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 2

[1,5,7,8,3,6,4,2] => [.,[[[.,[.,[.,.]]],[[.,.],.]],.]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2

[5,3,7,8,1,6,4,2] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[7,8,1,5,6,3,4,2] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2

[5,1,7,8,3,6,4,2] => [[.,.],[[[.,[.,.]],[[.,.],.]],.]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2

[3,1,7,8,5,6,4,2] => [[.,.],[[[[.,[.,.]],[.,.]],.],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[1,3,7,8,5,6,4,2] => [.,[[.,[[[.,[.,.]],[.,.]],.]],.]] => [1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 2

[7,1,5,8,3,6,4,2] => [[.,.],[[[.,[.,.]],[[.,.],.]],.]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2

[5,3,7,1,8,6,4,2] => [[[.,.],[.,.]],[[[[.,.],.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[3,5,7,1,8,6,4,2] => [[.,[.,[.,.]]],[[[[.,.],.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[5,7,3,1,8,6,4,2] => [[[.,[.,.]],.],[[[[.,.],.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2

[5,7,3,8,6,1,4,2] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[1,7,8,5,3,6,4,2] => [.,[[[[.,[.,.]],.],[[.,.],.]],.]] => [1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 2

[5,7,8,6,3,1,4,2] => [[[.,[[.,[.,.]],.]],.],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 2

[5,7,8,1,6,3,4,2] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[3,7,8,1,5,6,4,2] => [[.,[.,[.,.]]],[[[.,[.,.]],.],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[1,7,8,3,5,6,4,2] => [.,[[[.,[.,.]],[[.,[.,.]],.]],.]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 2

[3,7,1,8,5,6,4,2] => [[.,[.,.]],[[[[.,.],[.,.]],.],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 2

[5,7,1,8,3,6,4,2] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2

[5,7,1,8,6,3,4,2] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2

[7,5,8,1,6,3,4,2] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[7,8,5,1,6,3,4,2] => [[[.,[.,.]],.],[[[.,.],[.,.]],.]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[7,5,8,1,3,6,4,2] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[5,7,1,3,8,6,4,2] => [[.,[.,.]],[[.,[[[.,.],.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 2

[3,7,1,5,8,6,4,2] => [[.,[.,.]],[[[.,[[.,.],.]],.],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 2

[3,5,1,7,8,6,4,2] => [[.,[.,.]],[[[[.,[.,.]],.],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 2

[7,8,3,1,5,6,4,2] => [[[.,[.,.]],.],[[[.,[.,.]],.],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 2

[3,1,5,7,8,6,4,2] => [[.,.],[[[.,[[.,[.,.]],.]],.],.]] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2

[5,7,3,4,8,6,1,2] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[5,7,3,4,8,1,6,2] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[5,7,3,4,1,8,6,2] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[5,7,3,1,4,6,2,8] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[5,7,3,1,4,8,6,2] => [[[.,[.,.]],.],[[.,[[.,.],.]],.]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 2

[5,3,7,1,4,2,6,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[5,3,7,1,4,2,8,6] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[7,3,5,8,1,2,6,4] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[2,5,7,3,8,4,1,6] => [[.,[[.,[.,.]],[[.,.],.]]],[.,.]] => [1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2

[5,4,7,8,6,1,3,2] => [[[.,.],[[.,[.,.]],.]],[[.,.],.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[7,5,6,2,8,3,1,4] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[4,7,2,5,8,3,1,6] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[6,2,4,5,1,3,8,7] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[5,1,4,6,3,2,8,7] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3

[3,5,6,2,4,1,8,7] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[6,2,7,8,3,4,1,5] => [[[.,.],[[.,[.,.]],[.,.]]],[.,.]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[2,5,3,4,8,1,7,6] => [[.,[[.,.],[.,[.,.]]]],[[.,.],.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[3,7,8,1,5,4,6,2] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[7,1,3,4,6,8,5,2] => [[.,.],[[.,[.,[[.,[.,.]],.]]],.]] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[4,7,2,6,3,8,5,1] => [[[.,[.,.]],[[.,.],[[.,.],.]]],.] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 1

[4,7,8,6,3,1,2,5] => [[[.,[[.,[.,.]],.]],.],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 3

[3,8,1,5,6,7,2,4] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[6,7,2,4,8,5,3,1] => [[[.,[.,.]],[[.,[[.,.],.]],.]],.] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 1

[3,2,4,5,8,1,7,6] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[7,4,6,3,2,1,8,5] => [[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[4,7,3,2,1,8,6,5] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2

[6,4,8,1,7,3,2,5] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[4,2,3,1,8,7,5,6] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[7,6,8,1,3,5,2,4] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[6,7,5,2,3,1,8,4] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[4,7,2,6,5,1,8,3] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[6,7,8,2,5,3,1,4] => [[[.,[.,[.,.]]],[[.,.],.]],[.,.]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[2,1,5,7,8,4,6,3] => [[.,.],[[[.,[.,[.,.]]],[.,.]],.]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2

[2,5,7,8,3,6,1,4] => [[.,[[.,[.,[.,.]]],[.,.]]],[.,.]] => [1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[7,4,8,1,2,5,6,3] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[4,2,7,8,6,3,5,1] => [[[.,.],[[[.,[.,.]],.],[.,.]]],.] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1

[6,8,3,4,2,1,7,5] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[4,2,6,1,5,7,8,3] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[2,4,6,7,3,5,8,1] => [[.,[[.,[.,[.,.]]],[.,[.,.]]]],.] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1

[6,5,8,3,7,4,1,2] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[7,1,4,8,3,5,6,2] => [[.,.],[[[.,[.,.]],[.,[.,.]]],.]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[3,4,8,2,5,7,6,1] => [[[.,[.,[.,.]]],[.,[[.,.],.]]],.] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[2,5,7,4,8,6,1,3] => [[.,[[.,[.,.]],[[.,.],.]]],[.,.]] => [1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2

[6,3,7,2,8,5,1,4] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[3,6,2,5,8,7,1,4] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[3,1,5,6,2,8,7,4] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3

[1,2,4,6,3,8,7,5] => [.,[.,[[.,[.,.]],[[[.,.],.],.]]]] => [1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 4

[3,4,5,1,8,7,6,2] => [[.,[.,[.,.]]],[[[[.,.],.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[1,4,5,2,8,7,6,3] => [.,[[.,[.,.]],[[[[.,.],.],.],.]]] => [1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 3

[4,6,2,7,5,1,8,3] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[1,5,8,3,2,7,6,4] => [.,[[[.,[.,.]],.],[[[.,.],.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 3

[4,5,8,2,1,7,6,3] => [[[.,[.,[.,.]]],.],[[[.,.],.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[3,6,2,5,1,4,8,7] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[1,3,8,2,4,7,6,5] => [.,[[.,[.,.]],[.,[[[.,.],.],.]]]] => [1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 4

[3,5,2,1,7,4,8,6] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[4,5,1,2,8,7,6,3] => [[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 3

[5,2,8,1,3,7,6,4] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[4,7,5,6,8,3,1,2] => [[[.,[[.,.],[.,[.,.]]]],.],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2

[6,8,4,7,5,3,1,2] => [[[[.,[.,.]],[[.,.],.]],.],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2

[6,8,5,3,2,1,4,7] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 3

[5,7,2,6,4,1,3,8] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[8,2,3,1,4,6,5,7] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[2,4,8,3,1,5,6,7] => [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4

[3,4,2,7,1,5,6,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[4,7,3,8,2,1,5,6] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3

[8,3,7,2,1,5,4,6] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[1,3,7,2,8,4,6,5] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 4

[2,6,4,5,7,1,3,8] => [[.,[[.,.],[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[5,4,6,2,7,1,3,8] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[6,8,4,1,3,7,5,2] => [[[.,[.,.]],.],[[.,[[.,.],.]],.]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 2

[6,5,7,1,3,8,4,2] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[5,8,3,1,7,4,6,2] => [[[.,[.,.]],.],[[[.,.],[.,.]],.]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[2,3,1,8,7,4,5,6] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[2,4,1,8,5,7,3,6] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[5,8,2,1,7,6,3,4] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[6,2,7,1,8,5,3,4] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[2,1,7,8,4,6,3,5] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[5,8,2,7,1,6,4,3] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[4,6,3,8,5,2,1,7] => [[[[.,[.,.]],[[.,.],.]],.],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2

[4,6,3,7,5,2,8,1] => [[[[.,[.,.]],[[.,.],.]],[.,.]],.] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 1

[3,5,7,8,2,6,1,4] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,6,2,4,1,3,8,7] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[8,2,3,4,6,1,5,7] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[7,2,3,4,6,1,8,5] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[7,2,3,4,6,8,5,1] => [[[.,.],[.,[.,[[.,[.,.]],.]]]],.] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 1

[7,8,3,6,5,1,4,2] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[4,2,3,6,1,5,8,7] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[4,8,3,7,5,1,6,2] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[5,2,3,4,7,8,6,1] => [[[.,.],[.,[.,[[.,[.,.]],.]]]],.] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 1

[8,2,3,4,7,1,6,5] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[5,2,3,4,6,8,1,7] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2

[4,7,3,6,5,8,2,1] => [[[[.,[.,.]],[[.,.],[.,.]]],.],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 1

[4,8,3,7,5,2,1,6] => [[[[.,[.,.]],[[.,.],.]],.],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2

[5,8,1,7,3,6,4,2] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2

[5,2,7,8,4,6,3,1] => [[[.,.],[[[.,[.,.]],[.,.]],.]],.] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1

[6,8,3,2,5,7,1,4] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[6,7,3,8,5,4,2,1] => [[[[.,[.,.]],[[[.,.],.],.]],.],.] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 1

[8,2,3,4,1,7,5,6] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,2,3,4,1,8,5,7] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,8,3,1,5,7,4,2] => [[[.,[.,.]],.],[[[.,[.,.]],.],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 2

[7,2,3,4,1,8,6,5] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[7,2,3,4,1,5,8,6] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[8,6,7,4,1,5,3,2] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[8,5,7,1,4,6,3,2] => [[[.,.],[.,.]],[[[.,[.,.]],.],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[8,4,7,1,5,6,3,2] => [[[.,.],[.,.]],[[[.,[.,.]],.],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[5,7,1,8,2,6,3,4] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[5,7,1,8,2,3,6,4] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[4,8,3,6,1,7,5,2] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[4,7,1,8,2,6,5,3] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[8,2,7,1,6,3,4,5] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[8,2,7,1,3,6,4,5] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[2,8,3,6,7,1,5,4] => [[.,[[.,.],[.,[.,.]]]],[[.,.],.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[8,2,3,6,7,5,1,4] => [[[.,.],[.,[[.,[.,.]],.]]],[.,.]] => [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => 2

[8,3,7,2,5,6,1,4] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[8,1,3,7,2,5,6,4] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3

[1,7,8,2,3,6,5,4] => [.,[[.,[.,.]],[.,[[[.,.],.],.]]]] => [1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 4

[8,3,7,1,2,5,6,4] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[8,3,5,7,4,2,6,1] => [[[[.,.],[[.,[.,.]],.]],[.,.]],.] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[8,3,6,2,4,5,7,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1

[2,6,8,3,5,4,7,1] => [[.,[[.,[.,.]],[[.,.],[.,.]]]],.] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 1

[4,8,1,7,6,3,2,5] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[3,7,1,8,6,2,5,4] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[7,3,5,8,4,2,6,1] => [[[[.,.],[[.,[.,.]],.]],[.,.]],.] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[7,8,3,6,2,5,4,1] => [[[[.,[.,.]],[.,.]],[[.,.],.]],.] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 1

[7,4,8,2,1,6,3,5] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[7,8,5,2,1,4,3,6] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[7,4,6,2,3,8,1,5] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[4,7,1,5,3,8,2,6] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[4,7,8,1,3,6,2,5] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[5,7,1,3,4,6,2,8] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[5,7,1,4,2,3,6,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[5,8,1,3,2,4,6,7] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[8,4,6,2,1,3,7,5] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[6,8,3,7,2,5,4,1] => [[[[.,[.,.]],[.,.]],[[.,.],.]],.] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 1

[5,4,6,8,2,3,7,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1

[5,7,4,2,8,3,6,1] => [[[[.,[.,.]],.],[[.,.],[.,.]]],.] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 1

[6,4,7,2,1,8,3,5] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[6,8,5,4,1,3,2,7] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[6,3,7,8,2,5,1,4] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[7,3,5,6,4,2,1,8] => [[[[.,.],[[.,[.,.]],.]],.],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => 2

[5,3,7,8,2,6,4,1] => [[[[.,.],[.,[.,.]]],[[.,.],.]],.] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => 1

[5,3,7,8,6,2,4,1] => [[[[.,.],[[.,[.,.]],.]],[.,.]],.] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[5,4,6,2,8,7,1,3] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[5,7,3,8,6,2,4,1] => [[[[.,[.,.]],[[.,.],.]],[.,.]],.] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 1

[5,4,6,8,2,7,1,3] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,7,8,2,6,4,1,3] => [[[.,[.,[.,.]]],[[.,.],.]],[.,.]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[3,6,2,5,7,8,1,4] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[5,3,6,7,1,8,4,2] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[4,2,5,6,7,1,8,3] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[8,1,3,6,7,2,4,5] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[6,3,4,1,8,5,7,2] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[1,5,8,4,2,6,3,7] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 4

[3,5,7,4,1,6,8,2] => [[.,[[.,[.,.]],.]],[[.,[.,.]],.]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 2

[3,5,7,1,2,6,4,8] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[4,5,1,8,2,3,7,6] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[4,7,1,8,2,6,3,5] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[5,2,6,1,3,4,8,7] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[6,7,1,3,2,5,4,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[7,8,2,4,3,5,1,6] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[7,8,2,4,1,5,3,6] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,7,2,4,3,5,1,8] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[2,4,1,6,5,7,3,8] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[2,5,1,6,4,7,3,8] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[4,5,2,6,1,7,3,8] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,5,1,6,3,7,2,8] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[4,5,3,6,1,7,2,8] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,6,3,4,1,7,2,8] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,7,5,8,1,3,2,4] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,5,1,3,2,7,6,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[4,6,1,3,2,7,5,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[3,4,1,6,5,7,2,8] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[4,5,2,3,1,7,6,8] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,5,1,6,4,7,2,8] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[3,5,2,6,1,7,4,8] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,5,2,6,4,7,1,8] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[3,4,2,6,1,7,5,8] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,6,2,7,5,4,8,1] => [[[.,[.,.]],[[[.,.],.],[.,.]]],.] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 1

[4,6,1,7,3,8,2,5] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[5,2,6,7,4,3,8,1] => [[[.,.],[[[.,[.,.]],.],[.,.]]],.] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1

[3,5,2,7,6,4,8,1] => [[[.,[.,.]],[[[.,.],.],[.,.]]],.] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 1

[1,5,7,2,8,3,6,4] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 4

[2,5,7,3,1,8,4,6] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[2,1,5,6,8,4,3,7] => [[.,.],[[[.,[.,[.,.]]],.],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => 3

[1,3,7,2,8,5,4,6] => [.,[[.,[.,.]],[[[.,.],.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 4

[4,6,2,7,1,8,3,5] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,1,5,6,8,4,7,3] => [[.,.],[[[.,[.,[.,.]]],[.,.]],.]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2

[1,5,7,8,4,2,6,3] => [.,[[[.,[.,[.,.]]],.],[[.,.],.]]] => [1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3

[4,2,5,7,3,1,8,6] => [[[.,.],[[.,[.,.]],.]],[[.,.],.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[4,5,6,1,8,7,3,2] => [[.,[.,[.,.]]],[[[[.,.],.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[4,6,3,2,1,7,5,8] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[4,6,1,7,5,3,2,8] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[3,6,2,1,7,4,5,8] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[3,6,2,7,4,1,5,8] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[3,5,7,2,8,6,4,1] => [[[.,[.,[.,.]]],[[[.,.],.],.]],.] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1

[2,4,7,1,3,6,5,8] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[2,6,1,3,7,5,4,8] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 4

[2,6,1,5,4,3,7,8] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[3,8,2,6,5,4,1,7] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[4,3,7,2,5,6,1,8] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[6,7,1,4,3,2,5,8] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[3,4,2,6,7,1,5,8] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[3,7,1,6,5,2,4,8] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[3,5,6,2,4,7,1,8] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[1,7,8,2,5,4,3,6] => [.,[[.,[.,.]],[[[.,.],.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 4

[2,5,6,4,7,1,3,8] => [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[4,7,1,6,3,5,2,8] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[4,5,3,8,7,2,6,1] => [[[[.,[.,.]],[[.,.],.]],[.,.]],.] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 1

[1,4,5,3,7,8,2,6] => [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 3

[1,4,8,2,7,6,3,5] => [.,[[.,[.,.]],[[[.,.],.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 4

[4,7,3,5,1,8,6,2] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[4,7,8,3,5,2,1,6] => [[[[.,[.,[.,.]]],[.,.]],.],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[1,4,6,7,3,5,8,2] => [.,[[[.,[.,[.,.]]],[.,[.,.]]],.]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[8,3,6,2,1,7,5,4] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[2,3,1,8,4,7,6,5] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[6,3,7,2,8,5,4,1] => [[[[.,.],[.,.]],[[[.,.],.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1

[3,7,2,4,8,6,5,1] => [[[.,[.,.]],[.,[[[.,.],.],.]]],.] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 1

[3,4,2,8,7,6,1,5] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[3,7,8,5,2,4,1,6] => [[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => [1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[1,6,8,2,5,7,4,3] => [.,[[.,[.,.]],[[[.,[.,.]],.],.]]] => [1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 3

[6,7,2,5,8,4,3,1] => [[[.,[.,.]],[[[.,[.,.]],.],.]],.] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 1

[5,2,7,8,4,3,1,6] => [[[.,.],[[[.,[.,.]],.],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => 2

[1,5,8,2,7,4,6,3] => [.,[[.,[.,.]],[[[.,.],[.,.]],.]]] => [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 3

[5,7,2,8,4,6,3,1] => [[[.,[.,.]],[[[.,.],[.,.]],.]],.] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 1

[5,7,3,1,8,4,6,2] => [[[.,[.,.]],.],[[[.,.],[.,.]],.]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[8,4,7,3,1,6,5,2] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[2,6,8,5,7,4,1,3] => [[.,[[[.,[.,.]],[.,.]],.]],[.,.]] => [1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2

[5,7,4,6,2,1,8,3] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[5,6,4,8,3,7,2,1] => [[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1

[6,7,1,8,3,4,2,5] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[5,6,2,7,1,8,3,4] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,3,1,8,5,6,4,7] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[4,6,2,7,1,5,3,8] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,7,1,6,2,5,3,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[4,7,1,5,3,6,2,8] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[4,7,2,3,1,8,5,6] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,5,7,8,2,6,3,1] => [[[.,[.,[.,[.,.]]]],[[.,.],.]],.] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 1

[5,2,6,8,3,7,4,1] => [[[.,.],[[.,[.,.]],[[.,.],.]]],.] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1

[4,6,7,8,2,5,3,1] => [[[.,[.,[.,[.,.]]]],[[.,.],.]],.] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 1

[7,4,5,2,8,6,3,1] => [[[[.,.],[.,.]],[[[.,.],.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1

[6,8,2,5,3,7,4,1] => [[[.,[.,.]],[[.,.],[[.,.],.]]],.] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 1

[6,7,4,2,8,5,3,1] => [[[[.,[.,.]],.],[[[.,.],.],.]],.] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 1

[5,6,2,8,3,7,4,1] => [[[.,[.,.]],[[.,.],[[.,.],.]]],.] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 1

[5,7,8,3,2,6,4,1] => [[[[.,[.,[.,.]]],.],[[.,.],.]],.] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1

[1,5,8,2,7,3,6,4] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 4

[6,7,4,8,1,5,3,2] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[6,8,5,3,7,2,4,1] => [[[[[.,[.,.]],.],[.,.]],[.,.]],.] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1

[6,8,5,2,3,7,4,1] => [[[[.,[.,.]],.],[.,[[.,.],.]]],.] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 1

[6,7,3,4,8,5,2,1] => [[[[.,[.,.]],[.,[[.,.],.]]],.],.] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 1

[7,4,5,8,1,6,3,2] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[6,3,4,7,8,5,2,1] => [[[[.,.],[.,[[.,[.,.]],.]]],.],.] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1

[2,5,8,3,4,1,6,7] => [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[5,6,2,7,4,3,8,1] => [[[.,[.,.]],[[[.,.],.],[.,.]]],.] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 1

[4,6,7,3,2,5,8,1] => [[[[.,[.,[.,.]]],.],[.,[.,.]]],.] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1

[2,6,7,3,8,5,4,1] => [[.,[[.,[.,.]],[[[.,.],.],.]]],.] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 1

[2,5,7,8,4,3,6,1] => [[.,[[[.,[.,[.,.]]],.],[.,.]]],.] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1

[3,6,8,4,5,7,1,2] => [[.,[[.,[.,.]],[.,[.,.]]]],[.,.]] => [1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2

[1,6,8,4,7,2,3,5] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 4

[1,4,5,7,8,2,6,3] => [.,[[.,[.,[.,[.,.]]]],[[.,.],.]]] => [1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[3,4,5,7,8,6,1,2] => [[.,[.,[.,[[.,[.,.]],.]]]],[.,.]] => [1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 2

[3,6,7,4,8,5,1,2] => [[.,[[.,[.,.]],[[.,.],.]]],[.,.]] => [1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2

[1,2,5,8,3,6,4,7] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => [1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 5

[7,8,1,4,6,2,3,5] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[1,6,7,4,8,2,5,3] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 3

[1,4,5,6,8,2,7,3] => [.,[[.,[.,[.,[.,.]]]],[[.,.],.]]] => [1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[1,2,5,8,3,4,7,6] => [.,[.,[[.,[.,.]],[.,[[.,.],.]]]]] => [1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 5

[1,6,7,2,3,5,8,4] => [.,[[.,[.,.]],[.,[[.,[.,.]],.]]]] => [1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 4

[7,8,1,2,3,5,4,6] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 5

[1,6,7,2,3,5,4,8] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 5

[1,2,5,7,3,6,4,8] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => [1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 5

[1,2,5,7,3,6,8,4] => [.,[.,[[.,[.,.]],[[.,[.,.]],.]]]] => [1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 4

[1,6,8,2,3,5,7,4] => [.,[[.,[.,.]],[.,[[.,[.,.]],.]]]] => [1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 4

[1,6,8,4,5,2,3,7] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 4

[1,6,8,4,5,2,7,3] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 3

[1,6,8,2,3,4,7,5] => [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => [1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 5

[1,6,8,2,3,7,4,5] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 5

[7,8,1,4,5,2,6,3] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[7,8,1,2,3,4,6,5] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 5

[7,8,1,2,3,6,4,5] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 5

[1,6,7,2,3,8,5,4] => [.,[[.,[.,.]],[.,[[[.,.],.],.]]]] => [1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 4

[1,2,5,6,3,8,7,4] => [.,[.,[[.,[.,.]],[[[.,.],.],.]]]] => [1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 4

[6,8,2,1,4,3,7,5] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[6,7,3,8,4,2,5,1] => [[[[.,[.,.]],[[.,.],.]],[.,.]],.] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 1

[6,7,3,8,4,2,1,5] => [[[[.,[.,.]],[[.,.],.]],.],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2

[1,7,8,4,3,5,2,6] => [.,[[[[.,[.,.]],.],[.,.]],[.,.]]] => [1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 3

[7,1,4,8,3,5,2,6] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[7,4,8,1,5,6,2,3] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[6,7,3,1,8,4,5,2] => [[[.,[.,.]],.],[[[.,.],[.,.]],.]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[6,7,3,8,4,5,2,1] => [[[[.,[.,.]],[[.,.],[.,.]]],.],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 1

[6,7,1,4,8,3,5,2] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2

[6,7,4,1,3,8,2,5] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[1,6,7,8,4,3,2,5] => [.,[[[[.,[.,[.,.]]],.],.],[.,.]]] => [1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 3

[6,2,7,1,8,4,3,5] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[6,2,7,8,4,3,1,5] => [[[.,.],[[[.,[.,.]],.],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => 2

[6,2,7,8,4,3,5,1] => [[[.,.],[[[.,[.,.]],.],[.,.]]],.] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1

[2,6,7,4,8,3,5,1] => [[.,[[[.,[.,.]],[.,.]],[.,.]]],.] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1

[2,6,7,4,8,3,1,5] => [[.,[[[.,[.,.]],[.,.]],.]],[.,.]] => [1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2

[7,8,1,3,6,2,4,5] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[1,2,7,8,6,3,4,5] => [.,[.,[[[.,[.,.]],.],[.,[.,.]]]]] => [1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 5

[2,6,7,1,8,5,3,4] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[2,6,7,8,5,3,1,4] => [[.,[[[.,[.,[.,.]]],.],.]],[.,.]] => [1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 2

[2,6,7,8,5,3,4,1] => [[.,[[[.,[.,[.,.]]],.],[.,.]]],.] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1

[6,2,7,8,4,5,3,1] => [[[.,.],[[[.,[.,.]],[.,.]],.]],.] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1

[3,7,8,1,5,6,2,4] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[6,3,7,8,1,5,2,4] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,7,1,2,8,5,3,4] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 4

[1,6,7,8,4,2,5,3] => [.,[[[.,[.,[.,.]]],.],[[.,.],.]]] => [1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3

[6,1,2,4,7,3,8,5] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 4

[5,1,2,6,7,4,8,3] => [[.,.],[.,[[[.,[.,.]],[.,.]],.]]] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 3

[4,1,5,7,3,2,6,8] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[4,6,1,7,3,2,5,8] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[4,6,1,8,3,2,5,7] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[4,7,1,8,3,5,2,6] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[4,1,7,8,6,2,3,5] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[4,8,1,7,3,5,2,6] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[4,8,1,6,3,2,5,7] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[4,7,1,6,3,2,5,8] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[6,8,1,5,3,7,2,4] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[1,5,7,3,4,8,6,2] => [.,[[[.,[.,.]],[.,[[.,.],.]]],.]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 2

[1,5,8,3,4,7,6,2] => [.,[[[.,[.,.]],[.,[[.,.],.]]],.]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 2

[7,8,5,2,4,1,6,3] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[7,1,2,3,5,6,4,8] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => 5

[8,1,2,3,5,6,4,7] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => 5

[6,8,2,4,3,1,5,7] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[6,7,2,4,3,1,5,8] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[3,8,1,2,4,5,7,6] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 5

[3,7,1,8,6,4,2,5] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[3,1,2,6,7,5,8,4] => [[.,.],[.,[[[.,[.,.]],[.,.]],.]]] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 3

[3,8,1,7,6,4,2,5] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[1,5,7,3,4,6,8,2] => [.,[[[.,[.,.]],[.,[.,[.,.]]]],.]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2

[6,1,2,3,5,8,4,7] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => 5

[6,1,2,3,5,7,4,8] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => 5

[1,5,6,3,4,7,8,2] => [.,[[[.,[.,.]],[.,[.,[.,.]]]],.]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2

[7,4,5,2,3,8,6,1] => [[[[.,.],[.,.]],[.,[[.,.],.]]],.] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[8,4,7,3,2,5,1,6] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[5,4,6,3,1,2,8,7] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[4,6,2,3,1,5,8,7] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[8,2,3,4,5,7,1,6] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2

[7,3,4,6,8,5,1,2] => [[[.,.],[.,[[.,[.,.]],.]]],[.,.]] => [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => 2

[4,7,3,2,8,6,1,5] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[3,8,2,6,7,4,5,1] => [[[.,[.,.]],[[.,[.,.]],[.,.]]],.] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 1

[4,8,1,5,6,7,3,2] => [[.,[.,.]],[[[.,[.,[.,.]]],.],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2

[5,8,2,4,6,7,1,3] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[6,8,1,3,4,2,7,5] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[5,8,2,4,3,1,7,6] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[4,7,2,3,8,5,1,6] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[6,2,3,7,8,5,4,1] => [[[.,.],[.,[[[.,[.,.]],.],.]]],.] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 1

[7,2,3,6,8,4,1,5] => [[[.,.],[.,[[.,[.,.]],.]]],[.,.]] => [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => 2

[8,2,3,5,7,1,4,6] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[6,4,8,3,5,1,7,2] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[5,4,8,3,6,7,1,2] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[3,5,1,8,4,6,7,2] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 2

[3,6,1,8,4,5,2,7] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[4,6,8,3,5,2,7,1] => [[[[.,[.,[.,.]]],[.,.]],[.,.]],.] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[5,7,8,3,2,4,1,6] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[4,8,2,3,5,6,1,7] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[6,8,2,3,1,4,5,7] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[3,7,8,2,1,4,6,5] => [[[.,[.,[.,.]]],.],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[5,7,3,1,4,2,6,8] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[8,3,5,2,7,4,1,6] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[7,2,4,8,1,3,6,5] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[5,1,6,8,3,4,2,7] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[6,2,5,1,7,4,3,8] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[7,2,8,1,3,6,5,4] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[7,3,8,1,4,6,2,5] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[1,7,8,5,4,6,3,2] => [.,[[[[[.,[.,.]],.],[.,.]],.],.]] => [1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 2

[1,5,8,4,6,3,7,2] => [.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 2

[5,8,4,3,6,2,1,7] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[3,8,1,4,6,7,5,2] => [[.,[.,.]],[[.,[[.,[.,.]],.]],.]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 2

[3,8,2,5,1,7,6,4] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[4,3,8,2,5,1,6,7] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[6,7,3,5,1,4,8,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[5,7,8,4,2,6,3,1] => [[[[.,[.,[.,.]]],.],[[.,.],.]],.] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1

[5,7,4,1,6,8,3,2] => [[[.,[.,.]],.],[[[.,[.,.]],.],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 2

[6,8,4,5,7,1,3,2] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[5,8,4,6,1,7,3,2] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[5,6,1,4,7,8,3,2] => [[.,[.,.]],[[[.,[.,[.,.]]],.],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2

[5,6,7,2,4,8,3,1] => [[[.,[.,[.,.]]],[[.,[.,.]],.]],.] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[5,6,3,7,4,8,2,1] => [[[[.,[.,.]],[[.,.],[.,.]]],.],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 1

[5,3,6,7,4,8,2,1] => [[[[.,.],[[.,[.,.]],[.,.]]],.],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1

[5,4,8,2,6,7,3,1] => [[[[.,.],[.,.]],[[.,[.,.]],.]],.] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[4,6,8,5,7,2,3,1] => [[[.,[[.,[.,.]],[.,.]]],[.,.]],.] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[5,6,8,2,4,7,3,1] => [[[.,[.,[.,.]]],[[.,[.,.]],.]],.] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[5,6,3,8,4,7,2,1] => [[[[.,[.,.]],[[.,.],[.,.]]],.],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 1

[4,6,3,5,8,7,2,1] => [[[[.,[.,.]],[.,[[.,.],.]]],.],.] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 1

[4,6,3,2,8,7,5,1] => [[[[.,[.,.]],.],[[[.,.],.],.]],.] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 1

[5,6,3,8,2,7,4,1] => [[[[.,[.,.]],[.,.]],[[.,.],.]],.] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 1

[5,3,6,8,2,7,4,1] => [[[[.,.],[.,[.,.]]],[[.,.],.]],.] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => 1

[4,3,7,2,8,6,5,1] => [[[[.,.],[.,.]],[[[.,.],.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1

[5,4,7,2,6,8,3,1] => [[[[.,.],[.,.]],[[.,[.,.]],.]],.] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[6,7,3,8,5,2,4,1] => [[[[.,[.,.]],[[.,.],.]],[.,.]],.] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 1

[6,4,7,2,5,3,8,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[2,7,8,5,3,6,1,4] => [[.,[[[.,[.,.]],.],[.,.]]],[.,.]] => [1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 2

[6,3,7,8,4,2,5,1] => [[[[.,.],[[.,[.,.]],.]],[.,.]],.] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[3,5,7,8,4,6,2,1] => [[[.,[[.,[.,[.,.]]],[.,.]]],.],.] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1

[5,3,7,8,4,6,2,1] => [[[[.,.],[[.,[.,.]],[.,.]]],.],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1

[5,7,8,2,4,6,3,1] => [[[.,[.,[.,.]]],[[.,[.,.]],.]],.] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[2,5,8,4,3,7,6,1] => [[.,[[[.,[.,.]],.],[[.,.],.]]],.] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 1

[2,6,8,4,7,3,5,1] => [[.,[[[.,[.,.]],[.,.]],[.,.]]],.] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1

[4,5,7,3,8,6,2,1] => [[[[.,[.,[.,.]]],[[.,.],.]],.],.] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

[3,5,6,8,4,7,2,1] => [[[.,[[.,[.,[.,.]]],[.,.]]],.],.] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1

[5,4,8,1,7,6,3,2] => [[[.,.],[.,.]],[[[[.,.],.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[1,6,7,4,3,5,2,8] => [.,[[[[.,[.,.]],.],[.,.]],[.,.]]] => [1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 3

[2,6,8,4,3,5,7,1] => [[.,[[[.,[.,.]],.],[.,[.,.]]]],.] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 1

[7,5,8,3,2,1,6,4] => [[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[7,5,8,1,2,6,3,4] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[1,6,7,4,3,2,8,5] => [.,[[[[.,[.,.]],.],.],[[.,.],.]]] => [1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 3

[6,2,5,7,1,4,8,3] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[7,3,6,8,5,2,4,1] => [[[[.,.],[[.,[.,.]],.]],[.,.]],.] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[2,7,8,3,6,5,1,4] => [[.,[[.,[.,.]],[[.,.],.]]],[.,.]] => [1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2

[2,7,8,5,4,6,3,1] => [[.,[[[[.,[.,.]],.],[.,.]],.]],.] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 1

[6,2,5,7,4,1,3,8] => [[[.,.],[[.,[.,.]],.]],[.,[.,.]]] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[6,2,5,8,4,1,3,7] => [[[.,.],[[.,[.,.]],.]],[.,[.,.]]] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[2,7,8,4,6,1,3,5] => [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[6,2,5,7,8,1,3,4] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[4,7,3,1,5,6,2,8] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[5,8,3,4,1,6,7,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[1,7,8,4,5,6,2,3] => [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 3

[1,5,8,4,2,6,7,3] => [.,[[[.,[.,.]],.],[[.,[.,.]],.]]] => [1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3

[5,2,3,7,1,6,4,8] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,2,3,4,8,1,7,5] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[2,4,1,8,5,3,7,6] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[3,4,6,8,2,1,7,5] => [[[.,[.,[.,[.,.]]]],.],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[3,4,1,5,8,2,7,6] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[8,1,4,5,3,2,7,6] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3

[3,4,1,5,2,8,7,6] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[3,4,6,2,1,8,7,5] => [[[.,[.,[.,.]]],.],[[[.,.],.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[3,5,6,2,1,7,8,4] => [[[.,[.,[.,.]]],.],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[3,4,6,2,7,8,1,5] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[8,1,4,6,3,7,2,5] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[8,1,4,6,3,7,5,2] => [[.,.],[[[.,[.,.]],[[.,.],.]],.]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2

[3,5,6,2,1,7,4,8] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[8,1,5,6,7,3,4,2] => [[.,.],[[[.,[.,[.,.]]],[.,.]],.]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2

[8,1,5,6,7,3,2,4] => [[.,.],[[[.,[.,[.,.]]],.],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => 3

[3,4,1,6,8,7,2,5] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3

[3,5,6,1,8,7,2,4] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[2,4,1,8,6,7,5,3] => [[.,[.,.]],[[[[.,.],[.,.]],.],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 2

[3,5,6,1,8,7,4,2] => [[.,[.,[.,.]]],[[[[.,.],.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[3,4,1,6,8,7,5,2] => [[.,[.,.]],[[[.,[[.,.],.]],.],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 2

[8,1,4,6,2,7,5,3] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3

[3,5,1,6,7,8,4,2] => [[.,[.,.]],[[[.,[.,[.,.]]],.],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2

[4,5,6,1,7,8,3,2] => [[.,[.,[.,.]]],[[[.,[.,.]],.],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[4,5,6,1,7,3,8,2] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[3,5,1,6,7,4,8,2] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2

[8,1,5,6,7,4,2,3] => [[.,.],[[[.,[.,[.,.]]],.],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => 3

[8,1,5,6,7,4,3,2] => [[.,.],[[[[.,[.,[.,.]]],.],.],.]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => 2

[3,5,1,6,7,4,2,8] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[4,5,6,1,7,3,2,8] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[2,7,1,5,4,8,3,6] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[2,5,8,4,7,3,1,6] => [[.,[[[.,[.,.]],[.,.]],.]],[.,.]] => [1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2

[6,8,3,2,4,7,1,5] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[3,7,2,5,4,8,1,6] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[1,5,8,4,7,3,2,6] => [.,[[[[.,[.,.]],[.,.]],.],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 3

[5,8,2,4,7,3,1,6] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[6,8,4,3,7,5,1,2] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[5,7,3,4,6,8,2,1] => [[[[.,[.,.]],[.,[.,[.,.]]]],.],.] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1

[5,8,2,6,4,1,3,7] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[6,3,5,2,1,4,7,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[2,3,5,8,1,4,7,6] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[2,3,6,8,1,5,7,4] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[2,4,8,1,6,5,7,3] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[7,3,5,2,1,4,6,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[2,3,6,8,1,4,7,5] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[2,7,8,6,3,1,4,5] => [[.,[[[.,[.,.]],.],.]],[.,[.,.]]] => [1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 3

[2,3,6,1,8,4,7,5] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[8,3,5,2,1,4,6,7] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[2,4,8,1,3,7,5,6] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[2,5,8,1,7,3,6,4] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[2,7,1,5,8,3,4,6] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[7,3,6,1,2,8,4,5] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[7,4,8,1,6,5,2,3] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[4,6,1,8,7,5,2,3] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[4,5,1,8,7,2,3,6] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[5,6,8,3,7,1,4,2] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[6,4,7,1,2,8,5,3] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[6,8,5,7,4,1,2,3] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3

[7,3,8,1,5,2,4,6] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[2,5,8,3,4,6,7,1] => [[.,[[.,[.,.]],[.,[.,[.,.]]]]],.] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1

[4,6,2,1,5,7,8,3] => [[[.,[.,.]],.],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 2

[4,5,2,3,1,7,8,6] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[3,2,6,7,4,1,8,5] => [[[.,.],[[.,[.,.]],.]],[[.,.],.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[5,6,2,7,1,4,8,3] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[6,2,3,8,1,7,4,5] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,6,8,3,4,7,1,5] => [[.,[[.,[.,.]],[.,[.,.]]]],[.,.]] => [1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2

[4,6,2,7,5,1,3,8] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[2,4,3,7,8,1,5,6] => [[.,[[.,.],[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[3,5,6,4,7,8,1,2] => [[.,[[.,[.,.]],[.,[.,.]]]],[.,.]] => [1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2

[4,2,3,7,8,1,6,5] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[5,8,3,1,7,2,4,6] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[6,8,5,2,1,7,3,4] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[6,8,3,2,5,1,7,4] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[6,8,4,3,1,5,7,2] => [[[[.,[.,.]],.],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 2

[6,8,4,2,1,5,7,3] => [[[[.,[.,.]],.],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 2

[4,3,8,1,6,2,7,5] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[4,2,8,1,7,3,5,6] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[2,1,5,8,4,7,3,6] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[7,8,6,2,5,3,1,4] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[6,1,3,5,2,8,4,7] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[6,7,1,8,5,3,4,2] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2

[7,4,6,1,3,2,8,5] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[3,5,6,7,1,4,8,2] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[5,7,2,1,6,3,8,4] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[4,7,2,5,6,3,8,1] => [[[.,[.,.]],[[.,[.,.]],[.,.]]],.] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 1

[5,8,4,3,2,6,7,1] => [[[[[.,[.,.]],.],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1

[8,1,5,6,2,4,7,3] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3

[6,4,8,1,3,2,7,5] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[1,4,5,2,8,6,7,3] => [.,[[.,[.,.]],[[[.,.],[.,.]],.]]] => [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 3

[2,3,1,7,8,6,4,5] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[4,5,6,1,2,8,7,3] => [[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[8,4,5,2,1,6,7,3] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[3,1,2,6,8,4,7,5] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 4

[4,6,7,8,3,1,5,2] => [[[.,[.,[.,[.,.]]]],.],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[5,6,8,4,3,2,7,1] => [[[[[.,[.,[.,.]]],.],.],[.,.]],.] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1

[5,3,8,1,7,2,4,6] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[3,6,7,8,4,2,1,5] => [[[.,[[.,[.,[.,.]]],.]],.],[.,.]] => [1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 2

[2,5,8,3,1,6,7,4] => [[.,[[.,[.,.]],.]],[[.,[.,.]],.]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 2

[3,5,8,1,2,6,7,4] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[3,2,8,1,5,6,7,4] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[1,5,8,3,2,6,7,4] => [.,[[[.,[.,.]],.],[[.,[.,.]],.]]] => [1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3

[3,2,7,8,4,6,1,5] => [[[.,.],[[.,[.,.]],[.,.]]],[.,.]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[2,8,1,6,3,4,7,5] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[8,3,4,2,1,6,5,7] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[6,4,7,2,5,8,1,3] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[8,4,5,2,6,3,1,7] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[2,4,5,8,3,6,1,7] => [[.,[[.,[.,[.,.]]],[.,.]]],[.,.]] => [1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[3,5,8,1,2,6,4,7] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[5,8,4,6,1,3,2,7] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[7,3,4,5,2,8,1,6] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,7,4,3,6,1,8,2] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[5,6,1,7,4,2,8,3] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[6,3,5,7,8,1,4,2] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[6,4,7,8,2,1,3,5] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[6,7,3,8,4,1,2,5] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[2,7,8,3,4,6,1,5] => [[.,[[.,[.,.]],[.,[.,.]]]],[.,.]] => [1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2

[7,5,8,4,1,3,2,6] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[3,6,7,4,8,1,2,5] => [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[5,7,3,1,6,8,4,2] => [[[.,[.,.]],.],[[[.,[.,.]],.],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 2

[4,8,1,2,3,5,7,6] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 5

[7,6,8,1,2,4,3,5] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[7,6,8,5,1,3,2,4] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[8,4,5,2,7,6,1,3] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[6,7,1,3,5,2,8,4] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[5,7,2,3,6,8,1,4] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[3,4,6,7,5,8,1,2] => [[.,[.,[[.,[.,.]],[.,.]]]],[.,.]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 2

[2,6,4,5,7,8,3,1] => [[.,[[[.,.],[.,[.,[.,.]]]],.]],.] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[2,5,1,3,6,8,7,4] => [[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 3

[5,4,6,1,3,7,8,2] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[6,3,5,7,1,4,8,2] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[7,3,4,6,8,1,5,2] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[3,7,8,4,1,5,6,2] => [[.,[[.,[.,.]],.]],[[.,[.,.]],.]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 2

[6,7,2,5,1,8,4,3] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[3,6,1,2,5,8,4,7] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4

[1,4,5,8,2,3,7,6] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[3,6,1,5,8,2,4,7] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[5,2,6,1,4,8,3,7] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[2,5,1,8,4,7,3,6] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[2,7,1,4,3,6,8,5] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[2,4,1,3,8,6,7,5] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 3

[2,6,1,7,3,5,8,4] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[3,5,8,1,2,7,4,6] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[3,6,8,1,2,4,7,5] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[1,4,6,8,2,3,7,5] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[3,5,8,1,7,2,4,6] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[2,6,8,1,7,3,4,5] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[6,1,5,8,2,3,7,4] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[2,6,7,3,8,1,5,4] => [[.,[[.,[.,.]],[.,.]]],[[.,.],.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2

[3,7,2,8,6,1,5,4] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[5,1,7,8,4,2,6,3] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3

[4,7,2,8,3,6,5,1] => [[[.,[.,.]],[[.,.],[[.,.],.]]],.] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 1

[4,1,7,8,5,3,6,2] => [[.,.],[[[[.,[.,.]],.],[.,.]],.]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 2

[4,8,2,7,3,6,5,1] => [[[.,[.,.]],[[.,.],[[.,.],.]]],.] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 1

[4,7,2,6,3,5,8,1] => [[[.,[.,.]],[[.,.],[.,[.,.]]]],.] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 1

[6,8,2,4,3,7,5,1] => [[[.,[.,.]],[[.,.],[[.,.],.]]],.] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 1

[6,7,2,4,3,8,5,1] => [[[.,[.,.]],[[.,.],[[.,.],.]]],.] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 1

[6,8,2,7,3,5,4,1] => [[[.,[.,.]],[[.,.],[[.,.],.]]],.] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 1

[3,7,8,2,4,1,5,6] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[3,6,8,2,4,5,7,1] => [[[.,[.,[.,.]]],[.,[.,[.,.]]]],.] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1

[3,6,7,2,4,5,8,1] => [[[.,[.,[.,.]]],[.,[.,[.,.]]]],.] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1

[8,3,4,7,1,6,2,5] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,3,4,1,8,5,2,7] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[6,2,7,1,8,3,5,4] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[4,8,1,3,2,7,5,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[3,8,1,4,7,5,2,6] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3

[8,5,7,4,6,2,1,3] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[4,6,7,8,2,3,5,1] => [[[.,[.,[.,[.,.]]]],[.,[.,.]]],.] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1

[5,8,3,2,4,6,1,7] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[2,4,1,7,6,8,5,3] => [[.,[.,.]],[[[[.,.],[.,.]],.],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 2

[3,4,1,7,8,5,6,2] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2

[8,5,6,2,7,3,1,4] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[4,1,3,6,7,5,8,2] => [[.,.],[[.,[[.,[.,.]],[.,.]]],.]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 2

[6,1,4,7,8,3,5,2] => [[.,.],[[[.,[.,[.,.]]],[.,.]],.]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2

[3,6,4,7,8,1,5,2] => [[.,[[.,.],[.,[.,.]]]],[[.,.],.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[4,3,6,7,1,8,2,5] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,6,4,7,8,1,2,5] => [[.,[[.,.],[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[4,7,2,1,5,3,8,6] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[5,1,3,4,2,7,8,6] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3

[1,6,7,3,8,2,5,4] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 3

[6,1,4,7,8,5,2,3] => [[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3

[6,4,7,8,3,2,5,1] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1

[3,8,4,7,1,2,5,6] => [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[6,8,5,7,4,2,3,1] => [[[[[.,[.,.]],[.,.]],.],[.,.]],.] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1

[4,3,7,8,1,6,2,5] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,8,1,2,7,3,5,6] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5

[6,8,1,2,7,4,5,3] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 3

[5,6,8,4,1,3,7,2] => [[[.,[.,[.,.]]],.],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[5,7,1,8,4,6,2,3] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[2,3,7,8,5,6,1,4] => [[.,[.,[[.,[.,.]],[.,.]]]],[.,.]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 2

[2,6,7,8,5,1,3,4] => [[.,[[.,[.,[.,.]]],.]],[.,[.,.]]] => [1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[2,4,7,8,1,6,3,5] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,4,7,8,2,6,3,1] => [[[[.,.],[.,[.,.]]],[[.,.],.]],.] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => 1

[6,8,3,4,1,2,7,5] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[5,8,3,2,7,6,1,4] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[4,5,3,2,8,6,7,1] => [[[[.,[.,.]],.],[[.,.],[.,.]]],.] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 1

[5,8,2,3,7,6,1,4] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[4,6,8,5,3,2,7,1] => [[[[.,[[.,[.,.]],.]],.],[.,.]],.] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[2,5,1,3,8,6,7,4] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 3

[4,5,1,2,8,6,7,3] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 3

[5,4,8,1,3,6,7,2] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[6,1,5,7,2,4,8,3] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3

[7,4,5,1,2,3,8,6] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[5,7,2,3,6,4,8,1] => [[[.,[.,.]],[.,[[.,.],[.,.]]]],.] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 1

[5,7,2,4,8,3,6,1] => [[[.,[.,.]],[[.,[.,.]],[.,.]]],.] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 1

[4,7,3,2,1,8,5,6] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[7,8,6,1,3,2,5,4] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[3,8,1,2,5,7,4,6] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4

[6,8,5,4,2,7,3,1] => [[[[[.,[.,.]],.],.],[[.,.],.]],.] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 1

[6,8,3,1,2,4,5,7] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 5

[8,4,5,2,1,6,3,7] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[7,1,5,6,3,8,2,4] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[5,1,2,4,7,8,3,6] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 4

[5,6,8,1,7,3,2,4] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[7,4,6,8,2,1,5,3] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[6,5,8,4,3,1,2,7] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3

[2,5,8,3,6,7,4,1] => [[.,[[.,[.,.]],[[.,[.,.]],.]]],.] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 1

[1,5,8,3,7,4,2,6] => [.,[[[.,[.,.]],[[.,.],.]],[.,.]]] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 3

[3,8,2,7,1,5,6,4] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[5,8,2,3,6,4,1,7] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[6,8,2,3,4,7,5,1] => [[[.,[.,.]],[.,[.,[[.,.],.]]]],.] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 1

[3,6,8,5,2,7,4,1] => [[[.,[[.,[.,.]],.]],[[.,.],.]],.] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[2,1,7,8,4,6,5,3] => [[.,.],[[[.,[.,.]],[[.,.],.]],.]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2

[3,5,7,8,4,6,1,2] => [[.,[[.,[.,[.,.]]],[.,.]]],[.,.]] => [1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[7,8,2,4,3,1,5,6] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[6,2,7,1,3,5,8,4] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[7,2,4,1,6,3,8,5] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[4,7,1,8,5,2,6,3] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[5,3,4,2,8,7,1,6] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[5,8,2,7,3,4,6,1] => [[[.,[.,.]],[[.,.],[.,[.,.]]]],.] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 1

[6,8,2,5,4,3,1,7] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[6,7,2,4,5,3,8,1] => [[[.,[.,.]],[[.,[.,.]],[.,.]]],.] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 1

[5,7,2,8,3,6,1,4] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[6,8,3,7,5,4,2,1] => [[[[.,[.,.]],[[[.,.],.],.]],.],.] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 1

[6,2,3,1,4,7,8,5] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[8,3,7,1,4,6,5,2] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[6,7,2,1,5,8,4,3] => [[[.,[.,.]],.],[[[.,[.,.]],.],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 2

[7,6,8,1,5,4,3,2] => [[[.,.],[.,.]],[[[[.,.],.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[6,5,8,1,7,4,3,2] => [[[.,.],[.,.]],[[[[.,.],.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[6,1,4,8,2,3,5,7] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[5,7,4,1,2,3,8,6] => [[[.,[.,.]],.],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 4

[6,7,4,2,1,3,8,5] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 3

[6,8,4,2,3,1,5,7] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[7,4,8,2,3,1,5,6] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[8,3,7,2,1,4,5,6] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[6,5,7,4,1,8,2,3] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[4,8,1,3,5,7,2,6] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[7,8,4,1,3,6,2,5] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[6,5,8,1,3,7,2,4] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[5,3,6,1,8,2,4,7] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[4,7,3,1,8,2,5,6] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[2,8,1,4,7,3,5,6] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[4,1,5,8,3,7,6,2] => [[.,.],[[[.,[.,.]],[[.,.],.]],.]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2

[4,5,1,8,2,7,6,3] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[4,5,2,8,1,7,6,3] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[4,5,2,1,8,7,6,3] => [[[.,[.,.]],.],[[[[.,.],.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2

[5,6,2,7,8,1,4,3] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[4,6,2,8,7,1,5,3] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[4,6,8,2,7,5,1,3] => [[[.,[.,[.,.]]],[[.,.],.]],[.,.]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[4,6,2,8,7,5,1,3] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[5,6,2,7,4,1,8,3] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[5,6,7,2,3,1,8,4] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[5,6,7,2,8,3,1,4] => [[[.,[.,[.,.]]],[[.,.],.]],[.,.]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[5,6,7,2,1,8,3,4] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[5,6,7,2,1,3,8,4] => [[[.,[.,[.,.]]],.],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[5,6,1,7,8,2,4,3] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[5,6,1,7,2,4,8,3] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[5,1,6,7,8,3,4,2] => [[.,.],[[[.,[.,[.,.]]],[.,.]],.]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2

[5,1,6,7,4,8,3,2] => [[.,.],[[[[.,[.,.]],[.,.]],.],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[5,6,1,7,8,4,2,3] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[4,6,8,1,7,5,2,3] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[5,6,7,1,8,3,2,4] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[5,6,7,1,3,8,2,4] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[5,6,7,1,3,2,8,4] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[5,6,7,3,1,2,8,4] => [[[.,[.,[.,.]]],.],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[5,6,7,3,8,1,2,4] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[5,6,7,3,8,2,1,4] => [[[[.,[.,[.,.]]],[.,.]],.],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[7,4,6,2,3,5,1,8] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[7,4,5,6,1,8,3,2] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[3,2,5,1,4,8,7,6] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[5,4,8,3,7,1,6,2] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[4,7,1,8,2,5,3,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[8,4,6,1,3,5,2,7] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[8,1,6,7,2,5,3,4] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[6,1,4,7,2,8,3,5] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[7,8,4,6,3,2,1,5] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2

[4,5,3,6,8,1,7,2] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[3,5,2,6,1,8,7,4] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[1,5,4,6,7,8,2,3] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[7,4,5,2,6,8,1,3] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[7,8,1,3,5,6,2,4] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[1,7,8,3,5,6,2,4] => [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 3

[3,1,7,8,5,2,6,4] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3

[3,5,7,1,8,4,6,2] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[3,5,7,8,1,4,6,2] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[5,3,7,8,4,6,1,2] => [[[.,.],[[.,[.,.]],[.,.]]],[.,.]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[5,3,7,1,8,4,6,2] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[5,1,3,7,8,4,2,6] => [[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3

[3,6,2,1,4,5,8,7] => [[[.,[.,.]],.],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 4

[4,6,2,5,1,3,8,7] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[2,5,8,1,7,3,4,6] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[6,8,2,7,3,1,4,5] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[6,8,2,3,7,1,4,5] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[5,2,8,1,7,3,4,6] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[4,2,3,8,1,5,6,7] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[2,1,5,8,4,3,6,7] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[5,8,3,2,7,1,4,6] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[4,1,3,8,2,5,6,7] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[3,5,8,2,7,1,4,6] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[4,5,8,2,6,1,3,7] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[2,6,8,3,7,1,4,5] => [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[5,8,4,1,6,2,3,7] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[4,5,8,1,6,2,3,7] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[5,4,8,1,6,2,3,7] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[2,4,3,8,1,5,6,7] => [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[3,4,2,8,1,5,6,7] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[5,7,4,3,8,1,6,2] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[5,7,4,3,8,2,6,1] => [[[[[.,[.,.]],.],[.,.]],[.,.]],.] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1

[5,6,4,3,2,8,1,7] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2

[2,6,7,5,3,8,4,1] => [[.,[[[.,[.,.]],.],[[.,.],.]]],.] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 1

[6,7,4,8,2,5,3,1] => [[[[.,[.,.]],[.,.]],[[.,.],.]],.] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 1

[2,1,6,7,5,3,8,4] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3

[5,7,4,3,8,2,1,6] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[6,7,4,8,1,2,5,3] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[6,7,5,8,1,2,4,3] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[6,7,4,8,3,1,2,5] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3

[3,4,8,1,2,5,7,6] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[6,1,3,4,8,2,5,7] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[6,2,3,4,8,1,5,7] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[3,4,8,2,1,5,7,6] => [[[.,[.,[.,.]]],.],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[6,7,5,8,2,4,3,1] => [[[[.,[.,.]],[.,.]],[[.,.],.]],.] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 1

[6,7,5,8,3,1,4,2] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[3,4,8,1,5,7,6,2] => [[.,[.,[.,.]]],[[.,[[.,.],.]],.]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[6,7,4,8,2,3,5,1] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1

[6,7,4,8,1,3,5,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[2,6,7,5,1,3,8,4] => [[.,[[.,[.,.]],.]],[.,[[.,.],.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 3

[6,7,4,8,1,3,2,5] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,7,5,8,4,1,3,2] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[6,7,4,8,2,1,3,5] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3

[6,7,4,8,1,2,3,5] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[1,5,6,3,4,8,2,7] => [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 3

[8,1,3,4,7,2,6,5] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[6,7,8,2,3,5,4,1] => [[[.,[.,[.,.]]],[.,[[.,.],.]]],.] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[3,8,1,7,5,2,6,4] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[4,8,1,6,7,2,5,3] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[8,4,5,1,7,2,6,3] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[6,7,2,8,5,3,4,1] => [[[.,[.,.]],[[[.,.],.],[.,.]]],.] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 1

[5,2,7,8,6,3,4,1] => [[[.,.],[[[.,[.,.]],.],[.,.]]],.] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1

[5,1,7,8,6,4,2,3] => [[.,.],[[[[.,[.,.]],.],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => 3

[6,7,1,8,5,4,2,3] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[7,8,3,2,6,1,4,5] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[7,8,1,4,5,6,3,2] => [[.,[.,.]],[[[.,[.,[.,.]]],.],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2

[7,8,4,5,1,6,3,2] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[6,2,4,8,1,5,3,7] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[1,4,8,2,6,3,7,5] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 4

[5,3,8,1,4,6,7,2] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[1,2,7,8,5,3,4,6] => [.,[.,[[[.,[.,.]],.],[.,[.,.]]]]] => [1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 5

[3,2,7,8,5,1,4,6] => [[[.,.],[[.,[.,.]],.]],[.,[.,.]]] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[2,3,7,8,5,1,4,6] => [[.,[.,[[.,[.,.]],.]]],[.,[.,.]]] => [1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 3

[3,6,2,8,5,1,4,7] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[7,3,6,8,5,4,1,2] => [[[.,.],[[[.,[.,.]],.],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => 2

[6,5,7,1,8,4,3,2] => [[[.,.],[.,.]],[[[[.,.],.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[6,7,3,8,5,4,1,2] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[5,3,7,1,6,4,2,8] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[5,3,6,1,8,7,4,2] => [[[.,.],[.,.]],[[[[.,.],.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[2,3,1,8,7,5,4,6] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[2,4,5,1,3,8,7,6] => [[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[7,4,6,3,1,8,5,2] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[2,3,1,7,5,8,6,4] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2

[4,6,2,7,3,1,8,5] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[7,3,4,8,1,6,2,5] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,3,4,8,1,7,2,5] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,3,4,8,1,2,7,6] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[4,3,5,8,1,2,7,6] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[4,5,3,8,1,2,7,6] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[5,6,3,8,7,1,2,4] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[4,6,3,8,1,7,2,5] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,6,8,4,1,7,3,5] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[5,7,3,8,6,1,2,4] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[2,7,8,5,6,1,3,4] => [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[2,6,8,5,7,1,3,4] => [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[3,4,7,8,1,6,2,5] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,6,7,8,5,1,2,4] => [[.,[[.,[.,[.,.]]],.]],[.,[.,.]]] => [1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[2,7,8,6,5,1,3,4] => [[.,[[[.,[.,.]],.],.]],[.,[.,.]]] => [1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 3

[4,6,1,8,7,3,2,5] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[4,3,5,2,8,7,1,6] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[3,4,2,8,6,1,5,7] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[3,7,2,1,8,6,4,5] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[8,1,5,6,4,7,2,3] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[3,6,7,4,1,8,2,5] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[7,5,8,2,6,3,1,4] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[2,7,1,6,5,4,8,3] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2

[6,4,7,2,3,1,8,5] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[3,8,1,6,7,4,2,5] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[4,7,3,8,5,2,1,6] => [[[[.,[.,.]],[[.,.],.]],.],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2

[8,1,2,4,6,7,5,3] => [[.,.],[.,[[.,[[.,[.,.]],.]],.]]] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 3

[8,1,3,6,7,5,4,2] => [[.,.],[[.,[[[.,[.,.]],.],.]],.]] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2

[4,7,3,2,8,5,6,1] => [[[[.,[.,.]],.],[[.,.],[.,.]]],.] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 1

[7,5,8,4,2,3,6,1] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1

[3,5,1,6,8,4,7,2] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2

[6,1,5,7,3,8,4,2] => [[.,.],[[[.,[.,.]],[[.,.],.]],.]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2

[5,8,4,7,3,2,6,1] => [[[[[.,[.,.]],[.,.]],.],[.,.]],.] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1

[2,6,8,3,7,4,1,5] => [[.,[[.,[.,.]],[[.,.],.]]],[.,.]] => [1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2

[8,1,5,6,4,7,3,2] => [[.,.],[[[[.,[.,.]],[.,.]],.],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[2,5,8,1,6,4,7,3] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[5,2,6,8,3,1,7,4] => [[[.,.],[[.,[.,.]],.]],[[.,.],.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[7,3,6,1,8,4,5,2] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[7,3,8,2,5,6,4,1] => [[[[.,.],[.,.]],[[.,[.,.]],.]],.] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[5,7,3,1,6,4,8,2] => [[[.,[.,.]],.],[[[.,.],[.,.]],.]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[3,7,1,5,2,8,6,4] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[6,3,4,1,7,2,8,5] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[8,2,3,5,1,7,6,4] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[7,2,8,1,6,5,3,4] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[7,4,8,2,1,5,3,6] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[8,2,4,1,6,3,7,5] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[4,7,2,1,6,3,8,5] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[7,4,8,1,5,3,2,6] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[7,3,4,2,8,5,1,6] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[6,7,1,3,8,5,2,4] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3

[3,6,7,1,5,2,8,4] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[5,6,2,7,1,3,8,4] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[5,6,2,8,1,3,7,4] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[7,4,8,3,1,5,2,6] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[3,5,2,7,1,6,8,4] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[4,5,7,3,1,6,8,2] => [[[.,[.,[.,.]]],.],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[4,5,7,2,8,6,1,3] => [[[.,[.,[.,.]]],[[.,.],.]],[.,.]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[3,5,1,7,2,6,8,4] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[4,5,7,2,8,1,3,6] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[4,6,7,2,1,5,8,3] => [[[.,[.,[.,.]]],.],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[4,6,7,1,3,8,5,2] => [[.,[.,[.,.]]],[[.,[[.,.],.]],.]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[3,6,1,5,7,8,4,2] => [[.,[.,.]],[[[.,[.,[.,.]]],.],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2

[4,6,7,1,5,8,3,2] => [[.,[.,[.,.]]],[[[.,[.,.]],.],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[2,5,1,3,7,6,4,8] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 4

[2,5,1,4,3,8,6,7] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[3,7,2,1,5,8,6,4] => [[[.,[.,.]],.],[[.,[[.,.],.]],.]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 2

[6,2,7,1,4,8,5,3] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[7,2,6,1,5,4,3,8] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[8,5,7,4,3,6,2,1] => [[[[[[.,.],[.,.]],.],[.,.]],.],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1

[8,5,7,2,4,6,3,1] => [[[[.,.],[.,.]],[[.,[.,.]],.]],.] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[8,4,6,7,1,3,2,5] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[7,2,6,8,4,1,5,3] => [[[.,.],[[.,[.,.]],.]],[[.,.],.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[6,5,8,1,4,2,7,3] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[6,5,8,4,1,3,7,2] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[5,4,8,3,2,1,7,6] => [[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[4,3,7,2,1,6,5,8] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[2,5,8,1,4,3,7,6] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[3,6,8,2,1,5,7,4] => [[[.,[.,[.,.]]],.],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[5,7,4,8,1,3,6,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[5,7,1,4,8,2,6,3] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[3,5,1,8,4,2,7,6] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[4,1,5,7,3,6,2,8] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[4,2,5,8,3,1,7,6] => [[[.,.],[[.,[.,.]],.]],[[.,.],.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[6,1,2,7,8,3,5,4] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 4

[4,8,1,7,6,2,3,5] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[6,8,1,4,7,5,2,3] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3

[7,3,8,1,6,4,2,5] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[4,7,8,1,5,3,2,6] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[6,8,1,7,5,2,4,3] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[5,7,8,4,3,1,2,6] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3

[2,4,7,1,5,3,8,6] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[5,3,6,2,4,1,7,8] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[5,3,6,1,4,2,7,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[2,7,1,6,8,3,5,4] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[4,5,6,2,3,8,1,7] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[4,5,3,2,7,8,1,6] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[6,5,7,3,8,4,2,1] => [[[[[.,.],[.,.]],[[.,.],.]],.],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

[6,8,1,5,2,4,3,7] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[8,3,4,6,1,5,2,7] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,3,4,7,8,2,5,1] => [[[[.,.],[.,[.,[.,.]]]],[.,.]],.] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 1

[3,7,8,5,4,1,2,6] => [[.,[[[.,[.,.]],.],.]],[.,[.,.]]] => [1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 3

[7,5,6,4,1,3,8,2] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[1,5,6,8,4,7,3,2] => [.,[[[[.,[.,[.,.]]],[.,.]],.],.]] => [1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[3,4,1,7,5,8,6,2] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2

[8,5,7,4,3,1,6,2] => [[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[6,8,5,1,7,2,4,3] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[8,2,4,1,3,7,6,5] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[7,8,3,6,2,1,4,5] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3

[8,2,3,1,5,7,6,4] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[5,4,7,2,3,6,8,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1

[2,7,8,5,1,3,6,4] => [[.,[[.,[.,.]],.]],[.,[[.,.],.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 3

[8,2,5,6,7,1,3,4] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[6,7,1,5,8,2,4,3] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[7,8,1,5,3,2,6,4] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[6,5,7,3,8,2,1,4] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[8,1,4,7,2,5,6,3] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3

[7,3,4,6,1,5,8,2] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[8,3,4,5,7,1,6,2] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[4,2,6,8,3,1,5,7] => [[[.,.],[[.,[.,.]],.]],[.,[.,.]]] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[3,2,7,1,4,5,8,6] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[5,8,3,2,4,1,6,7] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[4,2,7,1,8,3,5,6] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[3,2,7,1,4,8,5,6] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[1,2,3,7,8,4,6,5] => [.,[.,[.,[[.,[.,.]],[[.,.],.]]]]] => [1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 5

[1,2,3,6,8,4,7,5] => [.,[.,[.,[[.,[.,.]],[[.,.],.]]]]] => [1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 5

[1,2,3,7,8,6,4,5] => [.,[.,[.,[[[.,[.,.]],.],[.,.]]]]] => [1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 5

[4,6,3,8,5,7,2,1] => [[[[.,[.,.]],[[.,.],[.,.]]],.],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 1

[2,6,8,3,7,4,5,1] => [[.,[[.,[.,.]],[[.,.],[.,.]]]],.] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 1

[2,5,8,3,7,4,6,1] => [[.,[[.,[.,.]],[[.,.],[.,.]]]],.] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 1

[4,5,3,8,6,7,2,1] => [[[[.,[.,.]],[[.,.],[.,.]]],.],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 1

[3,6,7,8,4,5,2,1] => [[[.,[[.,[.,[.,.]]],[.,.]]],.],.] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1

[2,6,8,5,4,7,3,1] => [[.,[[[[.,[.,.]],.],[.,.]],.]],.] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 1

[6,3,7,8,4,5,2,1] => [[[[.,.],[[.,[.,.]],[.,.]]],.],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1

[4,3,7,8,5,6,2,1] => [[[[.,.],[[.,[.,.]],[.,.]]],.],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1

[4,3,6,8,5,7,2,1] => [[[[.,.],[[.,[.,.]],[.,.]]],.],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1

[2,7,8,4,5,6,3,1] => [[.,[[[.,[.,.]],[.,[.,.]]],.]],.] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[5,7,4,6,8,3,2,1] => [[[[[.,[.,.]],[.,[.,.]]],.],.],.] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1

[2,6,8,4,5,7,3,1] => [[.,[[[.,[.,.]],[.,[.,.]]],.]],.] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[4,2,7,1,3,8,5,6] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[4,2,5,1,3,8,6,7] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[5,3,6,1,7,2,4,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[3,7,1,2,5,8,6,4] => [[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 3

[8,4,7,1,2,3,6,5] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[8,5,7,1,2,4,6,3] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[8,5,7,1,3,4,6,2] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[3,8,5,6,1,2,4,7] => [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[3,7,5,8,1,2,4,6] => [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[6,5,8,1,2,4,7,3] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[3,6,8,1,2,5,7,4] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[3,7,2,4,8,1,6,5] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[4,6,3,8,1,2,5,7] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[4,6,3,7,1,2,5,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[4,1,7,8,2,3,6,5] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[5,3,8,1,6,2,4,7] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[6,8,1,3,7,4,5,2] => [[.,[.,.]],[[.,[[.,.],[.,.]]],.]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 2

[7,2,8,1,6,3,4,5] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[4,7,8,2,5,1,3,6] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[6,8,2,7,1,4,5,3] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[7,8,4,1,2,5,3,6] => [[[.,[.,.]],.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[7,8,1,2,6,5,3,4] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 4

[1,4,8,2,7,5,3,6] => [.,[[.,[.,.]],[[[.,.],.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 4

[7,8,2,1,6,3,5,4] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[5,7,4,1,2,6,3,8] => [[[.,[.,.]],.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[4,8,1,2,6,7,3,5] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4

[4,8,2,1,6,3,7,5] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[3,7,8,5,2,1,6,4] => [[[.,[[.,[.,.]],.]],.],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 2

[5,1,3,4,6,7,2,8] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 3

[8,2,4,1,7,3,5,6] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[3,6,1,4,2,8,7,5] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[1,6,8,4,3,7,2,5] => [.,[[[[.,[.,.]],.],[.,.]],[.,.]]] => [1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 3

[3,1,4,7,8,5,2,6] => [[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3

[4,8,2,3,1,5,7,6] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[1,7,8,4,2,3,6,5] => [.,[[[.,[.,.]],.],[.,[[.,.],.]]]] => [1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 4

[4,7,1,3,8,2,6,5] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[1,4,7,3,6,2,8,5] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 3

[5,8,2,6,4,3,1,7] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[7,2,5,8,4,3,1,6] => [[[.,.],[[[.,[.,.]],.],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => 2

[3,8,4,5,6,2,1,7] => [[[.,[[.,.],[.,[.,.]]]],.],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2

[2,4,3,5,7,8,1,6] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[7,3,8,1,2,6,4,5] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[7,1,4,5,3,2,6,8] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[4,3,8,1,5,7,2,6] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[5,8,3,7,4,1,6,2] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[5,7,1,4,8,6,3,2] => [[.,[.,.]],[[[.,[[.,.],.]],.],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 2

[3,5,7,4,8,6,2,1] => [[[.,[[.,[.,.]],[[.,.],.]]],.],.] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 1

[7,5,8,4,1,6,3,2] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[2,7,8,4,5,1,6,3] => [[.,[[.,[.,.]],[.,.]]],[[.,.],.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2

[5,7,3,8,4,1,6,2] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[5,6,3,8,1,4,7,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[3,7,8,4,1,6,5,2] => [[.,[[.,[.,.]],.]],[[[.,.],.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2

[3,6,2,1,5,4,8,7] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[2,5,8,1,7,4,3,6] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[6,8,2,7,4,3,1,5] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[6,8,2,3,7,5,1,4] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[4,2,3,7,1,5,8,6] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[2,1,5,8,4,3,7,6] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3

[5,8,4,2,6,7,1,3] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[3,2,4,8,1,5,7,6] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[2,4,8,3,1,7,5,6] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[4,8,3,2,1,7,6,5] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2

[4,1,3,7,2,6,8,5] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3

[3,4,8,2,1,6,5,7] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[6,8,3,7,2,1,5,4] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[3,5,8,1,7,2,6,4] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[5,3,7,1,8,2,6,4] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[3,4,1,8,6,2,7,5] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[8,6,7,5,1,3,2,4] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[2,7,8,4,5,1,3,6] => [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[3,4,8,1,5,2,7,6] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[4,8,1,2,5,3,6,7] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5

[5,8,4,7,6,3,2,1] => [[[[[.,[.,.]],[[.,.],.]],.],.],.] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 1

[6,8,5,4,7,3,2,1] => [[[[[[.,[.,.]],.],[.,.]],.],.],.] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1

[7,5,8,4,6,3,1,2] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[7,6,8,2,5,1,4,3] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[3,5,2,4,7,6,1,8] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[3,5,7,4,6,1,8,2] => [[.,[[.,[.,.]],[.,.]]],[[.,.],.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2

[3,5,7,4,6,1,2,8] => [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[3,5,7,4,6,2,1,8] => [[[.,[[.,[.,.]],[.,.]]],.],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 2

[3,2,5,7,4,6,1,8] => [[[.,.],[[.,[.,.]],[.,.]]],[.,.]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[3,5,2,7,6,4,1,8] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[3,5,7,2,6,4,1,8] => [[[.,[.,[.,.]]],[[.,.],.]],[.,.]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[3,5,7,2,6,1,4,8] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[3,5,2,7,6,1,4,8] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[3,5,7,1,2,6,8,4] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[3,5,7,2,1,6,8,4] => [[[.,[.,[.,.]]],.],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[3,5,2,7,1,6,4,8] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,5,7,2,1,6,4,8] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[5,3,7,1,6,2,4,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[3,5,7,1,4,6,8,2] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[3,5,7,1,4,6,2,8] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[3,5,7,1,4,2,6,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[3,5,7,2,1,4,6,8] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[3,5,2,7,1,4,6,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[3,2,5,7,4,1,6,8] => [[[.,.],[[.,[.,.]],.]],[.,[.,.]]] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[3,5,2,7,4,1,6,8] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[3,5,7,4,2,1,6,8] => [[[.,[[.,[.,.]],.]],.],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 3

[3,5,7,4,1,2,6,8] => [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4

[3,5,4,7,1,2,6,8] => [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[3,5,7,4,1,2,8,6] => [[.,[[.,[.,.]],.]],[.,[[.,.],.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 3

[3,5,7,4,2,1,8,6] => [[[.,[[.,[.,.]],.]],.],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 2

[3,2,5,7,4,1,8,6] => [[[.,.],[[.,[.,.]],.]],[[.,.],.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[3,2,5,7,1,4,8,6] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[3,5,2,7,1,4,8,6] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[3,5,7,2,1,4,8,6] => [[[.,[.,[.,.]]],.],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[3,5,7,1,4,2,8,6] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[3,7,2,5,1,8,6,4] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[3,7,2,5,1,8,4,6] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,8,3,4,1,7,6,2] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[4,3,5,6,8,1,7,2] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[5,7,8,2,4,1,6,3] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[4,2,5,8,1,6,7,3] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[4,2,5,8,1,7,3,6] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,8,2,4,1,6,3,7] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,2,6,8,1,5,4,7] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,2,6,7,1,5,4,8] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[7,2,8,1,5,3,6,4] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[7,2,4,1,8,3,6,5] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[2,5,1,8,7,4,3,6] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[8,1,4,6,3,5,2,7] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[1,6,8,3,4,5,7,2] => [.,[[[.,[.,.]],[.,[.,[.,.]]]],.]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2

[5,7,4,8,6,1,3,2] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[6,8,2,3,1,7,5,4] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[8,3,7,2,1,5,6,4] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[5,7,8,2,4,3,1,6] => [[[.,[.,[.,.]]],[[.,.],.]],[.,.]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[8,4,7,3,2,6,1,5] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[3,2,5,7,4,8,1,6] => [[[.,.],[[.,[.,.]],[.,.]]],[.,.]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[2,8,5,6,7,1,4,3] => [[.,[[.,.],[.,[.,.]]]],[[.,.],.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[2,6,8,5,1,4,7,3] => [[.,[[.,[.,.]],.]],[[.,[.,.]],.]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 2

[3,5,1,6,8,7,2,4] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3

[7,3,4,2,5,8,6,1] => [[[[.,.],[.,.]],[.,[[.,.],.]]],.] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[8,1,4,5,2,6,7,3] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3

[8,5,6,2,1,3,7,4] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[7,3,5,2,4,6,1,8] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[5,3,7,2,4,6,1,8] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[5,7,3,2,4,6,1,8] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[5,7,3,2,1,4,6,8] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4

[5,7,3,2,4,1,6,8] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[3,7,2,5,4,1,6,8] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[7,1,3,5,2,4,6,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[5,1,3,7,2,4,6,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[5,7,3,1,2,4,6,8] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 5

[1,3,7,2,5,4,6,8] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 5

[3,2,5,1,4,7,6,8] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[5,7,1,3,2,4,6,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[3,7,1,5,2,4,6,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[3,7,1,2,5,4,6,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5

[3,7,2,1,5,4,6,8] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[6,8,5,1,2,7,4,3] => [[[.,[.,.]],.],[.,[[[.,.],.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 3

[2,8,1,4,7,6,5,3] => [[.,[.,.]],[[.,[[[.,.],.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 2

[8,5,6,3,7,4,2,1] => [[[[[.,.],[.,.]],[[.,.],.]],.],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

[8,5,6,2,7,4,3,1] => [[[[.,.],[.,.]],[[[.,.],.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1

[3,5,1,4,8,2,7,6] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[2,5,1,4,8,7,3,6] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3

[1,5,6,4,8,7,2,3] => [.,[[[.,[.,.]],[[.,.],.]],[.,.]]] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 3

[7,2,3,1,5,8,6,4] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[7,1,5,6,3,8,4,2] => [[.,.],[[[.,[.,.]],[[.,.],.]],.]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2

[1,5,6,4,8,3,7,2] => [.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 2

[3,5,6,8,2,1,7,4] => [[[.,[.,[.,[.,.]]]],.],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[3,5,6,8,1,7,2,4] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,5,3,1,7,2,8,6] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[3,5,7,1,8,4,2,6] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[4,3,6,1,2,7,5,8] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[5,1,3,4,2,6,7,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[4,2,6,1,3,7,5,8] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[4,6,2,7,1,3,5,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[3,6,1,7,2,5,8,4] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[6,2,4,5,1,8,3,7] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,6,8,1,4,5,7,3] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[1,6,7,5,8,2,3,4] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 4

[5,8,1,4,3,6,2,7] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[5,8,4,1,3,7,6,2] => [[[.,[.,.]],.],[[.,[[.,.],.]],.]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 2

[6,4,5,3,8,1,7,2] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[4,3,5,7,2,1,6,8] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[3,4,6,2,5,8,7,1] => [[[.,[.,[.,.]]],[.,[[.,.],.]]],.] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[1,3,7,2,6,5,8,4] => [.,[[.,[.,.]],[[[.,.],[.,.]],.]]] => [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 3

[3,2,6,7,8,1,4,5] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[3,4,8,1,7,6,2,5] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[6,7,4,8,5,1,3,2] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[6,4,8,3,1,7,5,2] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[5,7,4,8,2,6,3,1] => [[[[.,[.,.]],[.,.]],[[.,.],.]],.] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 1

[5,6,4,8,2,7,3,1] => [[[[.,[.,.]],[.,.]],[[.,.],.]],.] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 1

[5,6,8,3,1,7,4,2] => [[[.,[.,[.,.]]],.],[[[.,.],.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[5,3,8,1,7,2,6,4] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[6,4,8,1,3,7,5,2] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[7,8,4,2,5,3,1,6] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[4,2,7,8,5,3,1,6] => [[[.,.],[[[.,[.,.]],.],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => 2

[8,4,6,3,1,7,5,2] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[6,3,5,2,8,7,4,1] => [[[[.,.],[.,.]],[[[.,.],.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1

[6,3,5,2,7,4,1,8] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[4,5,7,2,6,3,1,8] => [[[.,[.,[.,.]]],[[.,.],.]],[.,.]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[1,4,7,3,5,2,6,8] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 4

[5,7,4,2,6,3,1,8] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[2,4,5,8,1,6,7,3] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[3,2,6,8,1,5,7,4] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[8,2,6,1,5,4,7,3] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[7,6,8,3,1,5,4,2] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[6,3,7,2,8,1,5,4] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[1,6,8,5,2,4,3,7] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 4

[4,5,7,2,8,1,6,3] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[4,5,6,8,3,1,7,2] => [[[.,[.,[.,[.,.]]]],.],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[4,5,3,1,7,2,6,8] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[7,8,1,2,4,3,6,5] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4

[6,1,3,4,2,8,5,7] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[5,2,4,1,3,7,8,6] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[4,7,2,8,5,6,3,1] => [[[.,[.,.]],[[[.,.],[.,.]],.]],.] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 1

[3,6,8,5,7,4,1,2] => [[.,[[[.,[.,.]],[.,.]],.]],[.,.]] => [1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2

[4,6,7,2,5,3,1,8] => [[[.,[.,[.,.]]],[[.,.],.]],[.,.]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[2,4,7,8,1,6,5,3] => [[.,[.,[.,[.,.]]]],[[[.,.],.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[2,6,8,4,1,7,5,3] => [[.,[[.,[.,.]],.]],[[[.,.],.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2

[4,6,7,1,2,8,5,3] => [[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[3,6,1,8,2,7,5,4] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[5,7,4,1,2,8,6,3] => [[[.,[.,.]],.],[.,[[[.,.],.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 3

[6,3,7,1,2,8,5,4] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[1,7,8,5,4,3,2,6] => [.,[[[[[.,[.,.]],.],.],.],[.,.]]] => [1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 3

[1,2,6,7,8,4,3,5] => [.,[.,[[[.,[.,[.,.]]],.],[.,.]]]] => [1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 4

[8,1,4,6,7,3,5,2] => [[.,.],[[[.,[.,[.,.]]],[.,.]],.]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2

[4,7,1,3,6,8,2,5] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[1,3,6,7,4,2,8,5] => [.,[[.,[[.,[.,.]],.]],[[.,.],.]]] => [1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 3

[8,1,6,7,5,3,2,4] => [[.,.],[[[[.,[.,.]],.],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => 3

[1,7,8,2,6,4,5,3] => [.,[[.,[.,.]],[[[.,.],[.,.]],.]]] => [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 3

[3,7,8,2,1,6,5,4] => [[[.,[.,[.,.]]],.],[[[.,.],.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[4,8,1,2,3,7,5,6] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 5

[3,5,8,4,7,2,6,1] => [[[.,[[.,[.,.]],[.,.]]],[.,.]],.] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[2,5,8,4,7,3,6,1] => [[.,[[[.,[.,.]],[.,.]],[.,.]]],.] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1

[4,5,8,1,7,6,2,3] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[3,5,8,4,7,1,6,2] => [[.,[[.,[.,.]],[.,.]]],[[.,.],.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2

[1,5,8,4,7,3,6,2] => [.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 2

[7,2,3,1,8,6,4,5] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[7,2,3,4,1,6,8,5] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[7,2,3,1,5,6,8,4] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[7,2,3,8,1,6,5,4] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[1,5,8,4,7,6,2,3] => [.,[[[.,[.,.]],[[.,.],.]],[.,.]]] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 3

[3,5,8,1,6,7,2,4] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[7,1,3,8,2,6,5,4] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3

[4,3,7,1,6,5,8,2] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[5,4,8,1,6,2,7,3] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[4,3,7,2,6,1,8,5] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[4,3,7,1,5,2,8,6] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[4,3,7,1,6,2,8,5] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[5,4,8,2,6,3,7,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[5,4,8,1,6,3,7,2] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[4,1,7,8,6,3,2,5] => [[.,.],[[[[.,[.,.]],.],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => 3

[1,2,6,8,3,7,4,5] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => [1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 5

[6,8,3,2,1,4,7,5] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 3

[7,2,4,1,6,5,8,3] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[7,5,8,4,3,1,6,2] => [[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[6,8,2,4,1,3,7,5] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[4,5,2,6,8,3,7,1] => [[[.,[.,.]],[[.,[.,.]],[.,.]]],.] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 1

[6,8,5,3,4,7,2,1] => [[[[[.,[.,.]],.],[.,[.,.]]],.],.] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1

[6,8,4,1,5,3,7,2] => [[[.,[.,.]],.],[[[.,.],[.,.]],.]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[6,8,3,5,1,4,7,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[6,8,5,4,2,3,7,1] => [[[[[.,[.,.]],.],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1

[8,1,3,4,2,6,5,7] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[8,1,2,4,5,3,7,6] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 4

[7,4,5,1,6,2,8,3] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[4,7,3,5,6,2,8,1] => [[[[.,[.,.]],[.,[.,.]]],[.,.]],.] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[6,7,8,4,1,3,5,2] => [[[.,[.,[.,.]]],.],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[3,1,6,8,4,7,5,2] => [[.,.],[[[.,[.,.]],[[.,.],.]],.]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2

[8,3,6,1,5,7,4,2] => [[[.,.],[.,.]],[[[.,[.,.]],.],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[2,5,4,7,8,1,6,3] => [[.,[[.,.],[.,[.,.]]]],[[.,.],.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[2,4,6,7,8,1,5,3] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[2,4,6,8,1,7,5,3] => [[.,[.,[.,[.,.]]]],[[[.,.],.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[2,4,7,8,3,5,6,1] => [[.,[[.,[.,[.,.]]],[.,[.,.]]]],.] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1

[3,2,6,8,1,7,4,5] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,3,6,2,1,8,5,7] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[4,6,2,3,7,5,8,1] => [[[.,[.,.]],[.,[[.,.],[.,.]]]],.] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 1

[5,8,4,2,3,6,7,1] => [[[[.,[.,.]],.],[.,[.,[.,.]]]],.] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1

[8,4,5,3,2,1,7,6] => [[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[5,8,3,4,2,1,7,6] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[6,4,8,3,2,7,1,5] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[5,8,3,7,2,1,6,4] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[2,5,6,4,7,1,8,3] => [[.,[[.,[.,.]],[.,.]]],[[.,.],.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2

[6,4,7,3,8,2,1,5] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[6,7,4,3,2,1,8,5] => [[[[[.,[.,.]],.],.],.],[[.,.],.]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2

[5,6,3,4,8,7,2,1] => [[[[.,[.,.]],[.,[[.,.],.]]],.],.] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 1

[5,8,1,2,3,4,7,6] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 5

[1,6,8,2,4,5,7,3] => [.,[[.,[.,.]],[[.,[.,[.,.]]],.]]] => [1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 3

[5,8,3,7,4,6,2,1] => [[[[.,[.,.]],[[.,.],[.,.]]],.],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 1

[2,3,4,6,8,5,7,1] => [[.,[.,[.,[[.,[.,.]],[.,.]]]]],.] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1

[2,3,5,7,4,8,6,1] => [[.,[.,[[.,[.,.]],[[.,.],.]]]],.] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 1

[2,4,6,3,7,8,5,1] => [[.,[[.,[.,.]],[[.,[.,.]],.]]],.] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 1

[2,5,7,1,8,6,3,4] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[8,2,4,5,1,3,7,6] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[2,6,7,1,8,4,5,3] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[5,8,3,1,4,2,6,7] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[2,4,1,8,5,6,3,7] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[3,5,2,6,7,8,4,1] => [[[.,[.,.]],[[.,[.,[.,.]]],.]],.] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[4,5,1,6,7,3,8,2] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2

[5,2,6,8,1,7,4,3] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[5,7,3,2,6,8,1,4] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[6,7,1,2,3,5,8,4] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 4

[3,1,6,7,8,4,2,5] => [[.,.],[[[.,[.,[.,.]]],.],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => 3

[8,2,4,5,7,3,1,6] => [[[.,.],[[.,[.,[.,.]]],.]],[.,.]] => [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => 2

[8,3,6,1,5,4,2,7] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[3,6,1,8,7,5,4,2] => [[.,[.,.]],[[[[[.,.],.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2

[3,8,1,5,7,6,4,2] => [[.,[.,.]],[[[.,[[.,.],.]],.],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 2

[3,5,2,8,7,6,4,1] => [[[.,[.,.]],[[[[.,.],.],.],.]],.] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1

[3,4,8,2,7,6,5,1] => [[[.,[.,[.,.]]],[[[.,.],.],.]],.] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1

[8,2,7,1,4,5,6,3] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[3,8,2,4,7,6,5,1] => [[[.,[.,.]],[.,[[[.,.],.],.]]],.] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 1

[8,2,3,7,1,6,5,4] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[8,2,7,1,3,6,5,4] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[8,2,4,1,7,6,5,3] => [[[.,.],[.,.]],[[[[.,.],.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[4,8,2,1,7,6,5,3] => [[[.,[.,.]],.],[[[[.,.],.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2

[5,8,1,3,7,6,2,4] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3

[4,8,1,3,7,6,5,2] => [[.,[.,.]],[[.,[[[.,.],.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 2

[4,3,8,1,7,6,5,2] => [[[.,.],[.,.]],[[[[.,.],.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[6,5,7,2,4,3,1,8] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[5,7,1,3,2,8,6,4] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[5,8,1,3,2,7,4,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[7,5,8,2,1,4,3,6] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[6,7,1,2,5,4,8,3] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 3

[6,8,1,2,5,7,4,3] => [[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 3

[1,7,8,2,3,5,6,4] => [.,[[.,[.,.]],[.,[[.,[.,.]],.]]]] => [1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 4

[7,5,8,2,3,1,4,6] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[6,2,8,1,5,7,3,4] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[6,7,4,2,1,8,5,3] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2

[6,7,3,2,1,8,5,4] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2

[6,5,8,1,7,3,4,2] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[6,5,8,2,3,7,4,1] => [[[[.,.],[.,.]],[.,[[.,.],.]]],.] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[3,5,8,2,6,1,7,4] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[2,7,1,5,8,4,3,6] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[6,7,8,4,2,5,3,1] => [[[[.,[.,[.,.]]],.],[[.,.],.]],.] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1

[6,1,2,5,7,8,4,3] => [[.,.],[.,[[[.,[.,[.,.]]],.],.]]] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => 3

[4,1,2,7,8,5,3,6] => [[.,.],[.,[[[.,[.,.]],.],[.,.]]]] => [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => 4

[4,7,3,1,2,6,8,5] => [[[.,[.,.]],.],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 3

[4,2,7,1,3,8,6,5] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[5,6,2,7,3,4,8,1] => [[[.,[.,.]],[[.,.],[.,[.,.]]]],.] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 1

[2,4,6,1,5,7,3,8] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[4,7,2,3,1,6,8,5] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[6,7,3,1,5,4,8,2] => [[[.,[.,.]],.],[[[.,.],[.,.]],.]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[7,4,6,2,8,3,5,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[7,3,5,1,4,8,2,6] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[4,3,8,2,6,7,5,1] => [[[[.,.],[.,.]],[[.,[.,.]],.]],.] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[4,2,6,1,5,3,8,7] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[6,7,2,3,1,5,8,4] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[4,5,1,7,6,3,8,2] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2

[4,5,1,6,2,8,7,3] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[4,8,3,6,1,7,2,5] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,2,7,8,3,4,5,1] => [[[.,.],[[.,[.,.]],[.,[.,.]]]],.] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1

[1,2,4,6,8,5,7,3] => [.,[.,[[.,[[.,[.,.]],[.,.]]],.]]] => [1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 3

[4,7,3,8,6,5,2,1] => [[[[.,[.,.]],[[[.,.],.],.]],.],.] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 1

[4,6,7,8,5,2,3,1] => [[[.,[[.,[.,[.,.]]],.]],[.,.]],.] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[4,5,3,8,2,7,6,1] => [[[[.,[.,.]],[.,.]],[[.,.],.]],.] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 1

[6,4,7,2,5,8,3,1] => [[[[.,.],[.,.]],[[.,[.,.]],.]],.] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[6,8,4,3,5,7,1,2] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[3,2,4,5,1,8,6,7] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,2,5,1,7,8,3,6] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[1,4,5,3,8,2,6,7] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 4

[4,8,3,1,6,7,2,5] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[3,4,8,2,6,5,7,1] => [[[.,[.,[.,.]]],[[.,.],[.,.]]],.] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[3,6,2,4,8,7,1,5] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[4,7,3,2,6,8,1,5] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[7,3,4,6,8,1,2,5] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[3,6,7,2,5,8,1,4] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[1,5,6,8,3,7,2,4] => [.,[[[.,[.,[.,.]]],[.,.]],[.,.]]] => [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[6,1,5,8,3,4,7,2] => [[.,.],[[[.,[.,.]],[.,[.,.]]],.]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[5,6,8,1,3,4,7,2] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[6,8,1,3,5,4,7,2] => [[.,[.,.]],[[.,[[.,.],[.,.]]],.]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 2

[7,1,2,5,8,4,6,3] => [[.,.],[.,[[[.,[.,.]],[.,.]],.]]] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 3

[6,2,4,8,1,7,3,5] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,1,7,8,5,4,6,2] => [[.,.],[[[[.,[.,.]],.],[.,.]],.]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 2

[2,7,1,8,4,3,5,6] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[6,7,1,8,3,2,4,5] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[2,7,5,6,8,1,3,4] => [[.,[[.,.],[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[6,7,2,8,1,3,4,5] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[7,4,6,8,5,3,1,2] => [[[[.,.],[[.,[.,.]],.]],.],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => 2

[4,6,2,5,7,1,8,3] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[1,6,8,3,2,5,4,7] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 4

[2,6,8,1,5,4,7,3] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[6,1,5,8,3,2,7,4] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3

[2,5,8,4,6,3,1,7] => [[.,[[[.,[.,.]],[.,.]],.]],[.,.]] => [1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2

[2,4,8,3,7,1,5,6] => [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[5,7,1,3,2,4,8,6] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[4,7,8,3,2,5,1,6] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[5,1,6,8,3,7,4,2] => [[.,.],[[[.,[.,.]],[[.,.],.]],.]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2

[8,2,3,7,1,4,5,6] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[2,8,3,7,1,4,5,6] => [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[5,6,2,7,4,3,1,8] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[3,7,8,5,2,1,4,6] => [[[.,[[.,[.,.]],.]],.],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 3

[6,8,4,7,3,1,5,2] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[3,4,5,1,7,6,8,2] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[8,4,6,7,1,2,5,3] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[5,7,2,6,1,8,4,3] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[5,7,2,6,1,3,8,4] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[5,8,2,6,1,4,7,3] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[6,8,4,7,2,1,5,3] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[4,8,2,1,3,5,6,7] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 5

[2,6,7,3,4,8,1,5] => [[.,[[.,[.,.]],[.,[.,.]]]],[.,.]] => [1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2

[2,1,5,7,4,3,8,6] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3

[7,4,6,1,2,3,8,5] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[1,7,8,6,2,3,5,4] => [.,[[[.,[.,.]],.],[.,[[.,.],.]]]] => [1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 4

[3,5,8,1,7,6,2,4] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[2,8,1,3,6,7,5,4] => [[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 3

[5,8,4,3,1,6,7,2] => [[[[.,[.,.]],.],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 2

[4,2,8,1,5,7,6,3] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[6,3,7,2,5,4,8,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[5,4,7,3,2,6,8,1] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1

[5,7,2,6,3,4,8,1] => [[[.,[.,.]],[[.,.],[.,[.,.]]]],.] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 1

[6,8,3,2,1,7,4,5] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[4,8,1,7,5,3,2,6] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[7,2,8,1,6,4,3,5] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[2,5,6,3,1,4,8,7] => [[.,[[.,[.,.]],.]],[.,[[.,.],.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 3

[2,4,7,8,5,3,1,6] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => [1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 2

[2,1,4,7,8,5,3,6] => [[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3

[8,5,6,7,3,1,4,2] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[3,8,5,6,7,1,2,4] => [[.,[[.,.],[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[2,5,8,1,4,6,7,3] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[7,8,3,4,1,6,5,2] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[8,4,5,2,3,7,1,6] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[4,7,2,8,6,3,1,5] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[4,6,3,8,7,5,1,2] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[2,5,8,3,7,1,6,4] => [[.,[[.,[.,.]],[.,.]]],[[.,.],.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2

[1,4,6,2,8,7,5,3] => [.,[[.,[.,.]],[[[[.,.],.],.],.]]] => [1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 3

[7,8,2,4,1,6,5,3] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[2,4,6,1,8,7,5,3] => [[.,[.,[.,.]]],[[[[.,.],.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[3,5,8,2,7,6,1,4] => [[[.,[.,[.,.]]],[[.,.],.]],[.,.]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[1,3,8,2,5,7,6,4] => [.,[[.,[.,.]],[[.,[[.,.],.]],.]]] => [1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 3

[2,3,8,1,5,7,6,4] => [[.,[.,[.,.]]],[[.,[[.,.],.]],.]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[2,6,1,8,7,5,3,4] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[3,2,8,1,5,7,6,4] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[2,8,1,4,5,7,6,3] => [[.,[.,.]],[[.,[.,[[.,.],.]]],.]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 2

[7,8,2,1,4,6,5,3] => [[[.,[.,.]],.],[[.,[[.,.],.]],.]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 2

[6,1,4,5,7,2,3,8] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[8,3,6,1,5,7,2,4] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[8,4,6,3,1,2,5,7] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[6,8,1,4,5,2,3,7] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[1,5,8,4,6,2,3,7] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 4

[5,6,8,1,4,2,3,7] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[5,7,4,8,1,2,3,6] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[4,7,8,1,2,6,3,5] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[3,7,1,6,2,4,8,5] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[1,6,8,5,7,2,3,4] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 4

[3,1,2,7,8,4,6,5] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 4

[5,7,8,1,2,6,3,4] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[7,1,6,8,5,2,3,4] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[7,8,6,1,5,2,3,4] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[7,8,6,3,1,5,2,4] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[7,8,1,3,4,5,2,6] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[7,6,8,4,1,5,3,2] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[6,4,7,3,2,5,1,8] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[6,4,5,7,8,1,3,2] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[4,8,2,5,3,7,1,6] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[5,7,8,4,6,3,2,1] => [[[[[.,[.,[.,.]]],[.,.]],.],.],.] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1

[6,8,1,2,7,4,3,5] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 4

[5,6,1,3,2,4,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[2,5,1,3,7,8,6,4] => [[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 3

[4,3,7,2,1,8,6,5] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[4,6,7,2,1,3,5,8] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[4,6,2,3,1,5,7,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[3,6,2,7,5,4,1,8] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[2,5,7,3,4,1,6,8] => [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[2,4,7,3,8,6,5,1] => [[.,[[.,[.,.]],[[[.,.],.],.]]],.] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 1

[3,4,2,7,5,8,6,1] => [[[.,[.,.]],[[.,.],[[.,.],.]]],.] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 1

[4,5,7,2,3,1,8,6] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[3,7,8,1,4,6,5,2] => [[.,[.,[.,.]]],[[.,[[.,.],.]],.]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[6,2,4,7,1,3,8,5] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[7,3,5,1,4,2,8,6] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[5,4,7,1,3,2,8,6] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[4,7,3,6,1,2,8,5] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[7,6,8,2,5,3,4,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[2,3,6,1,8,7,5,4] => [[.,[.,[.,.]]],[[[[.,.],.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[5,7,8,2,3,6,1,4] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[4,7,3,1,8,5,6,2] => [[[.,[.,.]],.],[[[.,.],[.,.]],.]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[2,6,7,5,3,4,8,1] => [[.,[[[.,[.,.]],.],[.,[.,.]]]],.] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 1

[6,1,4,5,8,3,7,2] => [[.,.],[[[.,[.,[.,.]]],[.,.]],.]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2

[4,1,5,6,8,3,7,2] => [[.,.],[[[.,[.,[.,.]]],[.,.]],.]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2

[4,5,7,2,6,8,1,3] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[4,2,7,8,6,1,3,5] => [[[.,.],[[.,[.,.]],.]],[.,[.,.]]] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[7,4,6,8,5,2,3,1] => [[[[.,.],[[.,[.,.]],.]],[.,.]],.] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[5,2,6,7,8,1,3,4] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[4,5,6,8,1,2,7,3] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[4,5,3,8,1,7,2,6] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,5,8,4,1,7,2,6] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[2,5,7,4,6,1,3,8] => [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[6,7,2,4,1,3,8,5] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[1,3,8,2,5,6,7,4] => [.,[[.,[.,.]],[[.,[.,[.,.]]],.]]] => [1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 3

[7,6,8,3,5,4,2,1] => [[[[[.,.],[.,.]],[[.,.],.]],.],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

[1,6,7,3,8,5,4,2] => [.,[[[.,[.,.]],[[[.,.],.],.]],.]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 2

[7,3,4,8,1,6,5,2] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[7,8,6,5,2,4,3,1] => [[[[[.,[.,.]],.],.],[[.,.],.]],.] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 1

[3,6,7,5,2,8,4,1] => [[[.,[[.,[.,.]],.]],[[.,.],.]],.] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[5,4,6,7,8,1,3,2] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[5,3,6,7,8,1,4,2] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[4,5,7,3,6,2,8,1] => [[[[.,[.,[.,.]]],[.,.]],[.,.]],.] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[4,5,6,3,8,2,7,1] => [[[[.,[.,[.,.]]],[.,.]],[.,.]],.] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[2,5,4,7,8,1,3,6] => [[.,[[.,.],[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[8,2,4,7,3,5,6,1] => [[[.,.],[[.,[.,.]],[.,[.,.]]]],.] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1

[4,5,6,2,7,3,8,1] => [[[.,[.,[.,.]]],[[.,.],[.,.]]],.] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[7,4,6,1,5,2,8,3] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[5,4,6,2,8,3,7,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[8,4,6,1,7,2,5,3] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[4,5,6,3,7,1,8,2] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[2,5,7,4,3,1,6,8] => [[.,[[[.,[.,.]],.],.]],[.,[.,.]]] => [1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 3

[5,3,4,2,7,1,6,8] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[4,2,5,1,3,8,7,6] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[4,3,5,1,2,7,6,8] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[3,7,2,4,1,6,5,8] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,5,4,6,1,3,7,8] => [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[2,5,6,4,1,3,7,8] => [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4

[7,1,5,6,3,2,4,8] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[2,4,1,6,5,3,7,8] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[6,1,4,5,3,2,7,8] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[5,8,3,1,7,6,4,2] => [[[.,[.,.]],.],[[[[.,.],.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2

[5,6,3,8,7,4,1,2] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[5,2,3,1,4,8,6,7] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[5,1,3,4,2,8,6,7] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[4,7,3,2,8,5,1,6] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[4,3,7,2,8,5,6,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[5,3,4,1,2,8,6,7] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[5,2,3,4,1,8,6,7] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,8,1,3,4,5,7,2] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2

[3,1,7,8,2,5,4,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[7,2,6,8,4,3,1,5] => [[[.,.],[[[.,[.,.]],.],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => 2

[3,7,2,8,6,5,1,4] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[3,6,7,5,1,2,4,8] => [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4

[7,4,5,1,8,2,3,6] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[7,2,3,1,8,4,5,6] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[2,1,4,8,3,7,5,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[4,8,1,6,7,3,2,5] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[1,2,7,8,4,3,6,5] => [.,[.,[[[.,[.,.]],.],[[.,.],.]]]] => [1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 4

[4,8,1,3,5,6,2,7] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[5,3,7,8,4,2,6,1] => [[[[.,.],[[.,[.,.]],.]],[.,.]],.] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[6,3,7,8,2,4,5,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1

[3,5,4,6,7,1,8,2] => [[.,[[.,.],[.,[.,.]]]],[[.,.],.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[2,5,1,4,3,8,7,6] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[4,8,1,3,2,6,5,7] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[8,3,5,1,2,6,4,7] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[8,3,5,7,4,1,2,6] => [[[.,.],[[.,[.,.]],.]],[.,[.,.]]] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[6,8,5,4,1,3,7,2] => [[[[.,[.,.]],.],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 2

[6,8,4,1,5,2,7,3] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[6,8,2,1,7,5,3,4] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[5,8,4,6,1,2,7,3] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[4,5,2,1,8,6,7,3] => [[[.,[.,.]],.],[[[.,.],[.,.]],.]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[4,5,8,3,1,6,7,2] => [[[.,[.,[.,.]]],.],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[5,7,2,8,4,6,1,3] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[6,7,3,2,4,8,5,1] => [[[[.,[.,.]],.],[.,[[.,.],.]]],.] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 1

[5,2,7,8,4,1,3,6] => [[[.,.],[[.,[.,.]],.]],[.,[.,.]]] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[2,7,8,6,4,1,3,5] => [[.,[[[.,[.,.]],.],.]],[.,[.,.]]] => [1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 3

[6,8,5,1,7,3,2,4] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[1,6,8,3,7,4,2,5] => [.,[[[.,[.,.]],[[.,.],.]],[.,.]]] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 3

[3,5,2,6,4,8,1,7] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[3,5,2,4,8,1,7,6] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[6,3,8,2,4,1,7,5] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[4,6,3,8,7,5,2,1] => [[[[.,[.,.]],[[[.,.],.],.]],.],.] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 1

[6,8,4,2,1,7,5,3] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2

[3,1,7,8,6,4,2,5] => [[.,.],[[[[.,[.,.]],.],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => 3

[3,8,1,7,6,2,5,4] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[1,5,6,3,8,2,4,7] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 4

[2,6,7,4,3,8,5,1] => [[.,[[[.,[.,.]],.],[[.,.],.]]],.] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 1

[5,2,4,7,3,8,6,1] => [[[.,.],[[.,[.,.]],[[.,.],.]]],.] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1

[8,3,7,2,5,1,6,4] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[3,7,2,8,1,5,4,6] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,2,6,1,5,8,4,7] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[7,2,8,1,4,3,6,5] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[1,7,8,3,2,6,5,4] => [.,[[[.,[.,.]],.],[[[.,.],.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 3

[1,7,4,5,6,8,2,3] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[2,5,8,4,6,1,7,3] => [[.,[[.,[.,.]],[.,.]]],[[.,.],.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2

[2,6,3,5,8,1,7,4] => [[.,[[.,.],[.,[.,.]]]],[[.,.],.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[5,8,4,6,1,3,7,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[8,3,5,7,2,6,4,1] => [[[[.,.],[.,[.,.]]],[[.,.],.]],.] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => 1

[2,4,6,8,5,3,7,1] => [[.,[[.,[[.,[.,.]],.]],[.,.]]],.] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[2,4,8,1,7,6,5,3] => [[.,[.,[.,.]]],[[[[.,.],.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[4,3,8,1,5,7,6,2] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[4,3,6,8,5,2,7,1] => [[[[.,.],[[.,[.,.]],.]],[.,.]],.] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[3,6,8,5,4,2,7,1] => [[[.,[[[.,[.,.]],.],.]],[.,.]],.] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1

[2,8,3,5,6,7,1,4] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[5,6,2,4,7,1,8,3] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[2,6,7,4,1,3,8,5] => [[.,[[.,[.,.]],.]],[.,[[.,.],.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 3

[6,5,7,4,1,3,8,2] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[2,4,6,3,5,7,8,1] => [[.,[[.,[.,.]],[.,[.,[.,.]]]]],.] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1

[2,3,6,1,5,7,8,4] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[4,3,6,2,5,7,8,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1

[4,6,1,2,5,7,8,3] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 3

[2,4,1,6,5,7,8,3] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 2

[4,7,3,1,8,6,5,2] => [[[.,[.,.]],.],[[[[.,.],.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2

[5,6,4,2,7,1,8,3] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[5,7,3,2,6,1,8,4] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[5,7,3,2,6,4,1,8] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[8,4,5,3,7,2,1,6] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[4,3,5,2,8,6,1,7] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[7,8,4,1,6,3,5,2] => [[[.,[.,.]],.],[[[.,.],[.,.]],.]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[3,4,2,8,7,5,1,6] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[7,5,8,4,1,3,6,2] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[6,4,7,1,3,2,8,5] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[7,5,8,1,6,3,2,4] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[7,4,6,1,3,2,5,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[8,4,5,7,2,6,1,3] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[4,5,2,6,7,3,1,8] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[4,3,5,1,6,7,8,2] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[3,6,7,5,1,2,8,4] => [[.,[[.,[.,.]],.]],[.,[[.,.],.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 3

[5,6,3,7,1,4,8,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[6,5,8,3,7,2,1,4] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[7,8,5,3,6,2,1,4] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[7,8,5,3,6,2,4,1] => [[[[[.,[.,.]],.],[.,.]],[.,.]],.] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1

[6,4,8,3,2,1,7,5] => [[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[5,2,3,6,1,4,8,7] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[7,2,3,4,5,8,1,6] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2

[7,2,8,1,5,3,4,6] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[4,8,2,5,7,3,1,6] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[5,8,2,3,4,7,1,6] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[6,3,4,7,8,2,1,5] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 2

[4,6,8,5,2,7,3,1] => [[[.,[[.,[.,.]],.]],[[.,.],.]],.] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[3,7,8,5,2,6,4,1] => [[[.,[[.,[.,.]],.]],[[.,.],.]],.] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[7,3,6,2,8,1,5,4] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[4,5,8,3,7,2,1,6] => [[[[.,[.,[.,.]]],[.,.]],.],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[3,7,2,8,4,5,1,6] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[3,5,1,8,4,6,2,7] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[4,6,2,7,8,3,1,5] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[4,6,1,3,8,2,5,7] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[4,3,6,2,1,8,7,5] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[3,6,4,5,8,2,1,7] => [[[.,[[.,.],[.,[.,.]]]],.],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2

[6,1,4,5,2,8,7,3] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3

[7,2,4,5,1,6,3,8] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,7,4,8,6,2,1,3] => [[[[.,[.,.]],[[.,.],.]],.],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2

[5,3,6,8,2,7,1,4] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,3,6,1,4,7,2,8] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[4,3,6,8,2,7,1,5] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,3,8,1,4,7,2,6] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[5,8,4,1,6,3,2,7] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[1,5,8,3,6,7,4,2] => [.,[[[.,[.,.]],[[.,[.,.]],.]],.]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 2

[7,8,4,1,6,5,2,3] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[6,3,8,1,5,7,2,4] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[5,1,3,4,7,8,2,6] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 3

[5,1,7,8,3,4,2,6] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[5,6,8,2,3,4,1,7] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[2,3,5,7,4,6,8,1] => [[.,[.,[[.,[.,.]],[.,[.,.]]]]],.] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1

[4,5,2,3,8,6,1,7] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[3,7,4,5,8,1,2,6] => [[.,[[.,.],[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[3,7,8,1,4,5,2,6] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[5,8,2,1,6,3,4,7] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[4,8,1,3,7,5,2,6] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3

[2,4,7,8,5,3,6,1] => [[.,[[.,[[.,[.,.]],.]],[.,.]]],.] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[3,7,8,4,1,5,2,6] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[1,3,6,8,5,4,2,7] => [.,[[.,[[[.,[.,.]],.],.]],[.,.]]] => [1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 3

[1,3,6,8,2,7,5,4] => [.,[[.,[.,[.,.]]],[[[.,.],.],.]]] => [1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3

[1,8,3,4,5,6,2,7] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[1,4,5,8,3,6,2,7] => [.,[[[.,[.,[.,.]]],[.,.]],[.,.]]] => [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[1,2,7,8,4,5,3,6] => [.,[.,[[[.,[.,.]],[.,.]],[.,.]]]] => [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 4

[1,4,7,3,2,6,8,5] => [.,[[[.,[.,.]],.],[[.,[.,.]],.]]] => [1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3

[1,5,7,3,6,2,8,4] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 3

[3,6,2,7,1,5,4,8] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[1,6,4,5,7,8,2,3] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[3,1,6,8,5,4,2,7] => [[.,.],[[[[.,[.,.]],.],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => 3

[5,3,8,2,7,6,1,4] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[7,8,5,2,1,6,4,3] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2

[4,5,1,8,6,7,3,2] => [[.,[.,.]],[[[[.,.],[.,.]],.],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 2

[4,7,1,5,6,2,8,3] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[3,8,4,5,6,7,2,1] => [[[.,[[.,.],[.,[.,[.,.]]]]],.],.] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1

[5,1,4,6,7,2,8,3] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[6,1,4,7,2,3,8,5] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[6,1,3,5,8,2,4,7] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[5,6,4,3,1,8,2,7] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[6,2,3,5,8,1,4,7] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[6,7,2,3,8,4,5,1] => [[[.,[.,.]],[.,[[.,.],[.,.]]]],.] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 1

[6,7,2,1,3,8,4,5] => [[[.,[.,.]],.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[5,7,4,1,8,3,2,6] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[6,7,1,3,8,4,5,2] => [[.,[.,.]],[[.,[[.,.],[.,.]]],.]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 2

[1,6,7,4,3,8,5,2] => [.,[[[[.,[.,.]],.],[[.,.],.]],.]] => [1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 2

[2,1,6,7,4,3,8,5] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3

[6,7,3,2,1,8,4,5] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[2,5,7,3,1,4,8,6] => [[.,[[.,[.,.]],.]],[.,[[.,.],.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 3

[6,7,3,2,8,4,5,1] => [[[[.,[.,.]],.],[[.,.],[.,.]]],.] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 1

[1,2,6,7,4,3,8,5] => [.,[.,[[[.,[.,.]],.],[[.,.],.]]]] => [1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 4

[2,7,1,8,4,6,3,5] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[6,7,1,8,4,5,3,2] => [[.,[.,.]],[[[[.,.],[.,.]],.],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 2

[8,2,5,7,1,4,6,3] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[8,2,4,7,1,5,6,3] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[8,2,3,4,7,1,5,6] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[8,4,6,7,5,1,2,3] => [[[.,.],[[.,[.,.]],.]],[.,[.,.]]] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[8,4,6,7,5,1,3,2] => [[[.,.],[[.,[.,.]],.]],[[.,.],.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[8,5,6,7,4,1,3,2] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[8,3,4,2,7,5,6,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[8,3,5,2,7,4,6,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[2,4,5,8,3,1,6,7] => [[.,[[.,[.,[.,.]]],.]],[.,[.,.]]] => [1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[7,8,3,2,5,4,6,1] => [[[[.,[.,.]],.],[[.,.],[.,.]]],.] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 1

[1,5,6,7,3,8,2,4] => [.,[[[.,[.,[.,.]]],[.,.]],[.,.]]] => [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[4,7,1,6,5,3,2,8] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[4,8,1,6,5,3,2,7] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[7,5,6,1,4,3,2,8] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[8,5,6,1,4,3,2,7] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[8,5,7,1,4,3,2,6] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[6,7,5,1,4,3,2,8] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[5,2,7,8,1,4,3,6] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,6,3,8,4,1,2,7] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[5,2,3,4,7,1,6,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[5,2,3,7,1,6,8,4] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[5,2,3,4,7,8,1,6] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2

[1,4,7,8,5,2,3,6] => [.,[[.,[[.,[.,.]],.]],[.,[.,.]]]] => [1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 4

[3,2,6,7,4,1,5,8] => [[[.,.],[[.,[.,.]],.]],[.,[.,.]]] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[5,8,3,7,6,4,1,2] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[3,6,7,1,4,2,5,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[7,8,1,5,4,2,3,6] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[3,4,6,8,1,5,7,2] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[6,8,1,7,5,4,2,3] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[7,1,3,6,8,2,4,5] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[1,2,5,7,8,4,6,3] => [.,[.,[[[.,[.,[.,.]]],[.,.]],.]]] => [1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 3

[6,7,4,1,3,2,8,5] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[1,6,3,5,7,8,2,4] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[1,5,3,4,7,8,2,6] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[5,1,4,6,7,8,2,3] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 3

[6,7,4,1,8,5,2,3] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[4,5,1,3,7,8,2,6] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[5,2,3,1,7,8,4,6] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[1,5,6,3,7,8,2,4] => [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 3

[3,7,2,8,6,4,5,1] => [[[.,[.,.]],[[[.,.],.],[.,.]]],.] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 1

[4,3,7,8,6,2,5,1] => [[[[.,.],[[.,[.,.]],.]],[.,.]],.] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[3,8,1,7,5,2,4,6] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[2,4,7,8,6,1,5,3] => [[.,[.,[[.,[.,.]],.]]],[[.,.],.]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 2

[8,2,4,6,3,7,5,1] => [[[.,.],[[.,[.,.]],[[.,.],.]]],.] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1

[4,5,3,8,2,1,7,6] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[1,4,6,2,7,5,3,8] => [.,[[.,[.,.]],[[[.,.],.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 4

[7,8,2,1,5,4,6,3] => [[[.,[.,.]],.],[[[.,.],[.,.]],.]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[5,2,3,7,8,1,6,4] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[4,7,8,1,6,5,3,2] => [[.,[.,[.,.]]],[[[[.,.],.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[7,3,8,1,6,5,4,2] => [[[.,.],[.,.]],[[[[.,.],.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[7,3,8,2,6,5,4,1] => [[[[.,.],[.,.]],[[[.,.],.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1

[2,4,1,8,7,3,6,5] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[3,5,1,7,8,2,6,4] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[5,4,7,8,2,1,6,3] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[6,4,7,1,5,3,2,8] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[3,4,6,2,1,8,5,7] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[4,5,7,2,1,6,3,8] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[5,6,4,8,3,2,1,7] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2

[5,7,4,8,2,1,6,3] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[5,7,4,2,6,3,8,1] => [[[[.,[.,.]],.],[[.,.],[.,.]]],.] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 1

[5,7,4,1,6,2,8,3] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[8,5,6,1,7,3,2,4] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[4,5,1,6,7,8,3,2] => [[.,[.,.]],[[[.,[.,[.,.]]],.],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2

[4,5,2,6,1,3,8,7] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[8,4,6,7,2,5,1,3] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[7,1,4,6,8,3,5,2] => [[.,.],[[[.,[.,[.,.]]],[.,.]],.]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2

[6,7,1,2,4,8,5,3] => [[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 3

[7,8,1,3,4,5,6,2] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2

[4,7,3,2,8,1,5,6] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[4,7,8,3,1,6,2,5] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[4,3,7,2,8,6,1,5] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[4,6,3,2,1,8,7,5] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2

[1,5,8,4,7,6,3,2] => [.,[[[[.,[.,.]],[[.,.],.]],.],.]] => [1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 2

[6,8,3,7,5,2,1,4] => [[[[.,[.,.]],[[.,.],.]],.],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2

[5,7,8,4,3,2,1,6] => [[[[[.,[.,[.,.]]],.],.],.],[.,.]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2

[4,5,3,2,8,6,1,7] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[3,2,7,8,5,4,1,6] => [[[.,.],[[[.,[.,.]],.],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => 2

[3,6,1,4,8,7,2,5] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3

[5,8,1,3,7,2,6,4] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[6,2,3,1,8,7,4,5] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[3,4,8,1,7,5,6,2] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[7,2,5,1,8,3,6,4] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[4,2,8,1,7,5,6,3] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[6,8,1,4,3,7,5,2] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2

[6,7,1,4,3,8,5,2] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2

[4,7,1,5,3,8,6,2] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2

[6,8,1,2,4,7,5,3] => [[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 3

[8,5,6,1,2,7,4,3] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[8,1,2,4,5,6,7,3] => [[.,.],[.,[[.,[.,[.,[.,.]]]],.]]] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 3

[4,6,7,2,1,8,3,5] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[3,7,1,8,2,5,4,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[4,6,7,1,5,3,8,2] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[4,6,7,2,1,8,5,3] => [[[.,[.,[.,.]]],.],[[[.,.],.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[4,2,5,6,7,8,3,1] => [[[.,.],[[.,[.,[.,[.,.]]]],.]],.] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 1

[4,1,3,5,6,7,8,2] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2

[3,7,8,4,5,1,6,2] => [[.,[[.,[.,.]],[.,.]]],[[.,.],.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2

[4,6,8,3,2,7,1,5] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[4,6,8,2,3,7,1,5] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[3,8,1,7,4,5,2,6] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[4,5,8,3,7,1,2,6] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[3,7,8,4,6,2,5,1] => [[[.,[[.,[.,.]],[.,.]]],[.,.]],.] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[3,6,1,5,7,8,2,4] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[3,8,2,5,4,7,1,6] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[4,6,8,5,2,7,1,3] => [[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => [1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[3,7,8,5,2,6,1,4] => [[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => [1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[3,7,8,5,4,1,6,2] => [[.,[[[.,[.,.]],.],.]],[[.,.],.]] => [1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 2

[4,6,8,5,3,1,7,2] => [[[.,[[.,[.,.]],.]],.],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 2

[7,8,2,3,5,4,1,6] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[5,7,3,1,2,4,8,6] => [[[.,[.,.]],.],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 4

[5,7,4,1,3,6,8,2] => [[[.,[.,.]],.],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 2

[7,8,1,4,6,5,3,2] => [[.,[.,.]],[[[.,[[.,.],.]],.],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 2

[6,2,7,8,3,1,4,5] => [[[.,.],[[.,[.,.]],.]],[.,[.,.]]] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[1,7,8,2,5,3,4,6] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 5

[3,8,1,5,7,2,6,4] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[6,8,4,3,1,7,2,5] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[4,8,1,3,7,5,6,2] => [[.,[.,.]],[[.,[[.,.],[.,.]]],.]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 2

[2,1,6,8,5,3,4,7] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[1,2,6,8,5,3,4,7] => [.,[.,[[[.,[.,.]],.],[.,[.,.]]]]] => [1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 5

[6,7,5,3,8,1,2,4] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[6,2,3,4,7,1,8,5] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[6,8,5,7,3,1,2,4] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3

[7,3,6,1,4,8,2,5] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[8,3,5,1,7,4,2,6] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[3,5,6,8,4,2,7,1] => [[[.,[[.,[.,[.,.]]],.]],[.,.]],.] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[5,8,2,6,4,3,7,1] => [[[.,[.,.]],[[[.,.],.],[.,.]]],.] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 1

[4,3,6,2,8,5,7,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[1,6,7,8,2,4,3,5] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[7,6,8,3,2,5,1,4] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[2,7,1,4,5,3,8,6] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[1,6,8,2,4,3,5,7] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 5

[1,6,7,2,5,3,4,8] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 5

[7,1,5,6,2,3,8,4] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[7,2,6,1,3,4,8,5] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[4,1,3,7,2,5,8,6] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[3,6,7,5,2,8,1,4] => [[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => [1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[7,8,4,1,5,6,2,3] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[5,8,1,3,6,7,2,4] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[3,8,4,6,7,1,2,5] => [[.,[[.,.],[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[7,1,3,8,2,4,5,6] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[8,1,3,7,2,4,5,6] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[3,5,4,7,8,1,2,6] => [[.,[[.,.],[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[5,2,3,6,7,8,1,4] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2

[1,3,7,8,5,6,2,4] => [.,[[.,[[.,[.,.]],[.,.]]],[.,.]]] => [1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 3

[8,2,6,7,5,1,3,4] => [[[.,.],[[.,[.,.]],.]],[.,[.,.]]] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[2,5,8,4,7,1,3,6] => [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[6,2,5,1,4,8,3,7] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[8,2,5,1,4,6,7,3] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[2,4,1,8,5,7,6,3] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2

[2,3,1,8,7,6,4,5] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[8,1,3,4,6,7,2,5] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 3

[3,4,8,2,6,7,1,5] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[3,6,8,2,5,1,7,4] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[3,8,2,5,7,4,6,1] => [[[.,[.,.]],[[.,[.,.]],[.,.]]],.] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 1

[6,8,5,4,1,7,2,3] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[2,8,1,5,7,6,3,4] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3

[8,5,7,1,6,4,2,3] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[8,4,7,2,1,6,5,3] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[3,5,8,1,7,4,6,2] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[8,4,7,1,3,6,5,2] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[3,8,1,2,5,6,4,7] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4

[3,7,1,2,5,6,4,8] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4

[4,8,1,6,5,2,7,3] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[4,5,2,6,7,1,8,3] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[7,2,6,8,4,3,5,1] => [[[.,.],[[[.,[.,.]],.],[.,.]]],.] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1

[5,2,4,6,1,3,8,7] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[7,2,3,4,6,8,1,5] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2

[8,3,4,6,7,5,1,2] => [[[.,.],[.,[[.,[.,.]],.]]],[.,.]] => [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => 2

[6,8,3,4,7,5,2,1] => [[[[.,[.,.]],[.,[[.,.],.]]],.],.] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 1

[4,8,1,5,7,6,3,2] => [[.,[.,.]],[[[.,[[.,.],.]],.],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 2

[3,7,4,6,8,2,5,1] => [[[.,[[.,.],[.,[.,.]]]],[.,.]],.] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[4,7,1,6,8,3,2,5] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[4,5,2,8,1,7,3,6] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[8,2,5,7,4,1,3,6] => [[[.,.],[[.,[.,.]],.]],[.,[.,.]]] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[7,2,4,5,6,8,1,3] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2

[7,1,3,5,6,2,8,4] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[7,1,5,8,4,6,3,2] => [[.,.],[[[[.,[.,.]],[.,.]],.],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[5,3,6,1,4,2,8,7] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[5,7,2,1,4,3,8,6] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[7,2,4,8,1,5,6,3] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[7,4,8,3,1,5,6,2] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[6,1,5,8,3,7,4,2] => [[.,.],[[[.,[.,.]],[[.,.],.]],.]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2

[7,8,4,1,3,5,6,2] => [[[.,[.,.]],.],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 2

[7,8,3,4,1,5,6,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[7,2,3,8,1,5,6,4] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[6,4,8,2,3,1,7,5] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[7,3,6,2,8,4,1,5] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[3,5,6,8,1,4,2,7] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,3,5,8,2,1,6,7] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[6,4,7,2,3,1,5,8] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[6,8,1,5,4,2,7,3] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[7,8,6,3,1,4,2,5] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[7,8,6,3,5,1,2,4] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[5,6,4,3,7,1,8,2] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[5,6,2,8,4,3,7,1] => [[[.,[.,.]],[[[.,.],.],[.,.]]],.] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 1

[4,6,2,7,8,3,5,1] => [[[.,[.,.]],[[.,[.,.]],[.,.]]],.] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 1

[5,1,2,4,6,7,8,3] => [[.,.],[.,[[.,[.,[.,[.,.]]]],.]]] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 3

[4,6,3,5,2,8,7,1] => [[[[.,[.,.]],[.,.]],[[.,.],.]],.] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 1

[5,6,3,4,8,2,7,1] => [[[[.,[.,.]],[.,[.,.]]],[.,.]],.] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[5,8,4,6,3,2,7,1] => [[[[[.,[.,.]],[.,.]],.],[.,.]],.] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1

[5,7,8,2,4,3,6,1] => [[[.,[.,[.,.]]],[[.,.],[.,.]]],.] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[5,6,2,4,8,3,7,1] => [[[.,[.,.]],[[.,[.,.]],[.,.]]],.] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 1

[6,4,7,8,2,3,5,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1

[6,4,7,3,2,5,8,1] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1

[5,7,3,2,8,4,6,1] => [[[[.,[.,.]],.],[[.,.],[.,.]]],.] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 1

[5,3,7,2,8,4,6,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[4,3,7,2,5,8,6,1] => [[[[.,.],[.,.]],[.,[[.,.],.]]],.] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[4,7,3,2,5,8,6,1] => [[[[.,[.,.]],.],[.,[[.,.],.]]],.] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 1

[4,7,3,2,6,8,5,1] => [[[[.,[.,.]],.],[[.,[.,.]],.]],.] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 1

[7,4,6,2,3,8,5,1] => [[[[.,.],[.,.]],[.,[[.,.],.]]],.] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[7,5,6,2,8,3,4,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[2,4,6,3,8,7,5,1] => [[.,[[.,[.,.]],[[[.,.],.],.]]],.] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 1

[2,4,6,3,8,7,1,5] => [[.,[[.,[.,.]],[[.,.],.]]],[.,.]] => [1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2

[2,4,6,8,5,7,3,1] => [[.,[[.,[[.,[.,.]],[.,.]]],.]],.] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1

[2,4,6,8,5,7,1,3] => [[.,[.,[[.,[.,.]],[.,.]]]],[.,.]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 2

[2,4,6,8,3,7,1,5] => [[.,[[.,[.,[.,.]]],[.,.]]],[.,.]] => [1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[2,4,6,8,1,7,3,5] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,4,6,8,5,1,7,3] => [[.,[.,[[.,[.,.]],.]]],[[.,.],.]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 2

[2,4,6,8,5,1,3,7] => [[.,[.,[[.,[.,.]],.]]],[.,[.,.]]] => [1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 3

[2,4,6,8,5,3,1,7] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => [1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 2

[4,6,1,7,8,5,3,2] => [[.,[.,.]],[[[[.,[.,.]],.],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 2

[6,1,2,7,8,4,5,3] => [[.,.],[.,[[[.,[.,.]],[.,.]],.]]] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 3

[5,6,3,1,7,4,8,2] => [[[.,[.,.]],.],[[[.,.],[.,.]],.]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[4,8,3,7,1,6,5,2] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[5,8,3,2,1,7,6,4] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2

[4,3,8,2,7,6,5,1] => [[[[.,.],[.,.]],[[[.,.],.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1

[4,8,2,7,6,5,3,1] => [[[.,[.,.]],[[[[.,.],.],.],.]],.] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1

[7,8,2,6,5,4,1,3] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[4,8,3,7,2,1,6,5] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[4,8,3,7,6,2,5,1] => [[[[.,[.,.]],[[.,.],.]],[.,.]],.] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 1

[5,8,2,7,6,4,1,3] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[1,3,6,8,2,7,4,5] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[1,4,8,2,5,6,3,7] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 4

[1,5,7,3,2,8,4,6] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 4

[1,4,8,3,2,5,6,7] => [.,[[[.,[.,.]],.],[.,[.,[.,.]]]]] => [1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 5

[6,2,3,5,8,1,7,4] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[5,2,4,8,1,6,7,3] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[2,5,6,3,4,7,1,8] => [[.,[[.,[.,.]],[.,[.,.]]]],[.,.]] => [1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2

[1,3,6,7,4,5,8,2] => [.,[[.,[[.,[.,.]],[.,[.,.]]]],.]] => [1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 2

[1,5,6,3,4,2,7,8] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 4

[1,5,7,3,6,4,8,2] => [.,[[[.,[.,.]],[[.,.],[.,.]]],.]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 2

[6,7,3,1,8,5,2,4] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[4,6,3,5,8,2,1,7] => [[[[.,[.,.]],[.,[.,.]]],.],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2

[7,4,5,2,1,8,6,3] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[4,5,7,3,1,2,8,6] => [[[.,[.,[.,.]]],.],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[4,5,1,8,3,2,7,6] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[5,7,4,6,3,2,1,8] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2

[3,6,1,2,4,8,7,5] => [[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 4

[2,3,1,7,8,5,6,4] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2

[3,7,8,5,1,4,2,6] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[4,5,3,8,2,1,6,7] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3

[3,7,2,1,8,4,6,5] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[3,5,7,8,2,4,6,1] => [[[.,[.,[.,[.,.]]]],[.,[.,.]]],.] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1

[7,8,2,5,4,3,6,1] => [[[.,[.,.]],[[[.,.],.],[.,.]]],.] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 1

[4,5,3,7,8,2,6,1] => [[[[.,[.,.]],[.,[.,.]]],[.,.]],.] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[4,6,8,2,7,3,5,1] => [[[.,[.,[.,.]]],[[.,.],[.,.]]],.] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[7,8,3,6,1,5,4,2] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[2,5,7,8,4,6,1,3] => [[.,[[.,[.,[.,.]]],[.,.]]],[.,.]] => [1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[7,5,6,3,8,4,2,1] => [[[[[.,.],[.,.]],[[.,.],.]],.],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

[2,6,8,4,7,5,1,3] => [[.,[[.,[.,.]],[[.,.],.]]],[.,.]] => [1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2

[6,7,5,1,4,8,3,2] => [[[.,[.,.]],.],[[[.,[.,.]],.],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 2

[5,8,2,7,3,6,4,1] => [[[.,[.,.]],[[.,.],[[.,.],.]]],.] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 1

[1,5,6,8,4,2,7,3] => [.,[[[.,[.,[.,.]]],.],[[.,.],.]]] => [1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3

[7,8,5,3,2,6,1,4] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2

[8,2,5,1,7,6,4,3] => [[[.,.],[.,.]],[[[[.,.],.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[6,7,4,3,8,2,5,1] => [[[[[.,[.,.]],.],[.,.]],[.,.]],.] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1

[3,4,2,7,8,6,1,5] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[7,8,6,1,4,3,2,5] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[2,4,7,8,6,1,3,5] => [[.,[.,[[.,[.,.]],.]]],[.,[.,.]]] => [1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 3

[3,7,8,6,5,2,4,1] => [[[.,[[[.,[.,.]],.],.]],[.,.]],.] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1

[4,5,2,7,8,6,3,1] => [[[.,[.,.]],[[[.,[.,.]],.],.]],.] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 1

[4,6,2,5,3,1,7,8] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[4,1,5,6,3,2,7,8] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[2,6,7,5,4,1,3,8] => [[.,[[[.,[.,.]],.],.]],[.,[.,.]]] => [1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 3

[4,1,6,7,5,3,2,8] => [[.,.],[[[[.,[.,.]],.],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => 3

[6,7,4,3,1,5,2,8] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[7,8,6,4,3,1,5,2] => [[[[[.,[.,.]],.],.],.],[[.,.],.]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2

[4,1,7,8,6,5,3,2] => [[.,.],[[[[[.,[.,.]],.],.],.],.]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2

[4,5,7,3,8,6,1,2] => [[[.,[.,[.,.]]],[[.,.],.]],[.,.]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[6,8,5,3,7,2,1,4] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[4,7,1,5,8,2,6,3] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[7,4,8,2,6,5,3,1] => [[[[.,.],[.,.]],[[[.,.],.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1

[4,3,8,1,6,5,2,7] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[8,3,4,1,2,6,7,5] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[7,2,4,5,1,8,3,6] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,8,2,3,5,7,6,1] => [[[.,[.,.]],[.,[.,[[.,.],.]]]],.] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 1

[4,5,2,3,8,6,7,1] => [[[.,[.,.]],[.,[[.,.],[.,.]]]],.] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 1

[6,7,4,8,5,3,2,1] => [[[[[.,[.,.]],[[.,.],.]],.],.],.] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 1

[4,3,5,6,1,7,8,2] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[3,5,2,6,4,7,8,1] => [[[.,[.,.]],[[.,.],[.,[.,.]]]],.] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 1

[3,1,5,6,4,7,8,2] => [[.,.],[[[.,[.,.]],[.,[.,.]]],.]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[3,1,4,6,7,5,8,2] => [[.,.],[[.,[[.,[.,.]],[.,.]]],.]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 2

[2,6,4,5,8,1,3,7] => [[.,[[.,.],[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[3,4,1,7,2,6,8,5] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[4,2,6,1,3,7,8,5] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[2,8,4,6,7,1,3,5] => [[.,[[.,.],[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[5,8,2,1,4,6,7,3] => [[[.,[.,.]],.],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 2

[8,4,6,1,2,5,7,3] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[5,6,2,8,7,1,3,4] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[7,8,1,4,3,5,6,2] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 2

[3,6,7,2,8,1,5,4] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[2,6,7,1,3,5,8,4] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[3,6,7,1,8,2,5,4] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[3,4,1,8,7,2,6,5] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[3,1,5,7,2,8,6,4] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3

[3,8,1,4,7,2,6,5] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[4,8,1,3,2,7,6,5] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[4,3,8,1,2,7,6,5] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[3,8,2,4,7,1,6,5] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[3,2,5,7,1,8,6,4] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[4,8,2,1,3,7,6,5] => [[[.,[.,.]],.],[.,[[[.,.],.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 3

[4,2,8,1,3,7,6,5] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[5,6,4,7,1,2,8,3] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[4,6,7,5,8,2,3,1] => [[[.,[[.,[.,.]],[.,.]]],[.,.]],.] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[4,5,7,1,6,8,3,2] => [[.,[.,[.,.]]],[[[.,[.,.]],.],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[4,5,1,7,6,8,2,3] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[6,7,2,8,3,1,4,5] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[6,2,7,8,4,1,3,5] => [[[.,.],[[.,[.,.]],.]],[.,[.,.]]] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[6,3,7,8,4,1,2,5] => [[[.,.],[[.,[.,.]],.]],[.,[.,.]]] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[7,8,5,2,4,1,3,6] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[4,2,5,1,3,7,8,6] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[3,4,1,7,8,5,2,6] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[4,1,3,7,8,5,2,6] => [[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3

[4,5,1,3,2,7,8,6] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[2,3,7,8,5,4,1,6] => [[.,[.,[[[.,[.,.]],.],.]]],[.,.]] => [1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 2

[8,3,5,6,1,7,2,4] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,5,8,1,2,6,7,3] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[5,3,6,7,8,2,1,4] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 2

[7,2,4,1,3,8,5,6] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[4,6,8,2,3,7,5,1] => [[[.,[.,[.,.]]],[.,[[.,.],.]]],.] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[4,5,7,2,3,6,1,8] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[6,7,2,3,4,8,1,5] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[3,5,2,4,6,7,8,1] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1

[6,7,5,3,8,2,1,4] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[5,2,6,8,3,7,1,4] => [[[.,.],[[.,[.,.]],[.,.]]],[.,.]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[2,4,7,8,5,1,3,6] => [[.,[.,[[.,[.,.]],.]]],[.,[.,.]]] => [1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 3

[2,4,8,3,5,7,1,6] => [[.,[[.,[.,.]],[.,[.,.]]]],[.,.]] => [1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2

[1,3,8,2,4,7,5,6] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 5

[1,3,7,2,4,6,5,8] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 5

[8,4,6,2,7,3,1,5] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[4,3,6,2,8,7,1,5] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[7,8,4,2,6,3,5,1] => [[[[.,[.,.]],.],[[.,.],[.,.]]],.] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 1

[3,2,7,8,6,4,5,1] => [[[.,.],[[[.,[.,.]],.],[.,.]]],.] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1

[5,7,8,6,3,2,4,1] => [[[[.,[[.,[.,.]],.]],.],[.,.]],.] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[6,8,5,3,1,7,2,4] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[1,5,7,3,2,6,4,8] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 4

[5,1,3,7,2,6,4,8] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[8,1,6,7,2,4,3,5] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[6,1,4,8,2,7,3,5] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[6,2,4,8,3,7,1,5] => [[[.,.],[[.,[.,.]],[.,.]]],[.,.]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[7,1,5,6,8,2,4,3] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[6,7,1,5,2,4,8,3] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[1,6,7,3,5,4,8,2] => [.,[[[.,[.,.]],[[.,.],[.,.]]],.]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 2

[1,7,8,3,6,4,5,2] => [.,[[[.,[.,.]],[[.,.],[.,.]]],.]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 2

[7,4,5,1,6,8,3,2] => [[[.,.],[.,.]],[[[.,[.,.]],.],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[5,6,7,4,3,1,8,2] => [[[[.,[.,[.,.]]],.],.],[[.,.],.]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[6,7,8,5,3,1,4,2] => [[[[.,[.,[.,.]]],.],.],[[.,.],.]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[1,4,6,2,5,3,7,8] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 5

[1,6,8,2,5,4,7,3] => [.,[[.,[.,.]],[[[.,.],[.,.]],.]]] => [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 3

[1,6,8,2,7,5,4,3] => [.,[[.,[.,.]],[[[[.,.],.],.],.]]] => [1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 3

[1,6,7,2,5,8,4,3] => [.,[[.,[.,.]],[[[.,[.,.]],.],.]]] => [1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 3

[1,5,8,3,2,7,4,6] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 4

[1,4,5,8,2,6,3,7] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[1,3,8,2,6,5,4,7] => [.,[[.,[.,.]],[[[.,.],.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 4

[5,8,3,1,2,6,4,7] => [[[.,[.,.]],.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[4,8,1,7,5,2,3,6] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[4,8,1,7,5,2,6,3] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[7,6,8,4,1,3,2,5] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[7,6,8,4,1,3,5,2] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[4,8,2,7,5,1,3,6] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[7,6,8,4,1,5,2,3] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[7,1,4,8,3,6,5,2] => [[.,.],[[[.,[.,.]],[[.,.],.]],.]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2

[7,8,5,2,4,3,6,1] => [[[[.,[.,.]],.],[[.,.],[.,.]]],.] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 1

[7,3,8,2,5,4,6,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[4,8,1,5,3,7,6,2] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2

[7,4,8,2,6,3,5,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[7,4,8,2,6,3,1,5] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[7,8,6,4,2,5,1,3] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2

[7,8,2,4,6,5,1,3] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[8,4,6,7,5,3,2,1] => [[[[[.,.],[[.,[.,.]],.]],.],.],.] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 1

[7,1,3,6,8,5,4,2] => [[.,.],[[.,[[[.,[.,.]],.],.]],.]] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2

[6,5,7,2,8,3,4,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[6,5,7,2,8,1,4,3] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[6,7,2,5,8,1,4,3] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[6,5,7,3,8,1,4,2] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[6,7,5,1,4,3,8,2] => [[[.,[.,.]],.],[[[.,.],[.,.]],.]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[7,8,5,1,4,3,6,2] => [[[.,[.,.]],.],[[[.,.],[.,.]],.]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[5,8,2,7,6,1,3,4] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[8,2,3,6,7,1,4,5] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[4,2,3,1,5,8,6,7] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[4,7,3,6,5,1,2,8] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[3,1,6,8,5,7,2,4] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[5,7,2,1,8,4,6,3] => [[[.,[.,.]],.],[[[.,.],[.,.]],.]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[5,8,3,7,4,2,1,6] => [[[[.,[.,.]],[[.,.],.]],.],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2

[8,4,7,3,5,2,1,6] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[5,4,8,1,3,2,6,7] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[4,5,8,2,1,3,6,7] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[8,1,3,5,2,4,6,7] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[1,5,7,3,6,8,2,4] => [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 3

[8,4,6,2,5,7,1,3] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[8,1,3,6,7,4,2,5] => [[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3

[1,2,4,7,8,5,3,6] => [.,[.,[[.,[[.,[.,.]],.]],[.,.]]]] => [1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 4

[6,7,8,2,4,5,1,3] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[3,8,2,6,5,7,1,4] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[3,8,1,7,5,4,2,6] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[6,7,1,2,8,4,3,5] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 4

[3,4,1,7,6,8,2,5] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[2,5,7,1,8,4,3,6] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[3,5,7,1,6,8,2,4] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[1,5,7,8,6,3,2,4] => [.,[[[.,[[.,[.,.]],.]],.],[.,.]]] => [1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 3

[8,4,6,7,5,2,1,3] => [[[[.,.],[[.,[.,.]],.]],.],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => 2

[5,2,7,8,6,3,1,4] => [[[.,.],[[[.,[.,.]],.],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => 2

[1,5,8,4,3,7,6,2] => [.,[[[[.,[.,.]],.],[[.,.],.]],.]] => [1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 2

[8,1,3,5,2,7,6,4] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3

[2,7,1,5,4,8,6,3] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2

[2,4,1,6,7,5,8,3] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2

[8,1,4,5,6,3,7,2] => [[.,.],[[[.,[.,[.,.]]],[.,.]],.]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2

[8,1,4,5,6,2,7,3] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[2,5,1,7,8,6,4,3] => [[.,[.,.]],[[[[.,[.,.]],.],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 2

[3,5,6,2,8,7,4,1] => [[[.,[.,[.,.]]],[[[.,.],.],.]],.] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1

[2,4,5,1,7,6,3,8] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[8,4,5,3,7,6,2,1] => [[[[[.,.],[.,.]],[[.,.],.]],.],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

[3,4,5,6,2,8,1,7] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[7,3,4,1,6,8,2,5] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[7,3,4,1,6,5,8,2] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[2,3,5,1,4,8,7,6] => [[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[2,7,1,3,6,8,5,4] => [[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 3

[2,7,1,3,8,4,6,5] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4

[8,4,5,7,3,2,6,1] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1

[8,3,7,2,4,1,5,6] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[8,6,7,2,1,4,3,5] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[7,3,4,6,2,1,5,8] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[6,4,7,2,1,5,8,3] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[7,4,8,2,6,1,5,3] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[4,7,2,5,3,6,1,8] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[7,8,3,4,6,1,5,2] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[6,1,4,8,3,2,5,7] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[6,8,2,5,1,4,7,3] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[4,5,2,1,6,8,7,3] => [[[.,[.,.]],.],[[.,[[.,.],.]],.]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 2

[1,7,8,6,2,4,3,5] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 4

[3,8,1,5,6,2,4,7] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[6,8,4,1,5,2,3,7] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[3,2,8,1,6,4,5,7] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[5,8,4,1,2,3,7,6] => [[[.,[.,.]],.],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 4

[1,6,7,3,2,8,4,5] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 4

[1,4,6,2,8,5,3,7] => [.,[[.,[.,.]],[[[.,.],.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 4

[1,5,6,2,8,4,3,7] => [.,[[.,[.,.]],[[[.,.],.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 4

[1,2,4,7,3,6,5,8] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => [1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 5

[1,2,5,7,4,6,8,3] => [.,[.,[[[.,[.,.]],[.,[.,.]]],.]]] => [1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 3

[2,3,7,1,8,6,4,5] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[2,6,1,7,8,5,3,4] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[4,8,3,1,6,5,7,2] => [[[.,[.,.]],.],[[[.,.],[.,.]],.]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[1,6,8,5,4,2,7,3] => [.,[[[[.,[.,.]],.],.],[[.,.],.]]] => [1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 3

[6,5,8,4,2,1,7,3] => [[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[1,7,8,6,5,4,2,3] => [.,[[[[[.,[.,.]],.],.],.],[.,.]]] => [1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 3

[5,3,7,2,6,8,4,1] => [[[[.,.],[.,.]],[[.,[.,.]],.]],.] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[5,7,2,3,4,6,8,1] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1

[5,7,1,2,3,8,6,4] => [[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 4

[7,8,6,2,4,1,5,3] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[7,4,6,2,8,1,5,3] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[7,1,5,8,2,3,6,4] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[7,3,6,2,1,8,5,4] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[5,6,2,1,8,4,7,3] => [[[.,[.,.]],.],[[[.,.],[.,.]],.]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[5,4,6,8,1,3,7,2] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[3,7,1,6,4,5,8,2] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 2

[3,5,2,1,4,6,7,8] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 5

[6,7,3,4,8,5,1,2] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[4,1,5,7,3,2,8,6] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3

[4,8,2,5,3,1,6,7] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[5,1,3,4,8,2,6,7] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[6,1,4,5,7,8,2,3] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 3

[6,3,4,7,1,8,5,2] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[7,8,5,1,3,4,6,2] => [[[.,[.,.]],.],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 2

[7,1,3,4,5,6,8,2] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2

[4,2,5,1,6,8,7,3] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[1,7,8,5,2,6,3,4] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 4

[1,5,7,3,8,6,2,4] => [.,[[[.,[.,.]],[[.,.],.]],[.,.]]] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 3

[6,7,5,1,8,2,3,4] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[6,7,2,1,5,3,8,4] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[4,8,3,1,7,6,5,2] => [[[.,[.,.]],.],[[[[.,.],.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2

[5,3,8,2,1,7,6,4] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[5,8,4,2,1,7,6,3] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2

[5,8,4,7,1,6,3,2] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[5,4,8,3,1,7,6,2] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[8,5,6,1,4,7,2,3] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[6,7,4,1,2,5,8,3] => [[[.,[.,.]],.],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 3

[1,6,7,4,2,5,8,3] => [.,[[[.,[.,.]],.],[[.,[.,.]],.]]] => [1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3

[3,6,7,5,8,1,2,4] => [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[1,6,7,5,8,3,2,4] => [.,[[[[.,[.,.]],[.,.]],.],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 3

[6,8,5,7,4,2,1,3] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2

[2,7,8,3,1,5,4,6] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[2,4,6,7,8,5,1,3] => [[.,[.,[[.,[.,[.,.]]],.]]],[.,.]] => [1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 2

[2,4,6,7,8,3,1,5] => [[.,[[.,[.,[.,[.,.]]]],.]],[.,.]] => [1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 2

[4,5,1,2,8,7,3,6] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 4

[5,6,1,2,8,3,7,4] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4

[8,5,6,1,7,2,4,3] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[7,5,6,1,3,8,4,2] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[6,7,1,4,2,8,5,3] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[7,4,5,1,3,8,6,2] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[1,5,7,8,4,2,3,6] => [.,[[[.,[.,[.,.]]],.],[.,[.,.]]]] => [1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[1,4,5,7,8,3,6,2] => [.,[[[.,[.,[.,[.,.]]]],[.,.]],.]] => [1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2

[1,5,7,8,3,6,2,4] => [.,[[[.,[.,[.,.]]],[.,.]],[.,.]]] => [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[1,5,7,8,2,4,3,6] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[6,8,4,7,3,2,1,5] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2

[6,8,5,4,2,7,1,3] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2

[3,5,6,1,4,2,7,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[3,6,7,8,2,1,4,5] => [[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[2,5,6,3,4,8,1,7] => [[.,[[.,[.,.]],[.,[.,.]]]],[.,.]] => [1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2

[5,2,4,7,8,6,1,3] => [[[.,.],[.,[[.,[.,.]],.]]],[.,.]] => [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => 2

[1,4,7,2,5,6,3,8] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 4

[7,3,5,8,2,6,1,4] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[3,4,8,2,5,1,7,6] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[1,4,6,7,8,3,5,2] => [.,[[[.,[.,[.,[.,.]]]],[.,.]],.]] => [1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2

[6,4,8,1,5,7,3,2] => [[[.,.],[.,.]],[[[.,[.,.]],.],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[1,6,8,3,5,2,7,4] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 3

[2,4,7,8,5,6,1,3] => [[.,[.,[[.,[.,.]],[.,.]]]],[.,.]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 2

[4,5,8,2,6,3,1,7] => [[[.,[.,[.,.]]],[[.,.],.]],[.,.]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[1,4,8,3,6,5,2,7] => [.,[[[.,[.,.]],[[.,.],.]],[.,.]]] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 3

[8,1,4,5,7,3,2,6] => [[.,.],[[[.,[.,[.,.]]],.],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => 3

[5,8,4,3,7,2,1,6] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[4,5,1,7,6,2,8,3] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[4,5,3,1,8,7,2,6] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[3,4,8,1,5,2,6,7] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[6,8,5,3,4,2,1,7] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[3,2,6,7,1,8,5,4] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[3,4,6,7,8,2,1,5] => [[[.,[.,[.,[.,[.,.]]]]],.],[.,.]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 2

[3,2,6,7,8,4,1,5] => [[[.,.],[[.,[.,[.,.]]],.]],[.,.]] => [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => 2

[6,7,1,3,8,5,4,2] => [[.,[.,.]],[[.,[[[.,.],.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 2

[6,7,1,8,5,2,4,3] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[1,2,6,7,8,5,3,4] => [.,[.,[[[.,[.,[.,.]]],.],[.,.]]]] => [1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 4

[1,6,7,4,8,3,2,5] => [.,[[[[.,[.,.]],[.,.]],.],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 3

[1,4,6,7,8,3,2,5] => [.,[[[.,[.,[.,[.,.]]]],.],[.,.]]] => [1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 3

[3,6,8,2,7,1,5,4] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[4,7,1,8,6,5,3,2] => [[.,[.,.]],[[[[[.,.],.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2

[3,8,1,5,2,4,7,6] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[7,5,6,4,1,3,2,8] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[7,8,6,4,1,3,2,5] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[2,7,1,3,5,6,8,4] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 3

[3,6,2,1,5,8,7,4] => [[[.,[.,.]],.],[[.,[[.,.],.]],.]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 2

[2,3,6,1,5,8,7,4] => [[.,[.,[.,.]]],[[.,[[.,.],.]],.]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[3,4,7,1,5,6,8,2] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[3,6,7,4,1,2,8,5] => [[.,[[.,[.,.]],.]],[.,[[.,.],.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 3

[7,4,8,1,5,6,3,2] => [[[.,.],[.,.]],[[[.,[.,.]],.],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[2,6,8,1,5,3,7,4] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[6,8,2,1,5,3,7,4] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[4,8,2,5,3,6,7,1] => [[[.,[.,.]],[[.,.],[.,[.,.]]]],.] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 1

[4,5,8,2,3,6,7,1] => [[[.,[.,[.,.]]],[.,[.,[.,.]]]],.] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1

[2,4,5,3,8,6,7,1] => [[.,[[.,[.,.]],[[.,.],[.,.]]]],.] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 1

[4,3,5,2,8,6,7,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[5,6,7,4,2,8,3,1] => [[[[.,[.,[.,.]]],.],[[.,.],.]],.] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1

[2,5,7,4,6,8,3,1] => [[.,[[[.,[.,.]],[.,[.,.]]],.]],.] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[6,8,1,2,5,4,7,3] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 3

[2,6,1,8,5,4,7,3] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2

[3,1,6,8,5,4,7,2] => [[.,.],[[[[.,[.,.]],.],[.,.]],.]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 2

[2,3,5,8,4,6,7,1] => [[.,[.,[[.,[.,.]],[.,[.,.]]]]],.] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1

[3,5,2,8,4,6,7,1] => [[[.,[.,.]],[[.,.],[.,[.,.]]]],.] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 1

[3,4,5,8,2,6,7,1] => [[[.,[.,[.,[.,.]]]],[.,[.,.]]],.] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1

[5,3,4,8,2,6,7,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1

[5,4,8,3,2,6,7,1] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1

[5,8,2,3,4,6,7,1] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1

[7,4,6,8,3,2,5,1] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1

[3,4,5,2,7,1,6,8] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[7,5,6,1,2,3,8,4] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[8,4,6,7,3,2,5,1] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1

[8,4,6,2,3,1,5,7] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[3,1,7,8,5,4,2,6] => [[.,.],[[[[.,[.,.]],.],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => 3

[3,4,5,2,1,8,6,7] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[3,2,7,8,6,1,4,5] => [[[.,.],[[.,[.,.]],.]],[.,[.,.]]] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[6,8,2,5,1,3,7,4] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[6,7,4,2,1,5,3,8] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[5,7,4,1,3,6,2,8] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[4,7,1,8,6,3,5,2] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2

[5,4,8,1,7,3,6,2] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[8,3,6,2,4,1,7,5] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[7,8,3,2,4,6,5,1] => [[[[.,[.,.]],.],[.,[[.,.],.]]],.] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 1

[3,6,8,1,7,4,2,5] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[7,8,6,3,1,4,5,2] => [[[[.,[.,.]],.],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 2

[4,7,8,5,6,2,3,1] => [[[.,[[.,[.,.]],[.,.]]],[.,.]],.] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[2,7,8,5,6,1,4,3] => [[.,[[.,[.,.]],[.,.]]],[[.,.],.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2

[6,7,8,4,2,1,5,3] => [[[[.,[.,[.,.]]],.],.],[[.,.],.]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[4,7,8,1,2,5,6,3] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[6,1,4,7,2,5,8,3] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3

[6,7,8,3,5,4,2,1] => [[[[.,[.,[.,.]]],[[.,.],.]],.],.] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

[6,7,8,2,1,5,3,4] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[5,6,3,2,7,4,1,8] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[7,2,3,6,1,8,4,5] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[8,5,7,2,4,1,6,3] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[7,4,8,2,1,5,6,3] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[2,3,6,7,8,5,1,4] => [[.,[.,[[.,[.,[.,.]]],.]]],[.,.]] => [1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 2

[8,3,7,1,6,4,2,5] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[5,7,4,1,6,8,2,3] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[5,6,8,1,3,7,2,4] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[1,6,8,5,3,2,4,7] => [.,[[[[.,[.,.]],.],.],[.,[.,.]]]] => [1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 4

[5,8,1,6,7,4,2,3] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[1,7,8,4,6,2,3,5] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 4

[5,1,4,6,7,3,8,2] => [[.,.],[[[.,[.,[.,.]]],[.,.]],.]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2

[7,1,3,4,6,2,8,5] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[4,7,2,8,5,3,1,6] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[4,7,1,6,8,3,5,2] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2

[1,5,6,4,2,3,7,8] => [.,[[[.,[.,.]],.],[.,[.,[.,.]]]]] => [1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 5

[5,7,3,6,8,4,2,1] => [[[[.,[.,.]],[[.,[.,.]],.]],.],.] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 1

[1,5,6,3,2,8,4,7] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 4

[1,2,5,8,4,6,3,7] => [.,[.,[[[.,[.,.]],[.,.]],[.,.]]]] => [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 4

[1,4,7,3,6,8,5,2] => [.,[[[.,[.,.]],[[.,[.,.]],.]],.]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 2

[1,5,6,3,2,7,8,4] => [.,[[[.,[.,.]],.],[[.,[.,.]],.]]] => [1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3

[6,8,5,2,1,7,4,3] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2

[1,2,6,8,4,3,7,5] => [.,[.,[[[.,[.,.]],.],[[.,.],.]]]] => [1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 4

[5,3,7,2,6,4,1,8] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[4,6,3,2,8,1,7,5] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[5,3,7,2,8,1,6,4] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[7,8,4,3,1,5,2,6] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[6,5,7,3,8,4,1,2] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[8,6,7,1,5,3,2,4] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[5,7,1,3,4,2,8,6] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[7,3,5,6,4,8,1,2] => [[[.,.],[[.,[.,.]],[.,.]]],[.,.]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[1,5,7,3,8,2,6,4] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 3

[3,1,2,5,7,8,6,4] => [[.,.],[.,[[.,[[.,[.,.]],.]],.]]] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 3

[3,7,1,2,8,5,6,4] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 3

[2,4,7,3,5,6,1,8] => [[.,[[.,[.,.]],[.,[.,.]]]],[.,.]] => [1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2

[7,4,8,2,5,6,1,3] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[5,8,2,4,6,1,3,7] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[3,4,5,8,1,6,7,2] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[5,6,8,4,7,3,1,2] => [[[[.,[.,[.,.]]],[.,.]],.],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[3,1,6,8,5,2,7,4] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3

[2,3,8,1,5,6,4,7] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[5,4,8,1,2,6,7,3] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[5,2,3,8,1,7,4,6] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,7,1,8,6,3,5,4] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[2,7,1,5,6,4,3,8] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[8,4,6,3,1,7,2,5] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[5,4,7,2,8,6,1,3] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[3,5,6,4,1,7,2,8] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[2,5,6,1,7,4,3,8] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[2,7,1,8,6,5,4,3] => [[.,[.,.]],[[[[[.,.],.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2

[2,7,8,3,1,4,5,6] => [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4

[1,5,6,7,3,2,8,4] => [.,[[[.,[.,[.,.]]],.],[[.,.],.]]] => [1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3

[1,6,7,8,3,2,4,5] => [.,[[[.,[.,[.,.]]],.],[.,[.,.]]]] => [1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[1,8,4,5,6,7,2,3] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[1,2,7,8,4,3,5,6] => [.,[.,[[[.,[.,.]],.],[.,[.,.]]]]] => [1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 5

[1,6,7,8,4,2,3,5] => [.,[[[.,[.,[.,.]]],.],[.,[.,.]]]] => [1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[1,6,7,8,3,4,2,5] => [.,[[[.,[.,[.,.]]],[.,.]],[.,.]]] => [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[1,7,8,4,2,3,5,6] => [.,[[[.,[.,.]],.],[.,[.,[.,.]]]]] => [1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 5

[1,7,8,3,4,2,5,6] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 4

[1,2,3,7,8,5,4,6] => [.,[.,[.,[[[.,[.,.]],.],[.,.]]]]] => [1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 5

[1,7,8,4,5,2,3,6] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 4

[1,7,8,3,4,5,2,6] => [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 3

[5,8,2,7,3,4,1,6] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[5,3,8,1,6,7,4,2] => [[[.,.],[.,.]],[[[.,[.,.]],.],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[5,8,2,1,3,7,6,4] => [[[.,[.,.]],.],[.,[[[.,.],.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 3

[3,5,2,4,7,6,8,1] => [[[.,[.,.]],[.,[[.,.],[.,.]]]],.] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 1

[7,3,5,2,8,4,6,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[3,5,2,7,4,6,8,1] => [[[.,[.,.]],[[.,.],[.,[.,.]]]],.] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 1

[3,2,5,7,4,6,8,1] => [[[.,.],[[.,[.,.]],[.,[.,.]]]],.] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1

[8,1,6,7,3,4,2,5] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[7,6,8,1,2,5,4,3] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[5,7,1,2,6,8,3,4] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4

[3,5,7,4,1,8,2,6] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[8,3,5,6,1,4,7,2] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[8,3,5,7,2,1,4,6] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[7,2,4,5,3,8,1,6] => [[[.,.],[[.,[.,.]],[.,.]]],[.,.]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[4,5,1,3,6,7,8,2] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2

[3,7,2,1,6,8,4,5] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[1,5,8,2,4,7,6,3] => [.,[[.,[.,.]],[[.,[[.,.],.]],.]]] => [1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 3

[5,8,1,6,4,7,3,2] => [[.,[.,.]],[[[[.,.],[.,.]],.],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 2

[6,8,1,4,7,3,5,2] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2

[1,6,8,2,7,4,5,3] => [.,[[.,[.,.]],[[[.,.],[.,.]],.]]] => [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 3

[5,7,2,1,8,4,3,6] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[5,7,1,6,8,3,2,4] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[5,6,2,1,8,3,4,7] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[8,2,5,6,7,1,4,3] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[7,2,4,6,8,3,1,5] => [[[.,.],[[.,[.,[.,.]]],.]],[.,.]] => [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => 2

[6,2,4,7,8,1,3,5] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[3,7,8,6,4,2,5,1] => [[[.,[[[.,[.,.]],.],.]],[.,.]],.] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1

[1,4,7,2,6,8,5,3] => [.,[[.,[.,.]],[[[.,[.,.]],.],.]]] => [1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 3

[6,5,8,1,4,2,3,7] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[4,5,7,3,1,6,2,8] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[5,3,6,2,8,7,4,1] => [[[[.,.],[.,.]],[[[.,.],.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1

[6,3,5,2,1,8,7,4] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[3,8,1,4,7,6,5,2] => [[.,[.,.]],[[.,[[[.,.],.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 2

[2,7,8,3,4,1,5,6] => [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[7,2,6,8,1,4,3,5] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,3,6,2,8,4,7,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[6,8,2,7,4,1,5,3] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[6,1,7,8,5,3,2,4] => [[.,.],[[[[.,[.,.]],.],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => 3

[5,8,3,4,6,1,7,2] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[4,8,3,1,5,7,6,2] => [[[.,[.,.]],.],[[.,[[.,.],.]],.]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 2

[5,3,8,2,7,1,6,4] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[8,3,4,5,2,7,1,6] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[3,7,1,5,2,6,8,4] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[6,7,1,8,3,4,5,2] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 2

[3,7,1,6,8,4,5,2] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2

[6,8,3,4,7,1,5,2] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[3,7,1,6,5,2,8,4] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[8,3,5,2,7,1,6,4] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[3,7,1,4,8,6,5,2] => [[.,[.,.]],[[.,[[[.,.],.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 2

[3,7,1,4,5,2,8,6] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[7,3,6,2,5,4,1,8] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[6,3,8,2,5,4,1,7] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[8,3,7,2,5,4,1,6] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[1,4,7,3,6,5,2,8] => [.,[[[.,[.,.]],[[.,.],.]],[.,.]]] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 3

[1,4,8,3,7,5,2,6] => [.,[[[.,[.,.]],[[.,.],.]],[.,.]]] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 3

[8,3,7,2,6,4,1,5] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[6,3,5,2,4,8,1,7] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[5,7,2,8,1,4,3,6] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,8,2,7,1,4,3,6] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,8,3,1,5,2,7,6] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[7,3,4,2,1,5,8,6] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[4,7,8,1,5,6,2,3] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[3,6,7,1,8,4,2,5] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[5,6,2,7,8,3,4,1] => [[[.,[.,.]],[[.,[.,.]],[.,.]]],.] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 1

[7,2,5,8,1,6,3,4] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,4,8,1,5,7,2,3] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[2,3,6,8,4,1,7,5] => [[.,[.,[[.,[.,.]],.]]],[[.,.],.]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 2

[3,2,4,6,7,8,1,5] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2

[5,2,6,8,1,3,7,4] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[4,8,1,6,3,7,5,2] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2

[8,3,5,2,6,1,4,7] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[6,7,2,4,3,5,8,1] => [[[.,[.,.]],[[.,.],[.,[.,.]]]],.] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 1

[4,3,8,2,1,5,7,6] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[4,5,8,3,2,7,1,6] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[6,8,5,2,7,3,4,1] => [[[[.,[.,.]],.],[[.,.],[.,.]]],.] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 1

[5,4,7,8,2,3,6,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1

[4,3,8,2,1,6,7,5] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[3,6,7,4,5,2,8,1] => [[[.,[[.,[.,.]],[.,.]]],[.,.]],.] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[3,5,7,4,6,2,8,1] => [[[.,[[.,[.,.]],[.,.]]],[.,.]],.] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[4,6,7,2,5,3,8,1] => [[[.,[.,[.,.]]],[[.,.],[.,.]]],.] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[6,4,7,8,3,1,5,2] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[5,8,1,7,6,4,2,3] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[5,6,7,1,8,3,4,2] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[1,5,8,2,6,4,7,3] => [.,[[.,[.,.]],[[[.,.],[.,.]],.]]] => [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 3

[1,5,7,4,6,8,3,2] => [.,[[[[.,[.,.]],[.,[.,.]]],.],.]] => [1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 2

[5,6,7,4,8,1,3,2] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[4,8,1,7,2,5,6,3] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[2,6,7,1,5,4,8,3] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[1,7,3,4,5,8,2,6] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[6,7,3,2,5,8,1,4] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[4,6,2,5,1,8,7,3] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[5,1,4,6,2,8,7,3] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3

[7,3,5,2,1,6,8,4] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[5,7,2,1,3,6,8,4] => [[[.,[.,.]],.],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 3

[3,7,2,6,8,1,5,4] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[7,1,6,8,5,2,4,3] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3

[1,5,7,8,6,2,4,3] => [.,[[.,[[.,[.,.]],.]],[[.,.],.]]] => [1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 3

[3,6,2,1,4,7,8,5] => [[[.,[.,.]],.],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 3

[6,8,2,7,5,4,3,1] => [[[.,[.,.]],[[[[.,.],.],.],.]],.] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1

[5,8,1,7,6,4,3,2] => [[.,[.,.]],[[[[[.,.],.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2

[4,7,3,6,1,8,5,2] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[5,3,8,2,6,7,1,4] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[8,2,5,1,7,6,3,4] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[8,2,4,6,3,7,1,5] => [[[.,.],[[.,[.,.]],[.,.]]],[.,.]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[7,3,6,2,4,5,8,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1

[8,3,7,2,1,4,6,5] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[7,3,8,2,1,5,6,4] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[6,2,5,7,4,3,8,1] => [[[.,.],[[[.,[.,.]],.],[.,.]]],.] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1

[7,2,6,8,1,3,5,4] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[6,1,5,7,4,8,3,2] => [[.,.],[[[[.,[.,.]],[.,.]],.],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[6,1,5,7,8,3,4,2] => [[.,.],[[[.,[.,[.,.]]],[.,.]],.]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2

[4,6,7,3,1,8,5,2] => [[[.,[.,[.,.]]],.],[[[.,.],.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[7,2,3,5,8,4,1,6] => [[[.,.],[.,[[.,[.,.]],.]]],[.,.]] => [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => 2

[8,2,3,5,1,4,6,7] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[7,1,4,8,3,6,2,5] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[6,1,5,8,3,4,2,7] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[6,7,5,1,3,2,4,8] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[5,2,6,1,7,3,4,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[4,2,6,8,3,7,1,5] => [[[.,.],[[.,[.,.]],[.,.]]],[.,.]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[6,8,5,1,4,2,3,7] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[7,8,4,5,1,3,6,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[1,7,8,5,3,4,6,2] => [.,[[[[.,[.,.]],.],[.,[.,.]]],.]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 2

[1,5,8,3,6,4,7,2] => [.,[[[.,[.,.]],[[.,.],[.,.]]],.]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 2

[6,3,8,1,4,2,7,5] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[4,8,1,5,6,3,7,2] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2

[3,8,1,7,2,6,5,4] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[7,3,8,1,2,6,5,4] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[8,3,7,1,5,4,6,2] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[8,4,7,1,5,3,6,2] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[5,8,4,3,6,2,7,1] => [[[[[.,[.,.]],.],[.,.]],[.,.]],.] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1

[5,8,4,3,1,7,2,6] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[3,6,8,5,2,4,7,1] => [[[.,[[.,[.,.]],.]],[.,[.,.]]],.] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 1

[5,7,8,4,3,2,6,1] => [[[[[.,[.,[.,.]]],.],.],[.,.]],.] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1

[6,7,1,3,2,8,5,4] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[5,7,4,2,8,6,1,3] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[2,6,3,7,1,4,5,8] => [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[7,6,8,4,3,1,5,2] => [[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[6,2,3,5,8,4,1,7] => [[[.,.],[.,[[.,[.,.]],.]]],[.,.]] => [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => 2

[7,2,6,1,5,8,3,4] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[4,7,3,8,6,2,5,1] => [[[[.,[.,.]],[[.,.],.]],[.,.]],.] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 1

[4,7,3,6,8,2,1,5] => [[[[.,[.,.]],[.,[.,.]]],.],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2

[5,4,7,3,8,2,1,6] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[4,3,5,7,2,6,1,8] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,4,8,3,6,2,1,7] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[6,8,2,5,7,1,4,3] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[5,8,4,2,7,3,6,1] => [[[[.,[.,.]],.],[[.,.],[.,.]]],.] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 1

[1,7,8,5,6,4,2,3] => [.,[[[[.,[.,.]],[.,.]],.],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 3

[8,1,5,6,4,2,3,7] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[2,6,8,1,5,4,3,7] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[3,5,8,2,1,4,7,6] => [[[.,[.,[.,.]]],.],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[6,4,5,1,8,3,2,7] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[5,4,7,8,3,1,2,6] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[4,5,8,1,3,7,2,6] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[4,7,2,6,8,3,5,1] => [[[.,[.,.]],[[.,[.,.]],[.,.]]],.] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 1

[4,7,3,2,5,1,6,8] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[7,5,6,1,8,3,2,4] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[4,5,6,2,7,3,1,8] => [[[.,[.,[.,.]]],[[.,.],.]],[.,.]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[3,5,1,4,6,8,2,7] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[8,5,7,4,2,1,3,6] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3

[4,6,2,7,5,8,1,3] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[7,8,1,4,2,3,5,6] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[4,3,8,1,5,2,6,7] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[4,1,3,6,7,2,8,5] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[7,8,1,6,5,2,4,3] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[3,7,8,6,5,1,2,4] => [[.,[[[.,[.,.]],.],.]],[.,[.,.]]] => [1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 3

[8,4,5,7,2,6,3,1] => [[[[.,.],[.,[.,.]]],[[.,.],.]],.] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => 1

[4,5,8,2,7,3,1,6] => [[[.,[.,[.,.]]],[[.,.],.]],[.,.]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[6,5,8,2,7,3,1,4] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[6,4,8,2,7,3,1,5] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[7,8,1,3,6,4,2,5] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3

[4,5,7,8,3,2,1,6] => [[[[.,[.,[.,[.,.]]]],.],.],[.,.]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2

[5,7,3,4,2,6,8,1] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1

[5,7,4,2,3,6,8,1] => [[[[.,[.,.]],.],[.,[.,[.,.]]]],.] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1

[5,4,7,3,2,8,1,6] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[6,8,3,2,4,5,1,7] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[5,8,3,4,6,1,2,7] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[6,4,8,2,3,5,1,7] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[5,4,6,8,2,3,1,7] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,6,8,4,1,2,3,7] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[7,4,8,3,1,2,5,6] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[5,7,8,2,3,1,4,6] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[5,4,7,8,2,1,3,6] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[6,8,5,2,1,3,4,7] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4

[5,6,1,3,2,4,8,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[4,3,8,1,2,5,7,6] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[4,6,3,2,8,5,7,1] => [[[[.,[.,.]],.],[[.,.],[.,.]]],.] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 1

[5,3,7,2,1,8,6,4] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[5,4,8,3,7,2,1,6] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[3,6,8,5,2,1,7,4] => [[[.,[[.,[.,.]],.]],.],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 2

[5,4,8,3,2,7,1,6] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[6,7,2,5,3,8,4,1] => [[[.,[.,.]],[[.,.],[[.,.],.]]],.] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 1

[6,3,4,8,1,2,7,5] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[6,8,5,7,3,4,2,1] => [[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1

[5,3,6,8,4,2,1,7] => [[[[.,.],[[.,[.,.]],.]],.],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => 2

[5,1,6,8,4,7,3,2] => [[.,.],[[[[.,[.,.]],[.,.]],.],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[2,4,1,8,7,6,3,5] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[1,3,5,8,4,7,2,6] => [.,[[.,[[.,[.,.]],[.,.]]],[.,.]]] => [1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 3

[4,1,3,5,6,2,8,7] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[8,2,4,6,1,3,7,5] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[8,2,3,5,6,1,4,7] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[4,3,5,6,8,2,7,1] => [[[[.,.],[.,[.,[.,.]]]],[.,.]],.] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 1

[8,2,3,4,6,1,7,5] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[3,8,2,7,6,4,1,5] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[5,3,6,2,1,8,4,7] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[3,1,6,8,2,7,5,4] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3

[2,7,1,4,6,5,3,8] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3

[4,7,1,2,6,5,8,3] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 3

[6,5,8,3,7,4,2,1] => [[[[[.,.],[.,.]],[[.,.],.]],.],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

[8,2,5,1,6,3,7,4] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[8,3,4,5,1,6,7,2] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[7,8,1,3,5,4,6,2] => [[.,[.,.]],[[.,[[.,.],[.,.]]],.]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 2

[1,3,7,8,5,4,6,2] => [.,[[.,[[[.,[.,.]],.],[.,.]]],.]] => [1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 2

[5,2,4,1,8,3,6,7] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[1,4,8,2,3,6,5,7] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 5

[1,4,6,7,3,5,2,8] => [.,[[[.,[.,[.,.]]],[.,.]],[.,.]]] => [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[1,4,8,2,6,7,5,3] => [.,[[.,[.,.]],[[[.,[.,.]],.],.]]] => [1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 3

[3,7,8,5,4,2,6,1] => [[[.,[[[.,[.,.]],.],.]],[.,.]],.] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1

[5,6,2,4,3,8,1,7] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[5,1,4,7,3,2,8,6] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3

[2,3,5,7,4,8,1,6] => [[.,[.,[[.,[.,.]],[.,.]]]],[.,.]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 2

[4,7,1,6,8,5,3,2] => [[.,[.,.]],[[[[.,[.,.]],.],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 2

[5,3,4,6,2,8,7,1] => [[[[.,.],[.,[.,.]]],[[.,.],.]],.] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => 1

[5,7,3,4,8,2,6,1] => [[[[.,[.,.]],[.,[.,.]]],[.,.]],.] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[5,6,4,2,7,8,3,1] => [[[[.,[.,.]],.],[[.,[.,.]],.]],.] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 1

[5,7,4,8,3,1,6,2] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[4,3,5,1,8,7,2,6] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[2,5,6,8,3,1,7,4] => [[.,[[.,[.,[.,.]]],.]],[[.,.],.]] => [1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[7,1,4,5,3,6,2,8] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[3,5,6,4,8,2,1,7] => [[[.,[[.,[.,.]],[.,.]]],.],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 2

[8,5,6,1,4,3,7,2] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[6,4,5,8,2,3,1,7] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[7,5,8,1,4,6,3,2] => [[[.,.],[.,.]],[[[.,[.,.]],.],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[4,2,6,7,8,1,5,3] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[3,4,6,7,8,1,5,2] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[4,7,3,8,5,1,6,2] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[7,8,4,1,3,6,5,2] => [[[.,[.,.]],.],[[.,[[.,.],.]],.]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 2

[7,3,8,2,4,1,6,5] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[6,2,3,7,8,1,5,4] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[6,3,7,8,1,5,4,2] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[2,6,3,7,8,1,5,4] => [[.,[[.,.],[.,[.,.]]]],[[.,.],.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[7,5,8,1,6,4,2,3] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[6,8,2,7,3,1,5,4] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[4,1,5,8,3,6,7,2] => [[.,.],[[[.,[.,.]],[.,[.,.]]],.]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[3,4,7,2,1,5,8,6] => [[[.,[.,[.,.]]],.],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[4,8,2,7,1,3,6,5] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[4,2,5,8,3,6,7,1] => [[[.,.],[[.,[.,.]],[.,[.,.]]]],.] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1

[5,1,6,8,3,2,7,4] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3

[4,1,5,6,8,2,7,3] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[4,5,2,8,7,3,1,6] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[6,2,3,1,7,8,5,4] => [[[.,.],[.,.]],[[[.,[.,.]],.],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[5,2,3,6,8,4,7,1] => [[[.,.],[.,[[.,[.,.]],[.,.]]]],.] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1

[5,2,7,8,4,1,6,3] => [[[.,.],[[.,[.,.]],.]],[[.,.],.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[6,2,7,8,3,5,4,1] => [[[.,.],[[.,[.,.]],[[.,.],.]]],.] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1

[6,7,8,3,2,5,4,1] => [[[[.,[.,[.,.]]],.],[[.,.],.]],.] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1

[5,7,2,6,4,8,1,3] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[6,2,3,4,7,8,5,1] => [[[.,.],[.,[.,[[.,[.,.]],.]]]],.] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 1

[6,2,3,7,8,1,4,5] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[6,1,4,7,2,8,5,3] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3

[1,6,7,2,4,8,5,3] => [.,[[.,[.,.]],[[.,[[.,.],.]],.]]] => [1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 3

[5,7,2,4,3,6,8,1] => [[[.,[.,.]],[[.,.],[.,[.,.]]]],.] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 1

[5,7,3,4,6,2,8,1] => [[[[.,[.,.]],[.,[.,.]]],[.,.]],.] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[7,3,8,2,1,4,5,6] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[6,3,5,8,1,7,4,2] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[4,3,5,2,8,1,6,7] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[5,4,6,8,1,3,2,7] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,6,1,5,8,4,7,2] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2

[6,4,8,3,5,7,2,1] => [[[[[.,.],[.,.]],[.,[.,.]]],.],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1

[3,5,8,2,4,1,7,6] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[5,8,1,2,4,3,6,7] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5

[6,3,5,8,2,4,7,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1

[7,5,6,2,8,4,3,1] => [[[[.,.],[.,.]],[[[.,.],.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1

[6,3,8,1,2,5,4,7] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[1,5,7,2,4,3,6,8] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 5

[1,4,7,2,6,5,3,8] => [.,[[.,[.,.]],[[[.,.],.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 4

[1,2,5,7,4,3,8,6] => [.,[.,[[[.,[.,.]],.],[[.,.],.]]]] => [1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 4

[1,5,7,4,2,3,8,6] => [.,[[[.,[.,.]],.],[.,[[.,.],.]]]] => [1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 4

[3,8,2,7,5,4,1,6] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[3,7,2,8,1,6,4,5] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,2,4,1,6,7,8,3] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[4,2,7,1,6,8,3,5] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[6,1,3,4,7,2,8,5] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[8,4,7,2,5,3,1,6] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[8,3,4,5,2,1,7,6] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[5,3,6,7,2,8,4,1] => [[[[.,.],[.,[.,.]]],[[.,.],.]],.] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => 1

[5,3,6,7,2,4,8,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1

[1,5,8,2,6,7,4,3] => [.,[[.,[.,.]],[[[.,[.,.]],.],.]]] => [1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 3

[7,6,8,1,3,5,4,2] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[1,2,4,6,8,5,3,7] => [.,[.,[[.,[[.,[.,.]],.]],[.,.]]]] => [1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 4

[2,5,4,6,8,1,3,7] => [[.,[[.,.],[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[8,1,4,7,2,3,5,6] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[4,3,7,1,8,5,2,6] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[4,7,3,1,8,5,2,6] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[3,7,8,2,5,6,1,4] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[7,8,6,1,2,4,5,3] => [[[.,[.,.]],.],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 3

[5,1,2,4,7,8,6,3] => [[.,.],[.,[[.,[[.,[.,.]],.]],.]]] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 3

[5,1,7,8,6,2,3,4] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[8,1,6,7,5,2,3,4] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[2,4,7,3,5,1,6,8] => [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[3,4,6,2,1,5,8,7] => [[[.,[.,[.,.]]],.],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[3,4,7,2,1,6,5,8] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[2,3,6,1,5,8,4,7] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[2,3,7,1,6,5,8,4] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[2,4,7,1,3,6,8,5] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[5,4,7,8,1,3,2,6] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,5,7,1,4,6,3,8] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[2,4,7,1,6,3,5,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[2,3,7,1,6,5,4,8] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[2,5,7,1,4,3,6,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[2,5,7,3,1,4,6,8] => [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4

[3,4,7,2,1,6,8,5] => [[[.,[.,[.,.]]],.],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[4,6,3,7,1,5,2,8] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,7,3,2,8,1,4,6] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[3,6,8,5,4,1,7,2] => [[.,[[[.,[.,.]],.],.]],[[.,.],.]] => [1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 2

[5,4,7,8,1,3,6,2] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[2,5,7,1,4,6,8,3] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[2,4,7,1,6,3,8,5] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[2,4,7,1,6,8,3,5] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[4,2,5,7,3,1,6,8] => [[[.,.],[[.,[.,.]],.]],[.,[.,.]]] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[8,2,4,5,3,1,6,7] => [[[.,.],[[.,[.,.]],.]],[.,[.,.]]] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[8,4,5,1,3,2,6,7] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[1,6,7,4,3,2,5,8] => [.,[[[[.,[.,.]],.],.],[.,[.,.]]]] => [1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 4

[1,4,5,7,3,2,6,8] => [.,[[[.,[.,[.,.]]],.],[.,[.,.]]]] => [1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[3,5,1,4,7,2,6,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[2,5,1,4,7,8,3,6] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[4,3,7,1,5,2,6,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[3,5,1,6,4,2,7,8] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[7,2,4,1,3,6,8,5] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[5,6,2,1,4,3,7,8] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[2,5,1,6,4,3,7,8] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[4,6,1,5,2,7,3,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[5,8,2,6,1,7,4,3] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[1,5,8,3,6,2,7,4] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 3

[1,2,7,8,3,5,6,4] => [.,[.,[[.,[.,.]],[[.,[.,.]],.]]]] => [1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 4

[2,7,4,5,8,1,6,3] => [[.,[[.,.],[.,[.,.]]]],[[.,.],.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[2,6,1,8,5,4,3,7] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[7,5,6,2,4,3,8,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[4,6,2,5,7,3,8,1] => [[[.,[.,.]],[[.,[.,.]],[.,.]]],.] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 1

[2,1,7,8,4,5,6,3] => [[.,.],[[[.,[.,.]],[.,[.,.]]],.]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[6,2,3,1,7,8,4,5] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[4,2,5,1,8,6,7,3] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[4,5,3,7,1,6,8,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[3,5,2,8,6,4,7,1] => [[[.,[.,.]],[[[.,.],.],[.,.]]],.] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 1

[7,3,5,1,6,4,8,2] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[5,1,4,7,2,6,8,3] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3

[2,7,1,4,8,5,6,3] => [[.,[.,.]],[[.,[[.,.],[.,.]]],.]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 2

[8,4,6,2,5,3,7,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[5,8,2,7,6,1,4,3] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[5,4,7,1,3,8,6,2] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[5,8,2,3,4,6,1,7] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[6,1,3,4,2,5,7,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[1,5,6,3,2,4,7,8] => [.,[[[.,[.,.]],.],[.,[.,[.,.]]]]] => [1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 5

[6,3,5,2,4,1,7,8] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[7,8,3,5,2,4,6,1] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1

[2,4,5,7,3,6,1,8] => [[.,[[.,[.,[.,.]]],[.,.]]],[.,.]] => [1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[5,7,4,3,2,6,1,8] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2

[2,6,7,8,4,3,5,1] => [[.,[[[.,[.,[.,.]]],.],[.,.]]],.] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1

[1,7,8,4,5,3,6,2] => [.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 2

[5,7,4,2,1,6,3,8] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[5,1,4,7,3,6,2,8] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[7,1,3,6,8,2,5,4] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[3,6,7,5,8,2,4,1] => [[[.,[[.,[.,.]],[.,.]]],[.,.]],.] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[3,6,7,4,2,8,5,1] => [[[.,[[.,[.,.]],.]],[[.,.],.]],.] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[4,6,3,2,7,8,5,1] => [[[[.,[.,.]],.],[[.,[.,.]],.]],.] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 1

[7,8,2,6,4,5,3,1] => [[[.,[.,.]],[[[.,.],[.,.]],.]],.] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 1

[7,1,2,4,5,6,3,8] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 4

[3,6,2,1,7,5,4,8] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[2,6,7,3,1,5,4,8] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[7,6,8,5,4,1,3,2] => [[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[7,8,6,3,1,5,4,2] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2

[7,1,5,6,4,3,2,8] => [[.,.],[[[[.,[.,.]],.],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => 3

[5,6,3,2,8,1,7,4] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[8,2,5,6,7,4,3,1] => [[[.,.],[[[.,[.,[.,.]]],.],.]],.] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => 1

[7,1,2,3,6,8,4,5] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => 5

[6,7,2,8,3,4,5,1] => [[[.,[.,.]],[[.,.],[.,[.,.]]]],.] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 1

[8,1,6,7,4,2,3,5] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[7,4,5,1,2,8,6,3] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[6,4,7,1,8,5,2,3] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[5,7,4,2,3,8,6,1] => [[[[.,[.,.]],.],[.,[[.,.],.]]],.] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 1

[3,8,2,5,1,7,4,6] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,8,4,2,3,7,1,6] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[4,6,8,3,7,1,2,5] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[3,5,2,8,4,7,1,6] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[6,4,8,3,7,2,1,5] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[3,6,2,8,7,4,1,5] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[6,8,4,2,7,3,1,5] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[3,4,7,8,5,1,2,6] => [[.,[.,[[.,[.,.]],.]]],[.,[.,.]]] => [1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 3

[4,7,3,2,5,6,8,1] => [[[[.,[.,.]],.],[.,[.,[.,.]]]],.] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1

[1,7,8,2,4,3,5,6] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 5

[5,7,4,8,1,3,2,6] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,3,7,8,1,5,2,6] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[1,5,8,2,4,3,6,7] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 5

[4,3,6,8,1,5,2,7] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,4,6,8,3,1,7,2] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[3,6,8,4,5,1,7,2] => [[.,[[.,[.,.]],[.,.]]],[[.,.],.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2

[3,2,7,8,6,4,1,5] => [[[.,.],[[[.,[.,.]],.],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => 2

[1,6,8,3,2,4,7,5] => [.,[[[.,[.,.]],.],[.,[[.,.],.]]]] => [1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 4

[5,6,2,8,4,1,3,7] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[3,5,8,4,2,1,6,7] => [[[.,[[.,[.,.]],.]],.],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 3

[2,5,8,3,1,4,6,7] => [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4

[2,8,1,3,5,7,4,6] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4

[5,4,7,8,3,2,6,1] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1

[3,6,8,2,5,1,4,7] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[2,4,6,7,8,3,5,1] => [[.,[[.,[.,[.,[.,.]]]],[.,.]]],.] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1

[1,2,6,8,3,5,4,7] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => [1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 5

[1,6,8,3,5,4,2,7] => [.,[[[.,[.,.]],[[.,.],.]],[.,.]]] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 3

[1,4,6,3,2,7,5,8] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 4

[1,4,6,3,2,8,7,5] => [.,[[[.,[.,.]],.],[[[.,.],.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 3

[6,4,7,1,5,3,8,2] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[4,3,8,2,6,5,7,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[5,7,1,4,8,2,3,6] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[6,5,7,1,4,3,8,2] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[1,3,4,2,8,5,7,6] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 4

[4,7,1,5,2,6,3,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[1,3,7,8,4,5,6,2] => [.,[[.,[[.,[.,.]],[.,[.,.]]]],.]] => [1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 2

[6,4,5,2,8,1,7,3] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[8,2,4,6,7,1,5,3] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[3,2,6,7,8,4,5,1] => [[[.,.],[[.,[.,[.,.]]],[.,.]]],.] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1

[5,6,4,1,3,8,2,7] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[4,5,3,1,8,7,6,2] => [[[.,[.,.]],.],[[[[.,.],.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2

[6,3,4,2,7,8,5,1] => [[[[.,.],[.,.]],[[.,[.,.]],.]],.] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[6,2,7,8,1,3,5,4] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[7,2,8,1,4,5,6,3] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[1,4,8,2,5,6,7,3] => [.,[[.,[.,.]],[[.,[.,[.,.]]],.]]] => [1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 3

[8,1,6,7,2,5,4,3] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3

[4,5,8,1,6,7,2,3] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[3,7,2,5,8,4,6,1] => [[[.,[.,.]],[[.,[.,.]],[.,.]]],.] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 1

[6,7,8,4,1,5,2,3] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[6,8,2,5,3,4,1,7] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[7,4,5,6,1,8,2,3] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,8,2,7,5,3,6,1] => [[[.,[.,.]],[[[.,.],.],[.,.]]],.] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 1

[1,3,8,2,5,4,6,7] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 5

[1,3,8,2,5,4,7,6] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 4

[1,6,7,5,2,4,8,3] => [.,[[[.,[.,.]],.],[[.,[.,.]],.]]] => [1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3

[1,5,6,4,7,2,3,8] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 4

[1,5,8,2,3,6,7,4] => [.,[[.,[.,.]],[.,[[.,[.,.]],.]]]] => [1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 4

[1,7,8,5,4,2,3,6] => [.,[[[[.,[.,.]],.],.],[.,[.,.]]]] => [1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 4

[1,4,8,3,2,7,5,6] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 4

[8,5,7,2,3,6,4,1] => [[[[.,.],[.,.]],[.,[[.,.],.]]],.] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[6,8,2,3,4,7,1,5] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[8,3,4,1,6,5,2,7] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[5,8,4,7,3,6,2,1] => [[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1

[6,5,8,2,1,7,4,3] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[5,6,3,8,7,2,1,4] => [[[[.,[.,.]],[[.,.],.]],.],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2

[2,5,8,4,7,1,6,3] => [[.,[[.,[.,.]],[.,.]]],[[.,.],.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2

[2,7,1,3,6,4,5,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5

[6,4,5,8,3,1,7,2] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[4,6,2,8,5,3,7,1] => [[[.,[.,.]],[[[.,.],.],[.,.]]],.] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 1

[5,8,3,7,6,4,2,1] => [[[[.,[.,.]],[[[.,.],.],.]],.],.] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 1

[1,2,5,7,4,8,6,3] => [.,[.,[[[.,[.,.]],[[.,.],.]],.]]] => [1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 3

[2,8,3,4,1,5,6,7] => [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[4,5,6,3,1,8,2,7] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[1,5,6,3,8,4,2,7] => [.,[[[.,[.,.]],[[.,.],.]],[.,.]]] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 3

[5,7,3,8,4,2,6,1] => [[[[.,[.,.]],[[.,.],.]],[.,.]],.] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 1

[5,3,6,2,8,4,1,7] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[5,3,7,1,2,8,4,6] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[6,8,4,1,7,5,2,3] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[8,1,4,6,7,5,2,3] => [[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3

[2,6,8,1,4,7,5,3] => [[.,[.,[.,.]]],[[.,[[.,.],.]],.]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[6,4,8,1,2,7,5,3] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[4,2,8,1,6,7,5,3] => [[[.,.],[.,.]],[[[.,[.,.]],.],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[4,8,1,2,6,7,5,3] => [[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 3

[4,8,2,1,6,7,5,3] => [[[.,[.,.]],.],[[[.,[.,.]],.],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 2

[8,2,4,6,1,7,5,3] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[3,6,8,4,1,5,2,7] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[4,6,1,3,2,8,7,5] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[7,1,4,8,2,3,6,5] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[4,5,3,6,7,1,8,2] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[1,4,7,8,3,5,2,6] => [.,[[[.,[.,[.,.]]],[.,.]],[.,.]]] => [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[2,4,5,6,8,3,1,7] => [[.,[[.,[.,[.,[.,.]]]],.]],[.,.]] => [1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 2

[4,5,1,8,6,3,7,2] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2

[8,3,7,2,1,6,5,4] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[8,4,7,3,6,2,1,5] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[1,5,6,3,8,2,7,4] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 3

[1,5,7,3,4,2,8,6] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 3

[1,4,5,3,8,2,7,6] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 3

[5,1,6,8,3,7,2,4] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[5,4,7,1,8,6,3,2] => [[[.,.],[.,.]],[[[[.,.],.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[1,4,8,2,6,5,3,7] => [.,[[.,[.,.]],[[[.,.],.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 4

[5,2,8,1,7,4,3,6] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[1,5,6,8,2,7,4,3] => [.,[[.,[.,[.,.]]],[[[.,.],.],.]]] => [1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3

[2,6,7,3,4,1,8,5] => [[.,[[.,[.,.]],[.,.]]],[[.,.],.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2

[1,5,6,7,2,8,4,3] => [.,[[.,[.,[.,.]]],[[[.,.],.],.]]] => [1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3

[1,3,7,2,6,4,8,5] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 4

[5,4,7,8,1,6,3,2] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[2,5,6,8,1,3,7,4] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[5,3,6,8,1,2,7,4] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[4,5,6,8,2,3,7,1] => [[[.,[.,[.,[.,.]]]],[.,[.,.]]],.] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1

[7,3,6,8,5,2,1,4] => [[[[.,.],[[.,[.,.]],.]],.],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => 2

[8,3,6,7,5,2,4,1] => [[[[.,.],[[.,[.,.]],.]],[.,.]],.] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[8,4,5,7,3,6,2,1] => [[[[[.,.],[.,[.,.]]],[.,.]],.],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1

[2,4,7,8,5,6,3,1] => [[.,[[.,[[.,[.,.]],[.,.]]],.]],.] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1

[6,4,7,8,5,1,3,2] => [[[.,.],[[.,[.,.]],.]],[[.,.],.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[7,8,4,6,5,3,1,2] => [[[[.,[.,.]],[[.,.],.]],.],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2

[6,8,4,7,5,1,3,2] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[5,8,3,7,1,4,6,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[1,3,4,7,2,6,5,8] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[2,5,1,4,3,6,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[5,3,8,2,4,6,1,7] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[4,5,8,3,2,6,1,7] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[5,8,2,1,4,6,3,7] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[4,1,5,8,3,6,2,7] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[4,5,8,3,6,1,2,7] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[3,2,7,1,8,5,4,6] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[4,7,8,5,2,3,1,6] => [[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => [1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[6,2,7,8,1,5,3,4] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[2,7,1,3,8,5,4,6] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 4

[2,6,7,8,4,1,3,5] => [[.,[[.,[.,[.,.]]],.]],[.,[.,.]]] => [1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[2,6,7,8,4,3,1,5] => [[.,[[[.,[.,[.,.]]],.],.]],[.,.]] => [1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 2

[7,4,8,3,1,2,6,5] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[8,4,5,3,1,6,7,2] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[8,2,3,1,6,7,4,5] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[7,2,6,8,4,1,3,5] => [[[.,.],[[.,[.,.]],.]],[.,[.,.]]] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[7,2,5,1,6,8,3,4] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[5,1,3,4,6,2,8,7] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[3,8,4,5,7,2,6,1] => [[[.,[[.,.],[.,[.,.]]]],[.,.]],.] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[3,5,6,8,4,7,1,2] => [[.,[[.,[.,[.,.]]],[.,.]]],[.,.]] => [1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[4,5,2,1,8,7,3,6] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[4,7,3,8,2,6,5,1] => [[[[.,[.,.]],[.,.]],[[.,.],.]],.] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 1

[4,7,3,1,8,6,2,5] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[6,3,7,1,2,5,8,4] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[5,1,4,7,8,2,6,3] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[7,2,5,8,1,3,6,4] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[8,3,6,7,2,4,5,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1

[6,8,3,2,5,7,4,1] => [[[[.,[.,.]],.],[[.,[.,.]],.]],.] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 1

[6,1,2,4,5,7,8,3] => [[.,.],[.,[[.,[.,[.,[.,.]]]],.]]] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 3

[4,5,1,3,7,6,8,2] => [[.,[.,.]],[[.,[[.,.],[.,.]]],.]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 2

[3,6,2,4,5,8,7,1] => [[[.,[.,.]],[.,[.,[[.,.],.]]]],.] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 1

[3,5,1,4,6,2,7,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[2,5,1,4,6,7,3,8] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[3,8,1,7,4,2,6,5] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[6,8,2,4,5,3,7,1] => [[[.,[.,.]],[[.,[.,.]],[.,.]]],.] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 1

[3,5,7,4,8,1,6,2] => [[.,[[.,[.,.]],[.,.]]],[[.,.],.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2

[2,8,1,3,5,4,6,7] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5

[3,6,8,4,1,2,5,7] => [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4

[4,7,8,5,2,1,3,6] => [[[.,[[.,[.,.]],.]],.],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 3

[8,1,3,5,7,4,2,6] => [[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3

[5,1,3,4,2,6,8,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[4,2,5,1,8,7,3,6] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[6,8,2,7,1,4,3,5] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,8,3,1,4,7,6,2] => [[[.,[.,.]],.],[[.,[[.,.],.]],.]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 2

[4,7,1,2,5,3,6,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5

[6,8,4,1,3,7,2,5] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[3,2,6,1,7,8,5,4] => [[[.,.],[.,.]],[[[.,[.,.]],.],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[8,2,4,6,1,7,3,5] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[1,5,7,2,3,6,8,4] => [.,[[.,[.,.]],[.,[[.,[.,.]],.]]]] => [1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 4

[4,3,5,1,6,2,7,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[4,8,1,7,6,3,5,2] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2

[5,4,8,3,1,7,2,6] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[5,1,4,8,3,2,7,6] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3

[4,8,1,7,6,5,2,3] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[8,2,5,7,4,3,6,1] => [[[.,.],[[[.,[.,.]],.],[.,.]]],.] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1

[5,4,8,2,1,3,7,6] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[2,6,8,3,1,7,4,5] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[7,8,2,6,3,5,4,1] => [[[.,[.,.]],[[.,.],[[.,.],.]]],.] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 1

[5,6,3,1,4,2,7,8] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[2,6,1,5,3,4,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[3,4,7,8,5,1,6,2] => [[.,[.,[[.,[.,.]],.]]],[[.,.],.]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 2

[3,6,2,4,7,8,5,1] => [[[.,[.,.]],[.,[[.,[.,.]],.]]],.] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 1

[5,8,3,1,2,7,6,4] => [[[.,[.,.]],.],[.,[[[.,.],.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 3

[8,4,6,1,3,7,2,5] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[4,5,1,3,8,6,2,7] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3

[2,1,6,7,4,8,3,5] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[7,8,1,3,6,4,5,2] => [[.,[.,.]],[[.,[[.,.],[.,.]]],.]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 2

[7,2,6,8,4,5,3,1] => [[[.,.],[[[.,[.,.]],[.,.]],.]],.] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1

[7,3,6,8,5,1,4,2] => [[[.,.],[[.,[.,.]],.]],[[.,.],.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[7,5,8,1,6,2,4,3] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[5,7,8,1,6,3,2,4] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[7,2,6,8,5,1,4,3] => [[[.,.],[[.,[.,.]],.]],[[.,.],.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[7,8,3,1,6,2,5,4] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[6,7,8,4,3,1,5,2] => [[[[.,[.,[.,.]]],.],.],[[.,.],.]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[7,8,3,6,4,1,5,2] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[7,3,8,1,6,4,5,2] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[3,7,8,2,6,5,1,4] => [[[.,[.,[.,.]]],[[.,.],.]],[.,.]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[3,7,8,2,1,6,4,5] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[7,8,1,6,3,5,4,2] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2

[6,7,8,2,5,4,3,1] => [[[.,[.,[.,.]]],[[[.,.],.],.]],.] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1

[6,7,8,3,1,5,4,2] => [[[.,[.,[.,.]]],.],[[[.,.],.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[7,8,1,6,2,5,4,3] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[5,6,1,4,3,8,2,7] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[5,1,6,8,3,4,7,2] => [[.,.],[[[.,[.,.]],[.,[.,.]]],.]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[7,1,6,8,5,4,3,2] => [[.,.],[[[[[.,[.,.]],.],.],.],.]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2

[5,6,8,1,2,3,7,4] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[4,8,1,2,7,6,5,3] => [[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 3

[4,6,1,2,8,5,7,3] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 3

[6,4,7,3,5,2,1,8] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[5,7,8,4,2,1,3,6] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3

[1,2,4,6,8,3,7,5] => [.,[.,[[.,[.,[.,.]]],[[.,.],.]]]] => [1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 4

[1,3,5,8,2,6,7,4] => [.,[[.,[.,[.,.]]],[[.,[.,.]],.]]] => [1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3

[6,1,3,7,2,8,5,4] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3

[6,4,5,8,3,7,1,2] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[2,6,8,4,3,1,7,5] => [[.,[[[.,[.,.]],.],.]],[[.,.],.]] => [1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 2

[1,6,7,4,2,8,3,5] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 4

[1,7,8,4,3,6,2,5] => [.,[[[[.,[.,.]],.],[.,.]],[.,.]]] => [1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 3

[1,4,7,2,3,6,8,5] => [.,[[.,[.,.]],[.,[[.,[.,.]],.]]]] => [1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 4

[3,1,2,6,7,8,5,4] => [[.,.],[.,[[[.,[.,[.,.]]],.],.]]] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => 3

[3,8,1,6,4,2,7,5] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[1,6,3,4,7,8,2,5] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[2,6,1,8,7,4,3,5] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[5,7,8,1,4,2,6,3] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[2,5,1,8,6,3,7,4] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[2,8,1,7,5,3,6,4] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[4,1,7,8,6,3,5,2] => [[.,.],[[[[.,[.,.]],.],[.,.]],.]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 2

[4,8,2,6,3,5,1,7] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[4,3,5,7,1,6,2,8] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,1,5,8,2,7,4,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[4,5,2,7,1,6,3,8] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,3,5,7,1,6,8,2] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[3,1,6,8,5,7,4,2] => [[.,.],[[[[.,[.,.]],[.,.]],.],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[2,6,1,8,5,7,4,3] => [[.,[.,.]],[[[[.,.],[.,.]],.],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 2

[2,1,6,8,5,3,7,4] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3

[3,2,6,8,5,4,7,1] => [[[.,.],[[[.,[.,.]],.],[.,.]]],.] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1

[3,1,6,8,5,2,4,7] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[3,6,2,4,8,5,7,1] => [[[.,[.,.]],[.,[[.,.],[.,.]]]],.] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 1

[3,5,1,8,4,7,6,2] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2

[3,6,1,8,5,4,7,2] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2

[2,4,8,3,7,6,5,1] => [[.,[[.,[.,.]],[[[.,.],.],.]]],.] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 1

[3,6,8,2,5,7,4,1] => [[[.,[.,[.,.]]],[[.,[.,.]],.]],.] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[2,6,8,5,4,3,7,1] => [[.,[[[[.,[.,.]],.],.],[.,.]]],.] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 1

[3,6,8,2,5,4,7,1] => [[[.,[.,[.,.]]],[[.,.],[.,.]]],.] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[4,6,8,3,2,5,7,1] => [[[[.,[.,[.,.]]],.],[.,[.,.]]],.] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1

[4,6,2,8,3,5,7,1] => [[[.,[.,.]],[[.,.],[.,[.,.]]]],.] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 1

[3,6,1,8,5,7,4,2] => [[.,[.,.]],[[[[.,.],[.,.]],.],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 2

[5,2,6,8,4,1,7,3] => [[[.,.],[[.,[.,.]],.]],[[.,.],.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[4,6,3,8,7,2,5,1] => [[[[.,[.,.]],[[.,.],.]],[.,.]],.] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 1

[3,5,8,2,7,4,6,1] => [[[.,[.,[.,.]]],[[.,.],[.,.]]],.] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[2,6,8,5,7,4,3,1] => [[.,[[[[.,[.,.]],[.,.]],.],.]],.] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[4,8,2,1,7,5,6,3] => [[[.,[.,.]],.],[[[.,.],[.,.]],.]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[6,2,8,1,7,5,3,4] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[3,5,1,8,7,6,2,4] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[5,6,2,7,8,1,3,4] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[4,7,8,3,5,6,1,2] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[3,2,5,6,8,4,7,1] => [[[.,.],[[.,[.,[.,.]]],[.,.]]],.] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1

[2,5,6,4,8,3,7,1] => [[.,[[[.,[.,.]],[.,.]],[.,.]]],.] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1

[4,2,5,7,3,8,1,6] => [[[.,.],[[.,[.,.]],[.,.]]],[.,.]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[4,7,3,1,6,8,2,5] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[4,7,2,5,6,3,1,8] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[6,1,5,8,3,7,2,4] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[5,6,4,1,8,3,2,7] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[4,5,2,1,7,8,3,6] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[2,3,7,8,5,1,6,4] => [[.,[.,[[.,[.,.]],.]]],[[.,.],.]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 2

[1,2,6,7,4,3,5,8] => [.,[.,[[[.,[.,.]],.],[.,[.,.]]]]] => [1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 5

[6,2,3,1,8,5,4,7] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[4,5,2,8,6,1,3,7] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[3,4,8,2,5,6,1,7] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[6,8,2,7,5,3,1,4] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[5,6,7,2,8,4,1,3] => [[[.,[.,[.,.]]],[[.,.],.]],[.,.]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[5,8,3,6,4,1,7,2] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[3,2,5,8,4,7,1,6] => [[[.,.],[[.,[.,.]],[.,.]]],[.,.]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[3,5,1,8,7,4,2,6] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[4,6,1,3,8,2,7,5] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[5,1,7,8,3,2,4,6] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[5,3,6,7,4,2,8,1] => [[[[.,.],[[.,[.,.]],.]],[.,.]],.] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[3,7,2,6,8,4,5,1] => [[[.,[.,.]],[[.,[.,.]],[.,.]]],.] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 1

[5,4,6,2,7,8,3,1] => [[[[.,.],[.,.]],[[.,[.,.]],.]],.] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[5,4,6,2,3,1,8,7] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[6,5,7,8,1,3,4,2] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[6,4,7,2,8,3,1,5] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[1,4,8,2,7,6,5,3] => [.,[[.,[.,.]],[[[[.,.],.],.],.]]] => [1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 3

[4,7,3,1,5,2,8,6] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[4,7,3,6,5,2,8,1] => [[[[.,[.,.]],[[.,.],.]],[.,.]],.] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 1

[2,4,7,3,8,5,1,6] => [[.,[[.,[.,.]],[[.,.],.]]],[.,.]] => [1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2

[6,7,5,2,1,4,8,3] => [[[[.,[.,.]],.],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 2

[1,2,6,8,3,4,7,5] => [.,[.,[[.,[.,.]],[.,[[.,.],.]]]]] => [1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 5

[3,4,2,8,6,7,5,1] => [[[.,[.,.]],[[[.,.],[.,.]],.]],.] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 1

[3,7,8,6,1,4,2,5] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[3,6,1,5,2,7,8,4] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[7,1,6,8,3,4,2,5] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[3,7,8,4,2,5,6,1] => [[[.,[[.,[.,.]],.]],[.,[.,.]]],.] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 1

[3,4,2,8,5,1,6,7] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[6,8,2,7,5,4,1,3] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[2,7,8,5,1,4,6,3] => [[.,[[.,[.,.]],.]],[[.,[.,.]],.]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 2

[2,7,8,1,5,4,6,3] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[2,7,8,1,4,5,6,3] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[5,4,7,8,6,3,1,2] => [[[[.,.],[[.,[.,.]],.]],.],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => 2

[4,5,7,8,2,6,1,3] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,7,3,4,2,1,6,8] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3

[6,8,2,7,5,1,4,3] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[8,3,4,5,6,1,7,2] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[5,4,6,2,7,3,1,8] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[4,3,7,2,8,5,1,6] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[4,3,6,2,8,5,1,7] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[5,3,7,2,8,6,1,4] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[4,8,1,7,3,2,5,6] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[3,7,8,2,5,4,6,1] => [[[.,[.,[.,.]]],[[.,.],[.,.]]],.] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[6,7,1,3,2,5,8,4] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[5,3,6,2,4,1,8,7] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[7,8,6,2,3,5,4,1] => [[[[.,[.,.]],.],[.,[[.,.],.]]],.] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 1

[5,8,2,6,3,7,4,1] => [[[.,[.,.]],[[.,.],[[.,.],.]]],.] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 1

[4,8,2,3,7,5,6,1] => [[[.,[.,.]],[.,[[.,.],[.,.]]]],.] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 1

[7,5,6,2,3,8,4,1] => [[[[.,.],[.,.]],[.,[[.,.],.]]],.] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[7,8,6,3,5,4,2,1] => [[[[[.,[.,.]],.],[[.,.],.]],.],.] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 1

[2,4,8,3,7,5,6,1] => [[.,[[.,[.,.]],[[.,.],[.,.]]]],.] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 1

[4,8,3,7,5,6,2,1] => [[[[.,[.,.]],[[.,.],[.,.]]],.],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 1

[6,2,5,8,3,7,4,1] => [[[.,.],[[.,[.,.]],[[.,.],.]]],.] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1

[4,7,3,8,2,5,6,1] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1

[8,2,5,6,3,7,4,1] => [[[.,.],[[.,[.,.]],[[.,.],.]]],.] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1

[4,5,3,7,1,2,6,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[8,5,6,4,1,3,2,7] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[6,7,2,8,4,3,1,5] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[6,7,3,2,8,4,1,5] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[4,7,8,3,1,5,2,6] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[4,5,8,1,3,2,6,7] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[4,7,8,1,6,3,2,5] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[4,7,1,3,8,6,5,2] => [[.,[.,.]],[[.,[[[.,.],.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 2

[5,7,2,8,3,4,6,1] => [[[.,[.,.]],[[.,.],[.,[.,.]]]],.] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 1

[3,7,2,8,5,6,4,1] => [[[.,[.,.]],[[[.,.],[.,.]],.]],.] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 1

[2,5,6,1,8,7,3,4] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[3,6,2,8,4,7,5,1] => [[[.,[.,.]],[[.,.],[[.,.],.]]],.] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 1

[8,5,6,3,1,4,2,7] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[5,7,8,3,4,6,2,1] => [[[[.,[.,[.,.]]],[.,[.,.]]],.],.] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1

[3,5,1,8,6,4,2,7] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[1,5,8,3,6,4,2,7] => [.,[[[.,[.,.]],[[.,.],.]],[.,.]]] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 3

[7,5,8,3,6,4,2,1] => [[[[[.,.],[.,.]],[[.,.],.]],.],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

[5,7,8,1,4,6,2,3] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[1,3,7,8,4,2,6,5] => [.,[[.,[[.,[.,.]],.]],[[.,.],.]]] => [1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 3

[6,7,3,5,4,1,2,8] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[8,1,6,7,3,5,4,2] => [[.,.],[[[.,[.,.]],[[.,.],.]],.]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2

[7,2,4,1,6,5,3,8] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[4,2,5,1,3,7,6,8] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[5,7,8,3,2,6,1,4] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[8,4,5,1,3,7,6,2] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[5,8,2,7,1,3,6,4] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[4,5,1,7,6,3,2,8] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[3,2,4,5,7,8,1,6] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2

[7,8,5,4,2,1,6,3] => [[[[[.,[.,.]],.],.],.],[[.,.],.]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2

[7,8,3,2,6,5,4,1] => [[[[.,[.,.]],.],[[[.,.],.],.]],.] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 1

[8,6,7,2,5,3,1,4] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[1,6,8,2,7,5,3,4] => [.,[[.,[.,.]],[[[.,.],.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 4

[1,7,8,6,4,2,3,5] => [.,[[[[.,[.,.]],.],.],[.,[.,.]]]] => [1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 4

[4,3,7,2,8,1,6,5] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[7,5,6,1,3,2,8,4] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[7,3,4,1,8,2,6,5] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[7,4,5,1,6,3,8,2] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[7,5,6,1,4,3,8,2] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[5,3,4,1,6,2,8,7] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[6,5,7,3,4,1,8,2] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[7,5,6,1,8,2,4,3] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[7,3,6,1,8,2,5,4] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[7,2,8,1,6,3,5,4] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[6,5,7,1,2,8,3,4] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[6,8,5,2,4,3,1,7] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[3,4,2,8,6,7,1,5] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[3,7,1,6,2,5,8,4] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[4,6,7,2,5,1,8,3] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[3,6,2,5,1,7,8,4] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[3,4,2,7,8,1,5,6] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[7,8,5,1,2,4,3,6] => [[[.,[.,.]],.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[5,8,1,4,3,6,7,2] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 2

[4,6,2,7,8,1,3,5] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[6,2,3,7,1,4,5,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[4,6,7,8,2,1,3,5] => [[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[6,1,3,4,2,5,8,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[5,1,3,6,2,4,8,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[5,7,1,3,8,4,2,6] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3

[2,6,1,4,3,7,8,5] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[1,5,6,3,7,8,4,2] => [.,[[[.,[.,.]],[[.,[.,.]],.]],.]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 2

[7,3,5,6,1,8,4,2] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[1,7,8,6,3,5,4,2] => [.,[[[[.,[.,.]],.],[[.,.],.]],.]] => [1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 2

[5,6,2,8,4,7,3,1] => [[[.,[.,.]],[[[.,.],[.,.]],.]],.] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 1

[7,8,5,1,3,2,4,6] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[7,1,3,8,2,5,4,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[6,8,5,3,2,7,1,4] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2

[8,3,7,2,6,5,1,4] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[4,6,2,7,1,3,8,5] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[3,5,1,4,7,2,8,6] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[6,1,3,4,2,7,8,5] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3

[7,4,8,2,3,5,1,6] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[3,1,6,8,4,2,7,5] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3

[5,6,2,3,7,4,1,8] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[6,2,4,7,3,5,1,8] => [[[.,.],[[.,[.,.]],[.,.]]],[.,.]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[2,5,6,3,1,8,4,7] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[4,5,1,2,7,8,6,3] => [[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 3

[4,6,7,5,1,2,8,3] => [[.,[[.,[.,.]],.]],[.,[[.,.],.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 3

[7,2,8,1,4,5,3,6] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[6,1,4,7,3,8,2,5] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[6,7,5,1,3,8,2,4] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[7,8,6,2,4,1,3,5] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[8,2,4,1,3,6,7,5] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[8,1,3,6,2,5,7,4] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3

[1,5,6,3,8,4,7,2] => [.,[[[.,[.,.]],[[.,.],[.,.]]],.]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 2

[5,6,1,3,7,2,8,4] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[5,6,1,8,2,3,7,4] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[5,6,1,2,8,4,7,3] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 3

[3,7,8,1,6,4,2,5] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[1,7,8,6,3,4,2,5] => [.,[[[[.,[.,.]],.],[.,.]],[.,.]]] => [1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 3

[5,7,1,8,6,4,2,3] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[7,8,1,5,6,4,2,3] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[8,1,3,5,6,4,2,7] => [[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3

[1,5,7,8,6,4,2,3] => [.,[[[.,[[.,[.,.]],.]],.],[.,.]]] => [1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 3

[2,7,8,4,1,3,5,6] => [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4

[6,8,1,2,3,7,4,5] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 5

[8,1,3,5,6,7,2,4] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 3

[1,4,7,8,5,6,3,2] => [.,[[[.,[[.,[.,.]],[.,.]]],.],.]] => [1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 2

[1,6,8,5,2,7,3,4] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 4

[3,6,1,4,5,7,8,2] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2

[5,7,8,2,4,6,1,3] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[3,8,1,6,4,2,5,7] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[8,2,3,1,7,4,5,6] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[3,1,7,8,6,2,5,4] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3

[4,8,1,2,6,5,7,3] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 3

[5,6,1,8,3,7,2,4] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[2,8,1,6,5,3,7,4] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[4,3,5,1,7,8,6,2] => [[[.,.],[.,.]],[[[.,[.,.]],.],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[1,5,8,2,3,4,7,6] => [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => [1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 5

[1,2,7,8,4,5,6,3] => [.,[.,[[[.,[.,.]],[.,[.,.]]],.]]] => [1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 3

[5,4,8,2,7,6,3,1] => [[[[.,.],[.,.]],[[[.,.],.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1

[3,2,5,6,4,8,1,7] => [[[.,.],[[.,[.,.]],[.,.]]],[.,.]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[2,3,7,1,5,8,4,6] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[2,3,6,1,7,5,8,4] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[4,6,1,7,5,8,3,2] => [[.,[.,.]],[[[[.,.],[.,.]],.],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 2

[3,5,6,2,1,4,7,8] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[3,5,6,4,2,8,1,7] => [[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => [1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[5,8,1,4,2,3,6,7] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[4,5,8,2,3,1,6,7] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[5,3,6,8,1,4,7,2] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[3,5,1,8,6,4,7,2] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2

[4,7,2,8,3,1,6,5] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[1,2,5,6,8,3,7,4] => [.,[.,[[.,[.,[.,.]]],[[.,.],.]]]] => [1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 4

[7,4,8,1,5,2,6,3] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[1,2,5,6,8,4,7,3] => [.,[.,[[[.,[.,[.,.]]],[.,.]],.]]] => [1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 3

[1,5,6,8,4,7,2,3] => [.,[[[.,[.,[.,.]]],[.,.]],[.,.]]] => [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[5,6,8,1,2,4,7,3] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[6,8,1,4,5,7,2,3] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[4,3,5,1,8,6,7,2] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[1,3,5,6,8,4,7,2] => [.,[[.,[[.,[.,[.,.]]],[.,.]]],.]] => [1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 2

[5,6,8,2,3,4,7,1] => [[[.,[.,[.,.]]],[.,[.,[.,.]]]],.] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1

[8,6,7,1,2,5,3,4] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[1,5,6,4,2,8,7,3] => [.,[[[.,[.,.]],.],[[[.,.],.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 3

[3,2,8,1,7,5,6,4] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[6,1,7,8,4,2,3,5] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[7,8,1,6,3,4,5,2] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 2

[6,8,1,7,3,4,2,5] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[4,5,6,3,8,1,7,2] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[7,8,3,5,2,1,6,4] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[6,2,4,5,7,3,1,8] => [[[.,.],[[.,[.,[.,.]]],.]],[.,.]] => [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => 2

[7,8,1,5,6,4,3,2] => [[.,[.,.]],[[[[.,[.,.]],.],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 2

[1,3,8,2,4,6,7,5] => [.,[[.,[.,.]],[.,[[.,[.,.]],.]]]] => [1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 4

[7,1,6,8,2,5,3,4] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[2,3,1,8,4,6,5,7] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[2,3,1,7,6,8,4,5] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[2,3,1,8,4,6,7,5] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[4,2,3,5,1,8,6,7] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,8,5,1,7,4,3,2] => [[[.,[.,.]],.],[[[[.,.],.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2

[6,8,5,2,7,4,1,3] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[7,5,8,1,6,4,3,2] => [[[.,.],[.,.]],[[[[.,.],.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[7,5,8,2,6,4,1,3] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[4,5,3,1,2,8,6,7] => [[[.,[.,.]],.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[2,4,5,3,1,8,6,7] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[2,5,7,4,1,3,6,8] => [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4

[5,7,4,1,3,2,6,8] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[2,6,8,4,5,3,1,7] => [[.,[[[.,[.,.]],[.,.]],.]],[.,.]] => [1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2

[4,5,1,6,3,2,7,8] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[4,2,5,1,6,3,7,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[8,5,7,2,4,3,6,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[6,8,5,2,7,1,3,4] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[6,3,4,7,2,8,5,1] => [[[[.,.],[.,[.,.]]],[[.,.],.]],.] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => 1

[6,8,4,3,1,5,2,7] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[1,4,5,8,3,2,6,7] => [.,[[[.,[.,[.,.]]],.],[.,[.,.]]]] => [1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[7,3,5,2,6,8,1,4] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[1,6,8,3,5,2,4,7] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 4

[1,4,7,3,2,8,6,5] => [.,[[[.,[.,.]],.],[[[.,.],.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 3

[1,6,8,4,3,2,5,7] => [.,[[[[.,[.,.]],.],.],[.,[.,.]]]] => [1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 4

[6,8,5,2,7,1,4,3] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[6,8,2,5,1,7,4,3] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[6,8,5,7,2,1,4,3] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[6,5,8,2,7,4,1,3] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[3,5,6,2,8,7,1,4] => [[[.,[.,[.,.]]],[[.,.],.]],[.,.]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[4,2,6,7,8,1,3,5] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[4,2,3,6,7,8,1,5] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2

[4,7,2,1,6,5,8,3] => [[[.,[.,.]],.],[[[.,.],[.,.]],.]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[2,4,3,6,7,8,1,5] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[6,8,5,2,7,3,1,4] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[7,1,2,4,6,3,8,5] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 4

[7,5,6,1,2,4,8,3] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[7,1,4,5,2,3,6,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[1,6,7,5,8,3,4,2] => [.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 2

[6,1,4,7,8,2,3,5] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[6,7,1,4,2,3,5,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[6,7,8,5,1,2,4,3] => [[[.,[.,[.,.]]],.],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[7,6,8,1,5,3,4,2] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[7,4,6,1,5,3,8,2] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[6,3,8,1,7,2,5,4] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[8,3,6,7,5,1,2,4] => [[[.,.],[[.,[.,.]],.]],[.,[.,.]]] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[4,6,8,2,3,5,1,7] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[6,8,2,1,3,5,4,7] => [[[.,[.,.]],.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[3,5,1,6,4,8,2,7] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[4,8,2,5,6,1,3,7] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[1,7,8,4,6,3,2,5] => [.,[[[[.,[.,.]],[.,.]],.],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 3

[7,8,3,4,6,5,2,1] => [[[[.,[.,.]],[.,[[.,.],.]]],.],.] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 1

[3,8,2,7,5,4,6,1] => [[[.,[.,.]],[[[.,.],.],[.,.]]],.] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 1

[8,3,4,1,2,5,7,6] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[4,7,2,6,5,8,3,1] => [[[.,[.,.]],[[[.,.],[.,.]],.]],.] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 1

[3,6,8,5,7,4,2,1] => [[[.,[[[.,[.,.]],[.,.]],.]],.],.] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[6,7,5,2,4,8,3,1] => [[[[.,[.,.]],.],[[.,[.,.]],.]],.] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 1

[6,7,5,4,8,1,3,2] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[8,3,5,6,4,7,2,1] => [[[[.,.],[[.,[.,.]],[.,.]]],.],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1

[8,5,6,2,4,3,7,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[6,5,8,1,3,4,2,7] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[6,8,4,5,1,3,2,7] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,7,1,4,3,2,8,5] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[7,2,5,1,4,8,3,6] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[5,8,1,3,4,2,7,6] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[1,5,6,3,2,8,7,4] => [.,[[[.,[.,.]],.],[[[.,.],.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 3

[1,6,7,3,2,8,5,4] => [.,[[[.,[.,.]],.],[[[.,.],.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 3

[2,6,1,5,7,4,8,3] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2

[3,5,8,2,1,4,6,7] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[3,5,8,2,4,6,7,1] => [[[.,[.,[.,.]]],[.,[.,[.,.]]]],.] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1

[5,3,8,2,1,4,6,7] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[5,1,3,8,2,4,6,7] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[1,5,8,4,2,3,6,7] => [.,[[[.,[.,.]],.],[.,[.,[.,.]]]]] => [1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 5

[5,8,2,1,4,3,6,7] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[5,8,2,4,1,6,7,3] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[5,8,2,4,6,3,1,7] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[5,8,2,4,3,6,1,7] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[5,8,1,4,6,2,3,7] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[1,5,8,4,6,7,2,3] => [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 3

[5,8,2,4,6,3,7,1] => [[[.,[.,.]],[[.,[.,.]],[.,.]]],.] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 1

[3,8,4,6,7,2,1,5] => [[[.,[[.,.],[.,[.,.]]]],.],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2

[3,8,4,6,7,2,5,1] => [[[.,[[.,.],[.,[.,.]]]],[.,.]],.] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[3,8,1,6,2,4,5,7] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[8,3,6,2,4,5,1,7] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[8,1,3,6,2,4,5,7] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[8,3,6,7,2,1,4,5] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[8,4,6,2,3,7,5,1] => [[[[.,.],[.,.]],[.,[[.,.],.]]],.] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[8,4,7,2,1,3,6,5] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[2,7,1,6,3,5,8,4] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[4,2,7,8,3,5,6,1] => [[[.,.],[[.,[.,.]],[.,[.,.]]]],.] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1

[7,3,5,6,4,2,8,1] => [[[[.,.],[[.,[.,.]],.]],[.,.]],.] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[2,6,8,1,5,3,4,7] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[3,2,5,6,8,1,4,7] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[3,8,1,6,4,5,2,7] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[5,7,2,3,1,4,8,6] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[3,2,5,7,8,4,6,1] => [[[.,.],[[.,[.,[.,.]]],[.,.]]],.] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1

[3,1,5,7,8,4,2,6] => [[.,.],[[[.,[.,[.,.]]],.],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => 3

[2,6,1,8,5,3,4,7] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[4,5,7,8,1,6,3,2] => [[.,[.,[.,[.,.]]]],[[[.,.],.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[2,5,7,8,4,6,3,1] => [[.,[[[.,[.,[.,.]]],[.,.]],.]],.] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1

[5,6,8,3,4,2,7,1] => [[[[.,[.,[.,.]]],[.,.]],[.,.]],.] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[7,3,5,1,4,8,6,2] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[5,1,7,8,2,4,3,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[4,8,1,7,3,5,6,2] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 2

[4,6,8,3,7,1,5,2] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[3,6,7,2,5,1,8,4] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[3,5,1,7,8,4,6,2] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2

[3,4,1,8,6,7,5,2] => [[.,[.,.]],[[[[.,.],[.,.]],.],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 2

[6,7,4,2,5,8,3,1] => [[[[.,[.,.]],.],[[.,[.,.]],.]],.] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 1

[5,3,7,1,4,6,8,2] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[5,7,2,6,1,4,8,3] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[2,5,6,4,8,1,7,3] => [[.,[[.,[.,.]],[.,.]]],[[.,.],.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2

[5,7,2,1,6,8,3,4] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[4,7,8,5,1,6,2,3] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[4,5,2,1,6,7,8,3] => [[[.,[.,.]],.],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 2

[4,5,6,3,1,7,8,2] => [[[.,[.,[.,.]]],.],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[3,5,6,7,4,1,8,2] => [[.,[[.,[.,[.,.]]],.]],[[.,.],.]] => [1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[3,5,1,4,2,8,7,6] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[3,5,1,4,2,6,8,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[3,5,1,4,2,6,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[1,4,8,3,2,7,6,5] => [.,[[[.,[.,.]],.],[[[.,.],.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 3

[4,2,7,8,3,6,1,5] => [[[.,.],[[.,[.,.]],[.,.]]],[.,.]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[4,6,3,7,5,8,2,1] => [[[[.,[.,.]],[[.,.],[.,.]]],.],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 1

[4,2,5,7,8,6,3,1] => [[[.,.],[[.,[[.,[.,.]],.]],.]],.] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1

[3,6,8,4,5,2,1,7] => [[[.,[[.,[.,.]],[.,.]]],.],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 2

[8,2,5,7,3,6,1,4] => [[[.,.],[[.,[.,.]],[.,.]]],[.,.]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[6,7,2,4,5,1,8,3] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[5,2,7,8,3,6,1,4] => [[[.,.],[[.,[.,.]],[.,.]]],[.,.]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[7,2,3,4,1,8,5,6] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[8,3,5,1,2,4,7,6] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[3,4,8,2,1,7,6,5] => [[[.,[.,[.,.]]],.],[[[.,.],.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[1,4,6,8,2,5,7,3] => [.,[[.,[.,[.,.]]],[[.,[.,.]],.]]] => [1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3

[3,6,2,4,8,1,7,5] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[7,3,8,2,4,6,1,5] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[4,5,3,1,8,2,6,7] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[5,1,7,8,3,6,2,4] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[5,8,2,1,3,4,6,7] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 5

[4,2,5,1,8,3,6,7] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[6,7,8,5,2,1,4,3] => [[[[.,[.,[.,.]]],.],.],[[.,.],.]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[7,3,4,1,8,6,2,5] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[1,4,7,8,6,2,5,3] => [.,[[.,[[.,[.,.]],.]],[[.,.],.]]] => [1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 3

[1,6,7,8,3,2,5,4] => [.,[[[.,[.,[.,.]]],.],[[.,.],.]]] => [1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3

[5,7,1,4,6,2,8,3] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[4,5,7,1,8,6,2,3] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[5,4,7,3,1,2,6,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[3,2,5,6,8,4,1,7] => [[[.,.],[[.,[.,[.,.]]],.]],[.,.]] => [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => 2

[7,2,6,8,5,4,3,1] => [[[.,.],[[[[.,[.,.]],.],.],.]],.] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 1

[4,2,5,1,3,6,8,7] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[5,3,4,2,7,1,8,6] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[2,4,3,5,6,8,1,7] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[8,4,7,1,2,5,3,6] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[7,4,6,1,8,5,2,3] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[8,5,6,7,2,1,4,3] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[2,5,6,3,8,4,7,1] => [[.,[[.,[.,.]],[[.,.],[.,.]]]],.] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 1

[8,2,5,6,4,3,1,7] => [[[.,.],[[[.,[.,.]],.],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => 2

[5,7,8,1,3,2,4,6] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[8,2,4,1,6,7,3,5] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[7,8,6,1,3,5,4,2] => [[[.,[.,.]],.],[[.,[[.,.],.]],.]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 2

[8,4,7,2,6,3,1,5] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[1,2,5,7,8,3,6,4] => [.,[.,[[.,[.,[.,.]]],[[.,.],.]]]] => [1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 4

[8,4,6,2,3,7,1,5] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[3,4,5,8,1,7,2,6] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,3,4,2,7,8,1,5] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[5,6,3,7,8,2,1,4] => [[[[.,[.,.]],[.,[.,.]]],.],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2

[4,5,6,2,7,8,3,1] => [[[.,[.,[.,.]]],[[.,[.,.]],.]],.] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[4,5,6,2,7,1,8,3] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[4,5,6,2,1,7,8,3] => [[[.,[.,[.,.]]],.],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[4,5,6,2,1,7,3,8] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[4,5,1,6,7,3,2,8] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[2,5,1,8,3,7,4,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[5,7,2,1,3,8,4,6] => [[[.,[.,.]],.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[2,7,4,5,6,8,1,3] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[2,3,4,6,8,1,7,5] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[2,3,5,8,1,6,7,4] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[7,3,4,6,2,8,1,5] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[2,5,1,4,6,3,8,7] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[3,1,5,6,4,2,8,7] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3

[8,5,6,4,3,1,7,2] => [[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[8,3,5,6,7,1,2,4] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[2,1,4,7,3,6,8,5] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3

[8,3,4,1,6,7,5,2] => [[[.,.],[.,.]],[[[.,[.,.]],.],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[5,8,1,4,3,2,6,7] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[5,6,4,3,8,2,7,1] => [[[[[.,[.,.]],.],[.,.]],[.,.]],.] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1

[7,8,1,4,3,2,5,6] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[7,1,2,4,5,6,8,3] => [[.,.],[.,[[.,[.,[.,[.,.]]]],.]]] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 3

[5,8,3,1,4,6,7,2] => [[[.,[.,.]],.],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 2

[5,6,3,4,1,7,8,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[6,8,2,3,1,5,7,4] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[5,2,3,1,4,7,8,6] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[5,2,4,7,8,6,3,1] => [[[.,.],[[.,[[.,[.,.]],.]],.]],.] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1

[8,1,4,5,3,6,2,7] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[8,3,5,1,4,6,2,7] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[5,8,2,1,7,4,3,6] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[6,5,7,2,1,8,4,3] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[3,6,8,4,1,7,2,5] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[3,5,2,4,7,8,6,1] => [[[.,[.,.]],[.,[[.,[.,.]],.]]],.] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 1

[7,5,6,3,8,2,1,4] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[7,3,4,5,1,6,8,2] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[8,4,7,1,2,6,5,3] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[5,7,8,1,6,2,4,3] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[6,8,4,5,7,2,1,3] => [[[[.,[.,.]],[.,[.,.]]],.],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2

[4,6,1,3,5,2,7,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[4,6,1,2,5,3,7,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5

[5,8,4,7,1,3,6,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[6,4,7,1,3,5,2,8] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[6,8,3,1,5,4,7,2] => [[[.,[.,.]],.],[[[.,.],[.,.]],.]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[5,1,3,6,7,4,2,8] => [[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3

[6,1,2,4,7,3,5,8] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 5

[4,2,8,1,6,5,7,3] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[5,6,1,4,8,3,2,7] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[2,4,1,3,7,8,6,5] => [[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 3

[2,6,1,5,7,8,4,3] => [[.,[.,.]],[[[.,[.,[.,.]]],.],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2

[8,4,6,3,7,5,1,2] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[5,7,4,8,1,2,6,3] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[3,6,7,5,8,1,4,2] => [[.,[[.,[.,.]],[.,.]]],[[.,.],.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2

[3,7,5,6,8,2,4,1] => [[[.,[[.,.],[.,[.,.]]]],[.,.]],.] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[2,7,1,6,8,4,5,3] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2

[2,4,5,8,3,1,7,6] => [[.,[[.,[.,[.,.]]],.]],[[.,.],.]] => [1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[4,7,8,6,2,5,1,3] => [[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => [1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[4,3,8,1,6,5,7,2] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[1,3,6,2,5,8,7,4] => [.,[[.,[.,.]],[[.,[[.,.],.]],.]]] => [1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 3

[6,2,5,1,3,4,8,7] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[5,6,4,1,2,7,3,8] => [[[.,[.,.]],.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[8,1,5,6,2,4,3,7] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[6,4,5,1,2,7,3,8] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[5,4,6,1,3,2,7,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[5,7,1,4,3,2,6,8] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[7,8,5,3,2,1,6,4] => [[[[[.,[.,.]],.],.],.],[[.,.],.]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2

[1,2,6,7,8,4,5,3] => [.,[.,[[[.,[.,[.,.]]],[.,.]],.]]] => [1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 3

[6,1,4,8,2,7,5,3] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3

[5,2,3,7,1,8,4,6] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[7,2,3,1,8,4,6,5] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[7,3,4,5,1,8,6,2] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[1,5,6,7,4,8,2,3] => [.,[[[.,[.,[.,.]]],[.,.]],[.,.]]] => [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[4,5,2,7,6,3,1,8] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[4,5,2,1,7,6,3,8] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[2,6,7,8,3,1,4,5] => [[.,[[.,[.,[.,.]]],.]],[.,[.,.]]] => [1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[4,6,3,7,8,2,1,5] => [[[[.,[.,.]],[.,[.,.]]],.],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2

[5,6,7,1,8,4,2,3] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[1,7,8,4,6,5,2,3] => [.,[[[.,[.,.]],[[.,.],.]],[.,.]]] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 3

[3,7,1,2,8,6,5,4] => [[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 3

[2,7,8,1,6,5,3,4] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[8,1,5,7,3,4,6,2] => [[.,.],[[[.,[.,.]],[.,[.,.]]],.]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[5,8,2,7,6,3,1,4] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[2,5,1,8,4,7,6,3] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2

[3,4,2,8,1,7,6,5] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[2,6,1,5,8,7,3,4] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3

[7,5,8,1,6,2,3,4] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[6,2,4,5,3,8,1,7] => [[[.,.],[[.,[.,.]],[.,.]]],[.,.]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[6,8,5,4,7,1,3,2] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[1,6,8,4,2,5,7,3] => [.,[[[.,[.,.]],.],[[.,[.,.]],.]]] => [1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3

[7,5,8,1,3,4,2,6] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[1,7,8,5,4,2,6,3] => [.,[[[[.,[.,.]],.],.],[[.,.],.]]] => [1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 3

[5,1,6,7,4,2,8,3] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3

[5,8,4,1,6,2,7,3] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[6,4,5,1,7,2,8,3] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[4,8,1,3,7,6,2,5] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3

[4,5,3,1,2,8,7,6] => [[[.,[.,.]],.],[.,[[[.,.],.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 3

[5,7,8,1,2,4,3,6] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[6,5,7,4,1,3,2,8] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[4,6,1,8,3,5,2,7] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[7,1,6,8,2,5,4,3] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3

[4,7,1,8,3,2,5,6] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[4,8,3,6,1,5,2,7] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[1,7,8,6,4,5,3,2] => [.,[[[[[.,[.,.]],.],[.,.]],.],.]] => [1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 2

[5,7,4,2,1,8,6,3] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2

[7,4,6,1,8,5,3,2] => [[[.,.],[.,.]],[[[[.,.],.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[7,4,6,3,8,1,5,2] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[7,4,8,1,6,3,2,5] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[7,4,8,3,6,2,1,5] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[4,6,8,2,5,7,1,3] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[6,4,8,2,5,7,1,3] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[6,2,4,5,8,3,7,1] => [[[.,.],[[.,[.,[.,.]]],[.,.]]],.] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1

[6,8,2,4,7,3,5,1] => [[[.,[.,.]],[[.,[.,.]],[.,.]]],.] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 1

[8,4,6,2,7,1,3,5] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[6,8,4,2,7,1,3,5] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[6,8,2,4,1,7,3,5] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,2,5,7,1,6,8,3] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[4,5,2,3,8,7,1,6] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[5,6,2,3,8,4,7,1] => [[[.,[.,.]],[.,[[.,.],[.,.]]]],.] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 1

[5,6,2,3,1,7,8,4] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[5,7,2,3,4,1,6,8] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[1,7,2,4,5,6,8,3] => [.,[[.,.],[[.,[.,[.,[.,.]]]],.]]] => [1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 3

[7,2,8,1,4,6,3,5] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[2,7,8,1,5,6,3,4] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[6,8,2,3,1,5,4,7] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,8,2,3,1,6,4,7] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,7,2,1,4,6,8,3] => [[[.,[.,.]],.],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 2

[4,2,7,1,5,6,8,3] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[4,2,3,8,1,7,5,6] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,1,3,4,2,7,6,8] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[6,1,3,4,2,7,5,8] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[4,5,7,2,8,3,6,1] => [[[.,[.,[.,.]]],[[.,.],[.,.]]],.] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[7,5,6,8,4,1,3,2] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[8,1,5,7,3,6,2,4] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[8,5,6,2,7,1,3,4] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[8,4,7,2,6,5,1,3] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[8,5,7,3,2,6,1,4] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[4,5,3,7,8,1,6,2] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[3,4,2,8,1,6,7,5] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[8,3,4,1,5,7,6,2] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[5,2,6,1,4,3,7,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[3,5,2,8,6,7,4,1] => [[[.,[.,.]],[[[.,.],[.,.]],.]],.] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 1

[7,4,8,2,3,5,6,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1

[5,6,2,8,7,1,4,3] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[4,6,3,5,2,7,8,1] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1

[3,1,5,7,4,6,8,2] => [[.,.],[[[.,[.,.]],[.,[.,.]]],.]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[4,3,6,1,5,7,8,2] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[4,6,7,1,3,5,8,2] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[5,6,1,3,4,7,2,8] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[4,6,2,1,3,7,8,5] => [[[.,[.,.]],.],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 3

[3,6,2,4,1,7,5,8] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,2,6,7,4,8,5,1] => [[[.,.],[[.,[.,.]],[[.,.],.]]],.] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1

[6,2,7,1,4,5,3,8] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[4,2,6,1,5,7,3,8] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[6,5,7,3,1,4,2,8] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[6,7,4,3,1,5,8,2] => [[[[.,[.,.]],.],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 2

[3,1,6,7,8,4,5,2] => [[.,.],[[[.,[.,[.,.]]],[.,.]],.]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2

[7,4,5,6,2,1,8,3] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[6,4,5,2,7,1,8,3] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[4,5,8,2,3,7,1,6] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[7,3,4,8,2,5,1,6] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,8,1,5,4,2,3,7] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[4,7,2,5,1,6,8,3] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[6,8,5,3,7,4,2,1] => [[[[[.,[.,.]],.],[[.,.],.]],.],.] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 1

[7,2,8,1,5,6,4,3] => [[[.,.],[.,.]],[[[.,[.,.]],.],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[7,5,6,1,4,8,2,3] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[5,7,2,6,3,8,4,1] => [[[.,[.,.]],[[.,.],[[.,.],.]]],.] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 1

[5,6,4,2,1,8,3,7] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[6,8,1,3,2,7,5,4] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[5,7,3,6,4,1,2,8] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[2,4,3,5,8,1,6,7] => [[.,[[.,.],[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[5,8,2,6,7,4,3,1] => [[[.,[.,.]],[[[.,[.,.]],.],.]],.] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 1

[6,5,8,2,7,3,4,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[4,6,1,3,7,8,5,2] => [[.,[.,.]],[[.,[[.,[.,.]],.]],.]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 2

[1,5,6,3,8,7,2,4] => [.,[[[.,[.,.]],[[.,.],.]],[.,.]]] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 3

[6,3,5,2,7,1,4,8] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[6,4,5,3,1,8,7,2] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[5,3,4,1,6,2,7,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[2,7,1,4,6,3,5,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[6,1,4,5,2,7,3,8] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[6,1,5,8,2,7,4,3] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3

[5,7,2,8,1,3,6,4] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[2,7,8,4,1,3,6,5] => [[.,[[.,[.,.]],.]],[.,[[.,.],.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 3

[2,4,6,7,5,8,1,3] => [[.,[.,[[.,[.,.]],[.,.]]]],[.,.]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 2

[2,4,6,3,7,8,1,5] => [[.,[[.,[.,.]],[.,[.,.]]]],[.,.]] => [1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2

[2,4,5,6,8,3,7,1] => [[.,[[.,[.,[.,[.,.]]]],[.,.]]],.] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1

[2,4,5,6,3,8,1,7] => [[.,[[.,[.,[.,.]]],[.,.]]],[.,.]] => [1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[2,3,4,6,8,5,1,7] => [[.,[.,[.,[[.,[.,.]],.]]]],[.,.]] => [1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 2

[4,8,2,7,6,5,1,3] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[6,5,8,2,7,1,4,3] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[7,5,8,2,1,6,4,3] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[3,4,1,8,7,6,2,5] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[8,1,5,7,4,2,6,3] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3

[4,6,1,3,2,8,5,7] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[6,7,8,2,4,5,3,1] => [[[.,[.,[.,.]]],[[.,[.,.]],.]],.] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[4,6,1,3,2,7,8,5] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[6,7,2,5,8,4,1,3] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[4,1,7,8,2,5,6,3] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3

[3,4,6,7,1,5,8,2] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[3,4,5,7,8,1,6,2] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[2,4,5,8,1,3,7,6] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[2,7,8,6,5,3,1,4] => [[.,[[[[.,[.,.]],.],.],.]],[.,.]] => [1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 2

[2,8,3,5,6,1,4,7] => [[.,[[.,.],[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[7,2,5,8,1,4,6,3] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[4,7,5,8,1,2,3,6] => [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[3,7,8,4,2,1,6,5] => [[[.,[[.,[.,.]],.]],.],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 2

[3,2,4,5,8,1,6,7] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[3,6,8,4,2,7,1,5] => [[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => [1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[4,8,3,7,6,2,1,5] => [[[[.,[.,.]],[[.,.],.]],.],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2

[1,3,6,8,2,4,7,5] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[1,6,7,4,3,8,2,5] => [.,[[[[.,[.,.]],.],[.,.]],[.,.]]] => [1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 3

[4,7,2,8,5,1,6,3] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[7,8,6,2,1,5,4,3] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2

[4,8,1,6,3,7,2,5] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[2,6,8,5,4,3,1,7] => [[.,[[[[.,[.,.]],.],.],.]],[.,.]] => [1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 2

[2,7,8,3,6,4,5,1] => [[.,[[.,[.,.]],[[.,.],[.,.]]]],.] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 1

[3,8,1,4,6,5,2,7] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3

[4,6,1,8,5,3,2,7] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[5,1,4,8,2,6,3,7] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[4,5,8,1,3,7,6,2] => [[.,[.,[.,.]]],[[.,[[.,.],.]],.]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[8,6,7,1,4,3,2,5] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[1,4,7,8,6,3,5,2] => [.,[[[.,[[.,[.,.]],.]],[.,.]],.]] => [1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 2

[8,3,6,1,2,7,4,5] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[6,8,1,5,4,7,2,3] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[6,7,2,5,4,8,1,3] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[3,5,6,2,8,1,4,7] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[1,6,8,2,5,3,4,7] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 5

[2,5,6,4,3,8,1,7] => [[.,[[[.,[.,.]],.],[.,.]]],[.,.]] => [1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 2

[4,6,3,8,5,2,7,1] => [[[[.,[.,.]],[[.,.],.]],[.,.]],.] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 1

[1,7,8,6,3,2,5,4] => [.,[[[[.,[.,.]],.],.],[[.,.],.]]] => [1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 3

[3,4,6,7,2,1,5,8] => [[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[7,2,5,1,6,3,8,4] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[5,8,2,7,4,6,3,1] => [[[.,[.,.]],[[[.,.],[.,.]],.]],.] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 1

[4,5,2,8,3,7,1,6] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[7,8,5,1,6,4,3,2] => [[[.,[.,.]],.],[[[[.,.],.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2

[4,5,8,3,1,2,7,6] => [[[.,[.,[.,.]]],.],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[1,4,6,3,7,5,2,8] => [.,[[[.,[.,.]],[[.,.],.]],[.,.]]] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 3

[3,8,2,1,5,7,6,4] => [[[.,[.,.]],.],[[.,[[.,.],.]],.]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 2

[4,6,3,7,8,1,2,5] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[2,4,5,8,3,7,6,1] => [[.,[[.,[.,[.,.]]],[[.,.],.]]],.] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1

[5,6,4,1,8,2,7,3] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[6,4,5,1,3,8,7,2] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[5,1,4,8,3,7,6,2] => [[.,.],[[[.,[.,.]],[[.,.],.]],.]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2

[4,8,3,2,7,6,5,1] => [[[[.,[.,.]],.],[[[.,.],.],.]],.] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 1

[8,5,7,3,1,2,4,6] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[6,7,1,5,2,8,4,3] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[4,8,1,3,6,2,7,5] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[6,2,3,8,1,5,7,4] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[2,5,7,4,8,3,6,1] => [[.,[[[.,[.,.]],[.,.]],[.,.]]],.] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1

[8,5,6,2,4,7,1,3] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[8,1,5,7,3,6,4,2] => [[.,.],[[[.,[.,.]],[[.,.],.]],.]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2

[4,3,7,1,2,8,5,6] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[4,8,1,6,2,5,3,7] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[5,8,3,1,2,4,6,7] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 5

[6,7,4,2,8,1,3,5] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[5,8,1,2,7,4,3,6] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 4

[4,6,3,7,8,1,5,2] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[6,5,8,1,4,3,7,2] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[6,8,3,1,2,5,4,7] => [[[.,[.,.]],.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[2,5,1,8,7,3,4,6] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[6,8,4,3,5,1,7,2] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[1,4,7,3,6,8,2,5] => [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 3

[3,7,1,4,6,8,2,5] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[2,4,7,3,6,8,1,5] => [[.,[[.,[.,.]],[.,[.,.]]]],[.,.]] => [1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2

[1,2,6,7,4,5,8,3] => [.,[.,[[[.,[.,.]],[.,[.,.]]],.]]] => [1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 3

[7,2,3,6,8,1,4,5] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[2,6,1,3,8,5,4,7] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 4

[5,8,1,4,2,7,3,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[2,3,1,6,8,7,4,5] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3

[6,4,8,2,1,7,3,5] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[2,3,1,8,7,5,6,4] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2

[1,5,6,7,2,4,3,8] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[6,8,3,7,1,2,5,4] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[6,7,4,5,1,3,8,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[3,2,4,6,1,8,7,5] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[3,6,7,4,1,2,5,8] => [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4

[1,6,8,4,7,3,2,5] => [.,[[[[.,[.,.]],[.,.]],.],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 3

[3,6,7,5,4,8,1,2] => [[.,[[[.,[.,.]],.],[.,.]]],[.,.]] => [1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 2

[4,5,7,2,6,3,8,1] => [[[.,[.,[.,.]]],[[.,.],[.,.]]],.] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[2,1,5,7,4,6,8,3] => [[.,.],[[[.,[.,.]],[.,[.,.]]],.]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[2,3,5,7,8,1,6,4] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[1,5,7,4,2,3,6,8] => [.,[[[.,[.,.]],.],[.,[.,[.,.]]]]] => [1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 5

[1,2,4,7,8,6,3,5] => [.,[.,[[.,[[.,[.,.]],.]],[.,.]]]] => [1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 4

[2,4,7,8,3,5,1,6] => [[.,[[.,[.,[.,.]]],[.,.]]],[.,.]] => [1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[1,3,6,2,5,8,4,7] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 4

[4,8,1,2,6,3,7,5] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4

[5,8,1,2,6,3,7,4] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4

[8,1,4,7,3,5,2,6] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[2,6,1,8,3,7,4,5] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[2,5,1,7,6,8,3,4] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[3,4,1,6,5,7,8,2] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 2

[4,8,3,1,6,2,7,5] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[6,2,7,1,5,8,4,3] => [[[.,.],[.,.]],[[[.,[.,.]],.],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[4,6,1,2,8,3,7,5] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4

[4,1,3,6,7,2,5,8] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[2,6,7,4,3,1,5,8] => [[.,[[[.,[.,.]],.],.]],[.,[.,.]]] => [1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 3

[2,3,6,7,1,5,4,8] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,1,6,7,3,2,4,8] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[5,6,1,4,7,2,3,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[1,2,5,7,8,6,3,4] => [.,[.,[[.,[[.,[.,.]],.]],[.,.]]]] => [1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 4

[1,2,7,8,4,6,3,5] => [.,[.,[[[.,[.,.]],[.,.]],[.,.]]]] => [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 4

[7,5,8,2,6,1,4,3] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[5,6,8,2,7,4,1,3] => [[[.,[.,[.,.]]],[[.,.],.]],[.,.]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[8,4,6,7,3,1,5,2] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[6,3,5,7,1,2,8,4] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[1,6,7,3,4,2,5,8] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 4

[1,6,8,3,4,2,5,7] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 4

[1,7,8,5,3,4,2,6] => [.,[[[[.,[.,.]],.],[.,.]],[.,.]]] => [1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 3

[1,7,8,6,4,3,2,5] => [.,[[[[[.,[.,.]],.],.],.],[.,.]]] => [1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 3

[5,1,7,8,4,2,3,6] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[3,8,2,1,6,7,5,4] => [[[.,[.,.]],.],[[[.,[.,.]],.],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 2

[8,5,6,2,1,4,7,3] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[5,7,8,3,4,2,1,6] => [[[[.,[.,[.,.]]],[.,.]],.],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[7,8,4,5,6,1,3,2] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[2,5,1,8,4,6,7,3] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 2

[6,5,8,3,4,2,1,7] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[3,4,5,8,2,1,6,7] => [[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[3,4,8,2,7,1,5,6] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[7,2,6,1,4,8,3,5] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[7,8,1,2,4,6,3,5] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4

[7,6,8,1,4,2,3,5] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[2,3,6,8,5,1,7,4] => [[.,[.,[[.,[.,.]],.]]],[[.,.],.]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 2

[2,1,3,7,8,4,6,5] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 4

[4,6,7,2,3,8,1,5] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[6,1,5,8,4,7,3,2] => [[.,.],[[[[.,[.,.]],[.,.]],.],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[1,4,6,8,5,7,2,3] => [.,[[.,[[.,[.,.]],[.,.]]],[.,.]]] => [1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 3

[2,4,7,1,8,3,6,5] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[6,4,5,1,2,8,3,7] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[4,6,2,5,3,8,1,7] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[5,8,4,3,6,7,2,1] => [[[[[.,[.,.]],.],[.,[.,.]]],.],.] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1

[6,8,2,1,5,3,4,7] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

[7,4,5,8,1,6,2,3] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,5,8,1,6,7,3,2] => [[.,[.,[.,.]]],[[[.,[.,.]],.],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[8,3,7,1,6,2,4,5] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[7,2,3,6,8,1,5,4] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[2,6,3,7,8,1,4,5] => [[.,[[.,.],[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[7,2,5,6,3,4,8,1] => [[[.,.],[[.,[.,.]],[.,[.,.]]]],.] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1

[7,2,3,6,8,5,4,1] => [[[.,.],[.,[[[.,[.,.]],.],.]]],.] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 1

[7,4,5,2,8,1,6,3] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[7,2,3,6,8,4,5,1] => [[[.,.],[.,[[.,[.,.]],[.,.]]]],.] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1

[7,4,5,2,8,3,6,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[6,4,5,3,8,1,2,7] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[7,2,4,6,3,8,5,1] => [[[.,.],[[.,[.,.]],[[.,.],.]]],.] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1

[3,7,2,5,8,6,4,1] => [[[.,[.,.]],[[.,[[.,.],.]],.]],.] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 1

[5,8,1,7,6,2,3,4] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[3,4,6,2,5,7,1,8] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[7,4,8,3,6,5,1,2] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[1,5,8,2,6,4,3,7] => [.,[[.,[.,.]],[[[.,.],.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 4

[3,5,6,2,4,7,8,1] => [[[.,[.,[.,.]]],[.,[.,[.,.]]]],.] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1

[3,5,6,7,2,4,8,1] => [[[.,[.,[.,[.,.]]]],[.,[.,.]]],.] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1

[3,5,7,2,6,8,4,1] => [[[.,[.,[.,.]]],[[.,[.,.]],.]],.] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[3,5,2,7,6,8,4,1] => [[[.,[.,.]],[[[.,.],[.,.]],.]],.] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 1

[3,5,7,4,2,6,8,1] => [[[.,[[.,[.,.]],.]],[.,[.,.]]],.] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 1

[3,4,5,7,2,6,8,1] => [[[.,[.,[.,[.,.]]]],[.,[.,.]]],.] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1

[3,4,5,7,2,8,6,1] => [[[.,[.,[.,[.,.]]]],[[.,.],.]],.] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 1

[3,5,4,7,8,2,6,1] => [[[.,[[.,.],[.,[.,.]]]],[.,.]],.] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[3,2,5,7,4,8,6,1] => [[[.,.],[[.,[.,.]],[[.,.],.]]],.] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1

[3,5,7,4,2,8,6,1] => [[[.,[[.,[.,.]],.]],[[.,.],.]],.] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[3,5,7,8,4,2,6,1] => [[[.,[[.,[.,[.,.]]],.]],[.,.]],.] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[2,3,5,7,8,4,6,1] => [[.,[.,[[.,[.,[.,.]]],[.,.]]]],.] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1

[3,5,2,7,8,6,4,1] => [[[.,[.,.]],[[[.,[.,.]],.],.]],.] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 1

[3,5,7,8,2,6,4,1] => [[[.,[.,[.,[.,.]]]],[[.,.],.]],.] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 1

[3,5,7,8,6,2,4,1] => [[[.,[.,[[.,[.,.]],.]]],[.,.]],.] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[4,2,5,6,7,3,8,1] => [[[.,.],[[.,[.,[.,.]]],[.,.]]],.] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1

[4,2,5,1,8,7,6,3] => [[[.,.],[.,.]],[[[[.,.],.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[5,2,4,8,1,7,6,3] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[1,4,5,7,3,8,2,6] => [.,[[[.,[.,[.,.]]],[.,.]],[.,.]]] => [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[4,6,8,1,2,5,3,7] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[3,5,6,8,2,1,4,7] => [[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[5,4,8,2,3,1,7,6] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[4,6,7,5,1,8,3,2] => [[.,[[.,[.,.]],.]],[[[.,.],.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2

[8,3,4,2,6,7,1,5] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[4,6,7,5,2,8,3,1] => [[[.,[[.,[.,.]],.]],[[.,.],.]],.] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[2,5,7,8,6,1,4,3] => [[.,[.,[[.,[.,.]],.]]],[[.,.],.]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 2

[7,2,6,8,4,5,1,3] => [[[.,.],[[.,[.,.]],[.,.]]],[.,.]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[4,6,7,2,1,5,3,8] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[5,7,1,6,2,3,4,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[6,2,5,8,3,4,1,7] => [[[.,.],[[.,[.,.]],[.,.]]],[.,.]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[6,1,5,7,8,4,2,3] => [[.,.],[[[.,[.,[.,.]]],.],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => 3

[5,6,8,3,7,4,2,1] => [[[[.,[.,[.,.]]],[[.,.],.]],.],.] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

[4,6,1,5,7,2,8,3] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[2,5,8,4,6,3,7,1] => [[.,[[[.,[.,.]],[.,.]],[.,.]]],.] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1

[4,3,7,1,2,6,8,5] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[6,8,1,5,2,7,4,3] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[4,5,8,2,3,7,6,1] => [[[.,[.,[.,.]]],[.,[[.,.],.]]],.] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[4,8,1,3,2,5,7,6] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[4,2,5,8,1,3,7,6] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[6,4,5,3,2,8,7,1] => [[[[[.,.],[.,.]],.],[[.,.],.]],.] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1

[8,2,3,4,1,5,7,6] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[2,7,8,1,4,3,6,5] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[6,5,8,1,3,2,4,7] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[7,8,1,5,2,4,6,3] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[5,7,2,8,4,1,6,3] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[2,5,6,3,8,1,4,7] => [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[7,4,5,6,8,1,3,2] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[7,6,8,1,4,5,3,2] => [[[.,.],[.,.]],[[[.,[.,.]],.],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[1,7,8,5,6,4,3,2] => [.,[[[[[.,[.,.]],[.,.]],.],.],.]] => [1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 2

[2,8,1,7,4,5,3,6] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[7,3,6,2,5,4,8,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[2,6,8,4,5,1,7,3] => [[.,[[.,[.,.]],[.,.]]],[[.,.],.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2

[4,6,5,7,8,1,3,2] => [[.,[[.,.],[.,[.,.]]]],[[.,.],.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[5,3,8,1,4,7,6,2] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[4,3,5,8,1,7,6,2] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[4,6,2,5,1,7,8,3] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[2,3,5,1,7,6,4,8] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[2,3,1,7,4,8,6,5] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[7,8,5,2,6,4,3,1] => [[[[.,[.,.]],.],[[[.,.],.],.]],.] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 1

[8,1,2,5,7,4,6,3] => [[.,.],[.,[[[.,[.,.]],[.,.]],.]]] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 3

[6,1,2,4,7,8,3,5] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 4

[3,5,2,1,7,8,6,4] => [[[.,[.,.]],.],[[[.,[.,.]],.],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 2

[4,2,7,8,6,5,1,3] => [[[.,.],[[[.,[.,.]],.],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => 2

[1,2,7,8,6,4,5,3] => [.,[.,[[[[.,[.,.]],.],[.,.]],.]]] => [1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 3

[4,8,1,2,6,5,3,7] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 4

[6,4,8,1,2,3,7,5] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[7,2,5,1,6,4,3,8] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[5,2,7,1,4,6,3,8] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[3,7,1,6,5,8,2,4] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[5,4,6,2,1,8,7,3] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[5,3,8,1,4,2,6,7] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[5,3,8,1,4,2,7,6] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[2,4,5,1,8,3,7,6] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[6,4,5,3,1,7,8,2] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[7,3,5,6,4,1,8,2] => [[[.,.],[[.,[.,.]],.]],[[.,.],.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[2,5,6,3,4,1,8,7] => [[.,[[.,[.,.]],[.,.]]],[[.,.],.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2

[4,6,2,1,5,8,3,7] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[4,6,7,2,3,8,5,1] => [[[.,[.,[.,.]]],[.,[[.,.],.]]],.] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[4,5,3,7,8,1,2,6] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[2,3,5,8,1,6,4,7] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,8,2,6,1,5,7,3] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[2,3,7,8,1,5,4,6] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,2,6,7,8,3,1,4] => [[[.,.],[[.,[.,[.,.]]],.]],[.,.]] => [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => 2

[5,6,2,7,8,3,1,4] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[3,7,8,5,1,4,6,2] => [[.,[[.,[.,.]],.]],[[.,[.,.]],.]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 2

[2,5,6,7,1,8,4,3] => [[.,[.,[.,[.,.]]]],[[[.,.],.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[2,3,7,8,5,4,6,1] => [[.,[.,[[[.,[.,.]],.],[.,.]]]],.] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 1

[6,4,7,8,1,2,5,3] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[7,5,8,1,2,3,6,4] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[1,3,8,2,7,4,6,5] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 4

[8,2,7,1,6,4,3,5] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[4,3,7,2,5,1,6,8] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[1,3,6,2,5,4,8,7] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 4

[4,6,7,5,1,3,8,2] => [[.,[[.,[.,.]],.]],[[.,[.,.]],.]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 2

[4,6,7,3,1,5,8,2] => [[[.,[.,[.,.]]],.],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[6,2,5,1,8,7,3,4] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[3,2,6,1,5,8,7,4] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[4,2,3,6,7,5,1,8] => [[[.,.],[.,[[.,[.,.]],.]]],[.,.]] => [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => 2

[6,2,3,5,7,4,1,8] => [[[.,.],[.,[[.,[.,.]],.]]],[.,.]] => [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => 2

[7,5,8,1,4,2,3,6] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[3,2,7,1,8,6,5,4] => [[[.,.],[.,.]],[[[[.,.],.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[6,2,4,1,5,7,8,3] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[5,8,4,1,3,6,7,2] => [[[.,[.,.]],.],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 2

[6,7,2,3,8,1,4,5] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[5,2,8,1,7,4,6,3] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[4,6,3,1,2,5,7,8] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 5

[7,4,6,8,3,1,2,5] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[2,5,6,4,8,1,3,7] => [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[2,7,8,1,4,5,3,6] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[3,7,8,1,2,4,6,5] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[7,3,4,1,2,6,8,5] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[3,8,2,7,4,5,1,6] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[8,2,6,1,3,5,4,7] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[8,2,4,5,1,7,3,6] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,8,2,4,5,1,7,3] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[4,3,8,1,7,5,6,2] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[8,3,4,7,2,6,5,1] => [[[[.,.],[.,[.,.]]],[[.,.],.]],.] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => 1

[8,3,7,1,4,5,6,2] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[8,2,7,1,3,4,6,5] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[8,2,4,7,3,1,6,5] => [[[.,.],[[.,[.,.]],.]],[[.,.],.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[6,8,1,4,7,3,2,5] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[8,5,7,2,6,3,1,4] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[5,8,2,7,3,1,6,4] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[8,1,2,6,7,5,4,3] => [[.,.],[.,[[[[.,[.,.]],.],.],.]]] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 3

[8,4,7,2,3,6,5,1] => [[[[.,.],[.,.]],[.,[[.,.],.]]],.] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[8,2,4,7,3,6,5,1] => [[[.,.],[[.,[.,.]],[[.,.],.]]],.] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1

[8,1,4,7,3,6,5,2] => [[.,.],[[[.,[.,.]],[[.,.],.]],.]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2

[2,8,1,5,3,7,6,4] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[5,8,2,3,7,4,1,6] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[1,3,5,6,4,8,2,7] => [.,[[.,[[.,[.,.]],[.,.]]],[.,.]]] => [1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 3

[4,6,1,8,2,7,5,3] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[5,6,1,7,4,3,8,2] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2

[3,7,2,1,5,6,8,4] => [[[.,[.,.]],.],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 2

[3,1,5,6,4,2,7,8] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[4,6,8,5,3,7,2,1] => [[[[.,[[.,[.,.]],.]],[.,.]],.],.] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[4,5,7,2,8,6,3,1] => [[[.,[.,[.,.]]],[[[.,.],.],.]],.] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1

[4,6,8,1,2,5,7,3] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[4,6,8,5,1,3,7,2] => [[.,[[.,[.,.]],.]],[[.,[.,.]],.]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 2

[3,7,8,4,6,1,5,2] => [[.,[[.,[.,.]],[.,.]]],[[.,.],.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2

[4,5,7,2,1,6,8,3] => [[[.,[.,[.,.]]],.],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[4,5,1,6,8,3,7,2] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2

[3,1,5,8,4,6,2,7] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[1,4,8,3,5,6,2,7] => [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 3

[3,7,2,4,5,8,1,6] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[7,4,6,2,1,3,8,5] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[3,6,7,2,4,1,8,5] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[8,4,7,2,3,5,6,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1

[5,7,1,8,4,3,6,2] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2

[8,4,6,3,1,5,2,7] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[3,6,1,5,2,4,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[2,7,1,5,3,4,6,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[8,4,5,1,2,7,6,3] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[7,2,6,8,5,1,3,4] => [[[.,.],[[.,[.,.]],.]],[.,[.,.]]] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[8,2,3,4,1,6,7,5] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[7,3,5,2,8,1,4,6] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[1,3,7,2,6,4,5,8] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 5

[1,5,8,2,3,6,4,7] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 5

[2,5,3,6,7,1,4,8] => [[.,[[.,.],[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[1,5,7,4,3,8,6,2] => [.,[[[[.,[.,.]],.],[[.,.],.]],.]] => [1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 2

[6,5,8,3,2,7,1,4] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[1,2,6,7,5,3,4,8] => [.,[.,[[[.,[.,.]],.],[.,[.,.]]]]] => [1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 5

[3,4,5,6,8,2,7,1] => [[[.,[.,[.,[.,[.,.]]]]],[.,.]],.] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 1

[1,5,6,7,3,4,2,8] => [.,[[[.,[.,[.,.]]],[.,.]],[.,.]]] => [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[4,6,8,5,2,1,7,3] => [[[.,[[.,[.,.]],.]],.],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 2

[1,6,7,8,2,4,5,3] => [.,[[.,[.,[.,.]]],[[.,[.,.]],.]]] => [1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3

[5,7,8,2,3,1,6,4] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[4,5,2,7,8,6,1,3] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[3,6,7,2,1,5,8,4] => [[[.,[.,[.,.]]],.],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[2,5,6,1,3,8,7,4] => [[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[6,7,1,4,5,2,8,3] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[7,2,5,6,1,3,8,4] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[4,7,3,5,2,6,8,1] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1

[6,8,4,1,5,7,3,2] => [[[.,[.,.]],.],[[[.,[.,.]],.],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 2

[8,4,5,2,7,3,6,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[7,3,4,2,8,5,6,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[6,3,8,2,7,4,5,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[8,3,6,2,7,4,5,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[1,7,8,4,3,6,5,2] => [.,[[[[.,[.,.]],.],[[.,.],.]],.]] => [1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 2

[1,7,8,3,6,5,4,2] => [.,[[[.,[.,.]],[[[.,.],.],.]],.]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 2

[5,8,1,7,2,4,3,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[2,5,7,3,8,1,4,6] => [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[8,3,5,2,1,6,7,4] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[5,6,8,2,4,7,1,3] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[2,4,1,7,5,6,3,8] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[1,5,7,3,6,4,2,8] => [.,[[[.,[.,.]],[[.,.],.]],[.,.]]] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 3

[1,6,7,2,4,8,3,5] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 4

[3,7,2,8,4,1,5,6] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[5,3,4,1,7,8,6,2] => [[[.,.],[.,.]],[[[.,[.,.]],.],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[1,2,6,8,4,3,5,7] => [.,[.,[[[.,[.,.]],.],[.,[.,.]]]]] => [1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 5

[5,8,4,1,3,7,2,6] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[3,4,2,1,6,8,5,7] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[8,1,3,5,6,4,7,2] => [[.,.],[[.,[[.,[.,.]],[.,.]]],.]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 2

[3,4,7,1,5,6,2,8] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[4,8,2,6,5,3,7,1] => [[[.,[.,.]],[[[.,.],.],[.,.]]],.] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 1

[8,3,5,1,4,6,7,2] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[8,4,5,1,2,6,7,3] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[6,8,5,4,7,2,3,1] => [[[[[.,[.,.]],.],[.,.]],[.,.]],.] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1

[2,5,7,3,4,8,1,6] => [[.,[[.,[.,.]],[.,[.,.]]]],[.,.]] => [1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2

[5,2,4,7,8,1,3,6] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3

[1,7,8,5,4,6,2,3] => [.,[[[[.,[.,.]],.],[.,.]],[.,.]]] => [1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 3

[4,6,8,1,5,2,7,3] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[5,6,2,8,1,7,3,4] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,8,4,5,1,3,7,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[5,2,3,8,1,4,6,7] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[1,6,8,3,2,4,5,7] => [.,[[[.,[.,.]],.],[.,[.,[.,.]]]]] => [1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 5

[7,3,6,8,4,5,1,2] => [[[.,.],[[.,[.,.]],[.,.]]],[.,.]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[2,6,7,4,8,5,1,3] => [[.,[[.,[.,.]],[[.,.],.]]],[.,.]] => [1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2

[8,1,4,7,3,5,6,2] => [[.,.],[[[.,[.,.]],[.,[.,.]]],.]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[8,3,7,2,4,5,6,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1

[8,1,4,5,7,3,6,2] => [[.,.],[[[.,[.,[.,.]]],[.,.]],.]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2

[5,6,3,4,2,8,7,1] => [[[[.,[.,.]],[.,.]],[[.,.],.]],.] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 1

[2,5,7,4,6,8,1,3] => [[.,[[.,[.,.]],[.,[.,.]]]],[.,.]] => [1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2

[2,5,6,4,1,3,8,7] => [[.,[[.,[.,.]],.]],[.,[[.,.],.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 3

[4,6,1,3,5,7,2,8] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[4,5,2,8,6,7,3,1] => [[[.,[.,.]],[[[.,.],[.,.]],.]],.] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 1

[4,2,3,6,8,5,1,7] => [[[.,.],[.,[[.,[.,.]],.]]],[.,.]] => [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => 2

[4,5,1,3,2,8,6,7] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[1,5,8,2,4,3,7,6] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 4

[4,3,7,8,2,6,5,1] => [[[[.,.],[.,[.,.]]],[[.,.],.]],.] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => 1

[2,4,7,8,3,6,5,1] => [[.,[[.,[.,[.,.]]],[[.,.],.]]],.] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1

[5,4,7,8,3,6,1,2] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,8,1,3,2,5,7,4] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[5,6,3,2,8,7,1,4] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[5,1,6,7,8,3,2,4] => [[.,.],[[[.,[.,[.,.]]],.],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => 3

[1,5,6,3,7,2,4,8] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 4

[1,5,6,7,4,2,3,8] => [.,[[[.,[.,[.,.]]],.],[.,[.,.]]]] => [1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[5,1,6,7,3,4,2,8] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[6,8,5,1,7,4,2,3] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[5,4,8,3,1,2,6,7] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[8,4,7,3,2,5,6,1] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1

[6,8,5,1,7,3,4,2] => [[[.,[.,.]],.],[[[.,.],[.,.]],.]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[1,7,8,3,6,5,2,4] => [.,[[[.,[.,.]],[[.,.],.]],[.,.]]] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 3

[4,6,7,5,1,8,2,3] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[3,5,2,6,8,7,4,1] => [[[.,[.,.]],[[.,[[.,.],.]],.]],.] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 1

[7,3,6,8,4,1,2,5] => [[[.,.],[[.,[.,.]],.]],[.,[.,.]]] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[3,5,8,1,2,7,6,4] => [[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[6,8,3,5,4,7,2,1] => [[[[.,[.,.]],[[.,.],[.,.]]],.],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 1

[8,5,7,1,4,2,6,3] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[4,8,2,5,6,3,7,1] => [[[.,[.,.]],[[.,[.,.]],[.,.]]],.] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 1

[8,1,5,7,4,6,2,3] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[4,7,1,5,6,3,2,8] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[4,5,7,1,6,3,8,2] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[2,7,1,4,8,3,6,5] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[2,7,1,5,6,8,4,3] => [[.,[.,.]],[[[.,[.,[.,.]]],.],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2

[2,3,1,8,7,4,6,5] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[4,6,8,2,1,5,3,7] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[5,6,8,4,7,2,3,1] => [[[[.,[.,[.,.]]],[.,.]],[.,.]],.] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[4,5,7,3,6,1,2,8] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[4,5,8,2,6,1,7,3] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[3,4,5,7,2,1,6,8] => [[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[4,5,6,8,3,2,7,1] => [[[[.,[.,[.,[.,.]]]],.],[.,.]],.] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1

[4,5,7,2,6,1,8,3] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[3,6,7,2,5,8,4,1] => [[[.,[.,[.,.]]],[[.,[.,.]],.]],.] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[5,3,6,7,4,8,1,2] => [[[.,.],[[.,[.,.]],[.,.]]],[.,.]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[4,2,7,8,3,6,5,1] => [[[.,.],[[.,[.,.]],[[.,.],.]]],.] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1

[4,2,7,8,5,6,1,3] => [[[.,.],[[.,[.,.]],[.,.]]],[.,.]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[3,5,7,8,4,2,1,6] => [[[.,[[.,[.,[.,.]]],.]],.],[.,.]] => [1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 2

[4,6,7,3,2,8,1,5] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[5,6,2,4,7,8,3,1] => [[[.,[.,.]],[[.,[.,[.,.]]],.]],.] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[5,6,3,2,8,4,7,1] => [[[[.,[.,.]],.],[[.,.],[.,.]]],.] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 1

[5,6,2,8,3,4,7,1] => [[[.,[.,.]],[[.,.],[.,[.,.]]]],.] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 1

[2,4,7,8,6,5,1,3] => [[.,[.,[[[.,[.,.]],.],.]]],[.,.]] => [1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 2

[5,2,6,7,8,1,4,3] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[4,8,2,7,5,3,1,6] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[3,5,8,1,7,4,2,6] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[3,7,8,6,1,4,5,2] => [[.,[[.,[.,.]],.]],[[.,[.,.]],.]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 2

[4,6,7,8,2,1,5,3] => [[[.,[.,[.,[.,.]]]],.],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[3,8,1,4,6,2,5,7] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[2,4,5,3,8,7,1,6] => [[.,[[.,[.,.]],[[.,.],.]]],[.,.]] => [1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2

[7,8,6,2,3,5,1,4] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[4,1,6,7,8,2,5,3] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[2,5,8,4,6,1,3,7] => [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[4,7,8,6,5,1,3,2] => [[.,[[[.,[.,.]],.],.]],[[.,.],.]] => [1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 2

[6,8,4,7,3,5,2,1] => [[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1

[7,4,5,8,3,6,2,1] => [[[[[.,.],[.,[.,.]]],[.,.]],.],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1

[4,8,1,3,6,7,5,2] => [[.,[.,.]],[[.,[[.,[.,.]],.]],.]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 2

[4,1,6,7,8,5,3,2] => [[.,.],[[[[.,[.,[.,.]]],.],.],.]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => 2

[3,7,8,6,4,1,5,2] => [[.,[[[.,[.,.]],.],.]],[[.,.],.]] => [1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 2

[4,6,1,5,7,2,3,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[5,4,8,1,3,7,2,6] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[8,4,5,3,1,7,2,6] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[7,4,5,3,1,8,6,2] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[5,7,8,6,4,2,3,1] => [[[[.,[[.,[.,.]],.]],.],[.,.]],.] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[3,8,2,6,7,5,1,4] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[6,7,4,1,8,2,5,3] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[3,4,7,8,6,1,2,5] => [[.,[.,[[.,[.,.]],.]]],[.,[.,.]]] => [1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 3

[2,1,4,7,8,6,3,5] => [[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3

[2,4,5,8,1,6,3,7] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,7,1,6,5,3,8,2] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2

[2,7,1,5,3,8,6,4] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[3,5,7,2,8,4,1,6] => [[[.,[.,[.,.]]],[[.,.],.]],[.,.]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[2,6,7,1,4,5,8,3] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[7,1,3,8,2,6,4,5] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[2,5,8,1,6,7,3,4] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[4,5,7,2,8,3,1,6] => [[[.,[.,[.,.]]],[[.,.],.]],[.,.]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[3,5,1,7,6,2,8,4] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[5,8,4,1,2,3,6,7] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 5

[3,5,8,1,4,2,7,6] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[8,1,2,4,6,3,7,5] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 4

[6,1,2,7,8,4,3,5] => [[.,.],[.,[[[.,[.,.]],.],[.,.]]]] => [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => 4

[7,8,1,2,5,3,4,6] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5

[8,4,7,2,1,6,3,5] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[4,5,8,2,1,6,7,3] => [[[.,[.,[.,.]]],.],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[3,1,6,7,5,2,4,8] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[4,8,1,5,3,6,7,2] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 2

[4,5,2,6,1,8,3,7] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,4,8,2,1,3,6,7] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[1,4,8,3,2,6,5,7] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 4

[5,7,3,2,8,6,4,1] => [[[[.,[.,.]],.],[[[.,.],.],.]],.] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 1

[4,5,1,6,8,2,7,3] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[4,5,2,1,3,7,6,8] => [[[.,[.,.]],.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[3,6,8,1,5,7,4,2] => [[.,[.,[.,.]]],[[[.,[.,.]],.],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[4,5,6,8,2,1,7,3] => [[[.,[.,[.,[.,.]]]],.],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[4,5,6,8,1,3,7,2] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[4,5,8,3,2,1,7,6] => [[[[.,[.,[.,.]]],.],.],[[.,.],.]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[4,5,1,3,2,6,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

[4,7,3,2,1,6,5,8] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[4,7,8,3,5,1,6,2] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[4,7,1,3,5,6,2,8] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[4,8,3,2,1,6,7,5] => [[[[.,[.,.]],.],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 2

[5,2,8,1,4,6,7,3] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[5,6,3,7,8,1,4,2] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[5,7,1,4,3,6,2,8] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[6,2,3,7,1,5,4,8] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,2,8,1,5,4,7,3] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[6,1,3,4,5,2,7,8] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[7,1,3,4,5,6,2,8] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 3

[7,2,5,1,3,6,4,8] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[1,3,6,7,5,2,4,8] => [.,[[.,[[.,[.,.]],.]],[.,[.,.]]]] => [1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 4

[4,8,5,7,1,2,3,6] => [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[4,6,3,2,5,8,7,1] => [[[[.,[.,.]],.],[.,[[.,.],.]]],.] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 1

[5,8,4,3,2,6,1,7] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2

[1,5,7,4,8,6,2,3] => [.,[[[.,[.,.]],[[.,.],.]],[.,.]]] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 3

[6,1,5,7,3,8,2,4] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[1,2,7,8,6,4,3,5] => [.,[.,[[[[.,[.,.]],.],.],[.,.]]]] => [1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 4

[3,5,1,7,8,6,2,4] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[5,2,4,1,7,6,8,3] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[7,2,3,1,6,8,4,5] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[5,7,8,1,6,2,3,4] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[4,8,2,1,5,7,3,6] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[5,2,7,1,6,3,4,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[4,8,2,5,1,6,3,7] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,8,1,2,4,6,3,7] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4

[3,2,7,1,6,4,5,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[7,3,6,8,4,5,2,1] => [[[[.,.],[[.,[.,.]],[.,.]]],.],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1

[5,6,2,8,3,1,7,4] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[5,2,4,8,3,1,6,7] => [[[.,.],[[.,[.,.]],.]],[.,[.,.]]] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[7,4,5,1,8,6,2,3] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[7,4,8,3,1,6,5,2] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[4,5,3,8,1,7,6,2] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[6,8,4,7,1,2,5,3] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[6,1,5,7,2,8,3,4] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[7,2,4,1,8,5,3,6] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[4,7,2,6,1,8,3,5] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,8,1,3,4,2,5,7] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[3,6,1,4,7,8,2,5] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[2,5,7,1,3,6,4,8] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[1,4,7,2,5,3,6,8] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 5

[4,5,3,1,2,6,8,7] => [[[.,[.,.]],.],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 4

[4,5,1,3,8,2,6,7] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[7,3,5,1,4,2,6,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[2,4,3,6,7,1,5,8] => [[.,[[.,.],[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[7,3,5,2,1,6,4,8] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[2,5,6,1,4,3,7,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[5,6,1,8,4,3,7,2] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2

[3,2,8,1,7,5,4,6] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[7,1,5,6,2,3,4,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[1,6,8,2,7,3,4,5] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 5

[4,1,2,6,7,8,5,3] => [[.,.],[.,[[[.,[.,[.,.]]],.],.]]] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => 3

[3,7,8,2,1,4,5,6] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[6,3,7,1,8,2,4,5] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[5,2,4,7,8,3,6,1] => [[[.,.],[[.,[.,[.,.]]],[.,.]]],.] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1

[5,1,4,7,8,3,6,2] => [[.,.],[[[.,[.,[.,.]]],[.,.]],.]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2

[5,6,4,1,7,3,8,2] => [[[.,[.,.]],.],[[[.,.],[.,.]],.]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[4,3,7,8,2,5,1,6] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[3,7,8,5,4,2,1,6] => [[[.,[[[.,[.,.]],.],.]],.],[.,.]] => [1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 2

[1,7,4,5,6,8,3,2] => [.,[[[[.,.],[.,[.,[.,.]]]],.],.]] => [1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2

[7,2,4,5,6,8,3,1] => [[[.,.],[[.,[.,[.,[.,.]]]],.]],.] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 1

[2,7,4,5,6,8,3,1] => [[.,[[[.,.],[.,[.,[.,.]]]],.]],.] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[2,4,7,8,3,1,6,5] => [[.,[[.,[.,[.,.]]],.]],[[.,.],.]] => [1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[3,7,4,5,8,1,6,2] => [[.,[[.,.],[.,[.,.]]]],[[.,.],.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[1,4,3,5,6,8,2,7] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[4,6,1,7,3,2,8,5] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[4,7,3,5,1,2,8,6] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[4,8,3,5,2,1,6,7] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3

[1,6,8,4,7,5,3,2] => [.,[[[[.,[.,.]],[[.,.],.]],.],.]] => [1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 2

[4,7,1,6,8,2,3,5] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[5,7,8,2,3,4,1,6] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[4,2,3,6,8,5,7,1] => [[[.,.],[.,[[.,[.,.]],[.,.]]]],.] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1

[4,7,3,2,6,5,1,8] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[4,3,7,8,2,1,6,5] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[7,3,8,2,5,1,6,4] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[4,5,3,8,6,1,2,7] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[6,3,5,8,4,1,2,7] => [[[.,.],[[.,[.,.]],.]],[.,[.,.]]] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[7,8,4,6,1,3,5,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[4,5,3,6,8,1,2,7] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[7,8,6,2,1,4,3,5] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[7,8,6,3,1,2,5,4] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 3

[6,8,2,1,4,5,3,7] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[7,5,8,1,2,4,6,3] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[4,6,3,5,7,1,2,8] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[1,4,7,2,6,5,8,3] => [.,[[.,[.,.]],[[[.,.],[.,.]],.]]] => [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 3

[1,5,7,2,6,4,8,3] => [.,[[.,[.,.]],[[[.,.],[.,.]],.]]] => [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 3

[7,2,4,6,1,8,3,5] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[1,2,7,8,3,5,4,6] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => [1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 5

[1,2,7,8,3,4,6,5] => [.,[.,[[.,[.,.]],[.,[[.,.],.]]]]] => [1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 5

[3,4,1,7,8,6,5,2] => [[.,[.,.]],[[[[.,[.,.]],.],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 2

[5,1,3,4,8,2,7,6] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[7,5,6,1,3,4,8,2] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[5,7,2,4,6,1,8,3] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[2,1,5,6,3,8,7,4] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3

[2,4,5,3,8,1,7,6] => [[.,[[.,[.,.]],[.,.]]],[[.,.],.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2

[7,2,5,1,3,6,8,4] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[2,4,8,3,6,5,7,1] => [[.,[[.,[.,.]],[[.,.],[.,.]]]],.] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 1

[4,6,7,8,5,2,1,3] => [[[.,[[.,[.,[.,.]]],.]],.],[.,.]] => [1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 2

[4,7,2,1,8,6,5,3] => [[[.,[.,.]],.],[[[[.,.],.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2

[5,6,2,8,4,1,7,3] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[5,7,2,4,8,6,1,3] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[6,7,2,4,8,5,1,3] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[6,7,3,2,8,5,1,4] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[7,2,3,1,8,6,5,4] => [[[.,.],[.,.]],[[[[.,.],.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[1,5,8,3,4,6,2,7] => [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 3

[5,7,1,6,4,8,3,2] => [[.,[.,.]],[[[[.,.],[.,.]],.],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 2

[7,4,5,8,1,3,6,2] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[1,4,6,3,2,8,5,7] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 4

[6,8,4,1,5,7,2,3] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[5,2,6,7,4,1,8,3] => [[[.,.],[[.,[.,.]],.]],[[.,.],.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[8,5,6,4,1,7,3,2] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[7,8,3,1,6,4,5,2] => [[[.,[.,.]],.],[[[.,.],[.,.]],.]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[5,8,2,6,3,1,7,4] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[4,5,8,1,6,3,7,2] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[8,1,4,6,2,5,7,3] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3

[4,5,8,1,6,2,7,3] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[5,2,6,8,1,4,3,7] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,7,3,8,2,1,4,5] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3

[1,5,8,3,4,7,2,6] => [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 3

[5,3,8,1,4,6,2,7] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[4,5,8,1,3,6,2,7] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[4,1,3,7,2,8,6,5] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3

[4,6,3,1,7,2,8,5] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[2,8,1,7,5,4,6,3] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2

[6,8,3,1,5,7,2,4] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[7,4,5,1,2,6,8,3] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[3,2,7,8,5,6,1,4] => [[[.,.],[[.,[.,.]],[.,.]]],[.,.]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[4,8,3,2,1,7,5,6] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[1,3,7,8,4,6,2,5] => [.,[[.,[[.,[.,.]],[.,.]]],[.,.]]] => [1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 3

[5,6,4,8,7,2,1,3] => [[[[.,[.,.]],[[.,.],.]],.],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2

[4,8,3,7,6,1,2,5] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[6,8,3,4,5,2,1,7] => [[[[.,[.,.]],[.,[.,.]]],.],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2

[3,7,1,4,5,6,2,8] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[3,6,1,4,5,2,7,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[3,8,2,4,5,1,7,6] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[3,7,2,1,5,6,4,8] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[3,6,8,1,5,4,7,2] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[1,6,8,5,4,3,7,2] => [.,[[[[[.,[.,.]],.],.],[.,.]],.]] => [1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 2

[2,5,7,8,4,3,1,6] => [[.,[[[.,[.,[.,.]]],.],.]],[.,.]] => [1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 2

[6,8,5,3,2,4,1,7] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2

[1,6,8,5,3,2,7,4] => [.,[[[[.,[.,.]],.],.],[[.,.],.]]] => [1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 3

[4,6,1,8,7,5,3,2] => [[.,[.,.]],[[[[[.,.],.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2

[4,1,7,8,6,5,2,3] => [[.,.],[[[[.,[.,.]],.],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => 3

[4,5,2,6,7,8,1,3] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[4,5,1,3,7,6,2,8] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3

[5,8,1,2,7,6,4,3] => [[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 3

[1,6,7,4,5,3,2,8] => [.,[[[[.,[.,.]],[.,.]],.],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 3

[4,3,7,1,5,8,2,6] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[6,1,3,5,7,2,8,4] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[2,8,1,5,6,4,3,7] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[1,6,7,5,8,4,2,3] => [.,[[[[.,[.,.]],[.,.]],.],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 3

[6,8,4,7,3,2,5,1] => [[[[[.,[.,.]],[.,.]],.],[.,.]],.] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1

[7,2,5,6,8,3,4,1] => [[[.,.],[[.,[.,[.,.]]],[.,.]]],.] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1

[8,6,7,2,3,5,4,1] => [[[[.,.],[.,.]],[.,[[.,.],.]]],.] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[1,5,7,2,4,3,8,6] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 4

[5,1,3,8,2,7,4,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[5,7,1,3,2,8,4,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[1,4,7,8,3,2,5,6] => [.,[[[.,[.,[.,.]]],.],[.,[.,.]]]] => [1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[2,8,1,3,5,6,4,7] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4

[4,1,3,6,2,5,8,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[7,1,4,6,3,2,5,8] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[6,7,2,3,8,4,1,5] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[2,7,8,1,5,4,3,6] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[4,7,1,5,2,6,8,3] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[3,1,6,7,5,2,8,4] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3

[8,6,7,5,2,1,4,3] => [[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[7,1,4,5,2,6,8,3] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3

[2,1,7,8,3,5,4,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[3,7,8,2,5,4,1,6] => [[[.,[.,[.,.]]],[[.,.],.]],[.,.]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[4,7,8,6,2,1,5,3] => [[[.,[[.,[.,.]],.]],.],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 2

[5,6,4,7,1,8,3,2] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2

[4,1,5,7,8,6,3,2] => [[.,.],[[[.,[[.,[.,.]],.]],.],.]] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2

[3,6,7,1,5,4,8,2] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[6,4,7,1,5,2,8,3] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[4,5,1,7,2,8,6,3] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[4,7,1,8,5,3,6,2] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2

[6,4,7,2,5,3,1,8] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[5,2,6,7,4,3,1,8] => [[[.,.],[[[.,[.,.]],.],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => 2

[8,4,6,2,1,5,7,3] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[6,7,1,4,8,5,3,2] => [[.,[.,.]],[[[.,[[.,.],.]],.],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 2

[8,3,5,2,4,7,1,6] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[4,3,7,8,6,1,5,2] => [[[.,.],[[.,[.,.]],.]],[[.,.],.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[6,1,3,7,8,5,4,2] => [[.,.],[[.,[[[.,[.,.]],.],.]],.]] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2

[3,6,8,5,4,2,1,7] => [[[.,[[[.,[.,.]],.],.]],.],[.,.]] => [1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 2

[4,5,1,8,6,2,7,3] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[5,6,1,8,7,2,3,4] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[4,5,1,6,8,7,3,2] => [[.,[.,.]],[[[.,[[.,.],.]],.],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 2

[3,2,8,1,5,6,4,7] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[2,8,1,3,7,5,6,4] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 3

[3,4,7,1,5,8,2,6] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[4,2,7,1,5,8,3,6] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[3,1,6,7,2,8,5,4] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3

[3,4,7,8,5,2,6,1] => [[[.,[.,[[.,[.,.]],.]]],[.,.]],.] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[4,8,1,7,5,6,3,2] => [[.,[.,.]],[[[[.,.],[.,.]],.],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 2

[1,4,7,2,3,6,5,8] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 5

[1,5,8,2,6,3,4,7] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 5

[6,8,3,2,7,5,1,4] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[7,3,6,8,1,2,5,4] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[4,1,5,7,2,6,3,8] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[5,7,2,1,3,6,4,8] => [[[.,[.,.]],.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[3,5,6,7,2,4,1,8] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[1,5,6,4,8,3,2,7] => [.,[[[[.,[.,.]],[.,.]],.],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 3

[2,1,5,6,4,8,3,7] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[5,1,4,7,8,6,2,3] => [[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3

[1,6,7,2,8,5,4,3] => [.,[[.,[.,.]],[[[[.,.],.],.],.]]] => [1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 3

[4,3,7,1,5,8,6,2] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[8,2,4,5,3,1,7,6] => [[[.,.],[[.,[.,.]],.]],[[.,.],.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[4,5,8,2,1,7,3,6] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[6,8,4,1,7,3,2,5] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[5,8,2,1,3,6,4,7] => [[[.,[.,.]],.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[3,4,6,1,8,5,7,2] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[2,5,8,4,6,7,1,3] => [[.,[[.,[.,.]],[.,[.,.]]]],[.,.]] => [1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2

[4,7,8,6,2,3,5,1] => [[[.,[[.,[.,.]],.]],[.,[.,.]]],.] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 1

[3,5,1,2,6,8,7,4] => [[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 3

[1,6,7,2,5,8,3,4] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 4

[7,8,5,6,2,4,3,1] => [[[[.,[.,.]],[.,.]],[[.,.],.]],.] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 1

[5,4,7,8,6,2,1,3] => [[[[.,.],[[.,[.,.]],.]],.],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => 2

[6,5,8,2,3,4,7,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1

[7,8,2,3,6,4,5,1] => [[[.,[.,.]],[.,[[.,.],[.,.]]]],.] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 1

[4,2,8,1,3,7,5,6] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[8,2,4,1,3,7,5,6] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[4,2,6,7,5,1,8,3] => [[[.,.],[[.,[.,.]],.]],[[.,.],.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[4,7,2,5,3,8,1,6] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[3,5,7,4,2,8,1,6] => [[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => [1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[4,6,8,5,1,2,3,7] => [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4

[4,6,5,7,1,2,3,8] => [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[5,2,6,7,4,8,3,1] => [[[.,.],[[[.,[.,.]],[.,.]],.]],.] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1

[6,5,8,1,7,3,2,4] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[6,4,8,1,5,2,3,7] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[7,2,4,1,6,3,5,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[2,6,1,5,3,4,8,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[5,7,8,2,3,6,4,1] => [[[.,[.,[.,.]]],[.,[[.,.],.]]],.] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[5,6,1,2,4,7,8,3] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 3

[7,8,5,1,4,6,2,3] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[4,6,7,1,3,2,8,5] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[8,4,6,3,1,5,7,2] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[6,7,1,5,4,3,2,8] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[5,8,4,1,3,2,7,6] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[4,5,2,1,6,3,8,7] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[4,5,2,1,6,7,3,8] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[2,5,1,6,4,3,8,7] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[3,6,2,8,5,7,1,4] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[4,6,8,1,5,7,2,3] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[4,8,1,2,7,5,6,3] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 3

[3,4,7,2,5,8,6,1] => [[[.,[.,[.,.]]],[.,[[.,.],.]]],.] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[2,5,1,8,6,4,7,3] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2

[2,5,1,8,3,6,4,7] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[5,8,4,7,3,2,1,6] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2

[7,2,3,5,6,8,4,1] => [[[.,.],[.,[[.,[.,[.,.]]],.]]],.] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => 1

[5,8,1,3,4,7,2,6] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[8,3,4,2,7,6,1,5] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[7,2,4,5,3,1,6,8] => [[[.,.],[[.,[.,.]],.]],[.,[.,.]]] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[5,3,4,7,8,1,6,2] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[5,1,4,8,2,3,7,6] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[5,7,1,2,6,3,4,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5

[5,1,4,7,2,3,6,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[4,8,1,2,3,6,5,7] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 5

[4,5,1,3,2,6,8,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[6,7,2,4,1,8,3,5] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,7,2,5,4,1,3,8] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[7,6,8,2,4,5,3,1] => [[[[.,.],[.,.]],[[.,[.,.]],.]],.] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[1,4,8,3,6,2,7,5] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 3

[3,6,2,5,7,4,8,1] => [[[.,[.,.]],[[.,[.,.]],[.,.]]],.] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 1

[2,7,1,5,8,6,4,3] => [[.,[.,.]],[[[.,[[.,.],.]],.],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 2

[7,2,4,1,6,8,5,3] => [[[.,.],[.,.]],[[[.,[.,.]],.],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[6,4,7,2,3,8,5,1] => [[[[.,.],[.,.]],[.,[[.,.],.]]],.] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[7,1,5,6,3,4,8,2] => [[.,.],[[[.,[.,.]],[.,[.,.]]],.]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[4,6,7,5,3,1,8,2] => [[[.,[[.,[.,.]],.]],.],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 2

[5,4,6,2,8,7,3,1] => [[[[.,.],[.,.]],[[[.,.],.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1

[2,3,4,7,8,6,1,5] => [[.,[.,[.,[[.,[.,.]],.]]]],[.,.]] => [1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 2

[6,3,7,1,4,2,8,5] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[3,4,6,7,8,2,5,1] => [[[.,[.,[.,[.,[.,.]]]]],[.,.]],.] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 1

[2,5,6,7,3,8,1,4] => [[.,[[.,[.,[.,.]]],[.,.]]],[.,.]] => [1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[5,8,4,6,2,1,7,3] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2

[1,6,8,3,4,2,7,5] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 3

[2,5,6,3,7,4,8,1] => [[.,[[.,[.,.]],[[.,.],[.,.]]]],.] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 1

[5,7,3,2,8,4,1,6] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[2,6,8,1,7,5,3,4] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[4,5,1,8,7,3,6,2] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2

[5,7,4,1,2,6,8,3] => [[[.,[.,.]],.],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 3

[8,4,7,3,1,2,5,6] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[4,8,3,2,6,1,7,5] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[7,2,4,1,5,3,8,6] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[5,6,7,2,3,8,4,1] => [[[.,[.,[.,.]]],[.,[[.,.],.]]],.] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[6,2,5,7,1,4,3,8] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[8,4,6,1,5,7,3,2] => [[[.,.],[.,.]],[[[.,[.,.]],.],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[6,4,7,2,1,3,8,5] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[6,7,3,1,2,4,8,5] => [[[.,[.,.]],.],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 4

[5,2,3,6,1,8,4,7] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,6,2,5,7,8,4,1] => [[[.,[.,.]],[[.,[.,[.,.]]],.]],.] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[2,7,1,8,6,5,3,4] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[7,6,8,2,4,3,5,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[7,4,5,3,8,1,6,2] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[7,3,6,1,4,2,8,5] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[7,1,4,6,8,5,3,2] => [[.,.],[[[.,[[.,[.,.]],.]],.],.]] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2

[7,2,5,1,6,4,8,3] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[2,7,1,5,6,4,8,3] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2

[1,5,7,8,4,6,3,2] => [.,[[[[.,[.,[.,.]]],[.,.]],.],.]] => [1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[2,8,1,5,6,4,7,3] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2

[3,7,2,8,1,5,6,4] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2

[3,6,2,1,8,4,7,5] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[3,5,1,7,6,4,8,2] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2

[3,5,2,8,7,1,6,4] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[4,5,2,6,7,3,8,1] => [[[.,[.,.]],[[.,[.,.]],[.,.]]],.] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 1

[8,6,7,4,3,1,5,2] => [[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[4,7,1,8,5,3,2,6] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[8,6,7,1,4,3,5,2] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[8,6,7,2,1,3,5,4] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3

[8,5,6,1,7,4,2,3] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[3,4,6,1,8,2,7,5] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[6,4,5,2,7,1,3,8] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[5,6,1,7,2,4,3,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4

[3,5,6,8,1,2,7,4] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[2,6,5,7,1,3,4,8] => [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[2,3,7,1,5,6,4,8] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[2,6,1,3,5,4,7,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5

[4,6,1,5,2,8,7,3] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3

[4,6,1,5,2,7,8,3] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[3,6,8,2,7,5,1,4] => [[[.,[.,[.,.]]],[[.,.],.]],[.,.]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[5,6,4,1,7,2,8,3] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[4,3,6,2,5,8,1,7] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[1,5,6,7,3,2,4,8] => [.,[[[.,[.,[.,.]]],.],[.,[.,.]]]] => [1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[7,6,8,2,1,5,3,4] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[7,1,6,8,3,2,4,5] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[5,7,2,6,4,1,8,3] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[4,5,6,1,3,8,2,7] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[6,3,5,7,4,2,8,1] => [[[[.,.],[[.,[.,.]],.]],[.,.]],.] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[1,6,8,5,4,7,2,3] => [.,[[[[.,[.,.]],.],[.,.]],[.,.]]] => [1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 3

[5,7,1,8,3,2,6,4] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[5,8,4,3,7,6,2,1] => [[[[[.,[.,.]],.],[[.,.],.]],.],.] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 1

[2,6,1,8,4,7,5,3] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2

[5,8,1,4,6,2,7,3] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3

[4,6,2,3,7,1,8,5] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[7,8,6,4,2,5,3,1] => [[[[[.,[.,.]],.],.],[[.,.],.]],.] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 1

[2,6,4,5,7,1,8,3] => [[.,[[.,.],[.,[.,.]]]],[[.,.],.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[4,6,7,5,8,2,1,3] => [[[.,[[.,[.,.]],[.,.]]],.],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 2

[5,1,4,6,2,7,8,3] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3

[4,8,3,5,1,2,7,6] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3

[6,1,3,7,2,8,4,5] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4

[3,1,5,8,2,6,7,4] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3

[6,2,4,5,7,1,8,3] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[6,8,2,5,4,7,3,1] => [[[.,[.,.]],[[[.,.],[.,.]],.]],.] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 1

[5,6,4,2,8,7,1,3] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[5,7,4,2,6,1,8,3] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[5,4,7,1,6,2,8,3] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[6,4,7,1,2,3,8,5] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4

[8,2,3,1,6,4,7,5] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[1,3,8,2,5,6,4,7] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 4

[8,2,3,6,7,4,5,1] => [[[.,.],[.,[[.,[.,.]],[.,.]]]],.] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1

[1,7,8,4,2,6,3,5] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 4

[6,2,5,1,3,8,7,4] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3

[4,1,7,8,3,6,5,2] => [[.,.],[[[.,[.,.]],[[.,.],.]],.]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2

[5,8,1,6,4,7,2,3] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3

[2,3,7,1,8,5,6,4] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[3,6,5,7,8,2,4,1] => [[[.,[[.,.],[.,[.,.]]]],[.,.]],.] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[7,8,1,2,5,4,3,6] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 4

[3,1,5,7,4,8,6,2] => [[.,.],[[[.,[.,.]],[[.,.],.]],.]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2

[7,3,5,6,1,4,2,8] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,8,3,1,6,7,4,2] => [[[.,[.,.]],.],[[[.,[.,.]],.],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 2

[4,5,8,1,7,3,6,2] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[4,7,1,6,8,5,2,3] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[5,7,1,6,4,2,8,3] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3

[2,7,1,6,5,8,4,3] => [[.,[.,.]],[[[[.,.],[.,.]],.],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 2

[2,3,6,1,7,5,4,8] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[2,7,1,4,8,6,5,3] => [[.,[.,.]],[[.,[[[.,.],.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 2

[6,7,5,4,1,3,2,8] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[6,2,7,1,4,3,5,8] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[2,6,8,4,7,1,3,5] => [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[7,8,6,3,2,5,4,1] => [[[[[.,[.,.]],.],.],[[.,.],.]],.] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 1

[1,4,7,3,5,8,6,2] => [.,[[[.,[.,.]],[.,[[.,.],.]]],.]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 2

[3,7,8,2,5,1,6,4] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[7,3,8,2,4,1,5,6] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[6,3,7,8,1,2,5,4] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[5,7,1,6,8,2,3,4] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[6,8,4,2,1,7,3,5] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3

[6,8,5,4,3,7,1,2] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2

[5,7,4,8,3,1,2,6] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3

[6,1,2,4,8,3,7,5] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 4

[2,7,8,5,1,4,3,6] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[8,5,6,2,4,7,3,1] => [[[[.,.],[.,.]],[[.,[.,.]],.]],.] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[7,1,2,4,8,3,5,6] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 5

[7,1,5,8,2,3,4,6] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[3,6,8,5,1,4,2,7] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3

[5,2,4,1,6,8,3,7] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[1,2,4,7,8,5,6,3] => [.,[.,[[.,[[.,[.,.]],[.,.]]],.]]] => [1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 3

[8,4,7,1,5,2,6,3] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[8,5,7,1,4,3,6,2] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[8,2,3,1,7,6,4,5] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[7,2,5,8,3,1,4,6] => [[[.,.],[[.,[.,.]],.]],[.,[.,.]]] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[6,8,2,3,1,7,4,5] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3

[8,2,5,7,3,1,4,6] => [[[.,.],[[.,[.,.]],.]],[.,[.,.]]] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[8,6,7,4,1,3,5,2] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[4,6,3,2,5,1,8,7] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2

[4,8,3,2,6,5,7,1] => [[[[.,[.,.]],.],[[.,.],[.,.]]],.] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 1

[4,8,3,6,5,2,7,1] => [[[[.,[.,.]],[[.,.],.]],[.,.]],.] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 1

[6,8,4,2,5,3,7,1] => [[[[.,[.,.]],.],[[.,.],[.,.]]],.] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 1

[6,8,4,3,5,2,7,1] => [[[[[.,[.,.]],.],[.,.]],[.,.]],.] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1

[7,3,5,6,1,8,2,4] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,6,7,2,3,5,8,1] => [[[.,[.,[.,.]]],[.,[.,[.,.]]]],.] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1

[5,7,4,3,6,2,1,8] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[8,5,6,1,3,2,7,4] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3

[5,3,7,8,2,6,1,4] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[4,5,8,3,6,1,7,2] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[5,7,1,3,6,2,4,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4

[4,7,1,3,2,5,8,6] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4

[3,7,8,5,6,2,4,1] => [[[.,[[.,[.,.]],[.,.]]],[.,.]],.] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[8,2,3,1,6,5,7,4] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[4,7,2,3,6,5,8,1] => [[[.,[.,.]],[.,[[.,.],[.,.]]]],.] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 1

[3,8,2,6,4,7,1,5] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[8,3,6,1,7,4,5,2] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[3,5,1,8,6,2,4,7] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[8,1,6,7,4,5,3,2] => [[.,.],[[[[.,[.,.]],[.,.]],.],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[6,4,8,1,5,3,7,2] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[5,7,1,8,6,3,2,4] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3

[4,3,6,1,2,7,8,5] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[7,2,6,1,3,5,8,4] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3

[6,2,7,1,5,8,3,4] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[5,8,3,6,7,2,4,1] => [[[[.,[.,.]],[.,[.,.]]],[.,.]],.] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[2,7,1,5,3,6,8,4] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3

[5,7,3,6,4,2,1,8] => [[[[.,[.,.]],[[.,.],.]],.],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2

[5,7,3,6,4,1,8,2] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[6,7,2,3,5,8,1,4] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2

[7,4,5,8,2,3,1,6] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,3,6,8,2,4,1,7] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[1,7,8,6,3,2,4,5] => [.,[[[[.,[.,.]],.],.],[.,[.,.]]]] => [1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 4

[1,8,3,4,5,7,2,6] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[7,8,2,6,5,4,3,1] => [[[.,[.,.]],[[[[.,.],.],.],.]],.] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1

[5,3,7,8,4,2,1,6] => [[[[.,.],[[.,[.,.]],.]],.],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => 2

[7,3,6,8,1,5,4,2] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[7,5,8,2,4,3,6,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[6,5,8,2,3,4,1,7] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[5,8,2,3,7,4,6,1] => [[[.,[.,.]],[.,[[.,.],[.,.]]]],.] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 1

[7,8,2,3,5,4,6,1] => [[[.,[.,.]],[.,[[.,.],[.,.]]]],.] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 1

[4,1,3,5,8,2,6,7] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[5,7,1,6,4,2,3,8] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

[4,8,2,7,5,1,6,3] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2

[2,8,4,6,7,1,5,3] => [[.,[[.,.],[.,[.,.]]]],[[.,.],.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[4,7,2,3,5,1,6,8] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[4,8,2,3,7,5,1,6] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[8,1,2,4,7,3,5,6] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 5

[6,8,1,5,7,3,2,4] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3

[4,6,7,5,2,3,1,8] => [[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => [1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[6,4,5,3,8,7,1,2] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[8,2,6,7,5,3,1,4] => [[[.,.],[[[.,[.,.]],.],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => 2

[8,4,6,7,5,3,1,2] => [[[[.,.],[[.,[.,.]],.]],.],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => 2

[6,7,2,4,5,3,1,8] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[6,5,8,4,7,2,1,3] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[6,8,1,2,4,7,3,5] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4

[4,6,1,3,5,8,2,7] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[4,5,1,3,8,7,2,6] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3

[6,2,7,1,8,3,4,5] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[6,4,5,8,1,7,2,3] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[3,4,2,6,8,5,7,1] => [[[.,[.,.]],[[.,[.,.]],[.,.]]],.] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 1

[6,8,1,2,7,3,4,5] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5

[1,6,8,5,7,4,3,2] => [.,[[[[[.,[.,.]],[.,.]],.],.],.]] => [1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 2

[3,8,1,2,4,7,6,5] => [[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 4

[1,4,5,7,3,6,8,2] => [.,[[[.,[.,[.,.]]],[.,[.,.]]],.]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[2,3,8,1,4,6,5,7] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4

[3,6,2,4,7,5,8,1] => [[[.,[.,.]],[.,[[.,.],[.,.]]]],.] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 1

[4,2,7,8,6,3,1,5] => [[[.,.],[[[.,[.,.]],.],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => 2

[8,4,6,3,5,1,7,2] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[2,4,5,7,1,6,8,3] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[4,1,5,7,8,6,2,3] => [[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3

[6,1,4,8,2,3,7,5] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

[2,5,7,8,6,4,1,3] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => [1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 2

[5,6,2,4,8,7,3,1] => [[[.,[.,.]],[[.,[[.,.],.]],.]],.] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 1

[8,5,6,2,3,7,4,1] => [[[[.,.],[.,.]],[.,[[.,.],.]]],.] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[7,8,1,4,5,6,2,3] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[1,2,6,7,8,3,5,4] => [.,[.,[[.,[.,[.,.]]],[[.,.],.]]]] => [1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 4

[2,6,1,4,7,5,8,3] => [[.,[.,.]],[[.,[[.,.],[.,.]]],.]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 2

[3,1,5,7,2,6,8,4] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3

[6,7,2,1,3,4,8,5] => [[[.,[.,.]],.],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 4

[4,6,3,1,2,7,8,5] => [[[.,[.,.]],.],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 3

[2,3,5,6,8,4,7,1] => [[.,[.,[[.,[.,[.,.]]],[.,.]]]],.] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1

[2,4,5,8,3,6,7,1] => [[.,[[.,[.,[.,.]]],[.,[.,.]]]],.] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1

[6,4,7,8,3,5,1,2] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[3,5,6,7,1,8,4,2] => [[.,[.,[.,[.,.]]]],[[[.,.],.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[3,5,2,4,8,6,7,1] => [[[.,[.,.]],[.,[[.,.],[.,.]]]],.] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 1

[8,4,7,1,5,6,2,3] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[4,5,8,1,7,3,2,6] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[4,6,7,1,3,8,2,5] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[7,3,4,1,6,8,5,2] => [[[.,.],[.,.]],[[[.,[.,.]],.],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[7,2,6,8,3,4,5,1] => [[[.,.],[[.,[.,.]],[.,[.,.]]]],.] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1

[1,6,7,5,4,8,2,3] => [.,[[[[.,[.,.]],.],[.,.]],[.,.]]] => [1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 3

[4,1,5,7,3,6,8,2] => [[.,.],[[[.,[.,.]],[.,[.,.]]],.]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[5,7,2,1,6,8,4,3] => [[[.,[.,.]],.],[[[.,[.,.]],.],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 2

[6,2,5,7,4,1,8,3] => [[[.,.],[[.,[.,.]],.]],[[.,.],.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[3,6,1,8,7,4,5,2] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2

[4,7,1,3,5,6,8,2] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2

[4,3,5,7,8,2,6,1] => [[[[.,.],[.,[.,[.,.]]]],[.,.]],.] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 1

[5,7,3,2,1,8,6,4] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2

[6,8,2,1,5,4,3,7] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[4,3,5,6,2,8,1,7] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,3,5,2,7,8,4,1] => [[[[.,.],[.,.]],[[.,[.,.]],.]],.] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[4,5,3,1,6,8,2,7] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3

[3,4,6,7,5,1,8,2] => [[.,[.,[[.,[.,.]],.]]],[[.,.],.]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 2

[4,8,2,6,7,1,5,3] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[6,5,8,3,7,1,4,2] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[8,1,2,4,6,3,5,7] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 5

[3,7,8,4,5,6,1,2] => [[.,[[.,[.,.]],[.,[.,.]]]],[.,.]] => [1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2

[5,7,1,3,6,4,8,2] => [[.,[.,.]],[[.,[[.,.],[.,.]]],.]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 2

[5,6,2,8,7,4,3,1] => [[[.,[.,.]],[[[[.,.],.],.],.]],.] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1

[7,8,2,6,4,3,5,1] => [[[.,[.,.]],[[[.,.],.],[.,.]]],.] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 1

[7,8,6,1,4,2,5,3] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3

[7,8,5,1,2,6,3,4] => [[[.,[.,.]],.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4

[6,4,5,1,8,7,3,2] => [[[.,.],[.,.]],[[[[.,.],.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[7,8,6,1,4,3,5,2] => [[[.,[.,.]],.],[[[.,.],[.,.]],.]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2

[4,3,6,2,5,7,1,8] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[5,6,7,1,3,2,4,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[1,7,8,6,2,5,4,3] => [.,[[[.,[.,.]],.],[[[.,.],.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 3

[7,2,5,6,4,8,3,1] => [[[.,.],[[[.,[.,.]],[.,.]],.]],.] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1

[7,4,6,2,8,5,3,1] => [[[[.,.],[.,.]],[[[.,.],.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1

[3,7,4,6,8,1,5,2] => [[.,[[.,.],[.,[.,.]]]],[[.,.],.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[4,8,3,1,7,6,2,5] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3

[5,6,1,4,3,8,7,2] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2

[4,1,3,7,8,6,5,2] => [[.,.],[[.,[[[.,[.,.]],.],.]],.]] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2

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$F_{2} = q + q^{2}$

$F_{3} = 2\ q + 3\ q^{2} + q^{3}$

$F_{4} = 6\ q + 11\ q^{2} + 6\ q^{3} + q^{4}$

$F_{5} = 24\ q + 50\ q^{2} + 35\ q^{3} + 10\ q^{4} + q^{5}$

$F_{6} = 120\ q + 274\ q^{2} + 225\ q^{3} + 85\ q^{4} + 15\ q^{5} + q^{6}$

$F_{7} = 720\ q + 1764\ q^{2} + 1624\ q^{3} + 735\ q^{4} + 175\ q^{5} + 21\ q^{6} + q^{7}$

Description

The number of up steps after the last double rise of a Dyck path.

Map

Lalanne-Kreweras involution

Description

The Lalanne-Kreweras involution on Dyck paths.
Label the upsteps from left to right and record the labels on the first up step of each double rise. Do the same for the downsteps. Then form the Dyck path whose ascent lengths and descent lengths are the consecutives differences of the labels.

Map

to Tamari-corresponding Dyck path

Description

Return the Dyck path associated with a binary tree in consistency with the Tamari order on Dyck words and binary trees.
The bijection is defined recursively as follows:

a leaf is associated with an empty Dyck path,
a tree with children $l,r$ is associated with the Dyck word $T(l) 1 T(r) 0$ where $T(l)$ and $T(r)$ are the images of this bijection to $l$ and $r$ .

Map

to increasing tree

Description

Sends a permutation to its associated increasing tree.
This tree is recursively obtained by sending the unique permutation of length

$0$ to the empty tree, and sending a permutation

$\sigma$ of length

$n \geq 1$ to a root node with two subtrees

$L$ and

$R$ by splitting

$\sigma$ at the index

$\sigma^{-1}(1)$ , normalizing both sides again to permutations and sending the permutations on the left and on the right of

$\sigma^{-1}(1)$ to the trees

$L$ and

$R$ , respectively.