- FindStat

Identifier

Mp00061: Permutations —to increasing tree⟶ Binary trees
Mp00020: Binary trees —to Tamari-corresponding Dyck path⟶ Dyck paths
St000674: Dyck paths ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 22591 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[6,3,1,2,4,5] => [[[.,.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2

[6,3,1,2,5,4] => [[[.,.],.],[.,[[.,.],.]]] => [1,0,1,0,1,1,1,0,1,0,0,0] => 2

[6,3,1,4,2,5] => [[[.,.],.],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,0] => 2

[6,3,1,4,5,2] => [[[.,.],.],[[.,[.,.]],.]] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2

[6,3,1,5,2,4] => [[[.,.],.],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,0] => 2

[6,3,1,5,4,2] => [[[.,.],.],[[[.,.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,0] => 2

[6,3,2,1,4,5] => [[[[.,.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3

[6,3,2,1,5,4] => [[[[.,.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,1,0,0] => 3

[6,3,2,4,1,5] => [[[[.,.],.],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2

[6,3,2,4,5,1] => [[[[.,.],.],[.,[.,.]]],.] => [1,0,1,0,1,1,1,0,0,0,1,0] => 3

[6,3,2,5,1,4] => [[[[.,.],.],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2

[6,3,2,5,4,1] => [[[[.,.],.],[[.,.],.]],.] => [1,0,1,0,1,1,0,1,0,0,1,0] => 3

[6,3,4,1,2,5] => [[[.,.],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => 1

[6,3,4,1,5,2] => [[[.,.],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,1,0,0] => 1

[6,3,4,2,1,5] => [[[[.,.],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2

[6,3,4,2,5,1] => [[[[.,.],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,3,4,5,1,2] => [[[.,.],[.,[.,.]]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0] => 1

[6,3,4,5,2,1] => [[[[.,.],[.,[.,.]]],.],.] => [1,0,1,1,1,0,0,0,1,0,1,0] => 3

[6,3,5,1,2,4] => [[[.,.],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => 1

[6,3,5,1,4,2] => [[[.,.],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,1,0,0] => 1

[6,3,5,2,1,4] => [[[[.,.],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2

[6,3,5,2,4,1] => [[[[.,.],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,3,5,4,1,2] => [[[.,.],[[.,.],.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0] => 1

[6,3,5,4,2,1] => [[[[.,.],[[.,.],.]],.],.] => [1,0,1,1,0,1,0,0,1,0,1,0] => 3

[6,4,1,2,3,5] => [[[.,.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2

[6,4,1,2,5,3] => [[[.,.],.],[.,[[.,.],.]]] => [1,0,1,0,1,1,1,0,1,0,0,0] => 2

[6,4,1,3,2,5] => [[[.,.],.],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,0] => 2

[6,4,1,3,5,2] => [[[.,.],.],[[.,[.,.]],.]] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2

[6,4,1,5,2,3] => [[[.,.],.],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,0] => 2

[6,4,1,5,3,2] => [[[.,.],.],[[[.,.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,0] => 2

[6,4,2,1,3,5] => [[[[.,.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3

[6,4,2,1,5,3] => [[[[.,.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,1,0,0] => 3

[6,4,2,3,1,5] => [[[[.,.],.],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2

[6,4,2,3,5,1] => [[[[.,.],.],[.,[.,.]]],.] => [1,0,1,0,1,1,1,0,0,0,1,0] => 3

[6,4,2,5,1,3] => [[[[.,.],.],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2

[6,4,2,5,3,1] => [[[[.,.],.],[[.,.],.]],.] => [1,0,1,0,1,1,0,1,0,0,1,0] => 3

[6,4,3,1,2,5] => [[[[.,.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3

[6,4,3,1,5,2] => [[[[.,.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,1,0,0] => 3

[6,4,3,2,1,5] => [[[[[.,.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0] => 4

[6,4,3,2,5,1] => [[[[[.,.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,0] => 4

[6,4,3,5,1,2] => [[[[.,.],.],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2

[6,4,3,5,2,1] => [[[[[.,.],.],[.,.]],.],.] => [1,0,1,0,1,1,0,0,1,0,1,0] => 4

[6,4,5,1,2,3] => [[[.,.],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => 1

[6,4,5,1,3,2] => [[[.,.],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,1,0,0] => 1

[6,4,5,2,1,3] => [[[[.,.],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2

[6,4,5,2,3,1] => [[[[.,.],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,4,5,3,1,2] => [[[[.,.],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2

[6,4,5,3,2,1] => [[[[[.,.],[.,.]],.],.],.] => [1,0,1,1,0,0,1,0,1,0,1,0] => 4

[6,5,1,2,3,4] => [[[.,.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2

[6,5,1,2,4,3] => [[[.,.],.],[.,[[.,.],.]]] => [1,0,1,0,1,1,1,0,1,0,0,0] => 2

[6,5,1,3,2,4] => [[[.,.],.],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,0] => 2

[6,5,1,3,4,2] => [[[.,.],.],[[.,[.,.]],.]] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2

[6,5,1,4,2,3] => [[[.,.],.],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,0] => 2

[6,5,1,4,3,2] => [[[.,.],.],[[[.,.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,0] => 2

[6,5,2,1,3,4] => [[[[.,.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3

[6,5,2,1,4,3] => [[[[.,.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,1,0,0] => 3

[6,5,2,3,1,4] => [[[[.,.],.],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2

[6,5,2,3,4,1] => [[[[.,.],.],[.,[.,.]]],.] => [1,0,1,0,1,1,1,0,0,0,1,0] => 3

[6,5,2,4,1,3] => [[[[.,.],.],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2

[6,5,2,4,3,1] => [[[[.,.],.],[[.,.],.]],.] => [1,0,1,0,1,1,0,1,0,0,1,0] => 3

[6,5,3,1,2,4] => [[[[.,.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3

[6,5,3,1,4,2] => [[[[.,.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,1,0,0] => 3

[6,5,3,2,1,4] => [[[[[.,.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0] => 4

[6,5,3,2,4,1] => [[[[[.,.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,0] => 4

[6,5,3,4,1,2] => [[[[.,.],.],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2

[6,5,3,4,2,1] => [[[[[.,.],.],[.,.]],.],.] => [1,0,1,0,1,1,0,0,1,0,1,0] => 4

[6,5,4,1,2,3] => [[[[.,.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3

[6,5,4,1,3,2] => [[[[.,.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,1,0,0] => 3

[6,5,4,2,1,3] => [[[[[.,.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0] => 4

[6,5,4,2,3,1] => [[[[[.,.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,0] => 4

[6,5,4,3,1,2] => [[[[[.,.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0] => 4

[6,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],.] => [1,0,1,0,1,0,1,0,1,0,1,0] => 6

[1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0

[1,2,3,4,5,7,6] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 0

[1,2,3,4,6,5,7] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 0

[1,2,3,4,6,7,5] => [.,[.,[.,[.,[[.,[.,.]],.]]]]] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 0

[1,2,3,4,7,5,6] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 0

[1,2,3,4,7,6,5] => [.,[.,[.,[.,[[[.,.],.],.]]]]] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 0

[1,2,3,5,4,6,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 0

[1,2,3,5,4,7,6] => [.,[.,[.,[[.,.],[[.,.],.]]]]] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 0

[1,2,3,5,6,4,7] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 0

[1,2,3,5,6,7,4] => [.,[.,[.,[[.,[.,[.,.]]],.]]]] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 0

[1,2,3,5,7,4,6] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 0

[1,2,3,5,7,6,4] => [.,[.,[.,[[.,[[.,.],.]],.]]]] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 0

[1,2,3,6,4,5,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 0

[1,2,3,6,4,7,5] => [.,[.,[.,[[.,.],[[.,.],.]]]]] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 0

[1,2,3,6,5,4,7] => [.,[.,[.,[[[.,.],.],[.,.]]]]] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 0

[1,2,3,6,5,7,4] => [.,[.,[.,[[[.,.],[.,.]],.]]]] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 0

[1,2,3,6,7,4,5] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 0

[1,2,3,6,7,5,4] => [.,[.,[.,[[[.,[.,.]],.],.]]]] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 0

[1,2,3,7,4,5,6] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 0

[1,2,3,7,4,6,5] => [.,[.,[.,[[.,.],[[.,.],.]]]]] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 0

[1,2,3,7,5,4,6] => [.,[.,[.,[[[.,.],.],[.,.]]]]] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 0

[1,2,3,7,5,6,4] => [.,[.,[.,[[[.,.],[.,.]],.]]]] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 0

[1,2,3,7,6,4,5] => [.,[.,[.,[[[.,.],.],[.,.]]]]] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 0

[1,2,3,7,6,5,4] => [.,[.,[.,[[[[.,.],.],.],.]]]] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 0

[1,2,4,3,5,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 0

[1,2,4,3,5,7,6] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 0

[1,2,4,3,6,5,7] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 0

[1,2,4,3,6,7,5] => [.,[.,[[.,.],[[.,[.,.]],.]]]] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 0

[1,2,4,3,7,5,6] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 0

[1,2,4,3,7,6,5] => [.,[.,[[.,.],[[[.,.],.],.]]]] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 0

[1,2,4,5,3,6,7] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 0

[1,2,4,5,3,7,6] => [.,[.,[[.,[.,.]],[[.,.],.]]]] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 0

[1,2,4,5,6,3,7] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 0

[1,2,4,5,6,7,3] => [.,[.,[[.,[.,[.,[.,.]]]],.]]] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 0

[1,2,4,5,7,3,6] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 0

[1,2,4,5,7,6,3] => [.,[.,[[.,[.,[[.,.],.]]],.]]] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 0

[1,2,4,6,3,5,7] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 0

[1,2,4,6,3,7,5] => [.,[.,[[.,[.,.]],[[.,.],.]]]] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 0

[1,2,4,6,5,3,7] => [.,[.,[[.,[[.,.],.]],[.,.]]]] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 0

[1,2,4,6,5,7,3] => [.,[.,[[.,[[.,.],[.,.]]],.]]] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 0

[1,2,4,6,7,3,5] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 0

[1,2,4,6,7,5,3] => [.,[.,[[.,[[.,[.,.]],.]],.]]] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 0

[1,2,4,7,3,5,6] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 0

[1,2,4,7,3,6,5] => [.,[.,[[.,[.,.]],[[.,.],.]]]] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 0

[1,2,4,7,5,3,6] => [.,[.,[[.,[[.,.],.]],[.,.]]]] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 0

[1,2,4,7,5,6,3] => [.,[.,[[.,[[.,.],[.,.]]],.]]] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 0

[1,2,4,7,6,3,5] => [.,[.,[[.,[[.,.],.]],[.,.]]]] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 0

[1,2,4,7,6,5,3] => [.,[.,[[.,[[[.,.],.],.]],.]]] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 0

[1,2,5,3,4,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 0

[1,2,5,3,4,7,6] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 0

[1,2,5,3,6,4,7] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 0

[1,2,5,3,6,7,4] => [.,[.,[[.,.],[[.,[.,.]],.]]]] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 0

[1,2,5,3,7,4,6] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 0

[1,2,5,3,7,6,4] => [.,[.,[[.,.],[[[.,.],.],.]]]] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 0

[1,2,5,4,3,6,7] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 0

[1,2,5,4,3,7,6] => [.,[.,[[[.,.],.],[[.,.],.]]]] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 0

[1,2,5,4,6,3,7] => [.,[.,[[[.,.],[.,.]],[.,.]]]] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 0

[1,2,5,4,6,7,3] => [.,[.,[[[.,.],[.,[.,.]]],.]]] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 0

[1,2,5,4,7,3,6] => [.,[.,[[[.,.],[.,.]],[.,.]]]] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 0

[1,2,5,4,7,6,3] => [.,[.,[[[.,.],[[.,.],.]],.]]] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 0

[1,2,5,6,3,4,7] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 0

[1,2,5,6,3,7,4] => [.,[.,[[.,[.,.]],[[.,.],.]]]] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 0

[1,2,5,6,4,3,7] => [.,[.,[[[.,[.,.]],.],[.,.]]]] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 0

[1,2,5,6,4,7,3] => [.,[.,[[[.,[.,.]],[.,.]],.]]] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 0

[1,2,5,6,7,3,4] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 0

[1,2,5,6,7,4,3] => [.,[.,[[[.,[.,[.,.]]],.],.]]] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 0

[1,2,5,7,3,4,6] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 0

[1,2,5,7,3,6,4] => [.,[.,[[.,[.,.]],[[.,.],.]]]] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 0

[1,2,5,7,4,3,6] => [.,[.,[[[.,[.,.]],.],[.,.]]]] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 0

[1,2,5,7,4,6,3] => [.,[.,[[[.,[.,.]],[.,.]],.]]] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 0

[1,2,5,7,6,3,4] => [.,[.,[[.,[[.,.],.]],[.,.]]]] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 0

[1,2,5,7,6,4,3] => [.,[.,[[[.,[[.,.],.]],.],.]]] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 0

[1,2,6,3,4,5,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 0

[1,2,6,3,4,7,5] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 0

[1,2,6,3,5,4,7] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 0

[1,2,6,3,5,7,4] => [.,[.,[[.,.],[[.,[.,.]],.]]]] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 0

[1,2,6,3,7,4,5] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 0

[1,2,6,3,7,5,4] => [.,[.,[[.,.],[[[.,.],.],.]]]] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 0

[1,2,6,4,3,5,7] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 0

[1,2,6,4,3,7,5] => [.,[.,[[[.,.],.],[[.,.],.]]]] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 0

[1,2,6,4,5,3,7] => [.,[.,[[[.,.],[.,.]],[.,.]]]] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 0

[1,2,6,4,5,7,3] => [.,[.,[[[.,.],[.,[.,.]]],.]]] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 0

[1,2,6,4,7,3,5] => [.,[.,[[[.,.],[.,.]],[.,.]]]] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 0

[1,2,6,4,7,5,3] => [.,[.,[[[.,.],[[.,.],.]],.]]] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 0

[1,2,6,5,3,4,7] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 0

[1,2,6,5,3,7,4] => [.,[.,[[[.,.],.],[[.,.],.]]]] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 0

[1,2,6,5,4,3,7] => [.,[.,[[[[.,.],.],.],[.,.]]]] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 0

[1,2,6,5,4,7,3] => [.,[.,[[[[.,.],.],[.,.]],.]]] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 0

[1,2,6,5,7,3,4] => [.,[.,[[[.,.],[.,.]],[.,.]]]] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 0

[1,2,6,5,7,4,3] => [.,[.,[[[[.,.],[.,.]],.],.]]] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 0

[1,2,6,7,3,4,5] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 0

[1,2,6,7,3,5,4] => [.,[.,[[.,[.,.]],[[.,.],.]]]] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 0

[1,2,6,7,4,3,5] => [.,[.,[[[.,[.,.]],.],[.,.]]]] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 0

[1,2,6,7,4,5,3] => [.,[.,[[[.,[.,.]],[.,.]],.]]] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 0

[1,2,6,7,5,3,4] => [.,[.,[[[.,[.,.]],.],[.,.]]]] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 0

[1,2,6,7,5,4,3] => [.,[.,[[[[.,[.,.]],.],.],.]]] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 0

[1,2,7,3,4,5,6] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 0

[1,2,7,3,4,6,5] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 0

[1,2,7,3,5,4,6] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 0

[1,2,7,3,5,6,4] => [.,[.,[[.,.],[[.,[.,.]],.]]]] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 0

[1,2,7,3,6,4,5] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 0

[1,2,7,3,6,5,4] => [.,[.,[[.,.],[[[.,.],.],.]]]] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 0

[1,2,7,4,3,5,6] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 0

[1,2,7,4,3,6,5] => [.,[.,[[[.,.],.],[[.,.],.]]]] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 0

[1,2,7,4,5,3,6] => [.,[.,[[[.,.],[.,.]],[.,.]]]] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 0

[1,2,7,4,5,6,3] => [.,[.,[[[.,.],[.,[.,.]]],.]]] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 0

[1,2,7,4,6,3,5] => [.,[.,[[[.,.],[.,.]],[.,.]]]] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 0

[1,2,7,4,6,5,3] => [.,[.,[[[.,.],[[.,.],.]],.]]] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 0

[1,2,7,5,3,4,6] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 0

[1,2,7,5,3,6,4] => [.,[.,[[[.,.],.],[[.,.],.]]]] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 0

[1,2,7,5,4,3,6] => [.,[.,[[[[.,.],.],.],[.,.]]]] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 0

[1,2,7,5,4,6,3] => [.,[.,[[[[.,.],.],[.,.]],.]]] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 0

[1,2,7,5,6,3,4] => [.,[.,[[[.,.],[.,.]],[.,.]]]] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 0

[1,2,7,5,6,4,3] => [.,[.,[[[[.,.],[.,.]],.],.]]] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 0

[1,2,7,6,3,4,5] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 0

[1,2,7,6,3,5,4] => [.,[.,[[[.,.],.],[[.,.],.]]]] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 0

[1,2,7,6,4,3,5] => [.,[.,[[[[.,.],.],.],[.,.]]]] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 0

[1,2,7,6,4,5,3] => [.,[.,[[[[.,.],.],[.,.]],.]]] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 0

[1,2,7,6,5,3,4] => [.,[.,[[[[.,.],.],.],[.,.]]]] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 0

[1,2,7,6,5,4,3] => [.,[.,[[[[[.,.],.],.],.],.]]] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 0

[1,3,2,4,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 0

[1,3,2,4,5,7,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 0

[1,3,2,4,6,5,7] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 0

[1,3,2,4,6,7,5] => [.,[[.,.],[.,[[.,[.,.]],.]]]] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 0

[1,3,2,4,7,5,6] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 0

[1,3,2,4,7,6,5] => [.,[[.,.],[.,[[[.,.],.],.]]]] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 0

[1,3,2,5,4,6,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 0

[1,3,2,5,4,7,6] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 0

[1,3,2,5,6,4,7] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 0

[1,3,2,5,6,7,4] => [.,[[.,.],[[.,[.,[.,.]]],.]]] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 0

[1,3,2,5,7,4,6] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 0

[1,3,2,5,7,6,4] => [.,[[.,.],[[.,[[.,.],.]],.]]] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 0

[1,3,2,6,4,5,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 0

[1,3,2,6,4,7,5] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 0

[1,3,2,6,5,4,7] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 0

[1,3,2,6,5,7,4] => [.,[[.,.],[[[.,.],[.,.]],.]]] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 0

[1,3,2,6,7,4,5] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 0

[1,3,2,6,7,5,4] => [.,[[.,.],[[[.,[.,.]],.],.]]] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 0

[1,3,2,7,4,5,6] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 0

[1,3,2,7,4,6,5] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 0

[1,3,2,7,5,4,6] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 0

[1,3,2,7,5,6,4] => [.,[[.,.],[[[.,.],[.,.]],.]]] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 0

[1,3,2,7,6,4,5] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 0

[1,3,2,7,6,5,4] => [.,[[.,.],[[[[.,.],.],.],.]]] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 0

[1,3,4,2,5,6,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 0

[1,3,4,2,5,7,6] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 0

[1,3,4,2,6,5,7] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 0

[1,3,4,2,6,7,5] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 0

[1,3,4,2,7,5,6] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 0

[1,3,4,2,7,6,5] => [.,[[.,[.,.]],[[[.,.],.],.]]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 0

[1,3,4,5,2,6,7] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 0

[1,3,4,5,2,7,6] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 0

[1,3,4,5,6,2,7] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 0

[1,3,4,5,6,7,2] => [.,[[.,[.,[.,[.,[.,.]]]]],.]] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 0

[1,3,4,5,7,2,6] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 0

[1,3,4,5,7,6,2] => [.,[[.,[.,[.,[[.,.],.]]]],.]] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 0

[1,3,4,6,2,5,7] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 0

[1,3,4,6,2,7,5] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 0

[1,3,4,6,5,2,7] => [.,[[.,[.,[[.,.],.]]],[.,.]]] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 0

[1,3,4,6,5,7,2] => [.,[[.,[.,[[.,.],[.,.]]]],.]] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 0

[1,3,4,6,7,2,5] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 0

[1,3,4,6,7,5,2] => [.,[[.,[.,[[.,[.,.]],.]]],.]] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 0

[1,3,4,7,2,5,6] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 0

[1,3,4,7,2,6,5] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 0

[1,3,4,7,5,2,6] => [.,[[.,[.,[[.,.],.]]],[.,.]]] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 0

[1,3,4,7,5,6,2] => [.,[[.,[.,[[.,.],[.,.]]]],.]] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 0

[1,3,4,7,6,2,5] => [.,[[.,[.,[[.,.],.]]],[.,.]]] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 0

[1,3,4,7,6,5,2] => [.,[[.,[.,[[[.,.],.],.]]],.]] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 0

[1,3,5,2,4,6,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 0

[1,3,5,2,4,7,6] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 0

[1,3,5,2,6,4,7] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 0

[1,3,5,2,6,7,4] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 0

[1,3,5,2,7,4,6] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 0

[1,3,5,2,7,6,4] => [.,[[.,[.,.]],[[[.,.],.],.]]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 0

[1,3,5,4,2,6,7] => [.,[[.,[[.,.],.]],[.,[.,.]]]] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 0

[1,3,5,4,2,7,6] => [.,[[.,[[.,.],.]],[[.,.],.]]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 0

[1,3,5,4,6,2,7] => [.,[[.,[[.,.],[.,.]]],[.,.]]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 0

[1,3,5,4,6,7,2] => [.,[[.,[[.,.],[.,[.,.]]]],.]] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 0

[1,3,5,4,7,2,6] => [.,[[.,[[.,.],[.,.]]],[.,.]]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 0

[1,3,5,4,7,6,2] => [.,[[.,[[.,.],[[.,.],.]]],.]] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 0

[1,3,5,6,2,4,7] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 0

[1,3,5,6,2,7,4] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 0

[1,3,5,6,4,2,7] => [.,[[.,[[.,[.,.]],.]],[.,.]]] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 0

[1,3,5,6,4,7,2] => [.,[[.,[[.,[.,.]],[.,.]]],.]] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 0

[1,3,5,6,7,2,4] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 0

[1,3,5,6,7,4,2] => [.,[[.,[[.,[.,[.,.]]],.]],.]] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 0

[1,3,5,7,2,4,6] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 0

[1,3,5,7,2,6,4] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 0

[1,3,5,7,4,2,6] => [.,[[.,[[.,[.,.]],.]],[.,.]]] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 0

[1,3,5,7,4,6,2] => [.,[[.,[[.,[.,.]],[.,.]]],.]] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 0

[1,3,5,7,6,2,4] => [.,[[.,[.,[[.,.],.]]],[.,.]]] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 0

[1,3,5,7,6,4,2] => [.,[[.,[[.,[[.,.],.]],.]],.]] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 0

[1,3,6,2,4,5,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 0

[1,3,6,2,4,7,5] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 0

[1,3,6,2,5,4,7] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 0

[1,3,6,2,5,7,4] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 0

[1,3,6,2,7,4,5] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 0

[1,3,6,2,7,5,4] => [.,[[.,[.,.]],[[[.,.],.],.]]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 0

[1,3,6,4,2,5,7] => [.,[[.,[[.,.],.]],[.,[.,.]]]] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 0

[1,3,6,4,2,7,5] => [.,[[.,[[.,.],.]],[[.,.],.]]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 0

[1,3,6,4,5,2,7] => [.,[[.,[[.,.],[.,.]]],[.,.]]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 0

[1,3,6,4,5,7,2] => [.,[[.,[[.,.],[.,[.,.]]]],.]] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 0

[1,3,6,4,7,2,5] => [.,[[.,[[.,.],[.,.]]],[.,.]]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 0

[1,3,6,4,7,5,2] => [.,[[.,[[.,.],[[.,.],.]]],.]] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 0

[1,3,6,5,2,4,7] => [.,[[.,[[.,.],.]],[.,[.,.]]]] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 0

[1,3,6,5,2,7,4] => [.,[[.,[[.,.],.]],[[.,.],.]]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 0

[1,3,6,5,4,2,7] => [.,[[.,[[[.,.],.],.]],[.,.]]] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 0

[1,3,6,5,4,7,2] => [.,[[.,[[[.,.],.],[.,.]]],.]] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 0

[1,3,6,5,7,2,4] => [.,[[.,[[.,.],[.,.]]],[.,.]]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 0

[1,3,6,5,7,4,2] => [.,[[.,[[[.,.],[.,.]],.]],.]] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 0

[1,3,6,7,2,4,5] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 0

[1,3,6,7,2,5,4] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 0

[1,3,6,7,4,2,5] => [.,[[.,[[.,[.,.]],.]],[.,.]]] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 0

[1,3,6,7,4,5,2] => [.,[[.,[[.,[.,.]],[.,.]]],.]] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 0

[1,3,6,7,5,2,4] => [.,[[.,[[.,[.,.]],.]],[.,.]]] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 0

[1,3,6,7,5,4,2] => [.,[[.,[[[.,[.,.]],.],.]],.]] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 0

[1,3,7,2,4,5,6] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 0

[1,3,7,2,4,6,5] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 0

[1,3,7,2,5,4,6] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 0

[1,3,7,2,5,6,4] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 0

[1,3,7,2,6,4,5] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 0

[1,3,7,2,6,5,4] => [.,[[.,[.,.]],[[[.,.],.],.]]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 0

[1,3,7,4,2,5,6] => [.,[[.,[[.,.],.]],[.,[.,.]]]] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 0

[1,3,7,4,2,6,5] => [.,[[.,[[.,.],.]],[[.,.],.]]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 0

[1,3,7,4,5,2,6] => [.,[[.,[[.,.],[.,.]]],[.,.]]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 0

[1,3,7,4,5,6,2] => [.,[[.,[[.,.],[.,[.,.]]]],.]] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 0

[1,3,7,4,6,2,5] => [.,[[.,[[.,.],[.,.]]],[.,.]]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 0

[1,3,7,4,6,5,2] => [.,[[.,[[.,.],[[.,.],.]]],.]] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 0

[1,3,7,5,2,4,6] => [.,[[.,[[.,.],.]],[.,[.,.]]]] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 0

[1,3,7,5,2,6,4] => [.,[[.,[[.,.],.]],[[.,.],.]]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 0

[1,3,7,5,4,2,6] => [.,[[.,[[[.,.],.],.]],[.,.]]] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 0

[1,3,7,5,4,6,2] => [.,[[.,[[[.,.],.],[.,.]]],.]] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 0

[1,3,7,5,6,2,4] => [.,[[.,[[.,.],[.,.]]],[.,.]]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 0

[1,3,7,5,6,4,2] => [.,[[.,[[[.,.],[.,.]],.]],.]] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 0

[1,3,7,6,2,4,5] => [.,[[.,[[.,.],.]],[.,[.,.]]]] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 0

[1,3,7,6,2,5,4] => [.,[[.,[[.,.],.]],[[.,.],.]]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 0

[1,3,7,6,4,2,5] => [.,[[.,[[[.,.],.],.]],[.,.]]] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 0

[1,3,7,6,4,5,2] => [.,[[.,[[[.,.],.],[.,.]]],.]] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 0

[1,3,7,6,5,2,4] => [.,[[.,[[[.,.],.],.]],[.,.]]] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 0

[1,3,7,6,5,4,2] => [.,[[.,[[[[.,.],.],.],.]],.]] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 0

[1,4,2,3,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 0

[1,4,2,3,5,7,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 0

[1,4,2,3,6,5,7] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 0

[1,4,2,3,6,7,5] => [.,[[.,.],[.,[[.,[.,.]],.]]]] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 0

[1,4,2,3,7,5,6] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 0

[1,4,2,3,7,6,5] => [.,[[.,.],[.,[[[.,.],.],.]]]] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 0

[1,4,2,5,3,6,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 0

[1,4,2,5,3,7,6] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 0

[1,4,2,5,6,3,7] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 0

[1,4,2,5,6,7,3] => [.,[[.,.],[[.,[.,[.,.]]],.]]] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 0

[1,4,2,5,7,3,6] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 0

[1,4,2,5,7,6,3] => [.,[[.,.],[[.,[[.,.],.]],.]]] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 0

[1,4,2,6,3,5,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 0

[1,4,2,6,3,7,5] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 0

[1,4,2,6,5,3,7] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 0

[1,4,2,6,5,7,3] => [.,[[.,.],[[[.,.],[.,.]],.]]] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 0

[1,4,2,6,7,3,5] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 0

[1,4,2,6,7,5,3] => [.,[[.,.],[[[.,[.,.]],.],.]]] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 0

[1,4,2,7,3,5,6] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 0

[1,4,2,7,3,6,5] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 0

[1,4,2,7,5,3,6] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 0

[1,4,2,7,5,6,3] => [.,[[.,.],[[[.,.],[.,.]],.]]] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 0

[1,4,2,7,6,3,5] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 0

[1,4,2,7,6,5,3] => [.,[[.,.],[[[[.,.],.],.],.]]] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 0

[1,4,3,2,5,6,7] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 0

[1,4,3,2,5,7,6] => [.,[[[.,.],.],[.,[[.,.],.]]]] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 0

[1,4,3,2,6,5,7] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 0

[1,4,3,2,6,7,5] => [.,[[[.,.],.],[[.,[.,.]],.]]] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 0

[1,4,3,2,7,5,6] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 0

[1,4,3,2,7,6,5] => [.,[[[.,.],.],[[[.,.],.],.]]] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 0

[1,4,3,5,2,6,7] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 0

[1,4,3,5,2,7,6] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 0

[1,4,3,5,6,2,7] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 0

[1,4,3,5,6,7,2] => [.,[[[.,.],[.,[.,[.,.]]]],.]] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 0

[1,4,3,5,7,2,6] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 0

[1,4,3,5,7,6,2] => [.,[[[.,.],[.,[[.,.],.]]],.]] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 0

[1,4,3,6,2,5,7] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 0

[1,4,3,6,2,7,5] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 0

[1,4,3,6,5,2,7] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 0

[1,4,3,6,5,7,2] => [.,[[[.,.],[[.,.],[.,.]]],.]] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 0

[1,4,3,6,7,2,5] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 0

[1,4,3,6,7,5,2] => [.,[[[.,.],[[.,[.,.]],.]],.]] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 0

[1,4,3,7,2,5,6] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 0

[1,4,3,7,2,6,5] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 0

[1,4,3,7,5,2,6] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 0

[1,4,3,7,5,6,2] => [.,[[[.,.],[[.,.],[.,.]]],.]] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 0

[1,4,3,7,6,2,5] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 0

[1,4,3,7,6,5,2] => [.,[[[.,.],[[[.,.],.],.]],.]] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 0

[1,4,5,2,3,6,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 0

[1,4,5,2,3,7,6] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 0

[1,4,5,2,6,3,7] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 0

[1,4,5,2,6,7,3] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 0

[1,4,5,2,7,3,6] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 0

[1,4,5,2,7,6,3] => [.,[[.,[.,.]],[[[.,.],.],.]]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 0

[1,4,5,3,2,6,7] => [.,[[[.,[.,.]],.],[.,[.,.]]]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 0

[1,4,5,3,2,7,6] => [.,[[[.,[.,.]],.],[[.,.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 0

[1,4,5,3,6,2,7] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 0

[1,4,5,3,6,7,2] => [.,[[[.,[.,.]],[.,[.,.]]],.]] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 0

[1,4,5,3,7,2,6] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 0

[1,4,5,3,7,6,2] => [.,[[[.,[.,.]],[[.,.],.]],.]] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 0

[1,4,5,6,2,3,7] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 0

[1,4,5,6,2,7,3] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 0

[1,4,5,6,3,2,7] => [.,[[[.,[.,[.,.]]],.],[.,.]]] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 0

[1,4,5,6,3,7,2] => [.,[[[.,[.,[.,.]]],[.,.]],.]] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 0

[1,4,5,6,7,2,3] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 0

[1,4,5,6,7,3,2] => [.,[[[.,[.,[.,[.,.]]]],.],.]] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 0

[1,4,5,7,2,3,6] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 0

[1,4,5,7,2,6,3] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 0

[1,4,5,7,3,2,6] => [.,[[[.,[.,[.,.]]],.],[.,.]]] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 0

[1,4,5,7,3,6,2] => [.,[[[.,[.,[.,.]]],[.,.]],.]] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 0

[1,4,5,7,6,2,3] => [.,[[.,[.,[[.,.],.]]],[.,.]]] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 0

[1,4,5,7,6,3,2] => [.,[[[.,[.,[[.,.],.]]],.],.]] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 0

[1,4,6,2,3,5,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 0

[1,4,6,2,3,7,5] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 0

[1,4,6,2,5,3,7] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 0

[1,4,6,2,5,7,3] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 0

[1,4,6,2,7,3,5] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 0

[1,4,6,2,7,5,3] => [.,[[.,[.,.]],[[[.,.],.],.]]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 0

[1,4,6,3,2,5,7] => [.,[[[.,[.,.]],.],[.,[.,.]]]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 0

[1,4,6,3,2,7,5] => [.,[[[.,[.,.]],.],[[.,.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 0

[1,4,6,3,5,2,7] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 0

[1,4,6,3,5,7,2] => [.,[[[.,[.,.]],[.,[.,.]]],.]] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 0

[1,4,6,3,7,2,5] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 0

[1,4,6,3,7,5,2] => [.,[[[.,[.,.]],[[.,.],.]],.]] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 0

[1,4,6,5,2,3,7] => [.,[[.,[[.,.],.]],[.,[.,.]]]] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 0

[1,4,6,5,2,7,3] => [.,[[.,[[.,.],.]],[[.,.],.]]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 0

[1,4,6,5,3,2,7] => [.,[[[.,[[.,.],.]],.],[.,.]]] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 0

[1,4,6,5,3,7,2] => [.,[[[.,[[.,.],.]],[.,.]],.]] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 0

[1,4,6,5,7,2,3] => [.,[[.,[[.,.],[.,.]]],[.,.]]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 0

[1,4,6,5,7,3,2] => [.,[[[.,[[.,.],[.,.]]],.],.]] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 0

[1,4,6,7,2,3,5] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 0

[1,4,6,7,2,5,3] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 0

[1,4,6,7,3,2,5] => [.,[[[.,[.,[.,.]]],.],[.,.]]] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 0

[1,4,6,7,3,5,2] => [.,[[[.,[.,[.,.]]],[.,.]],.]] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 0

[1,4,6,7,5,2,3] => [.,[[.,[[.,[.,.]],.]],[.,.]]] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 0

[1,4,6,7,5,3,2] => [.,[[[.,[[.,[.,.]],.]],.],.]] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 0

[1,4,7,2,3,5,6] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 0

[1,4,7,2,3,6,5] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 0

[1,4,7,2,5,3,6] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 0

[1,4,7,2,5,6,3] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 0

[1,4,7,2,6,3,5] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 0

[1,4,7,2,6,5,3] => [.,[[.,[.,.]],[[[.,.],.],.]]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 0

[1,4,7,3,2,5,6] => [.,[[[.,[.,.]],.],[.,[.,.]]]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 0

[1,4,7,3,2,6,5] => [.,[[[.,[.,.]],.],[[.,.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 0

[1,4,7,3,5,2,6] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 0

[1,4,7,3,5,6,2] => [.,[[[.,[.,.]],[.,[.,.]]],.]] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 0

[1,4,7,3,6,2,5] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 0

[1,4,7,3,6,5,2] => [.,[[[.,[.,.]],[[.,.],.]],.]] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 0

[1,4,7,5,2,3,6] => [.,[[.,[[.,.],.]],[.,[.,.]]]] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 0

[1,4,7,5,2,6,3] => [.,[[.,[[.,.],.]],[[.,.],.]]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 0

[1,4,7,5,3,2,6] => [.,[[[.,[[.,.],.]],.],[.,.]]] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 0

[1,4,7,5,3,6,2] => [.,[[[.,[[.,.],.]],[.,.]],.]] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 0

[1,4,7,5,6,2,3] => [.,[[.,[[.,.],[.,.]]],[.,.]]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 0

[1,4,7,5,6,3,2] => [.,[[[.,[[.,.],[.,.]]],.],.]] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 0

[1,4,7,6,2,3,5] => [.,[[.,[[.,.],.]],[.,[.,.]]]] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 0

[1,4,7,6,2,5,3] => [.,[[.,[[.,.],.]],[[.,.],.]]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 0

[1,4,7,6,3,2,5] => [.,[[[.,[[.,.],.]],.],[.,.]]] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 0

[1,4,7,6,3,5,2] => [.,[[[.,[[.,.],.]],[.,.]],.]] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 0

[1,4,7,6,5,2,3] => [.,[[.,[[[.,.],.],.]],[.,.]]] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 0

[1,4,7,6,5,3,2] => [.,[[[.,[[[.,.],.],.]],.],.]] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 0

[1,5,2,3,4,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 0

[1,5,2,3,4,7,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 0

[1,5,2,3,6,4,7] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 0

[1,5,2,3,6,7,4] => [.,[[.,.],[.,[[.,[.,.]],.]]]] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 0

[1,5,2,3,7,4,6] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 0

[1,5,2,3,7,6,4] => [.,[[.,.],[.,[[[.,.],.],.]]]] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 0

[1,5,2,4,3,6,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 0

[1,5,2,4,3,7,6] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 0

[1,5,2,4,6,3,7] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 0

[1,5,2,4,6,7,3] => [.,[[.,.],[[.,[.,[.,.]]],.]]] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 0

[1,5,2,4,7,3,6] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 0

[1,5,2,4,7,6,3] => [.,[[.,.],[[.,[[.,.],.]],.]]] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 0

[1,5,2,6,3,4,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 0

[1,5,2,6,3,7,4] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 0

[1,5,2,6,4,3,7] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 0

[1,5,2,6,4,7,3] => [.,[[.,.],[[[.,.],[.,.]],.]]] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 0

[1,5,2,6,7,3,4] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 0

[1,5,2,6,7,4,3] => [.,[[.,.],[[[.,[.,.]],.],.]]] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 0

[1,5,2,7,3,4,6] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 0

[1,5,2,7,3,6,4] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 0

[1,5,2,7,4,3,6] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 0

[1,5,2,7,4,6,3] => [.,[[.,.],[[[.,.],[.,.]],.]]] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 0

[1,5,2,7,6,3,4] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 0

[1,5,2,7,6,4,3] => [.,[[.,.],[[[[.,.],.],.],.]]] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 0

[1,5,3,2,4,6,7] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 0

[1,5,3,2,4,7,6] => [.,[[[.,.],.],[.,[[.,.],.]]]] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 0

[1,5,3,2,6,4,7] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 0

[1,5,3,2,6,7,4] => [.,[[[.,.],.],[[.,[.,.]],.]]] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 0

[1,5,3,2,7,4,6] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 0

[1,5,3,2,7,6,4] => [.,[[[.,.],.],[[[.,.],.],.]]] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 0

[1,5,3,4,2,6,7] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 0

[1,5,3,4,2,7,6] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 0

[1,5,3,4,6,2,7] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 0

[1,5,3,4,6,7,2] => [.,[[[.,.],[.,[.,[.,.]]]],.]] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 0

[1,5,3,4,7,2,6] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 0

[1,5,3,4,7,6,2] => [.,[[[.,.],[.,[[.,.],.]]],.]] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 0

[1,5,3,6,2,4,7] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 0

[1,5,3,6,2,7,4] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 0

[1,5,3,6,4,2,7] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 0

[1,5,3,6,4,7,2] => [.,[[[.,.],[[.,.],[.,.]]],.]] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 0

[1,5,3,6,7,2,4] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 0

[1,5,3,6,7,4,2] => [.,[[[.,.],[[.,[.,.]],.]],.]] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 0

[1,5,3,7,2,4,6] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 0

[1,5,3,7,2,6,4] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 0

[1,5,3,7,4,2,6] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 0

[1,5,3,7,4,6,2] => [.,[[[.,.],[[.,.],[.,.]]],.]] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 0

[1,5,3,7,6,2,4] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 0

[1,5,3,7,6,4,2] => [.,[[[.,.],[[[.,.],.],.]],.]] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 0

[1,5,4,2,3,6,7] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 0

[1,5,4,2,3,7,6] => [.,[[[.,.],.],[.,[[.,.],.]]]] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 0

[1,5,4,2,6,3,7] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 0

[1,5,4,2,6,7,3] => [.,[[[.,.],.],[[.,[.,.]],.]]] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 0

[1,5,4,2,7,3,6] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 0

[1,5,4,2,7,6,3] => [.,[[[.,.],.],[[[.,.],.],.]]] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 0

[1,5,4,3,2,6,7] => [.,[[[[.,.],.],.],[.,[.,.]]]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 0

[1,5,4,3,2,7,6] => [.,[[[[.,.],.],.],[[.,.],.]]] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 0

[1,5,4,3,6,2,7] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 0

[1,5,4,3,6,7,2] => [.,[[[[.,.],.],[.,[.,.]]],.]] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 0

[1,5,4,3,7,2,6] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 0

[1,5,4,3,7,6,2] => [.,[[[[.,.],.],[[.,.],.]],.]] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 0

[1,5,4,6,2,3,7] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 0

[1,5,4,6,2,7,3] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 0

[1,5,4,6,3,2,7] => [.,[[[[.,.],[.,.]],.],[.,.]]] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 0

[1,5,4,6,3,7,2] => [.,[[[[.,.],[.,.]],[.,.]],.]] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 0

[1,5,4,6,7,2,3] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 0

[1,5,4,6,7,3,2] => [.,[[[[.,.],[.,[.,.]]],.],.]] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 0

[1,5,4,7,2,3,6] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 0

[1,5,4,7,2,6,3] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 0

[1,5,4,7,3,2,6] => [.,[[[[.,.],[.,.]],.],[.,.]]] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 0

[1,5,4,7,3,6,2] => [.,[[[[.,.],[.,.]],[.,.]],.]] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 0

[1,5,4,7,6,2,3] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 0

[1,5,4,7,6,3,2] => [.,[[[[.,.],[[.,.],.]],.],.]] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 0

[1,5,6,2,3,4,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 0

[1,5,6,2,3,7,4] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 0

[1,5,6,2,4,3,7] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 0

[1,5,6,2,4,7,3] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 0

[1,5,6,2,7,3,4] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 0

[1,5,6,2,7,4,3] => [.,[[.,[.,.]],[[[.,.],.],.]]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 0

[1,5,6,3,2,4,7] => [.,[[[.,[.,.]],.],[.,[.,.]]]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 0

[1,5,6,3,2,7,4] => [.,[[[.,[.,.]],.],[[.,.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 0

[1,5,6,3,4,2,7] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 0

[1,5,6,3,4,7,2] => [.,[[[.,[.,.]],[.,[.,.]]],.]] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 0

[1,5,6,3,7,2,4] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 0

[1,5,6,3,7,4,2] => [.,[[[.,[.,.]],[[.,.],.]],.]] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 0

[1,5,6,4,2,3,7] => [.,[[[.,[.,.]],.],[.,[.,.]]]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 0

[1,5,6,4,2,7,3] => [.,[[[.,[.,.]],.],[[.,.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 0

[1,5,6,4,3,2,7] => [.,[[[[.,[.,.]],.],.],[.,.]]] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 0

[1,5,6,4,3,7,2] => [.,[[[[.,[.,.]],.],[.,.]],.]] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 0

[1,5,6,4,7,2,3] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 0

[1,5,6,4,7,3,2] => [.,[[[[.,[.,.]],[.,.]],.],.]] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 0

[1,5,6,7,2,3,4] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 0

[1,5,6,7,2,4,3] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 0

[1,5,6,7,3,2,4] => [.,[[[.,[.,[.,.]]],.],[.,.]]] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 0

[1,5,6,7,3,4,2] => [.,[[[.,[.,[.,.]]],[.,.]],.]] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 0

[1,5,6,7,4,2,3] => [.,[[[.,[.,[.,.]]],.],[.,.]]] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 0

[1,5,6,7,4,3,2] => [.,[[[[.,[.,[.,.]]],.],.],.]] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 0

[1,5,7,2,3,4,6] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 0

[1,5,7,2,3,6,4] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 0

[1,5,7,2,4,3,6] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 0

[1,5,7,2,4,6,3] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 0

[1,5,7,2,6,3,4] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 0

[1,5,7,2,6,4,3] => [.,[[.,[.,.]],[[[.,.],.],.]]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 0

[1,5,7,3,2,4,6] => [.,[[[.,[.,.]],.],[.,[.,.]]]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 0

[1,5,7,3,2,6,4] => [.,[[[.,[.,.]],.],[[.,.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 0

[1,5,7,3,4,2,6] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 0

[1,5,7,3,4,6,2] => [.,[[[.,[.,.]],[.,[.,.]]],.]] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 0

[1,5,7,3,6,2,4] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 0

[1,5,7,3,6,4,2] => [.,[[[.,[.,.]],[[.,.],.]],.]] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 0

[1,5,7,4,2,3,6] => [.,[[[.,[.,.]],.],[.,[.,.]]]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 0

[1,5,7,4,2,6,3] => [.,[[[.,[.,.]],.],[[.,.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 0

[1,5,7,4,3,2,6] => [.,[[[[.,[.,.]],.],.],[.,.]]] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 0

[1,5,7,4,3,6,2] => [.,[[[[.,[.,.]],.],[.,.]],.]] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 0

[1,5,7,4,6,2,3] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 0

[1,5,7,4,6,3,2] => [.,[[[[.,[.,.]],[.,.]],.],.]] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 0

[1,5,7,6,2,3,4] => [.,[[.,[[.,.],.]],[.,[.,.]]]] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 0

[1,5,7,6,2,4,3] => [.,[[.,[[.,.],.]],[[.,.],.]]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 0

[1,5,7,6,3,2,4] => [.,[[[.,[[.,.],.]],.],[.,.]]] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 0

[1,5,7,6,3,4,2] => [.,[[[.,[[.,.],.]],[.,.]],.]] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 0

[1,5,7,6,4,2,3] => [.,[[[.,[[.,.],.]],.],[.,.]]] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 0

[1,5,7,6,4,3,2] => [.,[[[[.,[[.,.],.]],.],.],.]] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 0

[1,6,2,3,4,5,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 0

[1,6,2,3,4,7,5] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 0

[1,6,2,3,5,4,7] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 0

[1,6,2,3,5,7,4] => [.,[[.,.],[.,[[.,[.,.]],.]]]] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 0

[1,6,2,3,7,4,5] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 0

[1,6,2,3,7,5,4] => [.,[[.,.],[.,[[[.,.],.],.]]]] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 0

[1,6,2,4,3,5,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 0

[1,6,2,4,3,7,5] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 0

[1,6,2,4,5,3,7] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 0

[1,6,2,4,5,7,3] => [.,[[.,.],[[.,[.,[.,.]]],.]]] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 0

[1,6,2,4,7,3,5] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 0

[1,6,2,4,7,5,3] => [.,[[.,.],[[.,[[.,.],.]],.]]] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 0

[1,6,2,5,3,4,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 0

[1,6,2,5,3,7,4] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 0

[1,6,2,5,4,3,7] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 0

[1,6,2,5,4,7,3] => [.,[[.,.],[[[.,.],[.,.]],.]]] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 0

[1,6,2,5,7,3,4] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 0

[1,6,2,5,7,4,3] => [.,[[.,.],[[[.,[.,.]],.],.]]] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 0

[1,6,2,7,3,4,5] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 0

[1,6,2,7,3,5,4] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 0

[1,6,2,7,4,3,5] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 0

[1,6,2,7,4,5,3] => [.,[[.,.],[[[.,.],[.,.]],.]]] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 0

[1,6,2,7,5,3,4] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 0

[1,6,2,7,5,4,3] => [.,[[.,.],[[[[.,.],.],.],.]]] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 0

[1,6,3,2,4,5,7] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 0

[1,6,3,2,4,7,5] => [.,[[[.,.],.],[.,[[.,.],.]]]] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 0

[1,6,3,2,5,4,7] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 0

[1,6,3,2,5,7,4] => [.,[[[.,.],.],[[.,[.,.]],.]]] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 0

[1,6,3,2,7,4,5] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 0

[1,6,3,2,7,5,4] => [.,[[[.,.],.],[[[.,.],.],.]]] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 0

[1,6,3,4,2,5,7] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 0

[1,6,3,4,2,7,5] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 0

[1,6,3,4,5,2,7] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 0

[1,6,3,4,5,7,2] => [.,[[[.,.],[.,[.,[.,.]]]],.]] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 0

[1,6,3,4,7,2,5] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 0

[1,6,3,4,7,5,2] => [.,[[[.,.],[.,[[.,.],.]]],.]] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 0

[1,6,3,5,2,4,7] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 0

[1,6,3,5,2,7,4] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 0

[1,6,3,5,4,2,7] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 0

[1,6,3,5,4,7,2] => [.,[[[.,.],[[.,.],[.,.]]],.]] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 0

[1,6,3,5,7,2,4] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 0

[1,6,3,5,7,4,2] => [.,[[[.,.],[[.,[.,.]],.]],.]] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 0

[1,6,3,7,2,4,5] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 0

[1,6,3,7,2,5,4] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 0

[1,6,3,7,4,2,5] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 0

[1,6,3,7,4,5,2] => [.,[[[.,.],[[.,.],[.,.]]],.]] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 0

[1,6,3,7,5,2,4] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 0

[1,6,3,7,5,4,2] => [.,[[[.,.],[[[.,.],.],.]],.]] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 0

[1,6,4,2,3,5,7] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 0

[1,6,4,2,3,7,5] => [.,[[[.,.],.],[.,[[.,.],.]]]] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 0

[1,6,4,2,5,3,7] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 0

[1,6,4,2,5,7,3] => [.,[[[.,.],.],[[.,[.,.]],.]]] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 0

[1,6,4,2,7,3,5] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 0

[1,6,4,2,7,5,3] => [.,[[[.,.],.],[[[.,.],.],.]]] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 0

[1,6,4,3,2,5,7] => [.,[[[[.,.],.],.],[.,[.,.]]]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 0

[1,6,4,3,2,7,5] => [.,[[[[.,.],.],.],[[.,.],.]]] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 0

[1,6,4,3,5,2,7] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 0

[1,6,4,3,5,7,2] => [.,[[[[.,.],.],[.,[.,.]]],.]] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 0

[1,6,4,3,7,2,5] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 0

[1,6,4,3,7,5,2] => [.,[[[[.,.],.],[[.,.],.]],.]] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 0

[1,6,4,5,2,3,7] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 0

[1,6,4,5,2,7,3] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 0

[1,6,4,5,3,2,7] => [.,[[[[.,.],[.,.]],.],[.,.]]] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 0

[1,6,4,5,3,7,2] => [.,[[[[.,.],[.,.]],[.,.]],.]] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 0

[1,6,4,5,7,2,3] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 0

[1,6,4,5,7,3,2] => [.,[[[[.,.],[.,[.,.]]],.],.]] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 0

[1,6,4,7,2,3,5] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 0

[1,6,4,7,2,5,3] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 0

[1,6,4,7,3,2,5] => [.,[[[[.,.],[.,.]],.],[.,.]]] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 0

[1,6,4,7,3,5,2] => [.,[[[[.,.],[.,.]],[.,.]],.]] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 0

[1,6,4,7,5,2,3] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 0

[1,6,4,7,5,3,2] => [.,[[[[.,.],[[.,.],.]],.],.]] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 0

[1,6,5,2,3,4,7] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 0

[1,6,5,2,3,7,4] => [.,[[[.,.],.],[.,[[.,.],.]]]] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 0

[1,6,5,2,4,3,7] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 0

[1,6,5,2,4,7,3] => [.,[[[.,.],.],[[.,[.,.]],.]]] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 0

[1,6,5,2,7,3,4] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 0

[1,6,5,2,7,4,3] => [.,[[[.,.],.],[[[.,.],.],.]]] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 0

[1,6,5,3,2,4,7] => [.,[[[[.,.],.],.],[.,[.,.]]]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 0

[1,6,5,3,2,7,4] => [.,[[[[.,.],.],.],[[.,.],.]]] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 0

[1,6,5,3,4,2,7] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 0

[1,6,5,3,4,7,2] => [.,[[[[.,.],.],[.,[.,.]]],.]] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 0

[1,6,5,3,7,2,4] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 0

[1,6,5,3,7,4,2] => [.,[[[[.,.],.],[[.,.],.]],.]] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 0

[1,6,5,4,2,3,7] => [.,[[[[.,.],.],.],[.,[.,.]]]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 0

[1,6,5,4,2,7,3] => [.,[[[[.,.],.],.],[[.,.],.]]] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 0

[1,6,5,4,3,2,7] => [.,[[[[[.,.],.],.],.],[.,.]]] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 0

[1,6,5,4,3,7,2] => [.,[[[[[.,.],.],.],[.,.]],.]] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 0

[1,6,5,4,7,2,3] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 0

[1,6,5,4,7,3,2] => [.,[[[[[.,.],.],[.,.]],.],.]] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 0

[1,6,5,7,2,3,4] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 0

[1,6,5,7,2,4,3] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 0

[1,6,5,7,3,2,4] => [.,[[[[.,.],[.,.]],.],[.,.]]] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 0

[1,6,5,7,3,4,2] => [.,[[[[.,.],[.,.]],[.,.]],.]] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 0

[1,6,5,7,4,2,3] => [.,[[[[.,.],[.,.]],.],[.,.]]] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 0

[1,6,5,7,4,3,2] => [.,[[[[[.,.],[.,.]],.],.],.]] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 0

[1,6,7,2,3,4,5] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 0

[1,6,7,2,3,5,4] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 0

[1,6,7,2,4,3,5] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 0

[1,6,7,2,4,5,3] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 0

[1,6,7,2,5,3,4] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 0

[1,6,7,2,5,4,3] => [.,[[.,[.,.]],[[[.,.],.],.]]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 0

[1,6,7,3,2,4,5] => [.,[[[.,[.,.]],.],[.,[.,.]]]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 0

[1,6,7,3,2,5,4] => [.,[[[.,[.,.]],.],[[.,.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 0

[1,6,7,3,4,2,5] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 0

[1,6,7,3,4,5,2] => [.,[[[.,[.,.]],[.,[.,.]]],.]] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 0

[1,6,7,3,5,2,4] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 0

[1,6,7,3,5,4,2] => [.,[[[.,[.,.]],[[.,.],.]],.]] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 0

[1,6,7,4,2,3,5] => [.,[[[.,[.,.]],.],[.,[.,.]]]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 0

[1,6,7,4,2,5,3] => [.,[[[.,[.,.]],.],[[.,.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 0

[1,6,7,4,3,2,5] => [.,[[[[.,[.,.]],.],.],[.,.]]] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 0

[1,6,7,4,3,5,2] => [.,[[[[.,[.,.]],.],[.,.]],.]] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 0

[1,6,7,4,5,2,3] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 0

[1,6,7,4,5,3,2] => [.,[[[[.,[.,.]],[.,.]],.],.]] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 0

[1,6,7,5,2,3,4] => [.,[[[.,[.,.]],.],[.,[.,.]]]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 0

[1,6,7,5,2,4,3] => [.,[[[.,[.,.]],.],[[.,.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 0

[1,6,7,5,3,2,4] => [.,[[[[.,[.,.]],.],.],[.,.]]] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 0

[1,6,7,5,3,4,2] => [.,[[[[.,[.,.]],.],[.,.]],.]] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 0

[1,6,7,5,4,2,3] => [.,[[[[.,[.,.]],.],.],[.,.]]] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 0

[1,6,7,5,4,3,2] => [.,[[[[[.,[.,.]],.],.],.],.]] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 0

[1,7,2,3,4,5,6] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 0

[1,7,2,3,4,6,5] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 0

[1,7,2,3,5,4,6] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 0

[1,7,2,3,5,6,4] => [.,[[.,.],[.,[[.,[.,.]],.]]]] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 0

[1,7,2,3,6,4,5] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 0

[1,7,2,3,6,5,4] => [.,[[.,.],[.,[[[.,.],.],.]]]] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 0

[1,7,2,4,3,5,6] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 0

[1,7,2,4,3,6,5] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 0

[1,7,2,4,5,3,6] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 0

[1,7,2,4,5,6,3] => [.,[[.,.],[[.,[.,[.,.]]],.]]] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 0

[1,7,2,4,6,3,5] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 0

[1,7,2,4,6,5,3] => [.,[[.,.],[[.,[[.,.],.]],.]]] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 0

[1,7,2,5,3,4,6] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 0

[1,7,2,5,3,6,4] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 0

[1,7,2,5,4,3,6] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 0

[1,7,2,5,4,6,3] => [.,[[.,.],[[[.,.],[.,.]],.]]] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 0

[1,7,2,5,6,3,4] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 0

[1,7,2,5,6,4,3] => [.,[[.,.],[[[.,[.,.]],.],.]]] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 0

[1,7,2,6,3,4,5] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 0

[1,7,2,6,3,5,4] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 0

[1,7,2,6,4,3,5] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 0

[1,7,2,6,4,5,3] => [.,[[.,.],[[[.,.],[.,.]],.]]] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 0

[1,7,2,6,5,3,4] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 0

[1,7,2,6,5,4,3] => [.,[[.,.],[[[[.,.],.],.],.]]] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 0

[1,7,3,2,4,5,6] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 0

[1,7,3,2,4,6,5] => [.,[[[.,.],.],[.,[[.,.],.]]]] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 0

[1,7,3,2,5,4,6] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 0

[1,7,3,2,5,6,4] => [.,[[[.,.],.],[[.,[.,.]],.]]] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 0

[1,7,3,2,6,4,5] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 0

[1,7,3,2,6,5,4] => [.,[[[.,.],.],[[[.,.],.],.]]] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 0

[1,7,3,4,2,5,6] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 0

[1,7,3,4,2,6,5] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 0

[1,7,3,4,5,2,6] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 0

[1,7,3,4,5,6,2] => [.,[[[.,.],[.,[.,[.,.]]]],.]] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 0

[1,7,3,4,6,2,5] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 0

[1,7,3,4,6,5,2] => [.,[[[.,.],[.,[[.,.],.]]],.]] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 0

[1,7,3,5,2,4,6] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 0

[1,7,3,5,2,6,4] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 0

[1,7,3,5,4,2,6] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 0

[1,7,3,5,4,6,2] => [.,[[[.,.],[[.,.],[.,.]]],.]] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 0

[1,7,3,5,6,2,4] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 0

[1,7,3,5,6,4,2] => [.,[[[.,.],[[.,[.,.]],.]],.]] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 0

[1,7,3,6,2,4,5] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 0

[1,7,3,6,2,5,4] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 0

[1,7,3,6,4,2,5] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 0

[1,7,3,6,4,5,2] => [.,[[[.,.],[[.,.],[.,.]]],.]] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 0

[1,7,3,6,5,2,4] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 0

[1,7,3,6,5,4,2] => [.,[[[.,.],[[[.,.],.],.]],.]] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 0

[1,7,4,2,3,5,6] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 0

[1,7,4,2,3,6,5] => [.,[[[.,.],.],[.,[[.,.],.]]]] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 0

[1,7,4,2,5,3,6] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 0

[1,7,4,2,5,6,3] => [.,[[[.,.],.],[[.,[.,.]],.]]] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 0

[1,7,4,2,6,3,5] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 0

[1,7,4,2,6,5,3] => [.,[[[.,.],.],[[[.,.],.],.]]] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 0

[1,7,4,3,2,5,6] => [.,[[[[.,.],.],.],[.,[.,.]]]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 0

[1,7,4,3,2,6,5] => [.,[[[[.,.],.],.],[[.,.],.]]] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 0

[1,7,4,3,5,2,6] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 0

[1,7,4,3,5,6,2] => [.,[[[[.,.],.],[.,[.,.]]],.]] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 0

[1,7,4,3,6,2,5] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 0

[1,7,4,3,6,5,2] => [.,[[[[.,.],.],[[.,.],.]],.]] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 0

[1,7,4,5,2,3,6] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 0

[1,7,4,5,2,6,3] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 0

[1,7,4,5,3,2,6] => [.,[[[[.,.],[.,.]],.],[.,.]]] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 0

[1,7,4,5,3,6,2] => [.,[[[[.,.],[.,.]],[.,.]],.]] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 0

[1,7,4,5,6,2,3] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 0

[1,7,4,5,6,3,2] => [.,[[[[.,.],[.,[.,.]]],.],.]] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 0

[1,7,4,6,2,3,5] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 0

[1,7,4,6,2,5,3] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 0

[1,7,4,6,3,2,5] => [.,[[[[.,.],[.,.]],.],[.,.]]] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 0

[1,7,4,6,3,5,2] => [.,[[[[.,.],[.,.]],[.,.]],.]] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 0

[1,7,4,6,5,2,3] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 0

[1,7,4,6,5,3,2] => [.,[[[[.,.],[[.,.],.]],.],.]] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 0

[1,7,5,2,3,4,6] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 0

[1,7,5,2,3,6,4] => [.,[[[.,.],.],[.,[[.,.],.]]]] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 0

[1,7,5,2,4,3,6] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 0

[1,7,5,2,4,6,3] => [.,[[[.,.],.],[[.,[.,.]],.]]] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 0

[1,7,5,2,6,3,4] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 0

[1,7,5,2,6,4,3] => [.,[[[.,.],.],[[[.,.],.],.]]] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 0

[1,7,5,3,2,4,6] => [.,[[[[.,.],.],.],[.,[.,.]]]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 0

[1,7,5,3,2,6,4] => [.,[[[[.,.],.],.],[[.,.],.]]] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 0

[1,7,5,3,4,2,6] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 0

[1,7,5,3,4,6,2] => [.,[[[[.,.],.],[.,[.,.]]],.]] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 0

[1,7,5,3,6,2,4] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 0

[1,7,5,3,6,4,2] => [.,[[[[.,.],.],[[.,.],.]],.]] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 0

[1,7,5,4,2,3,6] => [.,[[[[.,.],.],.],[.,[.,.]]]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 0

[1,7,5,4,2,6,3] => [.,[[[[.,.],.],.],[[.,.],.]]] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 0

[1,7,5,4,3,2,6] => [.,[[[[[.,.],.],.],.],[.,.]]] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 0

[1,7,5,4,3,6,2] => [.,[[[[[.,.],.],.],[.,.]],.]] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 0

[1,7,5,4,6,2,3] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 0

[1,7,5,4,6,3,2] => [.,[[[[[.,.],.],[.,.]],.],.]] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 0

[1,7,5,6,2,3,4] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 0

[1,7,5,6,2,4,3] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 0

[1,7,5,6,3,2,4] => [.,[[[[.,.],[.,.]],.],[.,.]]] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 0

[1,7,5,6,3,4,2] => [.,[[[[.,.],[.,.]],[.,.]],.]] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 0

[1,7,5,6,4,2,3] => [.,[[[[.,.],[.,.]],.],[.,.]]] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 0

[1,7,5,6,4,3,2] => [.,[[[[[.,.],[.,.]],.],.],.]] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 0

[1,7,6,2,3,4,5] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 0

[1,7,6,2,3,5,4] => [.,[[[.,.],.],[.,[[.,.],.]]]] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 0

[1,7,6,2,4,3,5] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 0

[1,7,6,2,4,5,3] => [.,[[[.,.],.],[[.,[.,.]],.]]] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 0

[1,7,6,2,5,3,4] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 0

[1,7,6,2,5,4,3] => [.,[[[.,.],.],[[[.,.],.],.]]] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 0

[1,7,6,3,2,4,5] => [.,[[[[.,.],.],.],[.,[.,.]]]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 0

[1,7,6,3,2,5,4] => [.,[[[[.,.],.],.],[[.,.],.]]] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 0

[1,7,6,3,4,2,5] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 0

[1,7,6,3,4,5,2] => [.,[[[[.,.],.],[.,[.,.]]],.]] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 0

[1,7,6,3,5,2,4] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 0

[1,7,6,3,5,4,2] => [.,[[[[.,.],.],[[.,.],.]],.]] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 0

[1,7,6,4,2,3,5] => [.,[[[[.,.],.],.],[.,[.,.]]]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 0

[1,7,6,4,2,5,3] => [.,[[[[.,.],.],.],[[.,.],.]]] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 0

[1,7,6,4,3,2,5] => [.,[[[[[.,.],.],.],.],[.,.]]] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 0

[1,7,6,4,3,5,2] => [.,[[[[[.,.],.],.],[.,.]],.]] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 0

[1,7,6,4,5,2,3] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 0

[1,7,6,4,5,3,2] => [.,[[[[[.,.],.],[.,.]],.],.]] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 0

[1,7,6,5,2,3,4] => [.,[[[[.,.],.],.],[.,[.,.]]]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 0

[1,7,6,5,2,4,3] => [.,[[[[.,.],.],.],[[.,.],.]]] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 0

[1,7,6,5,3,2,4] => [.,[[[[[.,.],.],.],.],[.,.]]] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 0

[1,7,6,5,3,4,2] => [.,[[[[[.,.],.],.],[.,.]],.]] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 0

[1,7,6,5,4,2,3] => [.,[[[[[.,.],.],.],.],[.,.]]] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 0

[1,7,6,5,4,3,2] => [.,[[[[[[.,.],.],.],.],.],.]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 0

[2,1,3,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1

[2,1,3,4,5,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 1

[2,1,3,4,6,5,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 1

[2,1,3,4,6,7,5] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 1

[2,1,3,4,7,5,6] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 1

[2,1,3,4,7,6,5] => [[.,.],[.,[.,[[[.,.],.],.]]]] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1

[2,1,3,5,4,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 1

[2,1,3,5,4,7,6] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 1

[2,1,3,5,6,4,7] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1

[2,1,3,5,6,7,4] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 1

[2,1,3,5,7,4,6] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1

[2,1,3,5,7,6,4] => [[.,.],[.,[[.,[[.,.],.]],.]]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 1

[2,1,3,6,4,5,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 1

[2,1,3,6,4,7,5] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 1

[2,1,3,6,5,4,7] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 1

[2,1,3,6,5,7,4] => [[.,.],[.,[[[.,.],[.,.]],.]]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 1

[2,1,3,6,7,4,5] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1

[2,1,3,6,7,5,4] => [[.,.],[.,[[[.,[.,.]],.],.]]] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 1

[2,1,3,7,4,5,6] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 1

[2,1,3,7,4,6,5] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 1

[2,1,3,7,5,4,6] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 1

[2,1,3,7,5,6,4] => [[.,.],[.,[[[.,.],[.,.]],.]]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 1

[2,1,3,7,6,4,5] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 1

[2,1,3,7,6,5,4] => [[.,.],[.,[[[[.,.],.],.],.]]] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 1

[2,1,4,3,5,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 1

[2,1,4,3,5,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 1

[2,1,4,3,6,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1

[2,1,4,3,6,7,5] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 1

[2,1,4,3,7,5,6] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1

[2,1,4,3,7,6,5] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 1

[2,1,4,5,3,6,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

[2,1,4,5,3,7,6] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 1

[2,1,4,5,6,3,7] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1

[2,1,4,5,6,7,3] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 1

[2,1,4,5,7,3,6] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1

[2,1,4,5,7,6,3] => [[.,.],[[.,[.,[[.,.],.]]],.]] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 1

[2,1,4,6,3,5,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

[2,1,4,6,3,7,5] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 1

[2,1,4,6,5,3,7] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1

[2,1,4,6,5,7,3] => [[.,.],[[.,[[.,.],[.,.]]],.]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 1

[2,1,4,6,7,3,5] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1

[2,1,4,6,7,5,3] => [[.,.],[[.,[[.,[.,.]],.]],.]] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 1

[2,1,4,7,3,5,6] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

[2,1,4,7,3,6,5] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 1

[2,1,4,7,5,3,6] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1

[2,1,4,7,5,6,3] => [[.,.],[[.,[[.,.],[.,.]]],.]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 1

[2,1,4,7,6,3,5] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1

[2,1,4,7,6,5,3] => [[.,.],[[.,[[[.,.],.],.]],.]] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 1

[2,1,5,3,4,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 1

[2,1,5,3,4,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 1

[2,1,5,3,6,4,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1

[2,1,5,3,6,7,4] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 1

[2,1,5,3,7,4,6] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1

[2,1,5,3,7,6,4] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 1

[2,1,5,4,3,6,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1

[2,1,5,4,3,7,6] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 1

[2,1,5,4,6,3,7] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1

[2,1,5,4,6,7,3] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 1

[2,1,5,4,7,3,6] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1

[2,1,5,4,7,6,3] => [[.,.],[[[.,.],[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 1

[2,1,5,6,3,4,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

[2,1,5,6,3,7,4] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 1

[2,1,5,6,4,3,7] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[2,1,5,6,4,7,3] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 1

[2,1,5,6,7,3,4] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1

[2,1,5,6,7,4,3] => [[.,.],[[[.,[.,[.,.]]],.],.]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 1

[2,1,5,7,3,4,6] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

[2,1,5,7,3,6,4] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 1

[2,1,5,7,4,3,6] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[2,1,5,7,4,6,3] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 1

[2,1,5,7,6,3,4] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1

[2,1,5,7,6,4,3] => [[.,.],[[[.,[[.,.],.]],.],.]] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 1

[2,1,6,3,4,5,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 1

[2,1,6,3,4,7,5] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 1

[2,1,6,3,5,4,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1

[2,1,6,3,5,7,4] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 1

[2,1,6,3,7,4,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1

[2,1,6,3,7,5,4] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 1

[2,1,6,4,3,5,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1

[2,1,6,4,3,7,5] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 1

[2,1,6,4,5,3,7] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1

[2,1,6,4,5,7,3] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 1

[2,1,6,4,7,3,5] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1

[2,1,6,4,7,5,3] => [[.,.],[[[.,.],[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 1

[2,1,6,5,3,4,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1

[2,1,6,5,3,7,4] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 1

[2,1,6,5,4,3,7] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 1

[2,1,6,5,4,7,3] => [[.,.],[[[[.,.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 1

[2,1,6,5,7,3,4] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1

[2,1,6,5,7,4,3] => [[.,.],[[[[.,.],[.,.]],.],.]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 1

[2,1,6,7,3,4,5] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

[2,1,6,7,3,5,4] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 1

[2,1,6,7,4,3,5] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[2,1,6,7,4,5,3] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 1

[2,1,6,7,5,3,4] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[2,1,6,7,5,4,3] => [[.,.],[[[[.,[.,.]],.],.],.]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 1

[2,1,7,3,4,5,6] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 1

[2,1,7,3,4,6,5] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 1

[2,1,7,3,5,4,6] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1

[2,1,7,3,5,6,4] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 1

[2,1,7,3,6,4,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1

[2,1,7,3,6,5,4] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 1

[2,1,7,4,3,5,6] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1

[2,1,7,4,3,6,5] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 1

[2,1,7,4,5,3,6] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1

[2,1,7,4,5,6,3] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 1

[2,1,7,4,6,3,5] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1

[2,1,7,4,6,5,3] => [[.,.],[[[.,.],[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 1

[2,1,7,5,3,4,6] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1

[2,1,7,5,3,6,4] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 1

[2,1,7,5,4,3,6] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 1

[2,1,7,5,4,6,3] => [[.,.],[[[[.,.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 1

[2,1,7,5,6,3,4] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1

[2,1,7,5,6,4,3] => [[.,.],[[[[.,.],[.,.]],.],.]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 1

[2,1,7,6,3,4,5] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1

[2,1,7,6,3,5,4] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 1

[2,1,7,6,4,3,5] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 1

[2,1,7,6,4,5,3] => [[.,.],[[[[.,.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 1

[2,1,7,6,5,3,4] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 1

[2,1,7,6,5,4,3] => [[.,.],[[[[[.,.],.],.],.],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1

[2,3,1,4,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0

[2,3,1,4,5,7,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 0

[2,3,1,4,6,5,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 0

[2,3,1,4,6,7,5] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 0

[2,3,1,4,7,5,6] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 0

[2,3,1,4,7,6,5] => [[.,[.,.]],[.,[[[.,.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 0

[2,3,1,5,4,6,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 0

[2,3,1,5,4,7,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 0

[2,3,1,5,6,4,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 0

[2,3,1,5,6,7,4] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 0

[2,3,1,5,7,4,6] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 0

[2,3,1,5,7,6,4] => [[.,[.,.]],[[.,[[.,.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 0

[2,3,1,6,4,5,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 0

[2,3,1,6,4,7,5] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 0

[2,3,1,6,5,4,7] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 0

[2,3,1,6,5,7,4] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 0

[2,3,1,6,7,4,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 0

[2,3,1,6,7,5,4] => [[.,[.,.]],[[[.,[.,.]],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 0

[2,3,1,7,4,5,6] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 0

[2,3,1,7,4,6,5] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 0

[2,3,1,7,5,4,6] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 0

[2,3,1,7,5,6,4] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 0

[2,3,1,7,6,4,5] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 0

[2,3,1,7,6,5,4] => [[.,[.,.]],[[[[.,.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 0

[2,3,4,1,5,6,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0

[2,3,4,1,5,7,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 0

[2,3,4,1,6,5,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 0

[2,3,4,1,6,7,5] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 0

[2,3,4,1,7,5,6] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 0

[2,3,4,1,7,6,5] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 0

[2,3,4,5,1,6,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0

[2,3,4,5,1,7,6] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 0

[2,3,4,5,6,1,7] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 0

[2,3,4,5,6,7,1] => [[.,[.,[.,[.,[.,[.,.]]]]]],.] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1

[2,3,4,5,7,1,6] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 0

[2,3,4,5,7,6,1] => [[.,[.,[.,[.,[[.,.],.]]]]],.] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 1

[2,3,4,6,1,5,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0

[2,3,4,6,1,7,5] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 0

[2,3,4,6,5,1,7] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 0

[2,3,4,6,5,7,1] => [[.,[.,[.,[[.,.],[.,.]]]]],.] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 1

[2,3,4,6,7,1,5] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 0

[2,3,4,6,7,5,1] => [[.,[.,[.,[[.,[.,.]],.]]]],.] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 1

[2,3,4,7,1,5,6] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0

[2,3,4,7,1,6,5] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 0

[2,3,4,7,5,1,6] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 0

[2,3,4,7,5,6,1] => [[.,[.,[.,[[.,.],[.,.]]]]],.] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 1

[2,3,4,7,6,1,5] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 0

[2,3,4,7,6,5,1] => [[.,[.,[.,[[[.,.],.],.]]]],.] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 1

[2,3,5,1,4,6,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0

[2,3,5,1,4,7,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 0

[2,3,5,1,6,4,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 0

[2,3,5,1,6,7,4] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 0

[2,3,5,1,7,4,6] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 0

[2,3,5,1,7,6,4] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 0

[2,3,5,4,1,6,7] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 0

[2,3,5,4,1,7,6] => [[.,[.,[[.,.],.]]],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 0

[2,3,5,4,6,1,7] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 0

[2,3,5,4,6,7,1] => [[.,[.,[[.,.],[.,[.,.]]]]],.] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 1

[2,3,5,4,7,1,6] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 0

[2,3,5,4,7,6,1] => [[.,[.,[[.,.],[[.,.],.]]]],.] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 1

[2,3,5,6,1,4,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0

[2,3,5,6,1,7,4] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 0

[2,3,5,6,4,1,7] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 0

[2,3,5,6,4,7,1] => [[.,[.,[[.,[.,.]],[.,.]]]],.] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 1

[2,3,5,6,7,1,4] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 0

[2,3,5,6,7,4,1] => [[.,[.,[[.,[.,[.,.]]],.]]],.] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 1

[2,3,5,7,1,4,6] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0

[2,3,5,7,1,6,4] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 0

[2,3,5,7,4,1,6] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 0

[2,3,5,7,4,6,1] => [[.,[.,[[.,[.,.]],[.,.]]]],.] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 1

[2,3,5,7,6,1,4] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 0

[2,3,5,7,6,4,1] => [[.,[.,[[.,[[.,.],.]],.]]],.] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 1

[2,3,6,1,4,5,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0

[2,3,6,1,4,7,5] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 0

[2,3,6,1,5,4,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 0

[2,3,6,1,5,7,4] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 0

[2,3,6,1,7,4,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 0

[2,3,6,1,7,5,4] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 0

[2,3,6,4,1,5,7] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 0

[2,3,6,4,1,7,5] => [[.,[.,[[.,.],.]]],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 0

[2,3,6,4,5,1,7] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 0

[2,3,6,4,5,7,1] => [[.,[.,[[.,.],[.,[.,.]]]]],.] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 1

[2,3,6,4,7,1,5] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 0

[2,3,6,4,7,5,1] => [[.,[.,[[.,.],[[.,.],.]]]],.] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 1

[2,3,6,5,1,4,7] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 0

[2,3,6,5,1,7,4] => [[.,[.,[[.,.],.]]],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 0

[2,3,6,5,4,1,7] => [[.,[.,[[[.,.],.],.]]],[.,.]] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 0

[2,3,6,5,4,7,1] => [[.,[.,[[[.,.],.],[.,.]]]],.] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 1

[2,3,6,5,7,1,4] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 0

[2,3,6,5,7,4,1] => [[.,[.,[[[.,.],[.,.]],.]]],.] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 1

[2,3,6,7,1,4,5] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0

[2,3,6,7,1,5,4] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 0

[2,3,6,7,4,1,5] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 0

[2,3,6,7,4,5,1] => [[.,[.,[[.,[.,.]],[.,.]]]],.] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 1

[2,3,6,7,5,1,4] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 0

[2,3,6,7,5,4,1] => [[.,[.,[[[.,[.,.]],.],.]]],.] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 1

[2,3,7,1,4,5,6] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0

[2,3,7,1,4,6,5] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 0

[2,3,7,1,5,4,6] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 0

[2,3,7,1,5,6,4] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 0

[2,3,7,1,6,4,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 0

[2,3,7,1,6,5,4] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 0

[2,3,7,4,1,5,6] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 0

[2,3,7,4,1,6,5] => [[.,[.,[[.,.],.]]],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 0

[2,3,7,4,5,1,6] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 0

[2,3,7,4,5,6,1] => [[.,[.,[[.,.],[.,[.,.]]]]],.] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 1

[2,3,7,4,6,1,5] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 0

[2,3,7,4,6,5,1] => [[.,[.,[[.,.],[[.,.],.]]]],.] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 1

[2,3,7,5,1,4,6] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 0

[2,3,7,5,1,6,4] => [[.,[.,[[.,.],.]]],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 0

[2,3,7,5,4,1,6] => [[.,[.,[[[.,.],.],.]]],[.,.]] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 0

[2,3,7,5,4,6,1] => [[.,[.,[[[.,.],.],[.,.]]]],.] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 1

[2,3,7,5,6,1,4] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 0

[2,3,7,5,6,4,1] => [[.,[.,[[[.,.],[.,.]],.]]],.] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 1

[2,3,7,6,1,4,5] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 0

[2,3,7,6,1,5,4] => [[.,[.,[[.,.],.]]],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 0

[2,3,7,6,4,1,5] => [[.,[.,[[[.,.],.],.]]],[.,.]] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 0

[2,3,7,6,4,5,1] => [[.,[.,[[[.,.],.],[.,.]]]],.] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 1

[2,3,7,6,5,1,4] => [[.,[.,[[[.,.],.],.]]],[.,.]] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 0

[2,3,7,6,5,4,1] => [[.,[.,[[[[.,.],.],.],.]]],.] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 1

[2,4,1,3,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0

[2,4,1,3,5,7,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 0

[2,4,1,3,6,5,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 0

[2,4,1,3,6,7,5] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 0

[2,4,1,3,7,5,6] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 0

[2,4,1,3,7,6,5] => [[.,[.,.]],[.,[[[.,.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 0

[2,4,1,5,3,6,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 0

[2,4,1,5,3,7,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 0

[2,4,1,5,6,3,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 0

[2,4,1,5,6,7,3] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 0

[2,4,1,5,7,3,6] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 0

[2,4,1,5,7,6,3] => [[.,[.,.]],[[.,[[.,.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 0

[2,4,1,6,3,5,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 0

[2,4,1,6,3,7,5] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 0

[2,4,1,6,5,3,7] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 0

[2,4,1,6,5,7,3] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 0

[2,4,1,6,7,3,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 0

[2,4,1,6,7,5,3] => [[.,[.,.]],[[[.,[.,.]],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 0

[2,4,1,7,3,5,6] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 0

[2,4,1,7,3,6,5] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 0

[2,4,1,7,5,3,6] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 0

[2,4,1,7,5,6,3] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 0

[2,4,1,7,6,3,5] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 0

[2,4,1,7,6,5,3] => [[.,[.,.]],[[[[.,.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 0

[2,4,3,1,5,6,7] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 0

[2,4,3,1,5,7,6] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 0

[2,4,3,1,6,5,7] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 0

[2,4,3,1,6,7,5] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 0

[2,4,3,1,7,5,6] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 0

[2,4,3,1,7,6,5] => [[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 0

[2,4,3,5,1,6,7] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 0

[2,4,3,5,1,7,6] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 0

[2,4,3,5,6,1,7] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 0

[2,4,3,5,6,7,1] => [[.,[[.,.],[.,[.,[.,.]]]]],.] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 1

[2,4,3,5,7,1,6] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 0

[2,4,3,5,7,6,1] => [[.,[[.,.],[.,[[.,.],.]]]],.] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 1

[2,4,3,6,1,5,7] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 0

[2,4,3,6,1,7,5] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 0

[2,4,3,6,5,1,7] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 0

[2,4,3,6,5,7,1] => [[.,[[.,.],[[.,.],[.,.]]]],.] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 1

[2,4,3,6,7,1,5] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 0

[2,4,3,6,7,5,1] => [[.,[[.,.],[[.,[.,.]],.]]],.] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 1

[2,4,3,7,1,5,6] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 0

[2,4,3,7,1,6,5] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 0

[2,4,3,7,5,1,6] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 0

[2,4,3,7,5,6,1] => [[.,[[.,.],[[.,.],[.,.]]]],.] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 1

[2,4,3,7,6,1,5] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 0

[2,4,3,7,6,5,1] => [[.,[[.,.],[[[.,.],.],.]]],.] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 1

[2,4,5,1,3,6,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0

[2,4,5,1,3,7,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 0

[2,4,5,1,6,3,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 0

[2,4,5,1,6,7,3] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 0

[2,4,5,1,7,3,6] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 0

[2,4,5,1,7,6,3] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 0

[2,4,5,3,1,6,7] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 0

[2,4,5,3,1,7,6] => [[.,[[.,[.,.]],.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 0

[2,4,5,3,6,1,7] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 0

[2,4,5,3,6,7,1] => [[.,[[.,[.,.]],[.,[.,.]]]],.] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 1

[2,4,5,3,7,1,6] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 0

[2,4,5,3,7,6,1] => [[.,[[.,[.,.]],[[.,.],.]]],.] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 1

[2,4,5,6,1,3,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0

[2,4,5,6,1,7,3] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 0

[2,4,5,6,3,1,7] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 0

[2,4,5,6,3,7,1] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 1

[2,4,5,6,7,1,3] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 0

[2,4,5,6,7,3,1] => [[.,[[.,[.,[.,[.,.]]]],.]],.] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 1

[2,4,5,7,1,3,6] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0

[2,4,5,7,1,6,3] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 0

[2,4,5,7,3,1,6] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 0

[2,4,5,7,3,6,1] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 1

[2,4,5,7,6,1,3] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 0

[2,4,5,7,6,3,1] => [[.,[[.,[.,[[.,.],.]]],.]],.] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 1

[2,4,6,1,3,5,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0

[2,4,6,1,3,7,5] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 0

[2,4,6,1,5,3,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 0

[2,4,6,1,5,7,3] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 0

[2,4,6,1,7,3,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 0

[2,4,6,1,7,5,3] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 0

[2,4,6,3,1,5,7] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 0

[2,4,6,3,1,7,5] => [[.,[[.,[.,.]],.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 0

[2,4,6,3,5,1,7] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 0

[2,4,6,3,5,7,1] => [[.,[[.,[.,.]],[.,[.,.]]]],.] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 1

[2,4,6,3,7,1,5] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 0

[2,4,6,3,7,5,1] => [[.,[[.,[.,.]],[[.,.],.]]],.] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 1

[2,4,6,5,1,3,7] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 0

[2,4,6,5,1,7,3] => [[.,[.,[[.,.],.]]],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 0

[2,4,6,5,3,1,7] => [[.,[[.,[[.,.],.]],.]],[.,.]] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 0

[2,4,6,5,3,7,1] => [[.,[[.,[[.,.],.]],[.,.]]],.] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 1

[2,4,6,5,7,1,3] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 0

[2,4,6,5,7,3,1] => [[.,[[.,[[.,.],[.,.]]],.]],.] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 1

[2,4,6,7,1,3,5] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0

[2,4,6,7,1,5,3] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 0

[2,4,6,7,3,1,5] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 0

[2,4,6,7,3,5,1] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 1

[2,4,6,7,5,1,3] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 0

[2,4,6,7,5,3,1] => [[.,[[.,[[.,[.,.]],.]],.]],.] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 1

[2,4,7,1,3,5,6] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0

[2,4,7,1,3,6,5] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 0

[2,4,7,1,5,3,6] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 0

[2,4,7,1,5,6,3] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 0

[2,4,7,1,6,3,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 0

[2,4,7,1,6,5,3] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 0

[2,4,7,3,1,5,6] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 0

[2,4,7,3,1,6,5] => [[.,[[.,[.,.]],.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 0

[2,4,7,3,5,1,6] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 0

[2,4,7,3,5,6,1] => [[.,[[.,[.,.]],[.,[.,.]]]],.] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 1

[2,4,7,3,6,1,5] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 0

[2,4,7,3,6,5,1] => [[.,[[.,[.,.]],[[.,.],.]]],.] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 1

[2,4,7,5,1,3,6] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 0

[2,4,7,5,1,6,3] => [[.,[.,[[.,.],.]]],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 0

[2,4,7,5,3,1,6] => [[.,[[.,[[.,.],.]],.]],[.,.]] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 0

[2,4,7,5,3,6,1] => [[.,[[.,[[.,.],.]],[.,.]]],.] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 1

[2,4,7,5,6,1,3] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 0

[2,4,7,5,6,3,1] => [[.,[[.,[[.,.],[.,.]]],.]],.] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 1

[2,4,7,6,1,3,5] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 0

[2,4,7,6,1,5,3] => [[.,[.,[[.,.],.]]],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 0

[2,4,7,6,3,1,5] => [[.,[[.,[[.,.],.]],.]],[.,.]] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 0

[2,4,7,6,3,5,1] => [[.,[[.,[[.,.],.]],[.,.]]],.] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 1

[2,4,7,6,5,1,3] => [[.,[.,[[[.,.],.],.]]],[.,.]] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 0

[2,4,7,6,5,3,1] => [[.,[[.,[[[.,.],.],.]],.]],.] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 1

[2,5,1,3,4,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0

[2,5,1,3,4,7,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 0

[2,5,1,3,6,4,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 0

[2,5,1,3,6,7,4] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 0

[2,5,1,3,7,4,6] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 0

[2,5,1,3,7,6,4] => [[.,[.,.]],[.,[[[.,.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 0

[2,5,1,4,3,6,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 0

[2,5,1,4,3,7,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 0

[2,5,1,4,6,3,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 0

[2,5,1,4,6,7,3] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 0

[2,5,1,4,7,3,6] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 0

[2,5,1,4,7,6,3] => [[.,[.,.]],[[.,[[.,.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 0

[2,5,1,6,3,4,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 0

[2,5,1,6,3,7,4] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 0

[2,5,1,6,4,3,7] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 0

[2,5,1,6,4,7,3] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 0

[2,5,1,6,7,3,4] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 0

[2,5,1,6,7,4,3] => [[.,[.,.]],[[[.,[.,.]],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 0

[2,5,1,7,3,4,6] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 0

[2,5,1,7,3,6,4] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 0

[2,5,1,7,4,3,6] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 0

[2,5,1,7,4,6,3] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 0

[2,5,1,7,6,3,4] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 0

[2,5,1,7,6,4,3] => [[.,[.,.]],[[[[.,.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 0

[2,5,3,1,4,6,7] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 0

[2,5,3,1,4,7,6] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 0

[2,5,3,1,6,4,7] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 0

[2,5,3,1,6,7,4] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 0

[2,5,3,1,7,4,6] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 0

[2,5,3,1,7,6,4] => [[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 0

[2,5,3,4,1,6,7] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 0

[2,5,3,4,1,7,6] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 0

[2,5,3,4,6,1,7] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 0

[2,5,3,4,6,7,1] => [[.,[[.,.],[.,[.,[.,.]]]]],.] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 1

[2,5,3,4,7,1,6] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 0

[2,5,3,4,7,6,1] => [[.,[[.,.],[.,[[.,.],.]]]],.] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 1

[2,5,3,6,1,4,7] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 0

[2,5,3,6,1,7,4] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 0

[2,5,3,6,4,1,7] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 0

[2,5,3,6,4,7,1] => [[.,[[.,.],[[.,.],[.,.]]]],.] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 1

[2,5,3,6,7,1,4] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 0

[2,5,3,6,7,4,1] => [[.,[[.,.],[[.,[.,.]],.]]],.] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 1

[2,5,3,7,1,4,6] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 0

[2,5,3,7,1,6,4] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 0

[2,5,3,7,4,1,6] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 0

[2,5,3,7,4,6,1] => [[.,[[.,.],[[.,.],[.,.]]]],.] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 1

[2,5,3,7,6,1,4] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 0

[2,5,3,7,6,4,1] => [[.,[[.,.],[[[.,.],.],.]]],.] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 1

[2,5,4,1,3,6,7] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 0

[2,5,4,1,3,7,6] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 0

[2,5,4,1,6,3,7] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 0

[2,5,4,1,6,7,3] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 0

[2,5,4,1,7,3,6] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 0

[2,5,4,1,7,6,3] => [[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 0

[2,5,4,3,1,6,7] => [[.,[[[.,.],.],.]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 0

[2,5,4,3,1,7,6] => [[.,[[[.,.],.],.]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 0

[2,5,4,3,6,1,7] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 0

[2,5,4,3,6,7,1] => [[.,[[[.,.],.],[.,[.,.]]]],.] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 1

[2,5,4,3,7,1,6] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 0

[2,5,4,3,7,6,1] => [[.,[[[.,.],.],[[.,.],.]]],.] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 1

[2,5,4,6,1,3,7] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 0

[2,5,4,6,1,7,3] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 0

[2,5,4,6,3,1,7] => [[.,[[[.,.],[.,.]],.]],[.,.]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 0

[2,5,4,6,3,7,1] => [[.,[[[.,.],[.,.]],[.,.]]],.] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 1

[2,5,4,6,7,1,3] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 0

[2,5,4,6,7,3,1] => [[.,[[[.,.],[.,[.,.]]],.]],.] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 1

[2,5,4,7,1,3,6] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 0

[2,5,4,7,1,6,3] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 0

[2,5,4,7,3,1,6] => [[.,[[[.,.],[.,.]],.]],[.,.]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 0

[2,5,4,7,3,6,1] => [[.,[[[.,.],[.,.]],[.,.]]],.] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 1

[2,5,4,7,6,1,3] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 0

[2,5,4,7,6,3,1] => [[.,[[[.,.],[[.,.],.]],.]],.] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 1

[2,5,6,1,3,4,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0

[2,5,6,1,3,7,4] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 0

[2,5,6,1,4,3,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 0

[2,5,6,1,4,7,3] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 0

[2,5,6,1,7,3,4] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 0

[2,5,6,1,7,4,3] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 0

[2,5,6,3,1,4,7] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 0

[2,5,6,3,1,7,4] => [[.,[[.,[.,.]],.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 0

[2,5,6,3,4,1,7] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 0

[2,5,6,3,4,7,1] => [[.,[[.,[.,.]],[.,[.,.]]]],.] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 1

[2,5,6,3,7,1,4] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 0

[2,5,6,3,7,4,1] => [[.,[[.,[.,.]],[[.,.],.]]],.] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 1

[2,5,6,4,1,3,7] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 0

[2,5,6,4,1,7,3] => [[.,[[.,[.,.]],.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 0

[2,5,6,4,3,1,7] => [[.,[[[.,[.,.]],.],.]],[.,.]] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 0

[2,5,6,4,3,7,1] => [[.,[[[.,[.,.]],.],[.,.]]],.] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 1

[2,5,6,4,7,1,3] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 0

[2,5,6,4,7,3,1] => [[.,[[[.,[.,.]],[.,.]],.]],.] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 1

[2,5,6,7,1,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0

[2,5,6,7,1,4,3] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 0

[2,5,6,7,3,1,4] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 0

[2,5,6,7,3,4,1] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 1

[2,5,6,7,4,1,3] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 0

[2,5,6,7,4,3,1] => [[.,[[[.,[.,[.,.]]],.],.]],.] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 1

[2,5,7,1,3,4,6] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0

[2,5,7,1,3,6,4] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 0

[2,5,7,1,4,3,6] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 0

[2,5,7,1,4,6,3] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 0

[2,5,7,1,6,3,4] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 0

[2,5,7,1,6,4,3] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 0

[2,5,7,3,1,4,6] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 0

[2,5,7,3,1,6,4] => [[.,[[.,[.,.]],.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 0

[2,5,7,3,4,1,6] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 0

[2,5,7,3,4,6,1] => [[.,[[.,[.,.]],[.,[.,.]]]],.] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 1

[2,5,7,3,6,1,4] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 0

[2,5,7,3,6,4,1] => [[.,[[.,[.,.]],[[.,.],.]]],.] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 1

[2,5,7,4,1,3,6] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 0

[2,5,7,4,1,6,3] => [[.,[[.,[.,.]],.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 0

[2,5,7,4,3,1,6] => [[.,[[[.,[.,.]],.],.]],[.,.]] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 0

[2,5,7,4,3,6,1] => [[.,[[[.,[.,.]],.],[.,.]]],.] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 1

[2,5,7,4,6,1,3] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 0

[2,5,7,4,6,3,1] => [[.,[[[.,[.,.]],[.,.]],.]],.] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 1

[2,5,7,6,1,3,4] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 0

[2,5,7,6,1,4,3] => [[.,[.,[[.,.],.]]],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 0

[2,5,7,6,3,1,4] => [[.,[[.,[[.,.],.]],.]],[.,.]] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 0

[2,5,7,6,3,4,1] => [[.,[[.,[[.,.],.]],[.,.]]],.] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 1

[2,5,7,6,4,1,3] => [[.,[[.,[[.,.],.]],.]],[.,.]] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 0

[2,5,7,6,4,3,1] => [[.,[[[.,[[.,.],.]],.],.]],.] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 1

[2,6,1,3,4,5,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0

[2,6,1,3,4,7,5] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 0

[2,6,1,3,5,4,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 0

[2,6,1,3,5,7,4] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 0

[2,6,1,3,7,4,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 0

[2,6,1,3,7,5,4] => [[.,[.,.]],[.,[[[.,.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 0

[2,6,1,4,3,5,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 0

[2,6,1,4,3,7,5] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 0

[2,6,1,4,5,3,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 0

[2,6,1,4,5,7,3] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 0

[2,6,1,4,7,3,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 0

[2,6,1,4,7,5,3] => [[.,[.,.]],[[.,[[.,.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 0

[2,6,1,5,3,4,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 0

[2,6,1,5,3,7,4] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 0

[2,6,1,5,4,3,7] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 0

[2,6,1,5,4,7,3] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 0

[2,6,1,5,7,3,4] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 0

[2,6,1,5,7,4,3] => [[.,[.,.]],[[[.,[.,.]],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 0

[2,6,1,7,3,4,5] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 0

[2,6,1,7,3,5,4] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 0

[2,6,1,7,4,3,5] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 0

[2,6,1,7,4,5,3] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 0

[2,6,1,7,5,3,4] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 0

[2,6,1,7,5,4,3] => [[.,[.,.]],[[[[.,.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 0

[2,6,3,1,4,5,7] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 0

[2,6,3,1,4,7,5] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 0

[2,6,3,1,5,4,7] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 0

[2,6,3,1,5,7,4] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 0

[2,6,3,1,7,4,5] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 0

[2,6,3,1,7,5,4] => [[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 0

[2,6,3,4,1,5,7] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 0

[2,6,3,4,1,7,5] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 0

[2,6,3,4,5,1,7] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 0

[2,6,3,4,5,7,1] => [[.,[[.,.],[.,[.,[.,.]]]]],.] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 1

[2,6,3,4,7,1,5] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 0

[2,6,3,4,7,5,1] => [[.,[[.,.],[.,[[.,.],.]]]],.] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 1

[2,6,3,5,1,4,7] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 0

[2,6,3,5,1,7,4] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 0

[2,6,3,5,4,1,7] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 0

[2,6,3,5,4,7,1] => [[.,[[.,.],[[.,.],[.,.]]]],.] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 1

[2,6,3,5,7,1,4] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 0

[2,6,3,5,7,4,1] => [[.,[[.,.],[[.,[.,.]],.]]],.] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 1

[2,6,3,7,1,4,5] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 0

[2,6,3,7,1,5,4] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 0

[2,6,3,7,4,1,5] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 0

[2,6,3,7,4,5,1] => [[.,[[.,.],[[.,.],[.,.]]]],.] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 1

[2,6,3,7,5,1,4] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 0

[2,6,3,7,5,4,1] => [[.,[[.,.],[[[.,.],.],.]]],.] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 1

[2,6,4,1,3,5,7] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 0

[2,6,4,1,3,7,5] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 0

[2,6,4,1,5,3,7] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 0

[2,6,4,1,5,7,3] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 0

[2,6,4,1,7,3,5] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 0

[2,6,4,1,7,5,3] => [[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 0

[2,6,4,3,1,5,7] => [[.,[[[.,.],.],.]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 0

[2,6,4,3,1,7,5] => [[.,[[[.,.],.],.]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 0

[2,6,4,3,5,1,7] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 0

[2,6,4,3,5,7,1] => [[.,[[[.,.],.],[.,[.,.]]]],.] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 1

[2,6,4,3,7,1,5] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 0

[2,6,4,3,7,5,1] => [[.,[[[.,.],.],[[.,.],.]]],.] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 1

[2,6,4,5,1,3,7] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 0

[2,6,4,5,1,7,3] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 0

[2,6,4,5,3,1,7] => [[.,[[[.,.],[.,.]],.]],[.,.]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 0

[2,6,4,5,3,7,1] => [[.,[[[.,.],[.,.]],[.,.]]],.] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 1

[2,6,4,5,7,1,3] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 0

[2,6,4,5,7,3,1] => [[.,[[[.,.],[.,[.,.]]],.]],.] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 1

[2,6,4,7,1,3,5] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 0

[2,6,4,7,1,5,3] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 0

[2,6,4,7,3,1,5] => [[.,[[[.,.],[.,.]],.]],[.,.]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 0

[2,6,4,7,3,5,1] => [[.,[[[.,.],[.,.]],[.,.]]],.] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 1

[2,6,4,7,5,1,3] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 0

[2,6,4,7,5,3,1] => [[.,[[[.,.],[[.,.],.]],.]],.] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 1

[2,6,5,1,3,4,7] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 0

[2,6,5,1,3,7,4] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 0

[2,6,5,1,4,3,7] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 0

[2,6,5,1,4,7,3] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 0

[2,6,5,1,7,3,4] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 0

[2,6,5,1,7,4,3] => [[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 0

[2,6,5,3,1,4,7] => [[.,[[[.,.],.],.]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 0

[2,6,5,3,1,7,4] => [[.,[[[.,.],.],.]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 0

[2,6,5,3,4,1,7] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 0

[2,6,5,3,4,7,1] => [[.,[[[.,.],.],[.,[.,.]]]],.] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 1

[2,6,5,3,7,1,4] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 0

[2,6,5,3,7,4,1] => [[.,[[[.,.],.],[[.,.],.]]],.] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 1

[2,6,5,4,1,3,7] => [[.,[[[.,.],.],.]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 0

[2,6,5,4,1,7,3] => [[.,[[[.,.],.],.]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 0

[2,6,5,4,3,1,7] => [[.,[[[[.,.],.],.],.]],[.,.]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 0

[2,6,5,4,3,7,1] => [[.,[[[[.,.],.],.],[.,.]]],.] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 1

[2,6,5,4,7,1,3] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 0

[2,6,5,4,7,3,1] => [[.,[[[[.,.],.],[.,.]],.]],.] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 1

[2,6,5,7,1,3,4] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 0

[2,6,5,7,1,4,3] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 0

[2,6,5,7,3,1,4] => [[.,[[[.,.],[.,.]],.]],[.,.]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 0

[2,6,5,7,3,4,1] => [[.,[[[.,.],[.,.]],[.,.]]],.] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 1

[2,6,5,7,4,1,3] => [[.,[[[.,.],[.,.]],.]],[.,.]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 0

[2,6,5,7,4,3,1] => [[.,[[[[.,.],[.,.]],.],.]],.] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 1

[2,6,7,1,3,4,5] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0

[2,6,7,1,3,5,4] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 0

[2,6,7,1,4,3,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 0

[2,6,7,1,4,5,3] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 0

[2,6,7,1,5,3,4] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 0

[2,6,7,1,5,4,3] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 0

[2,6,7,3,1,4,5] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 0

[2,6,7,3,1,5,4] => [[.,[[.,[.,.]],.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 0

[2,6,7,3,4,1,5] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 0

[2,6,7,3,4,5,1] => [[.,[[.,[.,.]],[.,[.,.]]]],.] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 1

[2,6,7,3,5,1,4] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 0

[2,6,7,3,5,4,1] => [[.,[[.,[.,.]],[[.,.],.]]],.] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 1

[2,6,7,4,1,3,5] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 0

[2,6,7,4,1,5,3] => [[.,[[.,[.,.]],.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 0

[2,6,7,4,3,1,5] => [[.,[[[.,[.,.]],.],.]],[.,.]] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 0

[2,6,7,4,3,5,1] => [[.,[[[.,[.,.]],.],[.,.]]],.] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 1

[2,6,7,4,5,1,3] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 0

[2,6,7,4,5,3,1] => [[.,[[[.,[.,.]],[.,.]],.]],.] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 1

[2,6,7,5,1,3,4] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 0

[2,6,7,5,1,4,3] => [[.,[[.,[.,.]],.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 0

[2,6,7,5,3,1,4] => [[.,[[[.,[.,.]],.],.]],[.,.]] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 0

[2,6,7,5,3,4,1] => [[.,[[[.,[.,.]],.],[.,.]]],.] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 1

[2,6,7,5,4,1,3] => [[.,[[[.,[.,.]],.],.]],[.,.]] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 0

[2,6,7,5,4,3,1] => [[.,[[[[.,[.,.]],.],.],.]],.] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 1

[2,7,1,3,4,5,6] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0

[2,7,1,3,4,6,5] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 0

[2,7,1,3,5,4,6] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 0

[2,7,1,3,5,6,4] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 0

[2,7,1,3,6,4,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 0

[2,7,1,3,6,5,4] => [[.,[.,.]],[.,[[[.,.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 0

[2,7,1,4,3,5,6] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 0

[2,7,1,4,3,6,5] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 0

[2,7,1,4,5,3,6] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 0

[2,7,1,4,5,6,3] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 0

[2,7,1,4,6,3,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 0

[2,7,1,4,6,5,3] => [[.,[.,.]],[[.,[[.,.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 0

[2,7,1,5,3,4,6] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 0

[2,7,1,5,3,6,4] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 0

[2,7,1,5,4,3,6] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 0

[2,7,1,5,4,6,3] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 0

[2,7,1,5,6,3,4] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 0

[2,7,1,5,6,4,3] => [[.,[.,.]],[[[.,[.,.]],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 0

[2,7,1,6,3,4,5] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 0

[2,7,1,6,3,5,4] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 0

[2,7,1,6,4,3,5] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 0

[2,7,1,6,4,5,3] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 0

[2,7,1,6,5,3,4] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 0

[2,7,1,6,5,4,3] => [[.,[.,.]],[[[[.,.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 0

[2,7,3,1,4,5,6] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 0

[2,7,3,1,4,6,5] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 0

[2,7,3,1,5,4,6] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 0

[2,7,3,1,5,6,4] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 0

[2,7,3,1,6,4,5] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 0

[2,7,3,1,6,5,4] => [[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 0

[2,7,3,4,1,5,6] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 0

[2,7,3,4,1,6,5] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 0

[2,7,3,4,5,1,6] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 0

[2,7,3,4,5,6,1] => [[.,[[.,.],[.,[.,[.,.]]]]],.] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 1

[2,7,3,4,6,1,5] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 0

[2,7,3,4,6,5,1] => [[.,[[.,.],[.,[[.,.],.]]]],.] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 1

[2,7,3,5,1,4,6] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 0

[2,7,3,5,1,6,4] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 0

[2,7,3,5,4,1,6] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 0

[2,7,3,5,4,6,1] => [[.,[[.,.],[[.,.],[.,.]]]],.] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 1

[2,7,3,5,6,1,4] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 0

[2,7,3,5,6,4,1] => [[.,[[.,.],[[.,[.,.]],.]]],.] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 1

[2,7,3,6,1,4,5] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 0

[2,7,3,6,1,5,4] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 0

[2,7,3,6,4,1,5] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 0

[2,7,3,6,4,5,1] => [[.,[[.,.],[[.,.],[.,.]]]],.] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 1

[2,7,3,6,5,1,4] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 0

[2,7,3,6,5,4,1] => [[.,[[.,.],[[[.,.],.],.]]],.] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 1

[2,7,4,1,3,5,6] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 0

[2,7,4,1,3,6,5] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 0

[2,7,4,1,5,3,6] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 0

[2,7,4,1,5,6,3] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 0

[2,7,4,1,6,3,5] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 0

[2,7,4,1,6,5,3] => [[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 0

[2,7,4,3,1,5,6] => [[.,[[[.,.],.],.]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 0

[2,7,4,3,1,6,5] => [[.,[[[.,.],.],.]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 0

[2,7,4,3,5,1,6] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 0

[2,7,4,3,5,6,1] => [[.,[[[.,.],.],[.,[.,.]]]],.] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 1

[2,7,4,3,6,1,5] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 0

[2,7,4,3,6,5,1] => [[.,[[[.,.],.],[[.,.],.]]],.] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 1

[2,7,4,5,1,3,6] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 0

[2,7,4,5,1,6,3] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 0

[2,7,4,5,3,1,6] => [[.,[[[.,.],[.,.]],.]],[.,.]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 0

[2,7,4,5,3,6,1] => [[.,[[[.,.],[.,.]],[.,.]]],.] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 1

[2,7,4,5,6,1,3] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 0

[2,7,4,5,6,3,1] => [[.,[[[.,.],[.,[.,.]]],.]],.] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 1

[2,7,4,6,1,3,5] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 0

[2,7,4,6,1,5,3] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 0

[2,7,4,6,3,1,5] => [[.,[[[.,.],[.,.]],.]],[.,.]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 0

[2,7,4,6,3,5,1] => [[.,[[[.,.],[.,.]],[.,.]]],.] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 1

[2,7,4,6,5,1,3] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 0

[2,7,4,6,5,3,1] => [[.,[[[.,.],[[.,.],.]],.]],.] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 1

[2,7,5,1,3,4,6] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 0

[2,7,5,1,3,6,4] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 0

[2,7,5,1,4,3,6] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 0

[2,7,5,1,4,6,3] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 0

[2,7,5,1,6,3,4] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 0

[2,7,5,1,6,4,3] => [[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 0

[2,7,5,3,1,4,6] => [[.,[[[.,.],.],.]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 0

[2,7,5,3,1,6,4] => [[.,[[[.,.],.],.]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 0

[2,7,5,3,4,1,6] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 0

[2,7,5,3,4,6,1] => [[.,[[[.,.],.],[.,[.,.]]]],.] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 1

[2,7,5,3,6,1,4] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 0

[2,7,5,3,6,4,1] => [[.,[[[.,.],.],[[.,.],.]]],.] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 1

[2,7,5,4,1,3,6] => [[.,[[[.,.],.],.]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 0

[2,7,5,4,1,6,3] => [[.,[[[.,.],.],.]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 0

[2,7,5,4,3,1,6] => [[.,[[[[.,.],.],.],.]],[.,.]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 0

[2,7,5,4,3,6,1] => [[.,[[[[.,.],.],.],[.,.]]],.] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 1

[2,7,5,4,6,1,3] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 0

[2,7,5,4,6,3,1] => [[.,[[[[.,.],.],[.,.]],.]],.] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 1

[2,7,5,6,1,3,4] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 0

[2,7,5,6,1,4,3] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 0

[2,7,5,6,3,1,4] => [[.,[[[.,.],[.,.]],.]],[.,.]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 0

[2,7,5,6,3,4,1] => [[.,[[[.,.],[.,.]],[.,.]]],.] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 1

[2,7,5,6,4,1,3] => [[.,[[[.,.],[.,.]],.]],[.,.]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 0

[2,7,5,6,4,3,1] => [[.,[[[[.,.],[.,.]],.],.]],.] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 1

[2,7,6,1,3,4,5] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 0

[2,7,6,1,3,5,4] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 0

[2,7,6,1,4,3,5] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 0

[2,7,6,1,4,5,3] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 0

[2,7,6,1,5,3,4] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 0

[2,7,6,1,5,4,3] => [[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 0

[2,7,6,3,1,4,5] => [[.,[[[.,.],.],.]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 0

[2,7,6,3,1,5,4] => [[.,[[[.,.],.],.]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 0

[2,7,6,3,4,1,5] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 0

[2,7,6,3,4,5,1] => [[.,[[[.,.],.],[.,[.,.]]]],.] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 1

[2,7,6,3,5,1,4] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 0

[2,7,6,3,5,4,1] => [[.,[[[.,.],.],[[.,.],.]]],.] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 1

[2,7,6,4,1,3,5] => [[.,[[[.,.],.],.]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 0

[2,7,6,4,1,5,3] => [[.,[[[.,.],.],.]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 0

[2,7,6,4,3,1,5] => [[.,[[[[.,.],.],.],.]],[.,.]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 0

[2,7,6,4,3,5,1] => [[.,[[[[.,.],.],.],[.,.]]],.] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 1

[2,7,6,4,5,1,3] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 0

[2,7,6,4,5,3,1] => [[.,[[[[.,.],.],[.,.]],.]],.] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 1

[2,7,6,5,1,3,4] => [[.,[[[.,.],.],.]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 0

[2,7,6,5,1,4,3] => [[.,[[[.,.],.],.]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 0

[2,7,6,5,3,1,4] => [[.,[[[[.,.],.],.],.]],[.,.]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 0

[2,7,6,5,3,4,1] => [[.,[[[[.,.],.],.],[.,.]]],.] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 1

[2,7,6,5,4,1,3] => [[.,[[[[.,.],.],.],.]],[.,.]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 0

[2,7,6,5,4,3,1] => [[.,[[[[[.,.],.],.],.],.]],.] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 1

[3,1,2,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1

[3,1,2,4,5,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 1

[3,1,2,4,6,5,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 1

[3,1,2,4,6,7,5] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 1

[3,1,2,4,7,5,6] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 1

[3,1,2,4,7,6,5] => [[.,.],[.,[.,[[[.,.],.],.]]]] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1

[3,1,2,5,4,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 1

[3,1,2,5,4,7,6] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 1

[3,1,2,5,6,4,7] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1

[3,1,2,5,6,7,4] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 1

[3,1,2,5,7,4,6] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1

[3,1,2,5,7,6,4] => [[.,.],[.,[[.,[[.,.],.]],.]]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 1

[3,1,2,6,4,5,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 1

[3,1,2,6,4,7,5] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 1

[3,1,2,6,5,4,7] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 1

[3,1,2,6,5,7,4] => [[.,.],[.,[[[.,.],[.,.]],.]]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 1

[3,1,2,6,7,4,5] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1

[3,1,2,6,7,5,4] => [[.,.],[.,[[[.,[.,.]],.],.]]] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 1

[3,1,2,7,4,5,6] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 1

[3,1,2,7,4,6,5] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 1

[3,1,2,7,5,4,6] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 1

[3,1,2,7,5,6,4] => [[.,.],[.,[[[.,.],[.,.]],.]]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 1

[3,1,2,7,6,4,5] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 1

[3,1,2,7,6,5,4] => [[.,.],[.,[[[[.,.],.],.],.]]] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 1

[3,1,4,2,5,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 1

[3,1,4,2,5,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 1

[3,1,4,2,6,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1

[3,1,4,2,6,7,5] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 1

[3,1,4,2,7,5,6] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1

[3,1,4,2,7,6,5] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 1

[3,1,4,5,2,6,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

[3,1,4,5,2,7,6] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 1

[3,1,4,5,6,2,7] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1

[3,1,4,5,6,7,2] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 1

[3,1,4,5,7,2,6] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1

[3,1,4,5,7,6,2] => [[.,.],[[.,[.,[[.,.],.]]],.]] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 1

[3,1,4,6,2,5,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

[3,1,4,6,2,7,5] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 1

[3,1,4,6,5,2,7] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1

[3,1,4,6,5,7,2] => [[.,.],[[.,[[.,.],[.,.]]],.]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 1

[3,1,4,6,7,2,5] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1

[3,1,4,6,7,5,2] => [[.,.],[[.,[[.,[.,.]],.]],.]] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 1

[3,1,4,7,2,5,6] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

[3,1,4,7,2,6,5] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 1

[3,1,4,7,5,2,6] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1

[3,1,4,7,5,6,2] => [[.,.],[[.,[[.,.],[.,.]]],.]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 1

[3,1,4,7,6,2,5] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1

[3,1,4,7,6,5,2] => [[.,.],[[.,[[[.,.],.],.]],.]] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 1

[3,1,5,2,4,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 1

[3,1,5,2,4,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 1

[3,1,5,2,6,4,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1

[3,1,5,2,6,7,4] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 1

[3,1,5,2,7,4,6] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1

[3,1,5,2,7,6,4] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 1

[3,1,5,4,2,6,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1

[3,1,5,4,2,7,6] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 1

[3,1,5,4,6,2,7] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1

[3,1,5,4,6,7,2] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 1

[3,1,5,4,7,2,6] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1

[3,1,5,4,7,6,2] => [[.,.],[[[.,.],[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 1

[3,1,5,6,2,4,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

[3,1,5,6,2,7,4] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 1

[3,1,5,6,4,2,7] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[3,1,5,6,4,7,2] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 1

[3,1,5,6,7,2,4] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1

[3,1,5,6,7,4,2] => [[.,.],[[[.,[.,[.,.]]],.],.]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 1

[3,1,5,7,2,4,6] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

[3,1,5,7,2,6,4] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 1

[3,1,5,7,4,2,6] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[3,1,5,7,4,6,2] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 1

[3,1,5,7,6,2,4] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1

[3,1,5,7,6,4,2] => [[.,.],[[[.,[[.,.],.]],.],.]] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 1

[3,1,6,2,4,5,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 1

[3,1,6,2,4,7,5] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 1

[3,1,6,2,5,4,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1

[3,1,6,2,5,7,4] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 1

[3,1,6,2,7,4,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1

[3,1,6,2,7,5,4] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 1

[3,1,6,4,2,5,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1

[3,1,6,4,2,7,5] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 1

[3,1,6,4,5,2,7] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1

[3,1,6,4,5,7,2] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 1

[3,1,6,4,7,2,5] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1

[3,1,6,4,7,5,2] => [[.,.],[[[.,.],[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 1

[3,1,6,5,2,4,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1

[3,1,6,5,2,7,4] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 1

[3,1,6,5,4,2,7] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 1

[3,1,6,5,4,7,2] => [[.,.],[[[[.,.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 1

[3,1,6,5,7,2,4] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1

[3,1,6,5,7,4,2] => [[.,.],[[[[.,.],[.,.]],.],.]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 1

[3,1,6,7,2,4,5] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

[3,1,6,7,2,5,4] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 1

[3,1,6,7,4,2,5] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[3,1,6,7,4,5,2] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 1

[3,1,6,7,5,2,4] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[3,1,6,7,5,4,2] => [[.,.],[[[[.,[.,.]],.],.],.]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 1

[3,1,7,2,4,5,6] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 1

[3,1,7,2,4,6,5] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 1

[3,1,7,2,5,4,6] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1

[3,1,7,2,5,6,4] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 1

[3,1,7,2,6,4,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1

[3,1,7,2,6,5,4] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 1

[3,1,7,4,2,5,6] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1

[3,1,7,4,2,6,5] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 1

[3,1,7,4,5,2,6] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1

[3,1,7,4,5,6,2] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 1

[3,1,7,4,6,2,5] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1

[3,1,7,4,6,5,2] => [[.,.],[[[.,.],[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 1

[3,1,7,5,2,4,6] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1

[3,1,7,5,2,6,4] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 1

[3,1,7,5,4,2,6] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 1

[3,1,7,5,4,6,2] => [[.,.],[[[[.,.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 1

[3,1,7,5,6,2,4] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1

[3,1,7,5,6,4,2] => [[.,.],[[[[.,.],[.,.]],.],.]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 1

[3,1,7,6,2,4,5] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1

[3,1,7,6,2,5,4] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 1

[3,1,7,6,4,2,5] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 1

[3,1,7,6,4,5,2] => [[.,.],[[[[.,.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 1

[3,1,7,6,5,2,4] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 1

[3,1,7,6,5,4,2] => [[.,.],[[[[[.,.],.],.],.],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1

[3,2,1,4,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2

[3,2,1,4,5,7,6] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 2

[3,2,1,4,6,5,7] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 2

[3,2,1,4,6,7,5] => [[[.,.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[3,2,1,4,7,5,6] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 2

[3,2,1,4,7,6,5] => [[[.,.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 2

[3,2,1,5,4,6,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 2

[3,2,1,5,4,7,6] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 2

[3,2,1,5,6,4,7] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 2

[3,2,1,5,6,7,4] => [[[.,.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[3,2,1,5,7,4,6] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 2

[3,2,1,5,7,6,4] => [[[.,.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 2

[3,2,1,6,4,5,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 2

[3,2,1,6,4,7,5] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 2

[3,2,1,6,5,4,7] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 2

[3,2,1,6,5,7,4] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2

[3,2,1,6,7,4,5] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 2

[3,2,1,6,7,5,4] => [[[.,.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2

[3,2,1,7,4,5,6] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 2

[3,2,1,7,4,6,5] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 2

[3,2,1,7,5,4,6] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 2

[3,2,1,7,5,6,4] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2

[3,2,1,7,6,4,5] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 2

[3,2,1,7,6,5,4] => [[[.,.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 2

[3,2,4,1,5,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1

[3,2,4,1,5,7,6] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 1

[3,2,4,1,6,5,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[3,2,4,1,6,7,5] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 1

[3,2,4,1,7,5,6] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[3,2,4,1,7,6,5] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1

[3,2,4,5,1,6,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1

[3,2,4,5,1,7,6] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 1

[3,2,4,5,6,1,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1

[3,2,4,5,6,7,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2

[3,2,4,5,7,1,6] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1

[3,2,4,5,7,6,1] => [[[.,.],[.,[.,[[.,.],.]]]],.] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 2

[3,2,4,6,1,5,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1

[3,2,4,6,1,7,5] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 1

[3,2,4,6,5,1,7] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1

[3,2,4,6,5,7,1] => [[[.,.],[.,[[.,.],[.,.]]]],.] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 2

[3,2,4,6,7,1,5] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1

[3,2,4,6,7,5,1] => [[[.,.],[.,[[.,[.,.]],.]]],.] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 2

[3,2,4,7,1,5,6] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1

[3,2,4,7,1,6,5] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 1

[3,2,4,7,5,1,6] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1

[3,2,4,7,5,6,1] => [[[.,.],[.,[[.,.],[.,.]]]],.] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 2

[3,2,4,7,6,1,5] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1

[3,2,4,7,6,5,1] => [[[.,.],[.,[[[.,.],.],.]]],.] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 2

[3,2,5,1,4,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1

[3,2,5,1,4,7,6] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 1

[3,2,5,1,6,4,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[3,2,5,1,6,7,4] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 1

[3,2,5,1,7,4,6] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[3,2,5,1,7,6,4] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1

[3,2,5,4,1,6,7] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1

[3,2,5,4,1,7,6] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1

[3,2,5,4,6,1,7] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[3,2,5,4,6,7,1] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 2

[3,2,5,4,7,1,6] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[3,2,5,4,7,6,1] => [[[.,.],[[.,.],[[.,.],.]]],.] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 2

[3,2,5,6,1,4,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1

[3,2,5,6,1,7,4] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 1

[3,2,5,6,4,1,7] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[3,2,5,6,4,7,1] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[3,2,5,6,7,1,4] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1

[3,2,5,6,7,4,1] => [[[.,.],[[.,[.,[.,.]]],.]],.] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 2

[3,2,5,7,1,4,6] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1

[3,2,5,7,1,6,4] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 1

[3,2,5,7,4,1,6] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[3,2,5,7,4,6,1] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[3,2,5,7,6,1,4] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1

[3,2,5,7,6,4,1] => [[[.,.],[[.,[[.,.],.]],.]],.] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 2

[3,2,6,1,4,5,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1

[3,2,6,1,4,7,5] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 1

[3,2,6,1,5,4,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[3,2,6,1,5,7,4] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 1

[3,2,6,1,7,4,5] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[3,2,6,1,7,5,4] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1

[3,2,6,4,1,5,7] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1

[3,2,6,4,1,7,5] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1

[3,2,6,4,5,1,7] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[3,2,6,4,5,7,1] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 2

[3,2,6,4,7,1,5] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[3,2,6,4,7,5,1] => [[[.,.],[[.,.],[[.,.],.]]],.] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 2

[3,2,6,5,1,4,7] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1

[3,2,6,5,1,7,4] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1

[3,2,6,5,4,1,7] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1

[3,2,6,5,4,7,1] => [[[.,.],[[[.,.],.],[.,.]]],.] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 2

[3,2,6,5,7,1,4] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[3,2,6,5,7,4,1] => [[[.,.],[[[.,.],[.,.]],.]],.] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 2

[3,2,6,7,1,4,5] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1

[3,2,6,7,1,5,4] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 1

[3,2,6,7,4,1,5] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[3,2,6,7,4,5,1] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[3,2,6,7,5,1,4] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[3,2,6,7,5,4,1] => [[[.,.],[[[.,[.,.]],.],.]],.] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 2

[3,2,7,1,4,5,6] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1

[3,2,7,1,4,6,5] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 1

[3,2,7,1,5,4,6] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[3,2,7,1,5,6,4] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 1

[3,2,7,1,6,4,5] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[3,2,7,1,6,5,4] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1

[3,2,7,4,1,5,6] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1

[3,2,7,4,1,6,5] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1

[3,2,7,4,5,1,6] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[3,2,7,4,5,6,1] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 2

[3,2,7,4,6,1,5] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[3,2,7,4,6,5,1] => [[[.,.],[[.,.],[[.,.],.]]],.] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 2

[3,2,7,5,1,4,6] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1

[3,2,7,5,1,6,4] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1

[3,2,7,5,4,1,6] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1

[3,2,7,5,4,6,1] => [[[.,.],[[[.,.],.],[.,.]]],.] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 2

[3,2,7,5,6,1,4] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[3,2,7,5,6,4,1] => [[[.,.],[[[.,.],[.,.]],.]],.] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 2

[3,2,7,6,1,4,5] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1

[3,2,7,6,1,5,4] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1

[3,2,7,6,4,1,5] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1

[3,2,7,6,4,5,1] => [[[.,.],[[[.,.],.],[.,.]]],.] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 2

[3,2,7,6,5,1,4] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1

[3,2,7,6,5,4,1] => [[[.,.],[[[[.,.],.],.],.]],.] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 2

[3,4,1,2,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0

[3,4,1,2,5,7,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 0

[3,4,1,2,6,5,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 0

[3,4,1,2,6,7,5] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 0

[3,4,1,2,7,5,6] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 0

[3,4,1,2,7,6,5] => [[.,[.,.]],[.,[[[.,.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 0

[3,4,1,5,2,6,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 0

[3,4,1,5,2,7,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 0

[3,4,1,5,6,2,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 0

[3,4,1,5,6,7,2] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 0

[3,4,1,5,7,2,6] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 0

[3,4,1,5,7,6,2] => [[.,[.,.]],[[.,[[.,.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 0

[3,4,1,6,2,5,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 0

[3,4,1,6,2,7,5] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 0

[3,4,1,6,5,2,7] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 0

[3,4,1,6,5,7,2] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 0

[3,4,1,6,7,2,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 0

[3,4,1,6,7,5,2] => [[.,[.,.]],[[[.,[.,.]],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 0

[3,4,1,7,2,5,6] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 0

[3,4,1,7,2,6,5] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 0

[3,4,1,7,5,2,6] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 0

[3,4,1,7,5,6,2] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 0

[3,4,1,7,6,2,5] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 0

[3,4,1,7,6,5,2] => [[.,[.,.]],[[[[.,.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 0

[3,4,2,1,5,6,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1

[3,4,2,1,5,7,6] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 1

[3,4,2,1,6,5,7] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[3,4,2,1,6,7,5] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 1

[3,4,2,1,7,5,6] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[3,4,2,1,7,6,5] => [[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1

[3,4,2,5,1,6,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0

[3,4,2,5,1,7,6] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 0

[3,4,2,5,6,1,7] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0

[3,4,2,5,6,7,1] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 1

[3,4,2,5,7,1,6] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0

[3,4,2,5,7,6,1] => [[[.,[.,.]],[.,[[.,.],.]]],.] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 1

[3,4,2,6,1,5,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0

[3,4,2,6,1,7,5] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 0

[3,4,2,6,5,1,7] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 0

[3,4,2,6,5,7,1] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 1

[3,4,2,6,7,1,5] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0

[3,4,2,6,7,5,1] => [[[.,[.,.]],[[.,[.,.]],.]],.] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 1

[3,4,2,7,1,5,6] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0

[3,4,2,7,1,6,5] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 0

[3,4,2,7,5,1,6] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 0

[3,4,2,7,5,6,1] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 1

[3,4,2,7,6,1,5] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 0

[3,4,2,7,6,5,1] => [[[.,[.,.]],[[[.,.],.],.]],.] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 1

[3,4,5,1,2,6,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0

[3,4,5,1,2,7,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 0

[3,4,5,1,6,2,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 0

[3,4,5,1,6,7,2] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 0

[3,4,5,1,7,2,6] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 0

[3,4,5,1,7,6,2] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 0

[3,4,5,2,1,6,7] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1

[3,4,5,2,1,7,6] => [[[.,[.,[.,.]]],.],[[.,.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 1

[3,4,5,2,6,1,7] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 0

[3,4,5,2,6,7,1] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 1

[3,4,5,2,7,1,6] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 0

[3,4,5,2,7,6,1] => [[[.,[.,[.,.]]],[[.,.],.]],.] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 1

[3,4,5,6,1,2,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0

[3,4,5,6,1,7,2] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 0

[3,4,5,6,2,1,7] => [[[.,[.,[.,[.,.]]]],.],[.,.]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1

[3,4,5,6,2,7,1] => [[[.,[.,[.,[.,.]]]],[.,.]],.] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 1

[3,4,5,6,7,1,2] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 0

[3,4,5,6,7,2,1] => [[[.,[.,[.,[.,[.,.]]]]],.],.] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 2

[3,4,5,7,1,2,6] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0

[3,4,5,7,1,6,2] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 0

[3,4,5,7,2,1,6] => [[[.,[.,[.,[.,.]]]],.],[.,.]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1

[3,4,5,7,2,6,1] => [[[.,[.,[.,[.,.]]]],[.,.]],.] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 1

[3,4,5,7,6,1,2] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 0

[3,4,5,7,6,2,1] => [[[.,[.,[.,[[.,.],.]]]],.],.] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 2

[3,4,6,1,2,5,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0

[3,4,6,1,2,7,5] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 0

[3,4,6,1,5,2,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 0

[3,4,6,1,5,7,2] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 0

[3,4,6,1,7,2,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 0

[3,4,6,1,7,5,2] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 0

[3,4,6,2,1,5,7] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1

[3,4,6,2,1,7,5] => [[[.,[.,[.,.]]],.],[[.,.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 1

[3,4,6,2,5,1,7] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 0

[3,4,6,2,5,7,1] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 1

[3,4,6,2,7,1,5] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 0

[3,4,6,2,7,5,1] => [[[.,[.,[.,.]]],[[.,.],.]],.] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 1

[3,4,6,5,1,2,7] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 0

[3,4,6,5,1,7,2] => [[.,[.,[[.,.],.]]],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 0

[3,4,6,5,2,1,7] => [[[.,[.,[[.,.],.]]],.],[.,.]] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 1

[3,4,6,5,2,7,1] => [[[.,[.,[[.,.],.]]],[.,.]],.] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 1

[3,4,6,5,7,1,2] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 0

[3,4,6,5,7,2,1] => [[[.,[.,[[.,.],[.,.]]]],.],.] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 2

[3,4,6,7,1,2,5] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0

[3,4,6,7,1,5,2] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 0

[3,4,6,7,2,1,5] => [[[.,[.,[.,[.,.]]]],.],[.,.]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1

[3,4,6,7,2,5,1] => [[[.,[.,[.,[.,.]]]],[.,.]],.] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 1

[3,4,6,7,5,1,2] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 0

[3,4,6,7,5,2,1] => [[[.,[.,[[.,[.,.]],.]]],.],.] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 2

[3,4,7,1,2,5,6] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0

[3,4,7,1,2,6,5] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 0

[3,4,7,1,5,2,6] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 0

[3,4,7,1,5,6,2] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 0

[3,4,7,1,6,2,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 0

[3,4,7,1,6,5,2] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 0

[3,4,7,2,1,5,6] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1

[3,4,7,2,1,6,5] => [[[.,[.,[.,.]]],.],[[.,.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 1

[3,4,7,2,5,1,6] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 0

[3,4,7,2,5,6,1] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 1

[3,4,7,2,6,1,5] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 0

[3,4,7,2,6,5,1] => [[[.,[.,[.,.]]],[[.,.],.]],.] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 1

[3,4,7,5,1,2,6] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 0

[3,4,7,5,1,6,2] => [[.,[.,[[.,.],.]]],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 0

[3,4,7,5,2,1,6] => [[[.,[.,[[.,.],.]]],.],[.,.]] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 1

[3,4,7,5,2,6,1] => [[[.,[.,[[.,.],.]]],[.,.]],.] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 1

[3,4,7,5,6,1,2] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 0

[3,4,7,5,6,2,1] => [[[.,[.,[[.,.],[.,.]]]],.],.] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 2

[3,4,7,6,1,2,5] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 0

[3,4,7,6,1,5,2] => [[.,[.,[[.,.],.]]],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 0

[3,4,7,6,2,1,5] => [[[.,[.,[[.,.],.]]],.],[.,.]] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 1

[3,4,7,6,2,5,1] => [[[.,[.,[[.,.],.]]],[.,.]],.] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 1

[3,4,7,6,5,1,2] => [[.,[.,[[[.,.],.],.]]],[.,.]] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 0

[3,4,7,6,5,2,1] => [[[.,[.,[[[.,.],.],.]]],.],.] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 2

[3,5,1,2,4,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0

[3,5,1,2,4,7,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 0

[3,5,1,2,6,4,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 0

[3,5,1,2,6,7,4] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 0

[3,5,1,2,7,4,6] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 0

[3,5,1,2,7,6,4] => [[.,[.,.]],[.,[[[.,.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 0

[3,5,1,4,2,6,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 0

[3,5,1,4,2,7,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 0

[3,5,1,4,6,2,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 0

[3,5,1,4,6,7,2] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 0

[3,5,1,4,7,2,6] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 0

[3,5,1,4,7,6,2] => [[.,[.,.]],[[.,[[.,.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 0

[3,5,1,6,2,4,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 0

[3,5,1,6,2,7,4] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 0

[3,5,1,6,4,2,7] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 0

[3,5,1,6,4,7,2] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 0

[3,5,1,6,7,2,4] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 0

[3,5,1,6,7,4,2] => [[.,[.,.]],[[[.,[.,.]],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 0

[3,5,1,7,2,4,6] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 0

[3,5,1,7,2,6,4] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 0

[3,5,1,7,4,2,6] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 0

[3,5,1,7,4,6,2] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 0

[3,5,1,7,6,2,4] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 0

[3,5,1,7,6,4,2] => [[.,[.,.]],[[[[.,.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 0

[3,5,2,1,4,6,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1

[3,5,2,1,4,7,6] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 1

[3,5,2,1,6,4,7] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[3,5,2,1,6,7,4] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 1

[3,5,2,1,7,4,6] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[3,5,2,1,7,6,4] => [[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1

[3,5,2,4,1,6,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0

[3,5,2,4,1,7,6] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 0

[3,5,2,4,6,1,7] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0

[3,5,2,4,6,7,1] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 1

[3,5,2,4,7,1,6] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0

[3,5,2,4,7,6,1] => [[[.,[.,.]],[.,[[.,.],.]]],.] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 1

[3,5,2,6,1,4,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0

[3,5,2,6,1,7,4] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 0

[3,5,2,6,4,1,7] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 0

[3,5,2,6,4,7,1] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 1

[3,5,2,6,7,1,4] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0

[3,5,2,6,7,4,1] => [[[.,[.,.]],[[.,[.,.]],.]],.] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 1

[3,5,2,7,1,4,6] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0

[3,5,2,7,1,6,4] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 0

[3,5,2,7,4,1,6] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 0

[3,5,2,7,4,6,1] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 1

[3,5,2,7,6,1,4] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 0

[3,5,2,7,6,4,1] => [[[.,[.,.]],[[[.,.],.],.]],.] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 1

[3,5,4,1,2,6,7] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 0

[3,5,4,1,2,7,6] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 0

[3,5,4,1,6,2,7] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 0

[3,5,4,1,6,7,2] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 0

[3,5,4,1,7,2,6] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 0

[3,5,4,1,7,6,2] => [[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 0

[3,5,4,2,1,6,7] => [[[.,[[.,.],.]],.],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 1

[3,5,4,2,1,7,6] => [[[.,[[.,.],.]],.],[[.,.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 1

[3,5,4,2,6,1,7] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 0

[3,5,4,2,6,7,1] => [[[.,[[.,.],.]],[.,[.,.]]],.] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 1

[3,5,4,2,7,1,6] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 0

[3,5,4,2,7,6,1] => [[[.,[[.,.],.]],[[.,.],.]],.] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 1

[3,5,4,6,1,2,7] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 0

[3,5,4,6,1,7,2] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 0

[3,5,4,6,2,1,7] => [[[.,[[.,.],[.,.]]],.],[.,.]] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 1

[3,5,4,6,2,7,1] => [[[.,[[.,.],[.,.]]],[.,.]],.] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 1

[3,5,4,6,7,1,2] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 0

[3,5,4,6,7,2,1] => [[[.,[[.,.],[.,[.,.]]]],.],.] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 2

[3,5,4,7,1,2,6] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 0

[3,5,4,7,1,6,2] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 0

[3,5,4,7,2,1,6] => [[[.,[[.,.],[.,.]]],.],[.,.]] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 1

[3,5,4,7,2,6,1] => [[[.,[[.,.],[.,.]]],[.,.]],.] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 1

[3,5,4,7,6,1,2] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 0

[3,5,4,7,6,2,1] => [[[.,[[.,.],[[.,.],.]]],.],.] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 2

[3,5,6,1,2,4,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0

[3,5,6,1,2,7,4] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 0

[3,5,6,1,4,2,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 0

[3,5,6,1,4,7,2] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 0

[3,5,6,1,7,2,4] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 0

[3,5,6,1,7,4,2] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 0

[3,5,6,2,1,4,7] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1

[3,5,6,2,1,7,4] => [[[.,[.,[.,.]]],.],[[.,.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 1

[3,5,6,2,4,1,7] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 0

[3,5,6,2,4,7,1] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 1

[3,5,6,2,7,1,4] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 0

[3,5,6,2,7,4,1] => [[[.,[.,[.,.]]],[[.,.],.]],.] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 1

[3,5,6,4,1,2,7] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 0

[3,5,6,4,1,7,2] => [[.,[[.,[.,.]],.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 0

[3,5,6,4,2,1,7] => [[[.,[[.,[.,.]],.]],.],[.,.]] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 1

[3,5,6,4,2,7,1] => [[[.,[[.,[.,.]],.]],[.,.]],.] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 1

[3,5,6,4,7,1,2] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 0

[3,5,6,4,7,2,1] => [[[.,[[.,[.,.]],[.,.]]],.],.] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 2

[3,5,6,7,1,2,4] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0

[3,5,6,7,1,4,2] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 0

[3,5,6,7,2,1,4] => [[[.,[.,[.,[.,.]]]],.],[.,.]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1

[3,5,6,7,2,4,1] => [[[.,[.,[.,[.,.]]]],[.,.]],.] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 1

[3,5,6,7,4,1,2] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 0

[3,5,6,7,4,2,1] => [[[.,[[.,[.,[.,.]]],.]],.],.] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 2

[3,5,7,1,2,4,6] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0

[3,5,7,1,2,6,4] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 0

[3,5,7,1,4,2,6] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 0

[3,5,7,1,4,6,2] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 0

[3,5,7,1,6,2,4] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 0

[3,5,7,1,6,4,2] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 0

[3,5,7,2,1,4,6] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1

[3,5,7,2,1,6,4] => [[[.,[.,[.,.]]],.],[[.,.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 1

[3,5,7,2,4,1,6] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 0

[3,5,7,2,4,6,1] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 1

[3,5,7,2,6,1,4] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 0

[3,5,7,2,6,4,1] => [[[.,[.,[.,.]]],[[.,.],.]],.] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 1

[3,5,7,4,1,2,6] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 0

[3,5,7,4,1,6,2] => [[.,[[.,[.,.]],.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 0

[3,5,7,4,2,1,6] => [[[.,[[.,[.,.]],.]],.],[.,.]] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 1

[3,5,7,4,2,6,1] => [[[.,[[.,[.,.]],.]],[.,.]],.] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 1

[3,5,7,4,6,1,2] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 0

[3,5,7,4,6,2,1] => [[[.,[[.,[.,.]],[.,.]]],.],.] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 2

[3,5,7,6,1,2,4] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 0

[3,5,7,6,1,4,2] => [[.,[.,[[.,.],.]]],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 0

[3,5,7,6,2,1,4] => [[[.,[.,[[.,.],.]]],.],[.,.]] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 1

[3,5,7,6,2,4,1] => [[[.,[.,[[.,.],.]]],[.,.]],.] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 1

[3,5,7,6,4,1,2] => [[.,[[.,[[.,.],.]],.]],[.,.]] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 0

[3,5,7,6,4,2,1] => [[[.,[[.,[[.,.],.]],.]],.],.] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 2

[3,6,1,2,4,5,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0

[3,6,1,2,4,7,5] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 0

[3,6,1,2,5,4,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 0

[3,6,1,2,5,7,4] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 0

[3,6,1,2,7,4,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 0

[3,6,1,2,7,5,4] => [[.,[.,.]],[.,[[[.,.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 0

[3,6,1,4,2,5,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 0

[3,6,1,4,2,7,5] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 0

[3,6,1,4,5,2,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 0

[3,6,1,4,5,7,2] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 0

[3,6,1,4,7,2,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 0

[3,6,1,4,7,5,2] => [[.,[.,.]],[[.,[[.,.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 0

[3,6,1,5,2,4,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 0

[3,6,1,5,2,7,4] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 0

[3,6,1,5,4,2,7] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 0

[3,6,1,5,4,7,2] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 0

[3,6,1,5,7,2,4] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 0

[3,6,1,5,7,4,2] => [[.,[.,.]],[[[.,[.,.]],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 0

[3,6,1,7,2,4,5] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 0

[3,6,1,7,2,5,4] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 0

[3,6,1,7,4,2,5] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 0

[3,6,1,7,4,5,2] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 0

[3,6,1,7,5,2,4] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 0

[3,6,1,7,5,4,2] => [[.,[.,.]],[[[[.,.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 0

[3,6,2,1,4,5,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1

[3,6,2,1,4,7,5] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 1

[3,6,2,1,5,4,7] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[3,6,2,1,5,7,4] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 1

[3,6,2,1,7,4,5] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[3,6,2,1,7,5,4] => [[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1

[3,6,2,4,1,5,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0

[3,6,2,4,1,7,5] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 0

[3,6,2,4,5,1,7] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0

[3,6,2,4,5,7,1] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 1

[3,6,2,4,7,1,5] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0

[3,6,2,4,7,5,1] => [[[.,[.,.]],[.,[[.,.],.]]],.] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 1

[3,6,2,5,1,4,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0

[3,6,2,5,1,7,4] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 0

[3,6,2,5,4,1,7] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 0

[3,6,2,5,4,7,1] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 1

[3,6,2,5,7,1,4] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0

[3,6,2,5,7,4,1] => [[[.,[.,.]],[[.,[.,.]],.]],.] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 1

[3,6,2,7,1,4,5] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0

[3,6,2,7,1,5,4] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 0

[3,6,2,7,4,1,5] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 0

[3,6,2,7,4,5,1] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 1

[3,6,2,7,5,1,4] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 0

[3,6,2,7,5,4,1] => [[[.,[.,.]],[[[.,.],.],.]],.] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 1

[3,6,4,1,2,5,7] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 0

[3,6,4,1,2,7,5] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 0

[3,6,4,1,5,2,7] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 0

[3,6,4,1,5,7,2] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 0

[3,6,4,1,7,2,5] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 0

[3,6,4,1,7,5,2] => [[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 0

[3,6,4,2,1,5,7] => [[[.,[[.,.],.]],.],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 1

[3,6,4,2,1,7,5] => [[[.,[[.,.],.]],.],[[.,.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 1

[3,6,4,2,5,1,7] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 0

[3,6,4,2,5,7,1] => [[[.,[[.,.],.]],[.,[.,.]]],.] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 1

[3,6,4,2,7,1,5] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 0

[3,6,4,2,7,5,1] => [[[.,[[.,.],.]],[[.,.],.]],.] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 1

[3,6,4,5,1,2,7] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 0

[3,6,4,5,1,7,2] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 0

[3,6,4,5,2,1,7] => [[[.,[[.,.],[.,.]]],.],[.,.]] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 1

[3,6,4,5,2,7,1] => [[[.,[[.,.],[.,.]]],[.,.]],.] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 1

[3,6,4,5,7,1,2] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 0

[3,6,4,5,7,2,1] => [[[.,[[.,.],[.,[.,.]]]],.],.] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 2

[3,6,4,7,1,2,5] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 0

[3,6,4,7,1,5,2] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 0

[3,6,4,7,2,1,5] => [[[.,[[.,.],[.,.]]],.],[.,.]] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 1

[3,6,4,7,2,5,1] => [[[.,[[.,.],[.,.]]],[.,.]],.] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 1

[3,6,4,7,5,1,2] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 0

[3,6,4,7,5,2,1] => [[[.,[[.,.],[[.,.],.]]],.],.] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 2

[3,6,5,1,2,4,7] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 0

[3,6,5,1,2,7,4] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 0

[3,6,5,1,4,2,7] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 0

[3,6,5,1,4,7,2] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 0

[3,6,5,1,7,2,4] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 0

[3,6,5,1,7,4,2] => [[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 0

[3,6,5,2,1,4,7] => [[[.,[[.,.],.]],.],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 1

[3,6,5,2,1,7,4] => [[[.,[[.,.],.]],.],[[.,.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 1

[3,6,5,2,4,1,7] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 0

[3,6,5,2,4,7,1] => [[[.,[[.,.],.]],[.,[.,.]]],.] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 1

[3,6,5,2,7,1,4] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 0

[3,6,5,2,7,4,1] => [[[.,[[.,.],.]],[[.,.],.]],.] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 1

[3,6,5,4,1,2,7] => [[.,[[[.,.],.],.]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 0

[3,6,5,4,1,7,2] => [[.,[[[.,.],.],.]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 0

[3,6,5,4,2,1,7] => [[[.,[[[.,.],.],.]],.],[.,.]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1

[3,6,5,4,2,7,1] => [[[.,[[[.,.],.],.]],[.,.]],.] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 1

[3,6,5,4,7,1,2] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 0

[3,6,5,4,7,2,1] => [[[.,[[[.,.],.],[.,.]]],.],.] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 2

[3,6,5,7,1,2,4] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 0

[3,6,5,7,1,4,2] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 0

[3,6,5,7,2,1,4] => [[[.,[[.,.],[.,.]]],.],[.,.]] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 1

[3,6,5,7,2,4,1] => [[[.,[[.,.],[.,.]]],[.,.]],.] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 1

[3,6,5,7,4,1,2] => [[.,[[[.,.],[.,.]],.]],[.,.]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 0

[3,6,5,7,4,2,1] => [[[.,[[[.,.],[.,.]],.]],.],.] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 2

[3,6,7,1,2,4,5] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0

[3,6,7,1,2,5,4] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 0

[3,6,7,1,4,2,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 0

[3,6,7,1,4,5,2] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 0

[3,6,7,1,5,2,4] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 0

[3,6,7,1,5,4,2] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 0

[3,6,7,2,1,4,5] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1

[3,6,7,2,1,5,4] => [[[.,[.,[.,.]]],.],[[.,.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 1

[3,6,7,2,4,1,5] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 0

[3,6,7,2,4,5,1] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 1

[3,6,7,2,5,1,4] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 0

[3,6,7,2,5,4,1] => [[[.,[.,[.,.]]],[[.,.],.]],.] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 1

[3,6,7,4,1,2,5] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 0

[3,6,7,4,1,5,2] => [[.,[[.,[.,.]],.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 0

[3,6,7,4,2,1,5] => [[[.,[[.,[.,.]],.]],.],[.,.]] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 1

[3,6,7,4,2,5,1] => [[[.,[[.,[.,.]],.]],[.,.]],.] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 1

[3,6,7,4,5,1,2] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 0

[3,6,7,4,5,2,1] => [[[.,[[.,[.,.]],[.,.]]],.],.] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 2

[3,6,7,5,1,2,4] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 0

[3,6,7,5,1,4,2] => [[.,[[.,[.,.]],.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 0

[3,6,7,5,2,1,4] => [[[.,[[.,[.,.]],.]],.],[.,.]] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 1

[3,6,7,5,2,4,1] => [[[.,[[.,[.,.]],.]],[.,.]],.] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 1

[3,6,7,5,4,1,2] => [[.,[[[.,[.,.]],.],.]],[.,.]] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 0

[3,6,7,5,4,2,1] => [[[.,[[[.,[.,.]],.],.]],.],.] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 2

[3,7,1,2,4,5,6] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0

[3,7,1,2,4,6,5] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 0

[3,7,1,2,5,4,6] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 0

[3,7,1,2,5,6,4] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 0

[3,7,1,2,6,4,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 0

[3,7,1,2,6,5,4] => [[.,[.,.]],[.,[[[.,.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 0

[3,7,1,4,2,5,6] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 0

[3,7,1,4,2,6,5] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 0

[3,7,1,4,5,2,6] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 0

[3,7,1,4,5,6,2] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 0

[3,7,1,4,6,2,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 0

[3,7,1,4,6,5,2] => [[.,[.,.]],[[.,[[.,.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 0

[3,7,1,5,2,4,6] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 0

[3,7,1,5,2,6,4] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 0

[3,7,1,5,4,2,6] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 0

[3,7,1,5,4,6,2] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 0

[3,7,1,5,6,2,4] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 0

[3,7,1,5,6,4,2] => [[.,[.,.]],[[[.,[.,.]],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 0

[3,7,1,6,2,4,5] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 0

[3,7,1,6,2,5,4] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 0

[3,7,1,6,4,2,5] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 0

[3,7,1,6,4,5,2] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 0

[3,7,1,6,5,2,4] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 0

[3,7,1,6,5,4,2] => [[.,[.,.]],[[[[.,.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 0

[3,7,2,1,4,5,6] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1

[3,7,2,1,4,6,5] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 1

[3,7,2,1,5,4,6] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[3,7,2,1,5,6,4] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 1

[3,7,2,1,6,4,5] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[3,7,2,1,6,5,4] => [[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1

[3,7,2,4,1,5,6] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0

[3,7,2,4,1,6,5] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 0

[3,7,2,4,5,1,6] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0

[3,7,2,4,5,6,1] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 1

[3,7,2,4,6,1,5] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0

[3,7,2,4,6,5,1] => [[[.,[.,.]],[.,[[.,.],.]]],.] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 1

[3,7,2,5,1,4,6] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0

[3,7,2,5,1,6,4] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 0

[3,7,2,5,4,1,6] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 0

[3,7,2,5,4,6,1] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 1

[3,7,2,5,6,1,4] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0

[3,7,2,5,6,4,1] => [[[.,[.,.]],[[.,[.,.]],.]],.] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 1

[3,7,2,6,1,4,5] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0

[3,7,2,6,1,5,4] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 0

[3,7,2,6,4,1,5] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 0

[3,7,2,6,4,5,1] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 1

[3,7,2,6,5,1,4] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 0

[3,7,2,6,5,4,1] => [[[.,[.,.]],[[[.,.],.],.]],.] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 1

[3,7,4,1,2,5,6] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 0

[3,7,4,1,2,6,5] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 0

[3,7,4,1,5,2,6] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 0

[3,7,4,1,5,6,2] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 0

[3,7,4,1,6,2,5] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 0

[3,7,4,1,6,5,2] => [[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 0

[3,7,4,2,1,5,6] => [[[.,[[.,.],.]],.],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 1

[3,7,4,2,1,6,5] => [[[.,[[.,.],.]],.],[[.,.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 1

[3,7,4,2,5,1,6] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 0

[3,7,4,2,5,6,1] => [[[.,[[.,.],.]],[.,[.,.]]],.] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 1

[3,7,4,2,6,1,5] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 0

[3,7,4,2,6,5,1] => [[[.,[[.,.],.]],[[.,.],.]],.] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 1

[3,7,4,5,1,2,6] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 0

[3,7,4,5,1,6,2] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 0

[3,7,4,5,2,1,6] => [[[.,[[.,.],[.,.]]],.],[.,.]] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 1

[3,7,4,5,2,6,1] => [[[.,[[.,.],[.,.]]],[.,.]],.] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 1

[3,7,4,5,6,1,2] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 0

[3,7,4,5,6,2,1] => [[[.,[[.,.],[.,[.,.]]]],.],.] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 2

[3,7,4,6,1,2,5] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 0

[3,7,4,6,1,5,2] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 0

[3,7,4,6,2,1,5] => [[[.,[[.,.],[.,.]]],.],[.,.]] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 1

[3,7,4,6,2,5,1] => [[[.,[[.,.],[.,.]]],[.,.]],.] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 1

[3,7,4,6,5,1,2] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 0

[3,7,4,6,5,2,1] => [[[.,[[.,.],[[.,.],.]]],.],.] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 2

[3,7,5,1,2,4,6] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 0

[3,7,5,1,2,6,4] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 0

[3,7,5,1,4,2,6] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 0

[3,7,5,1,4,6,2] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 0

[3,7,5,1,6,2,4] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 0

[3,7,5,1,6,4,2] => [[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 0

[3,7,5,2,1,4,6] => [[[.,[[.,.],.]],.],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 1

[3,7,5,2,1,6,4] => [[[.,[[.,.],.]],.],[[.,.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 1

[3,7,5,2,4,1,6] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 0

[3,7,5,2,4,6,1] => [[[.,[[.,.],.]],[.,[.,.]]],.] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 1

[3,7,5,2,6,1,4] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 0

[3,7,5,2,6,4,1] => [[[.,[[.,.],.]],[[.,.],.]],.] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 1

[3,7,5,4,1,2,6] => [[.,[[[.,.],.],.]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 0

[3,7,5,4,1,6,2] => [[.,[[[.,.],.],.]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 0

[3,7,5,4,2,1,6] => [[[.,[[[.,.],.],.]],.],[.,.]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1

[3,7,5,4,2,6,1] => [[[.,[[[.,.],.],.]],[.,.]],.] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 1

[3,7,5,4,6,1,2] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 0

[3,7,5,4,6,2,1] => [[[.,[[[.,.],.],[.,.]]],.],.] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 2

[3,7,5,6,1,2,4] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 0

[3,7,5,6,1,4,2] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 0

[3,7,5,6,2,1,4] => [[[.,[[.,.],[.,.]]],.],[.,.]] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 1

[3,7,5,6,2,4,1] => [[[.,[[.,.],[.,.]]],[.,.]],.] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 1

[3,7,5,6,4,1,2] => [[.,[[[.,.],[.,.]],.]],[.,.]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 0

[3,7,5,6,4,2,1] => [[[.,[[[.,.],[.,.]],.]],.],.] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 2

[3,7,6,1,2,4,5] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 0

[3,7,6,1,2,5,4] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 0

[3,7,6,1,4,2,5] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 0

[3,7,6,1,4,5,2] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 0

[3,7,6,1,5,2,4] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 0

[3,7,6,1,5,4,2] => [[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 0

[3,7,6,2,1,4,5] => [[[.,[[.,.],.]],.],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 1

[3,7,6,2,1,5,4] => [[[.,[[.,.],.]],.],[[.,.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 1

[3,7,6,2,4,1,5] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 0

[3,7,6,2,4,5,1] => [[[.,[[.,.],.]],[.,[.,.]]],.] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 1

[3,7,6,2,5,1,4] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 0

[3,7,6,2,5,4,1] => [[[.,[[.,.],.]],[[.,.],.]],.] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 1

[3,7,6,4,1,2,5] => [[.,[[[.,.],.],.]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 0

[3,7,6,4,1,5,2] => [[.,[[[.,.],.],.]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 0

[3,7,6,4,2,1,5] => [[[.,[[[.,.],.],.]],.],[.,.]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1

[3,7,6,4,2,5,1] => [[[.,[[[.,.],.],.]],[.,.]],.] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 1

[3,7,6,4,5,1,2] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 0

[3,7,6,4,5,2,1] => [[[.,[[[.,.],.],[.,.]]],.],.] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 2

[3,7,6,5,1,2,4] => [[.,[[[.,.],.],.]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 0

[3,7,6,5,1,4,2] => [[.,[[[.,.],.],.]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 0

[3,7,6,5,2,1,4] => [[[.,[[[.,.],.],.]],.],[.,.]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1

[3,7,6,5,2,4,1] => [[[.,[[[.,.],.],.]],[.,.]],.] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 1

[3,7,6,5,4,1,2] => [[.,[[[[.,.],.],.],.]],[.,.]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 0

[3,7,6,5,4,2,1] => [[[.,[[[[.,.],.],.],.]],.],.] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 2

[4,1,2,3,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1

[4,1,2,3,5,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 1

[4,1,2,3,6,5,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 1

[4,1,2,3,6,7,5] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 1

[4,1,2,3,7,5,6] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 1

[4,1,2,3,7,6,5] => [[.,.],[.,[.,[[[.,.],.],.]]]] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1

[4,1,2,5,3,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 1

[4,1,2,5,3,7,6] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 1

[4,1,2,5,6,3,7] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1

[4,1,2,5,6,7,3] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 1

[4,1,2,5,7,3,6] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1

[4,1,2,5,7,6,3] => [[.,.],[.,[[.,[[.,.],.]],.]]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 1

[4,1,2,6,3,5,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 1

[4,1,2,6,3,7,5] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 1

[4,1,2,6,5,3,7] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 1

[4,1,2,6,5,7,3] => [[.,.],[.,[[[.,.],[.,.]],.]]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 1

[4,1,2,6,7,3,5] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1

[4,1,2,6,7,5,3] => [[.,.],[.,[[[.,[.,.]],.],.]]] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 1

[4,1,2,7,3,5,6] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 1

[4,1,2,7,3,6,5] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 1

[4,1,2,7,5,3,6] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 1

[4,1,2,7,5,6,3] => [[.,.],[.,[[[.,.],[.,.]],.]]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 1

[4,1,2,7,6,3,5] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 1

[4,1,2,7,6,5,3] => [[.,.],[.,[[[[.,.],.],.],.]]] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 1

[4,1,3,2,5,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 1

[4,1,3,2,5,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 1

[4,1,3,2,6,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1

[4,1,3,2,6,7,5] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 1

[4,1,3,2,7,5,6] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1

[4,1,3,2,7,6,5] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 1

[4,1,3,5,2,6,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

[4,1,3,5,2,7,6] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 1

[4,1,3,5,6,2,7] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1

[4,1,3,5,6,7,2] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 1

[4,1,3,5,7,2,6] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1

[4,1,3,5,7,6,2] => [[.,.],[[.,[.,[[.,.],.]]],.]] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 1

[4,1,3,6,2,5,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

[4,1,3,6,2,7,5] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 1

[4,1,3,6,5,2,7] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1

[4,1,3,6,5,7,2] => [[.,.],[[.,[[.,.],[.,.]]],.]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 1

[4,1,3,6,7,2,5] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1

[4,1,3,6,7,5,2] => [[.,.],[[.,[[.,[.,.]],.]],.]] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 1

[4,1,3,7,2,5,6] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

[4,1,3,7,2,6,5] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 1

[4,1,3,7,5,2,6] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1

[4,1,3,7,5,6,2] => [[.,.],[[.,[[.,.],[.,.]]],.]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 1

[4,1,3,7,6,2,5] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1

[4,1,3,7,6,5,2] => [[.,.],[[.,[[[.,.],.],.]],.]] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 1

[4,1,5,2,3,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 1

[4,1,5,2,3,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 1

[4,1,5,2,6,3,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1

[4,1,5,2,6,7,3] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 1

[4,1,5,2,7,3,6] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1

[4,1,5,2,7,6,3] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 1

[4,1,5,3,2,6,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1

[4,1,5,3,2,7,6] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 1

[4,1,5,3,6,2,7] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1

[4,1,5,3,6,7,2] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 1

[4,1,5,3,7,2,6] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1

[4,1,5,3,7,6,2] => [[.,.],[[[.,.],[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 1

[4,1,5,6,2,3,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

[4,1,5,6,2,7,3] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 1

[4,1,5,6,3,2,7] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[4,1,5,6,3,7,2] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 1

[4,1,5,6,7,2,3] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1

[4,1,5,6,7,3,2] => [[.,.],[[[.,[.,[.,.]]],.],.]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 1

[4,1,5,7,2,3,6] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

[4,1,5,7,2,6,3] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 1

[4,1,5,7,3,2,6] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[4,1,5,7,3,6,2] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 1

[4,1,5,7,6,2,3] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1

[4,1,5,7,6,3,2] => [[.,.],[[[.,[[.,.],.]],.],.]] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 1

[4,1,6,2,3,5,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 1

[4,1,6,2,3,7,5] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 1

[4,1,6,2,5,3,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1

[4,1,6,2,5,7,3] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 1

[4,1,6,2,7,3,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1

[4,1,6,2,7,5,3] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 1

[4,1,6,3,2,5,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1

[4,1,6,3,2,7,5] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 1

[4,1,6,3,5,2,7] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1

[4,1,6,3,5,7,2] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 1

[4,1,6,3,7,2,5] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1

[4,1,6,3,7,5,2] => [[.,.],[[[.,.],[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 1

[4,1,6,5,2,3,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1

[4,1,6,5,2,7,3] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 1

[4,1,6,5,3,2,7] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 1

[4,1,6,5,3,7,2] => [[.,.],[[[[.,.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 1

[4,1,6,5,7,2,3] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1

[4,1,6,5,7,3,2] => [[.,.],[[[[.,.],[.,.]],.],.]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 1

[4,1,6,7,2,3,5] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

[4,1,6,7,2,5,3] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 1

[4,1,6,7,3,2,5] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[4,1,6,7,3,5,2] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 1

[4,1,6,7,5,2,3] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[4,1,6,7,5,3,2] => [[.,.],[[[[.,[.,.]],.],.],.]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 1

[4,1,7,2,3,5,6] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 1

[4,1,7,2,3,6,5] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 1

[4,1,7,2,5,3,6] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1

[4,1,7,2,5,6,3] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 1

[4,1,7,2,6,3,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1

[4,1,7,2,6,5,3] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 1

[4,1,7,3,2,5,6] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1

[4,1,7,3,2,6,5] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 1

[4,1,7,3,5,2,6] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1

[4,1,7,3,5,6,2] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 1

[4,1,7,3,6,2,5] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1

[4,1,7,3,6,5,2] => [[.,.],[[[.,.],[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 1

[4,1,7,5,2,3,6] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1

[4,1,7,5,2,6,3] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 1

[4,1,7,5,3,2,6] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 1

[4,1,7,5,3,6,2] => [[.,.],[[[[.,.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 1

[4,1,7,5,6,2,3] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1

[4,1,7,5,6,3,2] => [[.,.],[[[[.,.],[.,.]],.],.]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 1

[4,1,7,6,2,3,5] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1

[4,1,7,6,2,5,3] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 1

[4,1,7,6,3,2,5] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 1

[4,1,7,6,3,5,2] => [[.,.],[[[[.,.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 1

[4,1,7,6,5,2,3] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 1

[4,1,7,6,5,3,2] => [[.,.],[[[[[.,.],.],.],.],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1

[4,2,1,3,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2

[4,2,1,3,5,7,6] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 2

[4,2,1,3,6,5,7] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 2

[4,2,1,3,6,7,5] => [[[.,.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[4,2,1,3,7,5,6] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 2

[4,2,1,3,7,6,5] => [[[.,.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 2

[4,2,1,5,3,6,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 2

[4,2,1,5,3,7,6] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 2

[4,2,1,5,6,3,7] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 2

[4,2,1,5,6,7,3] => [[[.,.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[4,2,1,5,7,3,6] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 2

[4,2,1,5,7,6,3] => [[[.,.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 2

[4,2,1,6,3,5,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 2

[4,2,1,6,3,7,5] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 2

[4,2,1,6,5,3,7] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 2

[4,2,1,6,5,7,3] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2

[4,2,1,6,7,3,5] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 2

[4,2,1,6,7,5,3] => [[[.,.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2

[4,2,1,7,3,5,6] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 2

[4,2,1,7,3,6,5] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 2

[4,2,1,7,5,3,6] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 2

[4,2,1,7,5,6,3] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2

[4,2,1,7,6,3,5] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 2

[4,2,1,7,6,5,3] => [[[.,.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 2

[4,2,3,1,5,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1

[4,2,3,1,5,7,6] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 1

[4,2,3,1,6,5,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[4,2,3,1,6,7,5] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 1

[4,2,3,1,7,5,6] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[4,2,3,1,7,6,5] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1

[4,2,3,5,1,6,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1

[4,2,3,5,1,7,6] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 1

[4,2,3,5,6,1,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1

[4,2,3,5,6,7,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2

[4,2,3,5,7,1,6] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1

[4,2,3,5,7,6,1] => [[[.,.],[.,[.,[[.,.],.]]]],.] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 2

[4,2,3,6,1,5,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1

[4,2,3,6,1,7,5] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 1

[4,2,3,6,5,1,7] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1

[4,2,3,6,5,7,1] => [[[.,.],[.,[[.,.],[.,.]]]],.] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 2

[4,2,3,6,7,1,5] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1

[4,2,3,6,7,5,1] => [[[.,.],[.,[[.,[.,.]],.]]],.] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 2

[4,2,3,7,1,5,6] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1

[4,2,3,7,1,6,5] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 1

[4,2,3,7,5,1,6] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1

[4,2,3,7,5,6,1] => [[[.,.],[.,[[.,.],[.,.]]]],.] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 2

[4,2,3,7,6,1,5] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1

[4,2,3,7,6,5,1] => [[[.,.],[.,[[[.,.],.],.]]],.] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 2

[4,2,5,1,3,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1

[4,2,5,1,3,7,6] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 1

[4,2,5,1,6,3,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[4,2,5,1,6,7,3] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 1

[4,2,5,1,7,3,6] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[4,2,5,1,7,6,3] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1

[4,2,5,3,1,6,7] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1

[4,2,5,3,1,7,6] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1

[4,2,5,3,6,1,7] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[4,2,5,3,6,7,1] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 2

[4,2,5,3,7,1,6] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[4,2,5,3,7,6,1] => [[[.,.],[[.,.],[[.,.],.]]],.] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 2

[4,2,5,6,1,3,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1

[4,2,5,6,1,7,3] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 1

[4,2,5,6,3,1,7] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[4,2,5,6,3,7,1] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[4,2,5,6,7,1,3] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1

[4,2,5,6,7,3,1] => [[[.,.],[[.,[.,[.,.]]],.]],.] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 2

[4,2,5,7,1,3,6] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1

[4,2,5,7,1,6,3] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 1

[4,2,5,7,3,1,6] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[4,2,5,7,3,6,1] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[4,2,5,7,6,1,3] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1

[4,2,5,7,6,3,1] => [[[.,.],[[.,[[.,.],.]],.]],.] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 2

[4,2,6,1,3,5,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1

[4,2,6,1,3,7,5] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 1

[4,2,6,1,5,3,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[4,2,6,1,5,7,3] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 1

[4,2,6,1,7,3,5] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[4,2,6,1,7,5,3] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1

[4,2,6,3,1,5,7] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1

[4,2,6,3,1,7,5] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1

[4,2,6,3,5,1,7] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[4,2,6,3,5,7,1] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 2

[4,2,6,3,7,1,5] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[4,2,6,3,7,5,1] => [[[.,.],[[.,.],[[.,.],.]]],.] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 2

[4,2,6,5,1,3,7] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1

[4,2,6,5,1,7,3] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1

[4,2,6,5,3,1,7] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1

[4,2,6,5,3,7,1] => [[[.,.],[[[.,.],.],[.,.]]],.] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 2

[4,2,6,5,7,1,3] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[4,2,6,5,7,3,1] => [[[.,.],[[[.,.],[.,.]],.]],.] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 2

[4,2,6,7,1,3,5] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1

[4,2,6,7,1,5,3] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 1

[4,2,6,7,3,1,5] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[4,2,6,7,3,5,1] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[4,2,6,7,5,1,3] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[4,2,6,7,5,3,1] => [[[.,.],[[[.,[.,.]],.],.]],.] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 2

[4,2,7,1,3,5,6] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1

[4,2,7,1,3,6,5] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 1

[4,2,7,1,5,3,6] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[4,2,7,1,5,6,3] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 1

[4,2,7,1,6,3,5] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[4,2,7,1,6,5,3] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1

[4,2,7,3,1,5,6] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1

[4,2,7,3,1,6,5] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1

[4,2,7,3,5,1,6] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[4,2,7,3,5,6,1] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 2

[4,2,7,3,6,1,5] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[4,2,7,3,6,5,1] => [[[.,.],[[.,.],[[.,.],.]]],.] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 2

[4,2,7,5,1,3,6] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1

[4,2,7,5,1,6,3] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1

[4,2,7,5,3,1,6] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1

[4,2,7,5,3,6,1] => [[[.,.],[[[.,.],.],[.,.]]],.] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 2

[4,2,7,5,6,1,3] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[4,2,7,5,6,3,1] => [[[.,.],[[[.,.],[.,.]],.]],.] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 2

[4,2,7,6,1,3,5] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1

[4,2,7,6,1,5,3] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1

[4,2,7,6,3,1,5] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1

[4,2,7,6,3,5,1] => [[[.,.],[[[.,.],.],[.,.]]],.] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 2

[4,2,7,6,5,1,3] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1

[4,2,7,6,5,3,1] => [[[.,.],[[[[.,.],.],.],.]],.] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 2

[4,3,1,2,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2

[4,3,1,2,5,7,6] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 2

[4,3,1,2,6,5,7] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 2

[4,3,1,2,6,7,5] => [[[.,.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[4,3,1,2,7,5,6] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 2

[4,3,1,2,7,6,5] => [[[.,.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 2

[4,3,1,5,2,6,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 2

[4,3,1,5,2,7,6] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 2

[4,3,1,5,6,2,7] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 2

[4,3,1,5,6,7,2] => [[[.,.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[4,3,1,5,7,2,6] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 2

[4,3,1,5,7,6,2] => [[[.,.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 2

[4,3,1,6,2,5,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 2

[4,3,1,6,2,7,5] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 2

[4,3,1,6,5,2,7] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 2

[4,3,1,6,5,7,2] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2

[4,3,1,6,7,2,5] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 2

[4,3,1,6,7,5,2] => [[[.,.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2

[4,3,1,7,2,5,6] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 2

[4,3,1,7,2,6,5] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 2

[4,3,1,7,5,2,6] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 2

[4,3,1,7,5,6,2] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2

[4,3,1,7,6,2,5] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 2

[4,3,1,7,6,5,2] => [[[.,.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 2

[4,3,2,1,5,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3

[4,3,2,1,5,7,6] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 3

[4,3,2,1,6,5,7] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 3

[4,3,2,1,6,7,5] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3

[4,3,2,1,7,5,6] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 3

[4,3,2,1,7,6,5] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 3

[4,3,2,5,1,6,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2

[4,3,2,5,1,7,6] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[4,3,2,5,6,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2

[4,3,2,5,6,7,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 3

[4,3,2,5,7,1,6] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2

[4,3,2,5,7,6,1] => [[[[.,.],.],[.,[[.,.],.]]],.] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 3

[4,3,2,6,1,5,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2

[4,3,2,6,1,7,5] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[4,3,2,6,5,1,7] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2

[4,3,2,6,5,7,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 3

[4,3,2,6,7,1,5] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2

[4,3,2,6,7,5,1] => [[[[.,.],.],[[.,[.,.]],.]],.] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[4,3,2,7,1,5,6] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2

[4,3,2,7,1,6,5] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[4,3,2,7,5,1,6] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2

[4,3,2,7,5,6,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 3

[4,3,2,7,6,1,5] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2

[4,3,2,7,6,5,1] => [[[[.,.],.],[[[.,.],.],.]],.] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 3

[4,3,5,1,2,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1

[4,3,5,1,2,7,6] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 1

[4,3,5,1,6,2,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[4,3,5,1,6,7,2] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 1

[4,3,5,1,7,2,6] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[4,3,5,1,7,6,2] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1

[4,3,5,2,1,6,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2

[4,3,5,2,1,7,6] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[4,3,5,2,6,1,7] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[4,3,5,2,6,7,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[4,3,5,2,7,1,6] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[4,3,5,2,7,6,1] => [[[[.,.],[.,.]],[[.,.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 2

[4,3,5,6,1,2,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1

[4,3,5,6,1,7,2] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 1

[4,3,5,6,2,1,7] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 2

[4,3,5,6,2,7,1] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[4,3,5,6,7,1,2] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1

[4,3,5,6,7,2,1] => [[[[.,.],[.,[.,[.,.]]]],.],.] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3

[4,3,5,7,1,2,6] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1

[4,3,5,7,1,6,2] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 1

[4,3,5,7,2,1,6] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 2

[4,3,5,7,2,6,1] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[4,3,5,7,6,1,2] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1

[4,3,5,7,6,2,1] => [[[[.,.],[.,[[.,.],.]]],.],.] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 3

[4,3,6,1,2,5,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1

[4,3,6,1,2,7,5] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 1

[4,3,6,1,5,2,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[4,3,6,1,5,7,2] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 1

[4,3,6,1,7,2,5] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[4,3,6,1,7,5,2] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1

[4,3,6,2,1,5,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2

[4,3,6,2,1,7,5] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[4,3,6,2,5,1,7] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[4,3,6,2,5,7,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[4,3,6,2,7,1,5] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[4,3,6,2,7,5,1] => [[[[.,.],[.,.]],[[.,.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 2

[4,3,6,5,1,2,7] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1

[4,3,6,5,1,7,2] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1

[4,3,6,5,2,1,7] => [[[[.,.],[[.,.],.]],.],[.,.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 2

[4,3,6,5,2,7,1] => [[[[.,.],[[.,.],.]],[.,.]],.] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[4,3,6,5,7,1,2] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[4,3,6,5,7,2,1] => [[[[.,.],[[.,.],[.,.]]],.],.] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[4,3,6,7,1,2,5] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1

[4,3,6,7,1,5,2] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 1

[4,3,6,7,2,1,5] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 2

[4,3,6,7,2,5,1] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[4,3,6,7,5,1,2] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[4,3,6,7,5,2,1] => [[[[.,.],[[.,[.,.]],.]],.],.] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 3

[4,3,7,1,2,5,6] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1

[4,3,7,1,2,6,5] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 1

[4,3,7,1,5,2,6] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[4,3,7,1,5,6,2] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 1

[4,3,7,1,6,2,5] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[4,3,7,1,6,5,2] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1

[4,3,7,2,1,5,6] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2

[4,3,7,2,1,6,5] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[4,3,7,2,5,1,6] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[4,3,7,2,5,6,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[4,3,7,2,6,1,5] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[4,3,7,2,6,5,1] => [[[[.,.],[.,.]],[[.,.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 2

[4,3,7,5,1,2,6] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1

[4,3,7,5,1,6,2] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1

[4,3,7,5,2,1,6] => [[[[.,.],[[.,.],.]],.],[.,.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 2

[4,3,7,5,2,6,1] => [[[[.,.],[[.,.],.]],[.,.]],.] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[4,3,7,5,6,1,2] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[4,3,7,5,6,2,1] => [[[[.,.],[[.,.],[.,.]]],.],.] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[4,3,7,6,1,2,5] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1

[4,3,7,6,1,5,2] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1

[4,3,7,6,2,1,5] => [[[[.,.],[[.,.],.]],.],[.,.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 2

[4,3,7,6,2,5,1] => [[[[.,.],[[.,.],.]],[.,.]],.] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[4,3,7,6,5,1,2] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1

[4,3,7,6,5,2,1] => [[[[.,.],[[[.,.],.],.]],.],.] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 3

[4,5,1,2,3,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0

[4,5,1,2,3,7,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 0

[4,5,1,2,6,3,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 0

[4,5,1,2,6,7,3] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 0

[4,5,1,2,7,3,6] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 0

[4,5,1,2,7,6,3] => [[.,[.,.]],[.,[[[.,.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 0

[4,5,1,3,2,6,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 0

[4,5,1,3,2,7,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 0

[4,5,1,3,6,2,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 0

[4,5,1,3,6,7,2] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 0

[4,5,1,3,7,2,6] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 0

[4,5,1,3,7,6,2] => [[.,[.,.]],[[.,[[.,.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 0

[4,5,1,6,2,3,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 0

[4,5,1,6,2,7,3] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 0

[4,5,1,6,3,2,7] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 0

[4,5,1,6,3,7,2] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 0

[4,5,1,6,7,2,3] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 0

[4,5,1,6,7,3,2] => [[.,[.,.]],[[[.,[.,.]],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 0

[4,5,1,7,2,3,6] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 0

[4,5,1,7,2,6,3] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 0

[4,5,1,7,3,2,6] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 0

[4,5,1,7,3,6,2] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 0

[4,5,1,7,6,2,3] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 0

[4,5,1,7,6,3,2] => [[.,[.,.]],[[[[.,.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 0

[4,5,2,1,3,6,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1

[4,5,2,1,3,7,6] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 1

[4,5,2,1,6,3,7] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[4,5,2,1,6,7,3] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 1

[4,5,2,1,7,3,6] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[4,5,2,1,7,6,3] => [[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1

[4,5,2,3,1,6,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0

[4,5,2,3,1,7,6] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 0

[4,5,2,3,6,1,7] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0

[4,5,2,3,6,7,1] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 1

[4,5,2,3,7,1,6] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0

[4,5,2,3,7,6,1] => [[[.,[.,.]],[.,[[.,.],.]]],.] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 1

[4,5,2,6,1,3,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0

[4,5,2,6,1,7,3] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 0

[4,5,2,6,3,1,7] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 0

[4,5,2,6,3,7,1] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 1

[4,5,2,6,7,1,3] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0

[4,5,2,6,7,3,1] => [[[.,[.,.]],[[.,[.,.]],.]],.] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 1

[4,5,2,7,1,3,6] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0

[4,5,2,7,1,6,3] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 0

[4,5,2,7,3,1,6] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 0

[4,5,2,7,3,6,1] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 1

[4,5,2,7,6,1,3] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 0

[4,5,2,7,6,3,1] => [[[.,[.,.]],[[[.,.],.],.]],.] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 1

[4,5,3,1,2,6,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1

[4,5,3,1,2,7,6] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 1

[4,5,3,1,6,2,7] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[4,5,3,1,6,7,2] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 1

[4,5,3,1,7,2,6] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[4,5,3,1,7,6,2] => [[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1

[4,5,3,2,1,6,7] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 2

[4,5,3,2,1,7,6] => [[[[.,[.,.]],.],.],[[.,.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2

[4,5,3,2,6,1,7] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[4,5,3,2,6,7,1] => [[[[.,[.,.]],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2

[4,5,3,2,7,1,6] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[4,5,3,2,7,6,1] => [[[[.,[.,.]],.],[[.,.],.]],.] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 2

[4,5,3,6,1,2,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0

[4,5,3,6,1,7,2] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 0

[4,5,3,6,2,1,7] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1

[4,5,3,6,2,7,1] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 1

[4,5,3,6,7,1,2] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0

[4,5,3,6,7,2,1] => [[[[.,[.,.]],[.,[.,.]]],.],.] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 2

[4,5,3,7,1,2,6] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0

[4,5,3,7,1,6,2] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 0

[4,5,3,7,2,1,6] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1

[4,5,3,7,2,6,1] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 1

[4,5,3,7,6,1,2] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 0

[4,5,3,7,6,2,1] => [[[[.,[.,.]],[[.,.],.]],.],.] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 2

[4,5,6,1,2,3,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0

[4,5,6,1,2,7,3] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 0

[4,5,6,1,3,2,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 0

[4,5,6,1,3,7,2] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 0

[4,5,6,1,7,2,3] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 0

[4,5,6,1,7,3,2] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 0

[4,5,6,2,1,3,7] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1

[4,5,6,2,1,7,3] => [[[.,[.,[.,.]]],.],[[.,.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 1

[4,5,6,2,3,1,7] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 0

[4,5,6,2,3,7,1] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 1

[4,5,6,2,7,1,3] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 0

[4,5,6,2,7,3,1] => [[[.,[.,[.,.]]],[[.,.],.]],.] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 1

[4,5,6,3,1,2,7] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1

[4,5,6,3,1,7,2] => [[[.,[.,[.,.]]],.],[[.,.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 1

[4,5,6,3,2,1,7] => [[[[.,[.,[.,.]]],.],.],[.,.]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 2

[4,5,6,3,2,7,1] => [[[[.,[.,[.,.]]],.],[.,.]],.] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[4,5,6,3,7,1,2] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 0

[4,5,6,3,7,2,1] => [[[[.,[.,[.,.]]],[.,.]],.],.] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 2

[4,5,6,7,1,2,3] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0

[4,5,6,7,1,3,2] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 0

[4,5,6,7,2,1,3] => [[[.,[.,[.,[.,.]]]],.],[.,.]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1

[4,5,6,7,2,3,1] => [[[.,[.,[.,[.,.]]]],[.,.]],.] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 1

[4,5,6,7,3,1,2] => [[[.,[.,[.,[.,.]]]],.],[.,.]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1

[4,5,6,7,3,2,1] => [[[[.,[.,[.,[.,.]]]],.],.],.] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 3

[4,5,7,1,2,3,6] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0

[4,5,7,1,2,6,3] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 0

[4,5,7,1,3,2,6] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 0

[4,5,7,1,3,6,2] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 0

[4,5,7,1,6,2,3] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 0

[4,5,7,1,6,3,2] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 0

[4,5,7,2,1,3,6] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1

[4,5,7,2,1,6,3] => [[[.,[.,[.,.]]],.],[[.,.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 1

[4,5,7,2,3,1,6] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 0

[4,5,7,2,3,6,1] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 1

[4,5,7,2,6,1,3] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 0

[4,5,7,2,6,3,1] => [[[.,[.,[.,.]]],[[.,.],.]],.] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 1

[4,5,7,3,1,2,6] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1

[4,5,7,3,1,6,2] => [[[.,[.,[.,.]]],.],[[.,.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 1

[4,5,7,3,2,1,6] => [[[[.,[.,[.,.]]],.],.],[.,.]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 2

[4,5,7,3,2,6,1] => [[[[.,[.,[.,.]]],.],[.,.]],.] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[4,5,7,3,6,1,2] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 0

[4,5,7,3,6,2,1] => [[[[.,[.,[.,.]]],[.,.]],.],.] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 2

[4,5,7,6,1,2,3] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 0

[4,5,7,6,1,3,2] => [[.,[.,[[.,.],.]]],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 0

[4,5,7,6,2,1,3] => [[[.,[.,[[.,.],.]]],.],[.,.]] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 1

[4,5,7,6,2,3,1] => [[[.,[.,[[.,.],.]]],[.,.]],.] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 1

[4,5,7,6,3,1,2] => [[[.,[.,[[.,.],.]]],.],[.,.]] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 1

[4,5,7,6,3,2,1] => [[[[.,[.,[[.,.],.]]],.],.],.] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 3

[4,6,1,2,3,5,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0

[4,6,1,2,3,7,5] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 0

[4,6,1,2,5,3,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 0

[4,6,1,2,5,7,3] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 0

[4,6,1,2,7,3,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 0

[4,6,1,2,7,5,3] => [[.,[.,.]],[.,[[[.,.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 0

[4,6,1,3,2,5,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 0

[4,6,1,3,2,7,5] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 0

[4,6,1,3,5,2,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 0

[4,6,1,3,5,7,2] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 0

[4,6,1,3,7,2,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 0

[4,6,1,3,7,5,2] => [[.,[.,.]],[[.,[[.,.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 0

[4,6,1,5,2,3,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 0

[4,6,1,5,2,7,3] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 0

[4,6,1,5,3,2,7] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 0

[4,6,1,5,3,7,2] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 0

[4,6,1,5,7,2,3] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 0

[4,6,1,5,7,3,2] => [[.,[.,.]],[[[.,[.,.]],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 0

[4,6,1,7,2,3,5] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 0

[4,6,1,7,2,5,3] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 0

[4,6,1,7,3,2,5] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 0

[4,6,1,7,3,5,2] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 0

[4,6,1,7,5,2,3] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 0

[4,6,1,7,5,3,2] => [[.,[.,.]],[[[[.,.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 0

[4,6,2,1,3,5,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1

[4,6,2,1,3,7,5] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 1

[4,6,2,1,5,3,7] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[4,6,2,1,5,7,3] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 1

[4,6,2,1,7,3,5] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[4,6,2,1,7,5,3] => [[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1

[4,6,2,3,1,5,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0

[4,6,2,3,1,7,5] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 0

[4,6,2,3,5,1,7] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0

[4,6,2,3,5,7,1] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 1

[4,6,2,3,7,1,5] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0

[4,6,2,3,7,5,1] => [[[.,[.,.]],[.,[[.,.],.]]],.] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 1

[4,6,2,5,1,3,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0

[4,6,2,5,1,7,3] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 0

[4,6,2,5,3,1,7] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 0

[4,6,2,5,3,7,1] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 1

[4,6,2,5,7,1,3] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0

[4,6,2,5,7,3,1] => [[[.,[.,.]],[[.,[.,.]],.]],.] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 1

[4,6,2,7,1,3,5] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0

[4,6,2,7,1,5,3] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 0

[4,6,2,7,3,1,5] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 0

[4,6,2,7,3,5,1] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 1

[4,6,2,7,5,1,3] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 0

[4,6,2,7,5,3,1] => [[[.,[.,.]],[[[.,.],.],.]],.] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 1

[4,6,3,1,2,5,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1

[4,6,3,1,2,7,5] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 1

[4,6,3,1,5,2,7] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[4,6,3,1,5,7,2] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 1

[4,6,3,1,7,2,5] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[4,6,3,1,7,5,2] => [[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1

[4,6,3,2,1,5,7] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 2

[4,6,3,2,1,7,5] => [[[[.,[.,.]],.],.],[[.,.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2

[4,6,3,2,5,1,7] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[4,6,3,2,5,7,1] => [[[[.,[.,.]],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2

[4,6,3,2,7,1,5] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[4,6,3,2,7,5,1] => [[[[.,[.,.]],.],[[.,.],.]],.] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 2

[4,6,3,5,1,2,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0

[4,6,3,5,1,7,2] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 0

[4,6,3,5,2,1,7] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1

[4,6,3,5,2,7,1] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 1

[4,6,3,5,7,1,2] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0

[4,6,3,5,7,2,1] => [[[[.,[.,.]],[.,[.,.]]],.],.] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 2

[4,6,3,7,1,2,5] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0

[4,6,3,7,1,5,2] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 0

[4,6,3,7,2,1,5] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1

[4,6,3,7,2,5,1] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 1

[4,6,3,7,5,1,2] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 0

[4,6,3,7,5,2,1] => [[[[.,[.,.]],[[.,.],.]],.],.] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 2

[4,6,5,1,2,3,7] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 0

[4,6,5,1,2,7,3] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 0

[4,6,5,1,3,2,7] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 0

[4,6,5,1,3,7,2] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 0

[4,6,5,1,7,2,3] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 0

[4,6,5,1,7,3,2] => [[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 0

[4,6,5,2,1,3,7] => [[[.,[[.,.],.]],.],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 1

[4,6,5,2,1,7,3] => [[[.,[[.,.],.]],.],[[.,.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 1

[4,6,5,2,3,1,7] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 0

[4,6,5,2,3,7,1] => [[[.,[[.,.],.]],[.,[.,.]]],.] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 1

[4,6,5,2,7,1,3] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 0

[4,6,5,2,7,3,1] => [[[.,[[.,.],.]],[[.,.],.]],.] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 1

[4,6,5,3,1,2,7] => [[[.,[[.,.],.]],.],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 1

[4,6,5,3,1,7,2] => [[[.,[[.,.],.]],.],[[.,.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 1

[4,6,5,3,2,1,7] => [[[[.,[[.,.],.]],.],.],[.,.]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 2

[4,6,5,3,2,7,1] => [[[[.,[[.,.],.]],.],[.,.]],.] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2

[4,6,5,3,7,1,2] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 0

[4,6,5,3,7,2,1] => [[[[.,[[.,.],.]],[.,.]],.],.] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 2

[4,6,5,7,1,2,3] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 0

[4,6,5,7,1,3,2] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 0

[4,6,5,7,2,1,3] => [[[.,[[.,.],[.,.]]],.],[.,.]] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 1

[4,6,5,7,2,3,1] => [[[.,[[.,.],[.,.]]],[.,.]],.] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 1

[4,6,5,7,3,1,2] => [[[.,[[.,.],[.,.]]],.],[.,.]] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 1

[4,6,5,7,3,2,1] => [[[[.,[[.,.],[.,.]]],.],.],.] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 3

[4,6,7,1,2,3,5] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0

[4,6,7,1,2,5,3] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 0

[4,6,7,1,3,2,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 0

[4,6,7,1,3,5,2] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 0

[4,6,7,1,5,2,3] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 0

[4,6,7,1,5,3,2] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 0

[4,6,7,2,1,3,5] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1

[4,6,7,2,1,5,3] => [[[.,[.,[.,.]]],.],[[.,.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 1

[4,6,7,2,3,1,5] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 0

[4,6,7,2,3,5,1] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 1

[4,6,7,2,5,1,3] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 0

[4,6,7,2,5,3,1] => [[[.,[.,[.,.]]],[[.,.],.]],.] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 1

[4,6,7,3,1,2,5] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1

[4,6,7,3,1,5,2] => [[[.,[.,[.,.]]],.],[[.,.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 1

[4,6,7,3,2,1,5] => [[[[.,[.,[.,.]]],.],.],[.,.]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 2

[4,6,7,3,2,5,1] => [[[[.,[.,[.,.]]],.],[.,.]],.] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[4,6,7,3,5,1,2] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 0

[4,6,7,3,5,2,1] => [[[[.,[.,[.,.]]],[.,.]],.],.] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 2

[4,6,7,5,1,2,3] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 0

[4,6,7,5,1,3,2] => [[.,[[.,[.,.]],.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 0

[4,6,7,5,2,1,3] => [[[.,[[.,[.,.]],.]],.],[.,.]] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 1

[4,6,7,5,2,3,1] => [[[.,[[.,[.,.]],.]],[.,.]],.] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 1

[4,6,7,5,3,1,2] => [[[.,[[.,[.,.]],.]],.],[.,.]] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 1

[4,6,7,5,3,2,1] => [[[[.,[[.,[.,.]],.]],.],.],.] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 3

[4,7,1,2,3,5,6] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0

[4,7,1,2,3,6,5] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 0

[4,7,1,2,5,3,6] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 0

[4,7,1,2,5,6,3] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 0

[4,7,1,2,6,3,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 0

[4,7,1,2,6,5,3] => [[.,[.,.]],[.,[[[.,.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 0

[4,7,1,3,2,5,6] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 0

[4,7,1,3,2,6,5] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 0

[4,7,1,3,5,2,6] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 0

[4,7,1,3,5,6,2] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 0

[4,7,1,3,6,2,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 0

[4,7,1,3,6,5,2] => [[.,[.,.]],[[.,[[.,.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 0

[4,7,1,5,2,3,6] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 0

[4,7,1,5,2,6,3] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 0

[4,7,1,5,3,2,6] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 0

[4,7,1,5,3,6,2] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 0

[4,7,1,5,6,2,3] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 0

[4,7,1,5,6,3,2] => [[.,[.,.]],[[[.,[.,.]],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 0

[4,7,1,6,2,3,5] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 0

[4,7,1,6,2,5,3] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 0

[4,7,1,6,3,2,5] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 0

[4,7,1,6,3,5,2] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 0

[4,7,1,6,5,2,3] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 0

[4,7,1,6,5,3,2] => [[.,[.,.]],[[[[.,.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 0

[4,7,2,1,3,5,6] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1

[4,7,2,1,3,6,5] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 1

[4,7,2,1,5,3,6] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[4,7,2,1,5,6,3] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 1

[4,7,2,1,6,3,5] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[4,7,2,1,6,5,3] => [[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1

[4,7,2,3,1,5,6] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0

[4,7,2,3,1,6,5] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 0

[4,7,2,3,5,1,6] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0

[4,7,2,3,5,6,1] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 1

[4,7,2,3,6,1,5] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0

[4,7,2,3,6,5,1] => [[[.,[.,.]],[.,[[.,.],.]]],.] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 1

[4,7,2,5,1,3,6] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0

[4,7,2,5,1,6,3] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 0

[4,7,2,5,3,1,6] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 0

[4,7,2,5,3,6,1] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 1

[4,7,2,5,6,1,3] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0

[4,7,2,5,6,3,1] => [[[.,[.,.]],[[.,[.,.]],.]],.] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 1

[4,7,2,6,1,3,5] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0

[4,7,2,6,1,5,3] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 0

[4,7,2,6,3,1,5] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 0

[4,7,2,6,3,5,1] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 1

[4,7,2,6,5,1,3] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 0

[4,7,2,6,5,3,1] => [[[.,[.,.]],[[[.,.],.],.]],.] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 1

[4,7,3,1,2,5,6] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1

[4,7,3,1,2,6,5] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 1

[4,7,3,1,5,2,6] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[4,7,3,1,5,6,2] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 1

[4,7,3,1,6,2,5] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[4,7,3,1,6,5,2] => [[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1

[4,7,3,2,1,5,6] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 2

[4,7,3,2,1,6,5] => [[[[.,[.,.]],.],.],[[.,.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2

[4,7,3,2,5,1,6] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[4,7,3,2,5,6,1] => [[[[.,[.,.]],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2

[4,7,3,2,6,1,5] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[4,7,3,2,6,5,1] => [[[[.,[.,.]],.],[[.,.],.]],.] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 2

[4,7,3,5,1,2,6] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0

[4,7,3,5,1,6,2] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 0

[4,7,3,5,2,1,6] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1

[4,7,3,5,2,6,1] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 1

[4,7,3,5,6,1,2] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0

[4,7,3,5,6,2,1] => [[[[.,[.,.]],[.,[.,.]]],.],.] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 2

[4,7,3,6,1,2,5] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0

[4,7,3,6,1,5,2] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 0

[4,7,3,6,2,1,5] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1

[4,7,3,6,2,5,1] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 1

[4,7,3,6,5,1,2] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 0

[4,7,3,6,5,2,1] => [[[[.,[.,.]],[[.,.],.]],.],.] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 2

[4,7,5,1,2,3,6] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 0

[4,7,5,1,2,6,3] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 0

[4,7,5,1,3,2,6] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 0

[4,7,5,1,3,6,2] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 0

[4,7,5,1,6,2,3] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 0

[4,7,5,1,6,3,2] => [[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 0

[4,7,5,2,1,3,6] => [[[.,[[.,.],.]],.],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 1

[4,7,5,2,1,6,3] => [[[.,[[.,.],.]],.],[[.,.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 1

[4,7,5,2,3,1,6] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 0

[4,7,5,2,3,6,1] => [[[.,[[.,.],.]],[.,[.,.]]],.] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 1

[4,7,5,2,6,1,3] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 0

[4,7,5,2,6,3,1] => [[[.,[[.,.],.]],[[.,.],.]],.] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 1

[4,7,5,3,1,2,6] => [[[.,[[.,.],.]],.],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 1

[4,7,5,3,1,6,2] => [[[.,[[.,.],.]],.],[[.,.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 1

[4,7,5,3,2,1,6] => [[[[.,[[.,.],.]],.],.],[.,.]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 2

[4,7,5,3,2,6,1] => [[[[.,[[.,.],.]],.],[.,.]],.] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2

[4,7,5,3,6,1,2] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 0

[4,7,5,3,6,2,1] => [[[[.,[[.,.],.]],[.,.]],.],.] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 2

[4,7,5,6,1,2,3] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 0

[4,7,5,6,1,3,2] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 0

[4,7,5,6,2,1,3] => [[[.,[[.,.],[.,.]]],.],[.,.]] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 1

[4,7,5,6,2,3,1] => [[[.,[[.,.],[.,.]]],[.,.]],.] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 1

[4,7,5,6,3,1,2] => [[[.,[[.,.],[.,.]]],.],[.,.]] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 1

[4,7,5,6,3,2,1] => [[[[.,[[.,.],[.,.]]],.],.],.] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 3

[4,7,6,1,2,3,5] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 0

[4,7,6,1,2,5,3] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 0

[4,7,6,1,3,2,5] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 0

[4,7,6,1,3,5,2] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 0

[4,7,6,1,5,2,3] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 0

[4,7,6,1,5,3,2] => [[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 0

[4,7,6,2,1,3,5] => [[[.,[[.,.],.]],.],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 1

[4,7,6,2,1,5,3] => [[[.,[[.,.],.]],.],[[.,.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 1

[4,7,6,2,3,1,5] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 0

[4,7,6,2,3,5,1] => [[[.,[[.,.],.]],[.,[.,.]]],.] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 1

[4,7,6,2,5,1,3] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 0

[4,7,6,2,5,3,1] => [[[.,[[.,.],.]],[[.,.],.]],.] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 1

[4,7,6,3,1,2,5] => [[[.,[[.,.],.]],.],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 1

[4,7,6,3,1,5,2] => [[[.,[[.,.],.]],.],[[.,.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 1

[4,7,6,3,2,1,5] => [[[[.,[[.,.],.]],.],.],[.,.]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 2

[4,7,6,3,2,5,1] => [[[[.,[[.,.],.]],.],[.,.]],.] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2

[4,7,6,3,5,1,2] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 0

[4,7,6,3,5,2,1] => [[[[.,[[.,.],.]],[.,.]],.],.] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 2

[4,7,6,5,1,2,3] => [[.,[[[.,.],.],.]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 0

[4,7,6,5,1,3,2] => [[.,[[[.,.],.],.]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 0

[4,7,6,5,2,1,3] => [[[.,[[[.,.],.],.]],.],[.,.]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1

[4,7,6,5,2,3,1] => [[[.,[[[.,.],.],.]],[.,.]],.] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 1

[4,7,6,5,3,1,2] => [[[.,[[[.,.],.],.]],.],[.,.]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1

[4,7,6,5,3,2,1] => [[[[.,[[[.,.],.],.]],.],.],.] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 3

[5,1,2,3,4,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1

[5,1,2,3,4,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 1

[5,1,2,3,6,4,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 1

[5,1,2,3,6,7,4] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 1

[5,1,2,3,7,4,6] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 1

[5,1,2,3,7,6,4] => [[.,.],[.,[.,[[[.,.],.],.]]]] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1

[5,1,2,4,3,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 1

[5,1,2,4,3,7,6] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 1

[5,1,2,4,6,3,7] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1

[5,1,2,4,6,7,3] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 1

[5,1,2,4,7,3,6] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1

[5,1,2,4,7,6,3] => [[.,.],[.,[[.,[[.,.],.]],.]]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 1

[5,1,2,6,3,4,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 1

[5,1,2,6,3,7,4] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 1

[5,1,2,6,4,3,7] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 1

[5,1,2,6,4,7,3] => [[.,.],[.,[[[.,.],[.,.]],.]]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 1

[5,1,2,6,7,3,4] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1

[5,1,2,6,7,4,3] => [[.,.],[.,[[[.,[.,.]],.],.]]] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 1

[5,1,2,7,3,4,6] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 1

[5,1,2,7,3,6,4] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 1

[5,1,2,7,4,3,6] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 1

[5,1,2,7,4,6,3] => [[.,.],[.,[[[.,.],[.,.]],.]]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 1

[5,1,2,7,6,3,4] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 1

[5,1,2,7,6,4,3] => [[.,.],[.,[[[[.,.],.],.],.]]] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 1

[5,1,3,2,4,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 1

[5,1,3,2,4,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 1

[5,1,3,2,6,4,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1

[5,1,3,2,6,7,4] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 1

[5,1,3,2,7,4,6] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1

[5,1,3,2,7,6,4] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 1

[5,1,3,4,2,6,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

[5,1,3,4,2,7,6] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 1

[5,1,3,4,6,2,7] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1

[5,1,3,4,6,7,2] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 1

[5,1,3,4,7,2,6] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1

[5,1,3,4,7,6,2] => [[.,.],[[.,[.,[[.,.],.]]],.]] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 1

[5,1,3,6,2,4,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

[5,1,3,6,2,7,4] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 1

[5,1,3,6,4,2,7] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1

[5,1,3,6,4,7,2] => [[.,.],[[.,[[.,.],[.,.]]],.]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 1

[5,1,3,6,7,2,4] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1

[5,1,3,6,7,4,2] => [[.,.],[[.,[[.,[.,.]],.]],.]] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 1

[5,1,3,7,2,4,6] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

[5,1,3,7,2,6,4] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 1

[5,1,3,7,4,2,6] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1

[5,1,3,7,4,6,2] => [[.,.],[[.,[[.,.],[.,.]]],.]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 1

[5,1,3,7,6,2,4] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1

[5,1,3,7,6,4,2] => [[.,.],[[.,[[[.,.],.],.]],.]] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 1

[5,1,4,2,3,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 1

[5,1,4,2,3,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 1

[5,1,4,2,6,3,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1

[5,1,4,2,6,7,3] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 1

[5,1,4,2,7,3,6] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1

[5,1,4,2,7,6,3] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 1

[5,1,4,3,2,6,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1

[5,1,4,3,2,7,6] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 1

[5,1,4,3,6,2,7] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1

[5,1,4,3,6,7,2] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 1

[5,1,4,3,7,2,6] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1

[5,1,4,3,7,6,2] => [[.,.],[[[.,.],[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 1

[5,1,4,6,2,3,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

[5,1,4,6,2,7,3] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 1

[5,1,4,6,3,2,7] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[5,1,4,6,3,7,2] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 1

[5,1,4,6,7,2,3] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1

[5,1,4,6,7,3,2] => [[.,.],[[[.,[.,[.,.]]],.],.]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 1

[5,1,4,7,2,3,6] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

[5,1,4,7,2,6,3] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 1

[5,1,4,7,3,2,6] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[5,1,4,7,3,6,2] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 1

[5,1,4,7,6,2,3] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1

[5,1,4,7,6,3,2] => [[.,.],[[[.,[[.,.],.]],.],.]] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 1

[5,1,6,2,3,4,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 1

[5,1,6,2,3,7,4] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 1

[5,1,6,2,4,3,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1

[5,1,6,2,4,7,3] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 1

[5,1,6,2,7,3,4] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1

[5,1,6,2,7,4,3] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 1

[5,1,6,3,2,4,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1

[5,1,6,3,2,7,4] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 1

[5,1,6,3,4,2,7] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1

[5,1,6,3,4,7,2] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 1

[5,1,6,3,7,2,4] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1

[5,1,6,3,7,4,2] => [[.,.],[[[.,.],[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 1

[5,1,6,4,2,3,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1

[5,1,6,4,2,7,3] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 1

[5,1,6,4,3,2,7] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 1

[5,1,6,4,3,7,2] => [[.,.],[[[[.,.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 1

[5,1,6,4,7,2,3] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1

[5,1,6,4,7,3,2] => [[.,.],[[[[.,.],[.,.]],.],.]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 1

[5,1,6,7,2,3,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

[5,1,6,7,2,4,3] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 1

[5,1,6,7,3,2,4] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[5,1,6,7,3,4,2] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 1

[5,1,6,7,4,2,3] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[5,1,6,7,4,3,2] => [[.,.],[[[[.,[.,.]],.],.],.]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 1

[5,1,7,2,3,4,6] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 1

[5,1,7,2,3,6,4] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 1

[5,1,7,2,4,3,6] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1

[5,1,7,2,4,6,3] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 1

[5,1,7,2,6,3,4] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1

[5,1,7,2,6,4,3] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 1

[5,1,7,3,2,4,6] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1

[5,1,7,3,2,6,4] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 1

[5,1,7,3,4,2,6] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1

[5,1,7,3,4,6,2] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 1

[5,1,7,3,6,2,4] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1

[5,1,7,3,6,4,2] => [[.,.],[[[.,.],[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 1

[5,1,7,4,2,3,6] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1

[5,1,7,4,2,6,3] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 1

[5,1,7,4,3,2,6] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 1

[5,1,7,4,3,6,2] => [[.,.],[[[[.,.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 1

[5,1,7,4,6,2,3] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1

[5,1,7,4,6,3,2] => [[.,.],[[[[.,.],[.,.]],.],.]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 1

[5,1,7,6,2,3,4] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1

[5,1,7,6,2,4,3] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 1

[5,1,7,6,3,2,4] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 1

[5,1,7,6,3,4,2] => [[.,.],[[[[.,.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 1

[5,1,7,6,4,2,3] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 1

[5,1,7,6,4,3,2] => [[.,.],[[[[[.,.],.],.],.],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1

[5,2,1,3,4,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2

[5,2,1,3,4,7,6] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 2

[5,2,1,3,6,4,7] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 2

[5,2,1,3,6,7,4] => [[[.,.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[5,2,1,3,7,4,6] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 2

[5,2,1,3,7,6,4] => [[[.,.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 2

[5,2,1,4,3,6,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 2

[5,2,1,4,3,7,6] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 2

[5,2,1,4,6,3,7] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 2

[5,2,1,4,6,7,3] => [[[.,.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[5,2,1,4,7,3,6] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 2

[5,2,1,4,7,6,3] => [[[.,.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 2

[5,2,1,6,3,4,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 2

[5,2,1,6,3,7,4] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 2

[5,2,1,6,4,3,7] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 2

[5,2,1,6,4,7,3] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2

[5,2,1,6,7,3,4] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 2

[5,2,1,6,7,4,3] => [[[.,.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2

[5,2,1,7,3,4,6] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 2

[5,2,1,7,3,6,4] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 2

[5,2,1,7,4,3,6] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 2

[5,2,1,7,4,6,3] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2

[5,2,1,7,6,3,4] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 2

[5,2,1,7,6,4,3] => [[[.,.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 2

[5,2,3,1,4,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1

[5,2,3,1,4,7,6] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 1

[5,2,3,1,6,4,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[5,2,3,1,6,7,4] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 1

[5,2,3,1,7,4,6] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[5,2,3,1,7,6,4] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1

[5,2,3,4,1,6,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1

[5,2,3,4,1,7,6] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 1

[5,2,3,4,6,1,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1

[5,2,3,4,6,7,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2

[5,2,3,4,7,1,6] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1

[5,2,3,4,7,6,1] => [[[.,.],[.,[.,[[.,.],.]]]],.] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 2

[5,2,3,6,1,4,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1

[5,2,3,6,1,7,4] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 1

[5,2,3,6,4,1,7] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1

[5,2,3,6,4,7,1] => [[[.,.],[.,[[.,.],[.,.]]]],.] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 2

[5,2,3,6,7,1,4] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1

[5,2,3,6,7,4,1] => [[[.,.],[.,[[.,[.,.]],.]]],.] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 2

[5,2,3,7,1,4,6] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1

[5,2,3,7,1,6,4] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 1

[5,2,3,7,4,1,6] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1

[5,2,3,7,4,6,1] => [[[.,.],[.,[[.,.],[.,.]]]],.] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 2

[5,2,3,7,6,1,4] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1

[5,2,3,7,6,4,1] => [[[.,.],[.,[[[.,.],.],.]]],.] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 2

[5,2,4,1,3,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1

[5,2,4,1,3,7,6] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 1

[5,2,4,1,6,3,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[5,2,4,1,6,7,3] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 1

[5,2,4,1,7,3,6] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[5,2,4,1,7,6,3] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1

[5,2,4,3,1,6,7] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1

[5,2,4,3,1,7,6] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1

[5,2,4,3,6,1,7] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[5,2,4,3,6,7,1] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 2

[5,2,4,3,7,1,6] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[5,2,4,3,7,6,1] => [[[.,.],[[.,.],[[.,.],.]]],.] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 2

[5,2,4,6,1,3,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1

[5,2,4,6,1,7,3] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 1

[5,2,4,6,3,1,7] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[5,2,4,6,3,7,1] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[5,2,4,6,7,1,3] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1

[5,2,4,6,7,3,1] => [[[.,.],[[.,[.,[.,.]]],.]],.] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 2

[5,2,4,7,1,3,6] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1

[5,2,4,7,1,6,3] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 1

[5,2,4,7,3,1,6] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[5,2,4,7,3,6,1] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[5,2,4,7,6,1,3] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1

[5,2,4,7,6,3,1] => [[[.,.],[[.,[[.,.],.]],.]],.] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 2

[5,2,6,1,3,4,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1

[5,2,6,1,3,7,4] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 1

[5,2,6,1,4,3,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[5,2,6,1,4,7,3] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 1

[5,2,6,1,7,3,4] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[5,2,6,1,7,4,3] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1

[5,2,6,3,1,4,7] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1

[5,2,6,3,1,7,4] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1

[5,2,6,3,4,1,7] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[5,2,6,3,4,7,1] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 2

[5,2,6,3,7,1,4] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[5,2,6,3,7,4,1] => [[[.,.],[[.,.],[[.,.],.]]],.] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 2

[5,2,6,4,1,3,7] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1

[5,2,6,4,1,7,3] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1

[5,2,6,4,3,1,7] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1

[5,2,6,4,3,7,1] => [[[.,.],[[[.,.],.],[.,.]]],.] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 2

[5,2,6,4,7,1,3] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[5,2,6,4,7,3,1] => [[[.,.],[[[.,.],[.,.]],.]],.] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 2

[5,2,6,7,1,3,4] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1

[5,2,6,7,1,4,3] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 1

[5,2,6,7,3,1,4] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[5,2,6,7,3,4,1] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[5,2,6,7,4,1,3] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[5,2,6,7,4,3,1] => [[[.,.],[[[.,[.,.]],.],.]],.] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 2

[5,2,7,1,3,4,6] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1

[5,2,7,1,3,6,4] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 1

[5,2,7,1,4,3,6] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[5,2,7,1,4,6,3] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 1

[5,2,7,1,6,3,4] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[5,2,7,1,6,4,3] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1

[5,2,7,3,1,4,6] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1

[5,2,7,3,1,6,4] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1

[5,2,7,3,4,1,6] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[5,2,7,3,4,6,1] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 2

[5,2,7,3,6,1,4] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[5,2,7,3,6,4,1] => [[[.,.],[[.,.],[[.,.],.]]],.] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 2

[5,2,7,4,1,3,6] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1

[5,2,7,4,1,6,3] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1

[5,2,7,4,3,1,6] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1

[5,2,7,4,3,6,1] => [[[.,.],[[[.,.],.],[.,.]]],.] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 2

[5,2,7,4,6,1,3] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[5,2,7,4,6,3,1] => [[[.,.],[[[.,.],[.,.]],.]],.] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 2

[5,2,7,6,1,3,4] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1

[5,2,7,6,1,4,3] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1

[5,2,7,6,3,1,4] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1

[5,2,7,6,3,4,1] => [[[.,.],[[[.,.],.],[.,.]]],.] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 2

[5,2,7,6,4,1,3] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1

[5,2,7,6,4,3,1] => [[[.,.],[[[[.,.],.],.],.]],.] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 2

[5,3,1,2,4,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2

[5,3,1,2,4,7,6] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 2

[5,3,1,2,6,4,7] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 2

[5,3,1,2,6,7,4] => [[[.,.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[5,3,1,2,7,4,6] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 2

[5,3,1,2,7,6,4] => [[[.,.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 2

[5,3,1,4,2,6,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 2

[5,3,1,4,2,7,6] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 2

[5,3,1,4,6,2,7] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 2

[5,3,1,4,6,7,2] => [[[.,.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[5,3,1,4,7,2,6] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 2

[5,3,1,4,7,6,2] => [[[.,.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 2

[5,3,1,6,2,4,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 2

[5,3,1,6,2,7,4] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 2

[5,3,1,6,4,2,7] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 2

[5,3,1,6,4,7,2] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2

[5,3,1,6,7,2,4] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 2

[5,3,1,6,7,4,2] => [[[.,.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2

[5,3,1,7,2,4,6] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 2

[5,3,1,7,2,6,4] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 2

[5,3,1,7,4,2,6] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 2

[5,3,1,7,4,6,2] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2

[5,3,1,7,6,2,4] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 2

[5,3,1,7,6,4,2] => [[[.,.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 2

[5,3,2,1,4,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3

[5,3,2,1,4,7,6] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 3

[5,3,2,1,6,4,7] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 3

[5,3,2,1,6,7,4] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3

[5,3,2,1,7,4,6] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 3

[5,3,2,1,7,6,4] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 3

[5,3,2,4,1,6,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2

[5,3,2,4,1,7,6] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[5,3,2,4,6,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2

[5,3,2,4,6,7,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 3

[5,3,2,4,7,1,6] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2

[5,3,2,4,7,6,1] => [[[[.,.],.],[.,[[.,.],.]]],.] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 3

[5,3,2,6,1,4,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2

[5,3,2,6,1,7,4] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[5,3,2,6,4,1,7] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2

[5,3,2,6,4,7,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 3

[5,3,2,6,7,1,4] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2

[5,3,2,6,7,4,1] => [[[[.,.],.],[[.,[.,.]],.]],.] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,3,2,7,1,4,6] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2

[5,3,2,7,1,6,4] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[5,3,2,7,4,1,6] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2

[5,3,2,7,4,6,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 3

[5,3,2,7,6,1,4] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2

[5,3,2,7,6,4,1] => [[[[.,.],.],[[[.,.],.],.]],.] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 3

[5,3,4,1,2,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1

[5,3,4,1,2,7,6] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 1

[5,3,4,1,6,2,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[5,3,4,1,6,7,2] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 1

[5,3,4,1,7,2,6] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[5,3,4,1,7,6,2] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1

[5,3,4,2,1,6,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2

[5,3,4,2,1,7,6] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[5,3,4,2,6,1,7] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[5,3,4,2,6,7,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[5,3,4,2,7,1,6] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[5,3,4,2,7,6,1] => [[[[.,.],[.,.]],[[.,.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 2

[5,3,4,6,1,2,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1

[5,3,4,6,1,7,2] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 1

[5,3,4,6,2,1,7] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 2

[5,3,4,6,2,7,1] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[5,3,4,6,7,1,2] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1

[5,3,4,6,7,2,1] => [[[[.,.],[.,[.,[.,.]]]],.],.] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3

[5,3,4,7,1,2,6] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1

[5,3,4,7,1,6,2] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 1

[5,3,4,7,2,1,6] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 2

[5,3,4,7,2,6,1] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[5,3,4,7,6,1,2] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1

[5,3,4,7,6,2,1] => [[[[.,.],[.,[[.,.],.]]],.],.] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 3

[5,3,6,1,2,4,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1

[5,3,6,1,2,7,4] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 1

[5,3,6,1,4,2,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[5,3,6,1,4,7,2] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 1

[5,3,6,1,7,2,4] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[5,3,6,1,7,4,2] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1

[5,3,6,2,1,4,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2

[5,3,6,2,1,7,4] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[5,3,6,2,4,1,7] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[5,3,6,2,4,7,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[5,3,6,2,7,1,4] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[5,3,6,2,7,4,1] => [[[[.,.],[.,.]],[[.,.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 2

[5,3,6,4,1,2,7] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1

[5,3,6,4,1,7,2] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1

[5,3,6,4,2,1,7] => [[[[.,.],[[.,.],.]],.],[.,.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 2

[5,3,6,4,2,7,1] => [[[[.,.],[[.,.],.]],[.,.]],.] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[5,3,6,4,7,1,2] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[5,3,6,4,7,2,1] => [[[[.,.],[[.,.],[.,.]]],.],.] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[5,3,6,7,1,2,4] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1

[5,3,6,7,1,4,2] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 1

[5,3,6,7,2,1,4] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 2

[5,3,6,7,2,4,1] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[5,3,6,7,4,1,2] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[5,3,6,7,4,2,1] => [[[[.,.],[[.,[.,.]],.]],.],.] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 3

[5,3,7,1,2,4,6] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1

[5,3,7,1,2,6,4] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 1

[5,3,7,1,4,2,6] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[5,3,7,1,4,6,2] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 1

[5,3,7,1,6,2,4] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[5,3,7,1,6,4,2] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1

[5,3,7,2,1,4,6] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2

[5,3,7,2,1,6,4] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[5,3,7,2,4,1,6] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[5,3,7,2,4,6,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[5,3,7,2,6,1,4] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[5,3,7,2,6,4,1] => [[[[.,.],[.,.]],[[.,.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 2

[5,3,7,4,1,2,6] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1

[5,3,7,4,1,6,2] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1

[5,3,7,4,2,1,6] => [[[[.,.],[[.,.],.]],.],[.,.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 2

[5,3,7,4,2,6,1] => [[[[.,.],[[.,.],.]],[.,.]],.] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[5,3,7,4,6,1,2] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[5,3,7,4,6,2,1] => [[[[.,.],[[.,.],[.,.]]],.],.] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[5,3,7,6,1,2,4] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1

[5,3,7,6,1,4,2] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1

[5,3,7,6,2,1,4] => [[[[.,.],[[.,.],.]],.],[.,.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 2

[5,3,7,6,2,4,1] => [[[[.,.],[[.,.],.]],[.,.]],.] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[5,3,7,6,4,1,2] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1

[5,3,7,6,4,2,1] => [[[[.,.],[[[.,.],.],.]],.],.] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 3

[5,4,1,2,3,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2

[5,4,1,2,3,7,6] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 2

[5,4,1,2,6,3,7] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 2

[5,4,1,2,6,7,3] => [[[.,.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[5,4,1,2,7,3,6] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 2

[5,4,1,2,7,6,3] => [[[.,.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 2

[5,4,1,3,2,6,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 2

[5,4,1,3,2,7,6] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 2

[5,4,1,3,6,2,7] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 2

[5,4,1,3,6,7,2] => [[[.,.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[5,4,1,3,7,2,6] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 2

[5,4,1,3,7,6,2] => [[[.,.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 2

[5,4,1,6,2,3,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 2

[5,4,1,6,2,7,3] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 2

[5,4,1,6,3,2,7] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 2

[5,4,1,6,3,7,2] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2

[5,4,1,6,7,2,3] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 2

[5,4,1,6,7,3,2] => [[[.,.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2

[5,4,1,7,2,3,6] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 2

[5,4,1,7,2,6,3] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 2

[5,4,1,7,3,2,6] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 2

[5,4,1,7,3,6,2] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2

[5,4,1,7,6,2,3] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 2

[5,4,1,7,6,3,2] => [[[.,.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 2

[5,4,2,1,3,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3

[5,4,2,1,3,7,6] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 3

[5,4,2,1,6,3,7] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 3

[5,4,2,1,6,7,3] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3

[5,4,2,1,7,3,6] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 3

[5,4,2,1,7,6,3] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 3

[5,4,2,3,1,6,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2

[5,4,2,3,1,7,6] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[5,4,2,3,6,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2

[5,4,2,3,6,7,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 3

[5,4,2,3,7,1,6] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2

[5,4,2,3,7,6,1] => [[[[.,.],.],[.,[[.,.],.]]],.] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 3

[5,4,2,6,1,3,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2

[5,4,2,6,1,7,3] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[5,4,2,6,3,1,7] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2

[5,4,2,6,3,7,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 3

[5,4,2,6,7,1,3] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2

[5,4,2,6,7,3,1] => [[[[.,.],.],[[.,[.,.]],.]],.] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[5,4,2,7,1,3,6] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2

[5,4,2,7,1,6,3] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[5,4,2,7,3,1,6] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2

[5,4,2,7,3,6,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 3

[5,4,2,7,6,1,3] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2

[5,4,2,7,6,3,1] => [[[[.,.],.],[[[.,.],.],.]],.] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 3

[5,4,3,1,2,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3

[5,4,3,1,2,7,6] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 3

[5,4,3,1,6,2,7] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 3

[5,4,3,1,6,7,2] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3

[5,4,3,1,7,2,6] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 3

[5,4,3,1,7,6,2] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 3

[5,4,3,2,1,6,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 4

[5,4,3,2,1,7,6] => [[[[[.,.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 4

[5,4,3,2,6,1,7] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3

[5,4,3,2,6,7,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 4

[5,4,3,2,7,1,6] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3

[5,4,3,2,7,6,1] => [[[[[.,.],.],.],[[.,.],.]],.] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 4

[5,4,3,6,1,2,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2

[5,4,3,6,1,7,2] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[5,4,3,6,2,1,7] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3

[5,4,3,6,2,7,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3

[5,4,3,6,7,1,2] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2

[5,4,3,6,7,2,1] => [[[[[.,.],.],[.,[.,.]]],.],.] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 4

[5,4,3,7,1,2,6] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2

[5,4,3,7,1,6,2] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[5,4,3,7,2,1,6] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3

[5,4,3,7,2,6,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3

[5,4,3,7,6,1,2] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2

[5,4,3,7,6,2,1] => [[[[[.,.],.],[[.,.],.]],.],.] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[5,4,6,1,2,3,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1

[5,4,6,1,2,7,3] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 1

[5,4,6,1,3,2,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[5,4,6,1,3,7,2] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 1

[5,4,6,1,7,2,3] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[5,4,6,1,7,3,2] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1

[5,4,6,2,1,3,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2

[5,4,6,2,1,7,3] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[5,4,6,2,3,1,7] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[5,4,6,2,3,7,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[5,4,6,2,7,1,3] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[5,4,6,2,7,3,1] => [[[[.,.],[.,.]],[[.,.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 2

[5,4,6,3,1,2,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2

[5,4,6,3,1,7,2] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[5,4,6,3,2,1,7] => [[[[[.,.],[.,.]],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 3

[5,4,6,3,2,7,1] => [[[[[.,.],[.,.]],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3

[5,4,6,3,7,1,2] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[5,4,6,3,7,2,1] => [[[[[.,.],[.,.]],[.,.]],.],.] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[5,4,6,7,1,2,3] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1

[5,4,6,7,1,3,2] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 1

[5,4,6,7,2,1,3] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 2

[5,4,6,7,2,3,1] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[5,4,6,7,3,1,2] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 2

[5,4,6,7,3,2,1] => [[[[[.,.],[.,[.,.]]],.],.],.] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[5,4,7,1,2,3,6] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1

[5,4,7,1,2,6,3] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 1

[5,4,7,1,3,2,6] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[5,4,7,1,3,6,2] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 1

[5,4,7,1,6,2,3] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[5,4,7,1,6,3,2] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1

[5,4,7,2,1,3,6] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2

[5,4,7,2,1,6,3] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[5,4,7,2,3,1,6] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[5,4,7,2,3,6,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[5,4,7,2,6,1,3] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[5,4,7,2,6,3,1] => [[[[.,.],[.,.]],[[.,.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 2

[5,4,7,3,1,2,6] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2

[5,4,7,3,1,6,2] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[5,4,7,3,2,1,6] => [[[[[.,.],[.,.]],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 3

[5,4,7,3,2,6,1] => [[[[[.,.],[.,.]],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3

[5,4,7,3,6,1,2] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[5,4,7,3,6,2,1] => [[[[[.,.],[.,.]],[.,.]],.],.] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[5,4,7,6,1,2,3] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1

[5,4,7,6,1,3,2] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1

[5,4,7,6,2,1,3] => [[[[.,.],[[.,.],.]],.],[.,.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 2

[5,4,7,6,2,3,1] => [[[[.,.],[[.,.],.]],[.,.]],.] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[5,4,7,6,3,1,2] => [[[[.,.],[[.,.],.]],.],[.,.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 2

[5,4,7,6,3,2,1] => [[[[[.,.],[[.,.],.]],.],.],.] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 4

[5,6,1,2,3,4,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0

[5,6,1,2,3,7,4] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 0

[5,6,1,2,4,3,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 0

[5,6,1,2,4,7,3] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 0

[5,6,1,2,7,3,4] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 0

[5,6,1,2,7,4,3] => [[.,[.,.]],[.,[[[.,.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 0

[5,6,1,3,2,4,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 0

[5,6,1,3,2,7,4] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 0

[5,6,1,3,4,2,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 0

[5,6,1,3,4,7,2] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 0

[5,6,1,3,7,2,4] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 0

[5,6,1,3,7,4,2] => [[.,[.,.]],[[.,[[.,.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 0

[5,6,1,4,2,3,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 0

[5,6,1,4,2,7,3] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 0

[5,6,1,4,3,2,7] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 0

[5,6,1,4,3,7,2] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 0

[5,6,1,4,7,2,3] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 0

[5,6,1,4,7,3,2] => [[.,[.,.]],[[[.,[.,.]],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 0

[5,6,1,7,2,3,4] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 0

[5,6,1,7,2,4,3] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 0

[5,6,1,7,3,2,4] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 0

[5,6,1,7,3,4,2] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 0

[5,6,1,7,4,2,3] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 0

[5,6,1,7,4,3,2] => [[.,[.,.]],[[[[.,.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 0

[5,6,2,1,3,4,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1

[5,6,2,1,3,7,4] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 1

[5,6,2,1,4,3,7] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[5,6,2,1,4,7,3] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 1

[5,6,2,1,7,3,4] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[5,6,2,1,7,4,3] => [[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1

[5,6,2,3,1,4,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0

[5,6,2,3,1,7,4] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 0

[5,6,2,3,4,1,7] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0

[5,6,2,3,4,7,1] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 1

[5,6,2,3,7,1,4] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0

[5,6,2,3,7,4,1] => [[[.,[.,.]],[.,[[.,.],.]]],.] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 1

[5,6,2,4,1,3,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0

[5,6,2,4,1,7,3] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 0

[5,6,2,4,3,1,7] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 0

[5,6,2,4,3,7,1] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 1

[5,6,2,4,7,1,3] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0

[5,6,2,4,7,3,1] => [[[.,[.,.]],[[.,[.,.]],.]],.] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 1

[5,6,2,7,1,3,4] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0

[5,6,2,7,1,4,3] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 0

[5,6,2,7,3,1,4] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 0

[5,6,2,7,3,4,1] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 1

[5,6,2,7,4,1,3] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 0

[5,6,2,7,4,3,1] => [[[.,[.,.]],[[[.,.],.],.]],.] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 1

[5,6,3,1,2,4,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1

[5,6,3,1,2,7,4] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 1

[5,6,3,1,4,2,7] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[5,6,3,1,4,7,2] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 1

[5,6,3,1,7,2,4] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[5,6,3,1,7,4,2] => [[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1

[5,6,3,2,1,4,7] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 2

[5,6,3,2,1,7,4] => [[[[.,[.,.]],.],.],[[.,.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2

[5,6,3,2,4,1,7] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[5,6,3,2,4,7,1] => [[[[.,[.,.]],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2

[5,6,3,2,7,1,4] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[5,6,3,2,7,4,1] => [[[[.,[.,.]],.],[[.,.],.]],.] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 2

[5,6,3,4,1,2,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0

[5,6,3,4,1,7,2] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 0

[5,6,3,4,2,1,7] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1

[5,6,3,4,2,7,1] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 1

[5,6,3,4,7,1,2] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0

[5,6,3,4,7,2,1] => [[[[.,[.,.]],[.,[.,.]]],.],.] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 2

[5,6,3,7,1,2,4] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0

[5,6,3,7,1,4,2] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 0

[5,6,3,7,2,1,4] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1

[5,6,3,7,2,4,1] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 1

[5,6,3,7,4,1,2] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 0

[5,6,3,7,4,2,1] => [[[[.,[.,.]],[[.,.],.]],.],.] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 2

[5,6,4,1,2,3,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1

[5,6,4,1,2,7,3] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 1

[5,6,4,1,3,2,7] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[5,6,4,1,3,7,2] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 1

[5,6,4,1,7,2,3] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[5,6,4,1,7,3,2] => [[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1

[5,6,4,2,1,3,7] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 2

[5,6,4,2,1,7,3] => [[[[.,[.,.]],.],.],[[.,.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2

[5,6,4,2,3,1,7] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[5,6,4,2,3,7,1] => [[[[.,[.,.]],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2

[5,6,4,2,7,1,3] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[5,6,4,2,7,3,1] => [[[[.,[.,.]],.],[[.,.],.]],.] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 2

[5,6,4,3,1,2,7] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 2

[5,6,4,3,1,7,2] => [[[[.,[.,.]],.],.],[[.,.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2

[5,6,4,3,2,1,7] => [[[[[.,[.,.]],.],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 3

[5,6,4,3,2,7,1] => [[[[[.,[.,.]],.],.],[.,.]],.] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 3

[5,6,4,3,7,1,2] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[5,6,4,3,7,2,1] => [[[[[.,[.,.]],.],[.,.]],.],.] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[5,6,4,7,1,2,3] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0

[5,6,4,7,1,3,2] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 0

[5,6,4,7,2,1,3] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1

[5,6,4,7,2,3,1] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 1

[5,6,4,7,3,1,2] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1

[5,6,4,7,3,2,1] => [[[[[.,[.,.]],[.,.]],.],.],.] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 3

[5,6,7,1,2,3,4] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0

[5,6,7,1,2,4,3] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 0

[5,6,7,1,3,2,4] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 0

[5,6,7,1,3,4,2] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 0

[5,6,7,1,4,2,3] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 0

[5,6,7,1,4,3,2] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 0

[5,6,7,2,1,3,4] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1

[5,6,7,2,1,4,3] => [[[.,[.,[.,.]]],.],[[.,.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 1

[5,6,7,2,3,1,4] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 0

[5,6,7,2,3,4,1] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 1

[5,6,7,2,4,1,3] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 0

[5,6,7,2,4,3,1] => [[[.,[.,[.,.]]],[[.,.],.]],.] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 1

[5,6,7,3,1,2,4] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1

[5,6,7,3,1,4,2] => [[[.,[.,[.,.]]],.],[[.,.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 1

[5,6,7,3,2,1,4] => [[[[.,[.,[.,.]]],.],.],[.,.]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 2

[5,6,7,3,2,4,1] => [[[[.,[.,[.,.]]],.],[.,.]],.] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[5,6,7,3,4,1,2] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 0

[5,6,7,3,4,2,1] => [[[[.,[.,[.,.]]],[.,.]],.],.] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 2

[5,6,7,4,1,2,3] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1

[5,6,7,4,1,3,2] => [[[.,[.,[.,.]]],.],[[.,.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 1

[5,6,7,4,2,1,3] => [[[[.,[.,[.,.]]],.],.],[.,.]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 2

[5,6,7,4,2,3,1] => [[[[.,[.,[.,.]]],.],[.,.]],.] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2

[5,6,7,4,3,1,2] => [[[[.,[.,[.,.]]],.],.],[.,.]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 2

[5,6,7,4,3,2,1] => [[[[[.,[.,[.,.]]],.],.],.],.] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 4

[5,7,1,2,3,4,6] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0

[5,7,1,2,3,6,4] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 0

[5,7,1,2,4,3,6] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 0

[5,7,1,2,4,6,3] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 0

[5,7,1,2,6,3,4] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 0

[5,7,1,2,6,4,3] => [[.,[.,.]],[.,[[[.,.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 0

[5,7,1,3,2,4,6] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 0

[5,7,1,3,2,6,4] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 0

[5,7,1,3,4,2,6] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 0

[5,7,1,3,4,6,2] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 0

[5,7,1,3,6,2,4] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 0

[5,7,1,3,6,4,2] => [[.,[.,.]],[[.,[[.,.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 0

[5,7,1,4,2,3,6] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 0

[5,7,1,4,2,6,3] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 0

[5,7,1,4,3,2,6] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 0

[5,7,1,4,3,6,2] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 0

[5,7,1,4,6,2,3] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 0

[5,7,1,4,6,3,2] => [[.,[.,.]],[[[.,[.,.]],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 0

[5,7,1,6,2,3,4] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 0

[5,7,1,6,2,4,3] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 0

[5,7,1,6,3,2,4] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 0

[5,7,1,6,3,4,2] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 0

[5,7,1,6,4,2,3] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 0

[5,7,1,6,4,3,2] => [[.,[.,.]],[[[[.,.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 0

[5,7,2,1,3,4,6] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1

[5,7,2,1,3,6,4] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 1

[5,7,2,1,4,3,6] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[5,7,2,1,4,6,3] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 1

[5,7,2,1,6,3,4] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[5,7,2,1,6,4,3] => [[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1

[5,7,2,3,1,4,6] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0

[5,7,2,3,1,6,4] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 0

[5,7,2,3,4,1,6] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0

[5,7,2,3,4,6,1] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 1

[5,7,2,3,6,1,4] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0

[5,7,2,3,6,4,1] => [[[.,[.,.]],[.,[[.,.],.]]],.] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 1

[5,7,2,4,1,3,6] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0

[5,7,2,4,1,6,3] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 0

[5,7,2,4,3,1,6] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 0

[5,7,2,4,3,6,1] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 1

[5,7,2,4,6,1,3] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0

[5,7,2,4,6,3,1] => [[[.,[.,.]],[[.,[.,.]],.]],.] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 1

[5,7,2,6,1,3,4] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0

[5,7,2,6,1,4,3] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 0

[5,7,2,6,3,1,4] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 0

[5,7,2,6,3,4,1] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 1

[5,7,2,6,4,1,3] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 0

[5,7,2,6,4,3,1] => [[[.,[.,.]],[[[.,.],.],.]],.] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 1

[5,7,3,1,2,4,6] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1

[5,7,3,1,2,6,4] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 1

[5,7,3,1,4,2,6] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[5,7,3,1,4,6,2] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 1

[5,7,3,1,6,2,4] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[5,7,3,1,6,4,2] => [[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1

[5,7,3,2,1,4,6] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 2

[5,7,3,2,1,6,4] => [[[[.,[.,.]],.],.],[[.,.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2

[5,7,3,2,4,1,6] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[5,7,3,2,4,6,1] => [[[[.,[.,.]],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2

[5,7,3,2,6,1,4] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[5,7,3,2,6,4,1] => [[[[.,[.,.]],.],[[.,.],.]],.] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 2

[5,7,3,4,1,2,6] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0

[5,7,3,4,1,6,2] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 0

[5,7,3,4,2,1,6] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1

[5,7,3,4,2,6,1] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 1

[5,7,3,4,6,1,2] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0

[5,7,3,4,6,2,1] => [[[[.,[.,.]],[.,[.,.]]],.],.] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 2

[5,7,3,6,1,2,4] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0

[5,7,3,6,1,4,2] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 0

[5,7,3,6,2,1,4] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1

[5,7,3,6,2,4,1] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 1

[5,7,3,6,4,1,2] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 0

[5,7,3,6,4,2,1] => [[[[.,[.,.]],[[.,.],.]],.],.] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 2

[5,7,4,1,2,3,6] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1

[5,7,4,1,2,6,3] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 1

[5,7,4,1,3,2,6] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[5,7,4,1,3,6,2] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 1

[5,7,4,1,6,2,3] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[5,7,4,1,6,3,2] => [[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1

[5,7,4,2,1,3,6] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 2

[5,7,4,2,1,6,3] => [[[[.,[.,.]],.],.],[[.,.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2

[5,7,4,2,3,1,6] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[5,7,4,2,3,6,1] => [[[[.,[.,.]],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2

[5,7,4,2,6,1,3] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[5,7,4,2,6,3,1] => [[[[.,[.,.]],.],[[.,.],.]],.] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 2

[5,7,4,3,1,2,6] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 2

[5,7,4,3,1,6,2] => [[[[.,[.,.]],.],.],[[.,.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2

[5,7,4,3,2,1,6] => [[[[[.,[.,.]],.],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 3

[5,7,4,3,2,6,1] => [[[[[.,[.,.]],.],.],[.,.]],.] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 3

[5,7,4,3,6,1,2] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[5,7,4,3,6,2,1] => [[[[[.,[.,.]],.],[.,.]],.],.] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[5,7,4,6,1,2,3] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0

[5,7,4,6,1,3,2] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 0

[5,7,4,6,2,1,3] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1

[5,7,4,6,2,3,1] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 1

[5,7,4,6,3,1,2] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1

[5,7,4,6,3,2,1] => [[[[[.,[.,.]],[.,.]],.],.],.] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 3

[5,7,6,1,2,3,4] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 0

[5,7,6,1,2,4,3] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 0

[5,7,6,1,3,2,4] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 0

[5,7,6,1,3,4,2] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 0

[5,7,6,1,4,2,3] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 0

[5,7,6,1,4,3,2] => [[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 0

[5,7,6,2,1,3,4] => [[[.,[[.,.],.]],.],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 1

[5,7,6,2,1,4,3] => [[[.,[[.,.],.]],.],[[.,.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 1

[5,7,6,2,3,1,4] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 0

[5,7,6,2,3,4,1] => [[[.,[[.,.],.]],[.,[.,.]]],.] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 1

[5,7,6,2,4,1,3] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 0

[5,7,6,2,4,3,1] => [[[.,[[.,.],.]],[[.,.],.]],.] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 1

[5,7,6,3,1,2,4] => [[[.,[[.,.],.]],.],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 1

[5,7,6,3,1,4,2] => [[[.,[[.,.],.]],.],[[.,.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 1

[5,7,6,3,2,1,4] => [[[[.,[[.,.],.]],.],.],[.,.]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 2

[5,7,6,3,2,4,1] => [[[[.,[[.,.],.]],.],[.,.]],.] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2

[5,7,6,3,4,1,2] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 0

[5,7,6,3,4,2,1] => [[[[.,[[.,.],.]],[.,.]],.],.] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 2

[5,7,6,4,1,2,3] => [[[.,[[.,.],.]],.],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 1

[5,7,6,4,1,3,2] => [[[.,[[.,.],.]],.],[[.,.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 1

[5,7,6,4,2,1,3] => [[[[.,[[.,.],.]],.],.],[.,.]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 2

[5,7,6,4,2,3,1] => [[[[.,[[.,.],.]],.],[.,.]],.] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2

[5,7,6,4,3,1,2] => [[[[.,[[.,.],.]],.],.],[.,.]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 2

[5,7,6,4,3,2,1] => [[[[[.,[[.,.],.]],.],.],.],.] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 4

[6,1,2,3,4,5,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1

[6,1,2,3,4,7,5] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 1

[6,1,2,3,5,4,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 1

[6,1,2,3,5,7,4] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 1

[6,1,2,3,7,4,5] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 1

[6,1,2,3,7,5,4] => [[.,.],[.,[.,[[[.,.],.],.]]]] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1

[6,1,2,4,3,5,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 1

[6,1,2,4,3,7,5] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 1

[6,1,2,4,5,3,7] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1

[6,1,2,4,5,7,3] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 1

[6,1,2,4,7,3,5] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1

[6,1,2,4,7,5,3] => [[.,.],[.,[[.,[[.,.],.]],.]]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 1

[6,1,2,5,3,4,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 1

[6,1,2,5,3,7,4] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 1

[6,1,2,5,4,3,7] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 1

[6,1,2,5,4,7,3] => [[.,.],[.,[[[.,.],[.,.]],.]]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 1

[6,1,2,5,7,3,4] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1

[6,1,2,5,7,4,3] => [[.,.],[.,[[[.,[.,.]],.],.]]] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 1

[6,1,2,7,3,4,5] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 1

[6,1,2,7,3,5,4] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 1

[6,1,2,7,4,3,5] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 1

[6,1,2,7,4,5,3] => [[.,.],[.,[[[.,.],[.,.]],.]]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 1

[6,1,2,7,5,3,4] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 1

[6,1,2,7,5,4,3] => [[.,.],[.,[[[[.,.],.],.],.]]] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 1

[6,1,3,2,4,5,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 1

[6,1,3,2,4,7,5] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 1

[6,1,3,2,5,4,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1

[6,1,3,2,5,7,4] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 1

[6,1,3,2,7,4,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1

[6,1,3,2,7,5,4] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 1

[6,1,3,4,2,5,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

[6,1,3,4,2,7,5] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 1

[6,1,3,4,5,2,7] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1

[6,1,3,4,5,7,2] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 1

[6,1,3,4,7,2,5] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1

[6,1,3,4,7,5,2] => [[.,.],[[.,[.,[[.,.],.]]],.]] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 1

[6,1,3,5,2,4,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

[6,1,3,5,2,7,4] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 1

[6,1,3,5,4,2,7] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1

[6,1,3,5,4,7,2] => [[.,.],[[.,[[.,.],[.,.]]],.]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 1

[6,1,3,5,7,2,4] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1

[6,1,3,5,7,4,2] => [[.,.],[[.,[[.,[.,.]],.]],.]] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 1

[6,1,3,7,2,4,5] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

[6,1,3,7,2,5,4] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 1

[6,1,3,7,4,2,5] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1

[6,1,3,7,4,5,2] => [[.,.],[[.,[[.,.],[.,.]]],.]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 1

[6,1,3,7,5,2,4] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1

[6,1,3,7,5,4,2] => [[.,.],[[.,[[[.,.],.],.]],.]] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 1

[6,1,4,2,3,5,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 1

[6,1,4,2,3,7,5] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 1

[6,1,4,2,5,3,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1

[6,1,4,2,5,7,3] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 1

[6,1,4,2,7,3,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1

[6,1,4,2,7,5,3] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 1

[6,1,4,3,2,5,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1

[6,1,4,3,2,7,5] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 1

[6,1,4,3,5,2,7] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1

[6,1,4,3,5,7,2] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 1

[6,1,4,3,7,2,5] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1

[6,1,4,3,7,5,2] => [[.,.],[[[.,.],[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 1

[6,1,4,5,2,3,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

[6,1,4,5,2,7,3] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 1

[6,1,4,5,3,2,7] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[6,1,4,5,3,7,2] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 1

[6,1,4,5,7,2,3] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1

[6,1,4,5,7,3,2] => [[.,.],[[[.,[.,[.,.]]],.],.]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 1

[6,1,4,7,2,3,5] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

[6,1,4,7,2,5,3] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 1

[6,1,4,7,3,2,5] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[6,1,4,7,3,5,2] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 1

[6,1,4,7,5,2,3] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1

[6,1,4,7,5,3,2] => [[.,.],[[[.,[[.,.],.]],.],.]] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 1

[6,1,5,2,3,4,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 1

[6,1,5,2,3,7,4] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 1

[6,1,5,2,4,3,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1

[6,1,5,2,4,7,3] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 1

[6,1,5,2,7,3,4] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1

[6,1,5,2,7,4,3] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 1

[6,1,5,3,2,4,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1

[6,1,5,3,2,7,4] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 1

[6,1,5,3,4,2,7] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1

[6,1,5,3,4,7,2] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 1

[6,1,5,3,7,2,4] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1

[6,1,5,3,7,4,2] => [[.,.],[[[.,.],[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 1

[6,1,5,4,2,3,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1

[6,1,5,4,2,7,3] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 1

[6,1,5,4,3,2,7] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 1

[6,1,5,4,3,7,2] => [[.,.],[[[[.,.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 1

[6,1,5,4,7,2,3] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1

[6,1,5,4,7,3,2] => [[.,.],[[[[.,.],[.,.]],.],.]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 1

[6,1,5,7,2,3,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

[6,1,5,7,2,4,3] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 1

[6,1,5,7,3,2,4] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[6,1,5,7,3,4,2] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 1

[6,1,5,7,4,2,3] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[6,1,5,7,4,3,2] => [[.,.],[[[[.,[.,.]],.],.],.]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 1

[6,1,7,2,3,4,5] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 1

[6,1,7,2,3,5,4] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 1

[6,1,7,2,4,3,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1

[6,1,7,2,4,5,3] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 1

[6,1,7,2,5,3,4] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1

[6,1,7,2,5,4,3] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 1

[6,1,7,3,2,4,5] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1

[6,1,7,3,2,5,4] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 1

[6,1,7,3,4,2,5] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1

[6,1,7,3,4,5,2] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 1

[6,1,7,3,5,2,4] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1

[6,1,7,3,5,4,2] => [[.,.],[[[.,.],[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 1

[6,1,7,4,2,3,5] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1

[6,1,7,4,2,5,3] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 1

[6,1,7,4,3,2,5] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 1

[6,1,7,4,3,5,2] => [[.,.],[[[[.,.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 1

[6,1,7,4,5,2,3] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1

[6,1,7,4,5,3,2] => [[.,.],[[[[.,.],[.,.]],.],.]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 1

[6,1,7,5,2,3,4] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1

[6,1,7,5,2,4,3] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 1

[6,1,7,5,3,2,4] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 1

[6,1,7,5,3,4,2] => [[.,.],[[[[.,.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 1

[6,1,7,5,4,2,3] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 1

[6,1,7,5,4,3,2] => [[.,.],[[[[[.,.],.],.],.],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1

[6,2,1,3,4,5,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2

[6,2,1,3,4,7,5] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 2

[6,2,1,3,5,4,7] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 2

[6,2,1,3,5,7,4] => [[[.,.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[6,2,1,3,7,4,5] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 2

[6,2,1,3,7,5,4] => [[[.,.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 2

[6,2,1,4,3,5,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 2

[6,2,1,4,3,7,5] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 2

[6,2,1,4,5,3,7] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 2

[6,2,1,4,5,7,3] => [[[.,.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[6,2,1,4,7,3,5] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 2

[6,2,1,4,7,5,3] => [[[.,.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 2

[6,2,1,5,3,4,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 2

[6,2,1,5,3,7,4] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 2

[6,2,1,5,4,3,7] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 2

[6,2,1,5,4,7,3] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2

[6,2,1,5,7,3,4] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 2

[6,2,1,5,7,4,3] => [[[.,.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2

[6,2,1,7,3,4,5] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 2

[6,2,1,7,3,5,4] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 2

[6,2,1,7,4,3,5] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 2

[6,2,1,7,4,5,3] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2

[6,2,1,7,5,3,4] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 2

[6,2,1,7,5,4,3] => [[[.,.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 2

[6,2,3,1,4,5,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1

[6,2,3,1,4,7,5] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 1

[6,2,3,1,5,4,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[6,2,3,1,5,7,4] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 1

[6,2,3,1,7,4,5] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[6,2,3,1,7,5,4] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1

[6,2,3,4,1,5,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1

[6,2,3,4,1,7,5] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 1

[6,2,3,4,5,1,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1

[6,2,3,4,5,7,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2

[6,2,3,4,7,1,5] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1

[6,2,3,4,7,5,1] => [[[.,.],[.,[.,[[.,.],.]]]],.] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 2

[6,2,3,5,1,4,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1

[6,2,3,5,1,7,4] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 1

[6,2,3,5,4,1,7] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1

[6,2,3,5,4,7,1] => [[[.,.],[.,[[.,.],[.,.]]]],.] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 2

[6,2,3,5,7,1,4] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1

[6,2,3,5,7,4,1] => [[[.,.],[.,[[.,[.,.]],.]]],.] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 2

[6,2,3,7,1,4,5] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1

[6,2,3,7,1,5,4] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 1

[6,2,3,7,4,1,5] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1

[6,2,3,7,4,5,1] => [[[.,.],[.,[[.,.],[.,.]]]],.] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 2

[6,2,3,7,5,1,4] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1

[6,2,3,7,5,4,1] => [[[.,.],[.,[[[.,.],.],.]]],.] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 2

[6,2,4,1,3,5,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1

[6,2,4,1,3,7,5] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 1

[6,2,4,1,5,3,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[6,2,4,1,5,7,3] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 1

[6,2,4,1,7,3,5] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[6,2,4,1,7,5,3] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1

[6,2,4,3,1,5,7] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1

[6,2,4,3,1,7,5] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1

[6,2,4,3,5,1,7] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[6,2,4,3,5,7,1] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 2

[6,2,4,3,7,1,5] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[6,2,4,3,7,5,1] => [[[.,.],[[.,.],[[.,.],.]]],.] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 2

[6,2,4,5,1,3,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1

[6,2,4,5,1,7,3] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 1

[6,2,4,5,3,1,7] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[6,2,4,5,3,7,1] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[6,2,4,5,7,1,3] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1

[6,2,4,5,7,3,1] => [[[.,.],[[.,[.,[.,.]]],.]],.] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 2

[6,2,4,7,1,3,5] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1

[6,2,4,7,1,5,3] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 1

[6,2,4,7,3,1,5] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[6,2,4,7,3,5,1] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[6,2,4,7,5,1,3] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1

[6,2,4,7,5,3,1] => [[[.,.],[[.,[[.,.],.]],.]],.] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 2

[6,2,5,1,3,4,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1

[6,2,5,1,3,7,4] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 1

[6,2,5,1,4,3,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[6,2,5,1,4,7,3] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 1

[6,2,5,1,7,3,4] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[6,2,5,1,7,4,3] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1

[6,2,5,3,1,4,7] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1

[6,2,5,3,1,7,4] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1

[6,2,5,3,4,1,7] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[6,2,5,3,4,7,1] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 2

[6,2,5,3,7,1,4] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[6,2,5,3,7,4,1] => [[[.,.],[[.,.],[[.,.],.]]],.] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 2

[6,2,5,4,1,3,7] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1

[6,2,5,4,1,7,3] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1

[6,2,5,4,3,1,7] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1

[6,2,5,4,3,7,1] => [[[.,.],[[[.,.],.],[.,.]]],.] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 2

[6,2,5,4,7,1,3] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[6,2,5,4,7,3,1] => [[[.,.],[[[.,.],[.,.]],.]],.] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 2

[6,2,5,7,1,3,4] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1

[6,2,5,7,1,4,3] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 1

[6,2,5,7,3,1,4] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[6,2,5,7,3,4,1] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[6,2,5,7,4,1,3] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[6,2,5,7,4,3,1] => [[[.,.],[[[.,[.,.]],.],.]],.] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 2

[6,2,7,1,3,4,5] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1

[6,2,7,1,3,5,4] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 1

[6,2,7,1,4,3,5] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[6,2,7,1,4,5,3] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 1

[6,2,7,1,5,3,4] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[6,2,7,1,5,4,3] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1

[6,2,7,3,1,4,5] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1

[6,2,7,3,1,5,4] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1

[6,2,7,3,4,1,5] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[6,2,7,3,4,5,1] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 2

[6,2,7,3,5,1,4] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[6,2,7,3,5,4,1] => [[[.,.],[[.,.],[[.,.],.]]],.] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 2

[6,2,7,4,1,3,5] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1

[6,2,7,4,1,5,3] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1

[6,2,7,4,3,1,5] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1

[6,2,7,4,3,5,1] => [[[.,.],[[[.,.],.],[.,.]]],.] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 2

[6,2,7,4,5,1,3] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[6,2,7,4,5,3,1] => [[[.,.],[[[.,.],[.,.]],.]],.] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 2

[6,2,7,5,1,3,4] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1

[6,2,7,5,1,4,3] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1

[6,2,7,5,3,1,4] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1

[6,2,7,5,3,4,1] => [[[.,.],[[[.,.],.],[.,.]]],.] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 2

[6,2,7,5,4,1,3] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1

[6,2,7,5,4,3,1] => [[[.,.],[[[[.,.],.],.],.]],.] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 2

[6,3,1,2,4,5,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2

[6,3,1,2,4,7,5] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 2

[6,3,1,2,5,4,7] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 2

[6,3,1,2,5,7,4] => [[[.,.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[6,3,1,2,7,4,5] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 2

[6,3,1,2,7,5,4] => [[[.,.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 2

[6,3,1,4,2,5,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 2

[6,3,1,4,2,7,5] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 2

[6,3,1,4,5,2,7] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 2

[6,3,1,4,5,7,2] => [[[.,.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[6,3,1,4,7,2,5] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 2

[6,3,1,4,7,5,2] => [[[.,.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 2

[6,3,1,5,2,4,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 2

[6,3,1,5,2,7,4] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 2

[6,3,1,5,4,2,7] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 2

[6,3,1,5,4,7,2] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2

[6,3,1,5,7,2,4] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 2

[6,3,1,5,7,4,2] => [[[.,.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2

[6,3,1,7,2,4,5] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 2

[6,3,1,7,2,5,4] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 2

[6,3,1,7,4,2,5] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 2

[6,3,1,7,4,5,2] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2

[6,3,1,7,5,2,4] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 2

[6,3,1,7,5,4,2] => [[[.,.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 2

[6,3,2,1,4,5,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3

[6,3,2,1,4,7,5] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 3

[6,3,2,1,5,4,7] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 3

[6,3,2,1,5,7,4] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3

[6,3,2,1,7,4,5] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 3

[6,3,2,1,7,5,4] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 3

[6,3,2,4,1,5,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2

[6,3,2,4,1,7,5] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[6,3,2,4,5,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2

[6,3,2,4,5,7,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 3

[6,3,2,4,7,1,5] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2

[6,3,2,4,7,5,1] => [[[[.,.],.],[.,[[.,.],.]]],.] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 3

[6,3,2,5,1,4,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2

[6,3,2,5,1,7,4] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[6,3,2,5,4,1,7] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2

[6,3,2,5,4,7,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 3

[6,3,2,5,7,1,4] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2

[6,3,2,5,7,4,1] => [[[[.,.],.],[[.,[.,.]],.]],.] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,3,2,7,1,4,5] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2

[6,3,2,7,1,5,4] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[6,3,2,7,4,1,5] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2

[6,3,2,7,4,5,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 3

[6,3,2,7,5,1,4] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2

[6,3,2,7,5,4,1] => [[[[.,.],.],[[[.,.],.],.]],.] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 3

[6,3,4,1,2,5,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1

[6,3,4,1,2,7,5] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 1

[6,3,4,1,5,2,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[6,3,4,1,5,7,2] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 1

[6,3,4,1,7,2,5] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[6,3,4,1,7,5,2] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1

[6,3,4,2,1,5,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2

[6,3,4,2,1,7,5] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[6,3,4,2,5,1,7] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[6,3,4,2,5,7,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[6,3,4,2,7,1,5] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[6,3,4,2,7,5,1] => [[[[.,.],[.,.]],[[.,.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 2

[6,3,4,5,1,2,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1

[6,3,4,5,1,7,2] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 1

[6,3,4,5,2,1,7] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 2

[6,3,4,5,2,7,1] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[6,3,4,5,7,1,2] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1

[6,3,4,5,7,2,1] => [[[[.,.],[.,[.,[.,.]]]],.],.] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3

[6,3,4,7,1,2,5] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1

[6,3,4,7,1,5,2] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 1

[6,3,4,7,2,1,5] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 2

[6,3,4,7,2,5,1] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[6,3,4,7,5,1,2] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1

[6,3,4,7,5,2,1] => [[[[.,.],[.,[[.,.],.]]],.],.] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 3

[6,3,5,1,2,4,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1

[6,3,5,1,2,7,4] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 1

[6,3,5,1,4,2,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[6,3,5,1,4,7,2] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 1

[6,3,5,1,7,2,4] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[6,3,5,1,7,4,2] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1

[6,3,5,2,1,4,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2

[6,3,5,2,1,7,4] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[6,3,5,2,4,1,7] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[6,3,5,2,4,7,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[6,3,5,2,7,1,4] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[6,3,5,2,7,4,1] => [[[[.,.],[.,.]],[[.,.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 2

[6,3,5,4,1,2,7] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1

[6,3,5,4,1,7,2] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1

[6,3,5,4,2,1,7] => [[[[.,.],[[.,.],.]],.],[.,.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 2

[6,3,5,4,2,7,1] => [[[[.,.],[[.,.],.]],[.,.]],.] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[6,3,5,4,7,1,2] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[6,3,5,4,7,2,1] => [[[[.,.],[[.,.],[.,.]]],.],.] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[6,3,5,7,1,2,4] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1

[6,3,5,7,1,4,2] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 1

[6,3,5,7,2,1,4] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 2

[6,3,5,7,2,4,1] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[6,3,5,7,4,1,2] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[6,3,5,7,4,2,1] => [[[[.,.],[[.,[.,.]],.]],.],.] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 3

[6,3,7,1,2,4,5] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1

[6,3,7,1,2,5,4] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 1

[6,3,7,1,4,2,5] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[6,3,7,1,4,5,2] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 1

[6,3,7,1,5,2,4] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[6,3,7,1,5,4,2] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1

[6,3,7,2,1,4,5] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2

[6,3,7,2,1,5,4] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[6,3,7,2,4,1,5] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[6,3,7,2,4,5,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[6,3,7,2,5,1,4] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[6,3,7,2,5,4,1] => [[[[.,.],[.,.]],[[.,.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 2

[6,3,7,4,1,2,5] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1

[6,3,7,4,1,5,2] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1

[6,3,7,4,2,1,5] => [[[[.,.],[[.,.],.]],.],[.,.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 2

[6,3,7,4,2,5,1] => [[[[.,.],[[.,.],.]],[.,.]],.] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[6,3,7,4,5,1,2] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[6,3,7,4,5,2,1] => [[[[.,.],[[.,.],[.,.]]],.],.] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[6,3,7,5,1,2,4] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1

[6,3,7,5,1,4,2] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1

[6,3,7,5,2,1,4] => [[[[.,.],[[.,.],.]],.],[.,.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 2

[6,3,7,5,2,4,1] => [[[[.,.],[[.,.],.]],[.,.]],.] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[6,3,7,5,4,1,2] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1

[6,3,7,5,4,2,1] => [[[[.,.],[[[.,.],.],.]],.],.] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 3

[6,4,1,2,3,5,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2

[6,4,1,2,3,7,5] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 2

[6,4,1,2,5,3,7] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 2

[6,4,1,2,5,7,3] => [[[.,.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[6,4,1,2,7,3,5] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 2

[6,4,1,2,7,5,3] => [[[.,.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 2

[6,4,1,3,2,5,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 2

[6,4,1,3,2,7,5] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 2

[6,4,1,3,5,2,7] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 2

[6,4,1,3,5,7,2] => [[[.,.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[6,4,1,3,7,2,5] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 2

[6,4,1,3,7,5,2] => [[[.,.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 2

[6,4,1,5,2,3,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 2

[6,4,1,5,2,7,3] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 2

[6,4,1,5,3,2,7] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 2

[6,4,1,5,3,7,2] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2

[6,4,1,5,7,2,3] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 2

[6,4,1,5,7,3,2] => [[[.,.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2

[6,4,1,7,2,3,5] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 2

[6,4,1,7,2,5,3] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 2

[6,4,1,7,3,2,5] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 2

[6,4,1,7,3,5,2] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2

[6,4,1,7,5,2,3] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 2

[6,4,1,7,5,3,2] => [[[.,.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 2

[6,4,2,1,3,5,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3

[6,4,2,1,3,7,5] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 3

[6,4,2,1,5,3,7] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 3

[6,4,2,1,5,7,3] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3

[6,4,2,1,7,3,5] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 3

[6,4,2,1,7,5,3] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 3

[6,4,2,3,1,5,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2

[6,4,2,3,1,7,5] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[6,4,2,3,5,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2

[6,4,2,3,5,7,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 3

[6,4,2,3,7,1,5] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2

[6,4,2,3,7,5,1] => [[[[.,.],.],[.,[[.,.],.]]],.] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 3

[6,4,2,5,1,3,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2

[6,4,2,5,1,7,3] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[6,4,2,5,3,1,7] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2

[6,4,2,5,3,7,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 3

[6,4,2,5,7,1,3] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2

[6,4,2,5,7,3,1] => [[[[.,.],.],[[.,[.,.]],.]],.] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,4,2,7,1,3,5] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2

[6,4,2,7,1,5,3] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[6,4,2,7,3,1,5] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2

[6,4,2,7,3,5,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 3

[6,4,2,7,5,1,3] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2

[6,4,2,7,5,3,1] => [[[[.,.],.],[[[.,.],.],.]],.] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 3

[6,4,3,1,2,5,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3

[6,4,3,1,2,7,5] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 3

[6,4,3,1,5,2,7] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 3

[6,4,3,1,5,7,2] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3

[6,4,3,1,7,2,5] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 3

[6,4,3,1,7,5,2] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 3

[6,4,3,2,1,5,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 4

[6,4,3,2,1,7,5] => [[[[[.,.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 4

[6,4,3,2,5,1,7] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3

[6,4,3,2,5,7,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 4

[6,4,3,2,7,1,5] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3

[6,4,3,2,7,5,1] => [[[[[.,.],.],.],[[.,.],.]],.] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 4

[6,4,3,5,1,2,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2

[6,4,3,5,1,7,2] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[6,4,3,5,2,1,7] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3

[6,4,3,5,2,7,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3

[6,4,3,5,7,1,2] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2

[6,4,3,5,7,2,1] => [[[[[.,.],.],[.,[.,.]]],.],.] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 4

[6,4,3,7,1,2,5] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2

[6,4,3,7,1,5,2] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[6,4,3,7,2,1,5] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3

[6,4,3,7,2,5,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3

[6,4,3,7,5,1,2] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2

[6,4,3,7,5,2,1] => [[[[[.,.],.],[[.,.],.]],.],.] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[6,4,5,1,2,3,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1

[6,4,5,1,2,7,3] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 1

[6,4,5,1,3,2,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[6,4,5,1,3,7,2] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 1

[6,4,5,1,7,2,3] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[6,4,5,1,7,3,2] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1

[6,4,5,2,1,3,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2

[6,4,5,2,1,7,3] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[6,4,5,2,3,1,7] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[6,4,5,2,3,7,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[6,4,5,2,7,1,3] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[6,4,5,2,7,3,1] => [[[[.,.],[.,.]],[[.,.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 2

[6,4,5,3,1,2,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2

[6,4,5,3,1,7,2] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[6,4,5,3,2,1,7] => [[[[[.,.],[.,.]],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 3

[6,4,5,3,2,7,1] => [[[[[.,.],[.,.]],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3

[6,4,5,3,7,1,2] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[6,4,5,3,7,2,1] => [[[[[.,.],[.,.]],[.,.]],.],.] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[6,4,5,7,1,2,3] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1

[6,4,5,7,1,3,2] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 1

[6,4,5,7,2,1,3] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 2

[6,4,5,7,2,3,1] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[6,4,5,7,3,1,2] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 2

[6,4,5,7,3,2,1] => [[[[[.,.],[.,[.,.]]],.],.],.] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[6,4,7,1,2,3,5] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1

[6,4,7,1,2,5,3] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 1

[6,4,7,1,3,2,5] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[6,4,7,1,3,5,2] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 1

[6,4,7,1,5,2,3] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[6,4,7,1,5,3,2] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1

[6,4,7,2,1,3,5] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2

[6,4,7,2,1,5,3] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[6,4,7,2,3,1,5] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[6,4,7,2,3,5,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[6,4,7,2,5,1,3] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[6,4,7,2,5,3,1] => [[[[.,.],[.,.]],[[.,.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 2

[6,4,7,3,1,2,5] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2

[6,4,7,3,1,5,2] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[6,4,7,3,2,1,5] => [[[[[.,.],[.,.]],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 3

[6,4,7,3,2,5,1] => [[[[[.,.],[.,.]],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3

[6,4,7,3,5,1,2] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[6,4,7,3,5,2,1] => [[[[[.,.],[.,.]],[.,.]],.],.] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[6,4,7,5,1,2,3] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1

[6,4,7,5,1,3,2] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1

[6,4,7,5,2,1,3] => [[[[.,.],[[.,.],.]],.],[.,.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 2

[6,4,7,5,2,3,1] => [[[[.,.],[[.,.],.]],[.,.]],.] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[6,4,7,5,3,1,2] => [[[[.,.],[[.,.],.]],.],[.,.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 2

[6,4,7,5,3,2,1] => [[[[[.,.],[[.,.],.]],.],.],.] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 4

[6,5,1,2,3,4,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2

[6,5,1,2,3,7,4] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 2

[6,5,1,2,4,3,7] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 2

[6,5,1,2,4,7,3] => [[[.,.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[6,5,1,2,7,3,4] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 2

[6,5,1,2,7,4,3] => [[[.,.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 2

[6,5,1,3,2,4,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 2

[6,5,1,3,2,7,4] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 2

[6,5,1,3,4,2,7] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 2

[6,5,1,3,4,7,2] => [[[.,.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[6,5,1,3,7,2,4] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 2

[6,5,1,3,7,4,2] => [[[.,.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 2

[6,5,1,4,2,3,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 2

[6,5,1,4,2,7,3] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 2

[6,5,1,4,3,2,7] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 2

[6,5,1,4,3,7,2] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2

[6,5,1,4,7,2,3] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 2

[6,5,1,4,7,3,2] => [[[.,.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2

[6,5,1,7,2,3,4] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 2

[6,5,1,7,2,4,3] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 2

[6,5,1,7,3,2,4] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 2

[6,5,1,7,3,4,2] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2

[6,5,1,7,4,2,3] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 2

[6,5,1,7,4,3,2] => [[[.,.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 2

[6,5,2,1,3,4,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3

[6,5,2,1,3,7,4] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 3

[6,5,2,1,4,3,7] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 3

[6,5,2,1,4,7,3] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3

[6,5,2,1,7,3,4] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 3

[6,5,2,1,7,4,3] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 3

[6,5,2,3,1,4,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2

[6,5,2,3,1,7,4] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[6,5,2,3,4,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2

[6,5,2,3,4,7,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 3

[6,5,2,3,7,1,4] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2

[6,5,2,3,7,4,1] => [[[[.,.],.],[.,[[.,.],.]]],.] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 3

[6,5,2,4,1,3,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2

[6,5,2,4,1,7,3] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[6,5,2,4,3,1,7] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2

[6,5,2,4,3,7,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 3

[6,5,2,4,7,1,3] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2

[6,5,2,4,7,3,1] => [[[[.,.],.],[[.,[.,.]],.]],.] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[6,5,2,7,1,3,4] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2

[6,5,2,7,1,4,3] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[6,5,2,7,3,1,4] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2

[6,5,2,7,3,4,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 3

[6,5,2,7,4,1,3] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2

[6,5,2,7,4,3,1] => [[[[.,.],.],[[[.,.],.],.]],.] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 3

[6,5,3,1,2,4,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3

[6,5,3,1,2,7,4] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 3

[6,5,3,1,4,2,7] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 3

[6,5,3,1,4,7,2] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3

[6,5,3,1,7,2,4] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 3

[6,5,3,1,7,4,2] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 3

[6,5,3,2,1,4,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 4

[6,5,3,2,1,7,4] => [[[[[.,.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 4

[6,5,3,2,4,1,7] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3

[6,5,3,2,4,7,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 4

[6,5,3,2,7,1,4] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3

[6,5,3,2,7,4,1] => [[[[[.,.],.],.],[[.,.],.]],.] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 4

[6,5,3,4,1,2,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2

[6,5,3,4,1,7,2] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[6,5,3,4,2,1,7] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3

[6,5,3,4,2,7,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3

[6,5,3,4,7,1,2] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2

[6,5,3,4,7,2,1] => [[[[[.,.],.],[.,[.,.]]],.],.] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 4

[6,5,3,7,1,2,4] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2

[6,5,3,7,1,4,2] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[6,5,3,7,2,1,4] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3

[6,5,3,7,2,4,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3

[6,5,3,7,4,1,2] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2

[6,5,3,7,4,2,1] => [[[[[.,.],.],[[.,.],.]],.],.] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[6,5,4,1,2,3,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3

[6,5,4,1,2,7,3] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 3

[6,5,4,1,3,2,7] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 3

[6,5,4,1,3,7,2] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3

[6,5,4,1,7,2,3] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 3

[6,5,4,1,7,3,2] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 3

[6,5,4,2,1,3,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 4

[6,5,4,2,1,7,3] => [[[[[.,.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 4

[6,5,4,2,3,1,7] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3

[6,5,4,2,3,7,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 4

[6,5,4,2,7,1,3] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3

[6,5,4,2,7,3,1] => [[[[[.,.],.],.],[[.,.],.]],.] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 4

[6,5,4,3,1,2,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 4

[6,5,4,3,1,7,2] => [[[[[.,.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 4

[6,5,4,3,2,1,7] => [[[[[[.,.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 5

[6,5,4,3,2,7,1] => [[[[[[.,.],.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 5

[6,5,4,3,7,1,2] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3

[6,5,4,3,7,2,1] => [[[[[[.,.],.],.],[.,.]],.],.] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 5

[6,5,4,7,1,2,3] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2

[6,5,4,7,1,3,2] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[6,5,4,7,2,1,3] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3

[6,5,4,7,2,3,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3

[6,5,4,7,3,1,2] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3

[6,5,4,7,3,2,1] => [[[[[[.,.],.],[.,.]],.],.],.] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 5

[6,5,7,1,2,3,4] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1

[6,5,7,1,2,4,3] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 1

[6,5,7,1,3,2,4] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[6,5,7,1,3,4,2] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 1

[6,5,7,1,4,2,3] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[6,5,7,1,4,3,2] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1

[6,5,7,2,1,3,4] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2

[6,5,7,2,1,4,3] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[6,5,7,2,3,1,4] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[6,5,7,2,3,4,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[6,5,7,2,4,1,3] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[6,5,7,2,4,3,1] => [[[[.,.],[.,.]],[[.,.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 2

[6,5,7,3,1,2,4] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2

[6,5,7,3,1,4,2] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[6,5,7,3,2,1,4] => [[[[[.,.],[.,.]],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 3

[6,5,7,3,2,4,1] => [[[[[.,.],[.,.]],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3

[6,5,7,3,4,1,2] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[6,5,7,3,4,2,1] => [[[[[.,.],[.,.]],[.,.]],.],.] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[6,5,7,4,1,2,3] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2

[6,5,7,4,1,3,2] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[6,5,7,4,2,1,3] => [[[[[.,.],[.,.]],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 3

[6,5,7,4,2,3,1] => [[[[[.,.],[.,.]],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3

[6,5,7,4,3,1,2] => [[[[[.,.],[.,.]],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 3

[6,5,7,4,3,2,1] => [[[[[[.,.],[.,.]],.],.],.],.] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[6,7,1,2,3,4,5] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0

[6,7,1,2,3,5,4] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 0

[6,7,1,2,4,3,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 0

[6,7,1,2,4,5,3] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 0

[6,7,1,2,5,3,4] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 0

[6,7,1,2,5,4,3] => [[.,[.,.]],[.,[[[.,.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 0

[6,7,1,3,2,4,5] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 0

[6,7,1,3,2,5,4] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 0

[6,7,1,3,4,2,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 0

[6,7,1,3,4,5,2] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 0

[6,7,1,3,5,2,4] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 0

[6,7,1,3,5,4,2] => [[.,[.,.]],[[.,[[.,.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 0

[6,7,1,4,2,3,5] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 0

[6,7,1,4,2,5,3] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 0

[6,7,1,4,3,2,5] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 0

[6,7,1,4,3,5,2] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 0

[6,7,1,4,5,2,3] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 0

[6,7,1,4,5,3,2] => [[.,[.,.]],[[[.,[.,.]],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 0

[6,7,1,5,2,3,4] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 0

[6,7,1,5,2,4,3] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 0

[6,7,1,5,3,2,4] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 0

[6,7,1,5,3,4,2] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 0

[6,7,1,5,4,2,3] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 0

[6,7,1,5,4,3,2] => [[.,[.,.]],[[[[.,.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 0

[6,7,2,1,3,4,5] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1

[6,7,2,1,3,5,4] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 1

[6,7,2,1,4,3,5] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[6,7,2,1,4,5,3] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 1

[6,7,2,1,5,3,4] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[6,7,2,1,5,4,3] => [[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1

[6,7,2,3,1,4,5] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0

[6,7,2,3,1,5,4] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 0

[6,7,2,3,4,1,5] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0

[6,7,2,3,4,5,1] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 1

[6,7,2,3,5,1,4] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0

[6,7,2,3,5,4,1] => [[[.,[.,.]],[.,[[.,.],.]]],.] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 1

[6,7,2,4,1,3,5] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0

[6,7,2,4,1,5,3] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 0

[6,7,2,4,3,1,5] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 0

[6,7,2,4,3,5,1] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 1

[6,7,2,4,5,1,3] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0

[6,7,2,4,5,3,1] => [[[.,[.,.]],[[.,[.,.]],.]],.] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 1

[6,7,2,5,1,3,4] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0

[6,7,2,5,1,4,3] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 0

[6,7,2,5,3,1,4] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 0

[6,7,2,5,3,4,1] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 1

[6,7,2,5,4,1,3] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 0

[6,7,2,5,4,3,1] => [[[.,[.,.]],[[[.,.],.],.]],.] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 1

[6,7,3,1,2,4,5] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1

[6,7,3,1,2,5,4] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 1

[6,7,3,1,4,2,5] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[6,7,3,1,4,5,2] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 1

[6,7,3,1,5,2,4] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[6,7,3,1,5,4,2] => [[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1

[6,7,3,2,1,4,5] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 2

[6,7,3,2,1,5,4] => [[[[.,[.,.]],.],.],[[.,.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2

[6,7,3,2,4,1,5] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[6,7,3,2,4,5,1] => [[[[.,[.,.]],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2

[6,7,3,2,5,1,4] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[6,7,3,2,5,4,1] => [[[[.,[.,.]],.],[[.,.],.]],.] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 2

[6,7,3,4,1,2,5] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0

[6,7,3,4,1,5,2] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 0

[6,7,3,4,2,1,5] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1

[6,7,3,4,2,5,1] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 1

[6,7,3,4,5,1,2] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0

[6,7,3,4,5,2,1] => [[[[.,[.,.]],[.,[.,.]]],.],.] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 2

[6,7,3,5,1,2,4] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0

[6,7,3,5,1,4,2] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 0

[6,7,3,5,2,1,4] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1

[6,7,3,5,2,4,1] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 1

[6,7,3,5,4,1,2] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 0

[6,7,3,5,4,2,1] => [[[[.,[.,.]],[[.,.],.]],.],.] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 2

[6,7,4,1,2,3,5] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1

[6,7,4,1,2,5,3] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 1

[6,7,4,1,3,2,5] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[6,7,4,1,3,5,2] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 1

[6,7,4,1,5,2,3] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[6,7,4,1,5,3,2] => [[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1

[6,7,4,2,1,3,5] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 2

[6,7,4,2,1,5,3] => [[[[.,[.,.]],.],.],[[.,.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2

[6,7,4,2,3,1,5] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[6,7,4,2,3,5,1] => [[[[.,[.,.]],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2

[6,7,4,2,5,1,3] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[6,7,4,2,5,3,1] => [[[[.,[.,.]],.],[[.,.],.]],.] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 2

[6,7,4,3,1,2,5] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 2

[6,7,4,3,1,5,2] => [[[[.,[.,.]],.],.],[[.,.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2

[6,7,4,3,2,1,5] => [[[[[.,[.,.]],.],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 3

[6,7,4,3,2,5,1] => [[[[[.,[.,.]],.],.],[.,.]],.] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 3

[6,7,4,3,5,1,2] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[6,7,4,3,5,2,1] => [[[[[.,[.,.]],.],[.,.]],.],.] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[6,7,4,5,1,2,3] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0

[6,7,4,5,1,3,2] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 0

[6,7,4,5,2,1,3] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1

[6,7,4,5,2,3,1] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 1

[6,7,4,5,3,1,2] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1

[6,7,4,5,3,2,1] => [[[[[.,[.,.]],[.,.]],.],.],.] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 3

[6,7,5,1,2,3,4] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1

[6,7,5,1,2,4,3] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 1

[6,7,5,1,3,2,4] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[6,7,5,1,3,4,2] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 1

[6,7,5,1,4,2,3] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[6,7,5,1,4,3,2] => [[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1

[6,7,5,2,1,3,4] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 2

[6,7,5,2,1,4,3] => [[[[.,[.,.]],.],.],[[.,.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2

[6,7,5,2,3,1,4] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[6,7,5,2,3,4,1] => [[[[.,[.,.]],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2

[6,7,5,2,4,1,3] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[6,7,5,2,4,3,1] => [[[[.,[.,.]],.],[[.,.],.]],.] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 2

[6,7,5,3,1,2,4] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 2

[6,7,5,3,1,4,2] => [[[[.,[.,.]],.],.],[[.,.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2

[6,7,5,3,2,1,4] => [[[[[.,[.,.]],.],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 3

[6,7,5,3,2,4,1] => [[[[[.,[.,.]],.],.],[.,.]],.] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 3

[6,7,5,3,4,1,2] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[6,7,5,3,4,2,1] => [[[[[.,[.,.]],.],[.,.]],.],.] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[6,7,5,4,1,2,3] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 2

[6,7,5,4,1,3,2] => [[[[.,[.,.]],.],.],[[.,.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2

[6,7,5,4,2,1,3] => [[[[[.,[.,.]],.],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 3

[6,7,5,4,2,3,1] => [[[[[.,[.,.]],.],.],[.,.]],.] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 3

[6,7,5,4,3,1,2] => [[[[[.,[.,.]],.],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 3

[6,7,5,4,3,2,1] => [[[[[[.,[.,.]],.],.],.],.],.] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 5

[7,1,2,3,4,5,6] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1

[7,1,2,3,4,6,5] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 1

[7,1,2,3,5,4,6] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 1

[7,1,2,3,5,6,4] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 1

[7,1,2,3,6,4,5] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 1

[7,1,2,3,6,5,4] => [[.,.],[.,[.,[[[.,.],.],.]]]] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1

[7,1,2,4,3,5,6] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 1

[7,1,2,4,3,6,5] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 1

[7,1,2,4,5,3,6] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1

[7,1,2,4,5,6,3] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 1

[7,1,2,4,6,3,5] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1

[7,1,2,4,6,5,3] => [[.,.],[.,[[.,[[.,.],.]],.]]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 1

[7,1,2,5,3,4,6] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 1

[7,1,2,5,3,6,4] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 1

[7,1,2,5,4,3,6] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 1

[7,1,2,5,4,6,3] => [[.,.],[.,[[[.,.],[.,.]],.]]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 1

[7,1,2,5,6,3,4] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1

[7,1,2,5,6,4,3] => [[.,.],[.,[[[.,[.,.]],.],.]]] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 1

[7,1,2,6,3,4,5] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 1

[7,1,2,6,3,5,4] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 1

[7,1,2,6,4,3,5] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 1

[7,1,2,6,4,5,3] => [[.,.],[.,[[[.,.],[.,.]],.]]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 1

[7,1,2,6,5,3,4] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 1

[7,1,2,6,5,4,3] => [[.,.],[.,[[[[.,.],.],.],.]]] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 1

[7,1,3,2,4,5,6] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 1

[7,1,3,2,4,6,5] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 1

[7,1,3,2,5,4,6] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1

[7,1,3,2,5,6,4] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 1

[7,1,3,2,6,4,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1

[7,1,3,2,6,5,4] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 1

[7,1,3,4,2,5,6] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

[7,1,3,4,2,6,5] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 1

[7,1,3,4,5,2,6] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1

[7,1,3,4,5,6,2] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 1

[7,1,3,4,6,2,5] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1

[7,1,3,4,6,5,2] => [[.,.],[[.,[.,[[.,.],.]]],.]] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 1

[7,1,3,5,2,4,6] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

[7,1,3,5,2,6,4] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 1

[7,1,3,5,4,2,6] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1

[7,1,3,5,4,6,2] => [[.,.],[[.,[[.,.],[.,.]]],.]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 1

[7,1,3,5,6,2,4] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1

[7,1,3,5,6,4,2] => [[.,.],[[.,[[.,[.,.]],.]],.]] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 1

[7,1,3,6,2,4,5] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

[7,1,3,6,2,5,4] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 1

[7,1,3,6,4,2,5] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1

[7,1,3,6,4,5,2] => [[.,.],[[.,[[.,.],[.,.]]],.]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 1

[7,1,3,6,5,2,4] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1

[7,1,3,6,5,4,2] => [[.,.],[[.,[[[.,.],.],.]],.]] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 1

[7,1,4,2,3,5,6] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 1

[7,1,4,2,3,6,5] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 1

[7,1,4,2,5,3,6] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1

[7,1,4,2,5,6,3] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 1

[7,1,4,2,6,3,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1

[7,1,4,2,6,5,3] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 1

[7,1,4,3,2,5,6] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1

[7,1,4,3,2,6,5] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 1

[7,1,4,3,5,2,6] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1

[7,1,4,3,5,6,2] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 1

[7,1,4,3,6,2,5] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1

[7,1,4,3,6,5,2] => [[.,.],[[[.,.],[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 1

[7,1,4,5,2,3,6] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

[7,1,4,5,2,6,3] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 1

[7,1,4,5,3,2,6] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[7,1,4,5,3,6,2] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 1

[7,1,4,5,6,2,3] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1

[7,1,4,5,6,3,2] => [[.,.],[[[.,[.,[.,.]]],.],.]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 1

[7,1,4,6,2,3,5] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

[7,1,4,6,2,5,3] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 1

[7,1,4,6,3,2,5] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[7,1,4,6,3,5,2] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 1

[7,1,4,6,5,2,3] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1

[7,1,4,6,5,3,2] => [[.,.],[[[.,[[.,.],.]],.],.]] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 1

[7,1,5,2,3,4,6] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 1

[7,1,5,2,3,6,4] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 1

[7,1,5,2,4,3,6] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1

[7,1,5,2,4,6,3] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 1

[7,1,5,2,6,3,4] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1

[7,1,5,2,6,4,3] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 1

[7,1,5,3,2,4,6] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1

[7,1,5,3,2,6,4] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 1

[7,1,5,3,4,2,6] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1

[7,1,5,3,4,6,2] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 1

[7,1,5,3,6,2,4] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1

[7,1,5,3,6,4,2] => [[.,.],[[[.,.],[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 1

[7,1,5,4,2,3,6] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1

[7,1,5,4,2,6,3] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 1

[7,1,5,4,3,2,6] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 1

[7,1,5,4,3,6,2] => [[.,.],[[[[.,.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 1

[7,1,5,4,6,2,3] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1

[7,1,5,4,6,3,2] => [[.,.],[[[[.,.],[.,.]],.],.]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 1

[7,1,5,6,2,3,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1

[7,1,5,6,2,4,3] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 1

[7,1,5,6,3,2,4] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[7,1,5,6,3,4,2] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 1

[7,1,5,6,4,2,3] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1

[7,1,5,6,4,3,2] => [[.,.],[[[[.,[.,.]],.],.],.]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 1

[7,1,6,2,3,4,5] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 1

[7,1,6,2,3,5,4] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 1

[7,1,6,2,4,3,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1

[7,1,6,2,4,5,3] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 1

[7,1,6,2,5,3,4] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1

[7,1,6,2,5,4,3] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 1

[7,1,6,3,2,4,5] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1

[7,1,6,3,2,5,4] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 1

[7,1,6,3,4,2,5] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1

[7,1,6,3,4,5,2] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 1

[7,1,6,3,5,2,4] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1

[7,1,6,3,5,4,2] => [[.,.],[[[.,.],[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 1

[7,1,6,4,2,3,5] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1

[7,1,6,4,2,5,3] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 1

[7,1,6,4,3,2,5] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 1

[7,1,6,4,3,5,2] => [[.,.],[[[[.,.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 1

[7,1,6,4,5,2,3] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1

[7,1,6,4,5,3,2] => [[.,.],[[[[.,.],[.,.]],.],.]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 1

[7,1,6,5,2,3,4] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1

[7,1,6,5,2,4,3] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 1

[7,1,6,5,3,2,4] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 1

[7,1,6,5,3,4,2] => [[.,.],[[[[.,.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 1

[7,1,6,5,4,2,3] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 1

[7,1,6,5,4,3,2] => [[.,.],[[[[[.,.],.],.],.],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1

[7,2,1,3,4,5,6] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2

[7,2,1,3,4,6,5] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 2

[7,2,1,3,5,4,6] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 2

[7,2,1,3,5,6,4] => [[[.,.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[7,2,1,3,6,4,5] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 2

[7,2,1,3,6,5,4] => [[[.,.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 2

[7,2,1,4,3,5,6] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 2

[7,2,1,4,3,6,5] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 2

[7,2,1,4,5,3,6] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 2

[7,2,1,4,5,6,3] => [[[.,.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[7,2,1,4,6,3,5] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 2

[7,2,1,4,6,5,3] => [[[.,.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 2

[7,2,1,5,3,4,6] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 2

[7,2,1,5,3,6,4] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 2

[7,2,1,5,4,3,6] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 2

[7,2,1,5,4,6,3] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2

[7,2,1,5,6,3,4] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 2

[7,2,1,5,6,4,3] => [[[.,.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2

[7,2,1,6,3,4,5] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 2

[7,2,1,6,3,5,4] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 2

[7,2,1,6,4,3,5] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 2

[7,2,1,6,4,5,3] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2

[7,2,1,6,5,3,4] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 2

[7,2,1,6,5,4,3] => [[[.,.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 2

[7,2,3,1,4,5,6] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1

[7,2,3,1,4,6,5] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 1

[7,2,3,1,5,4,6] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[7,2,3,1,5,6,4] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 1

[7,2,3,1,6,4,5] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[7,2,3,1,6,5,4] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1

[7,2,3,4,1,5,6] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1

[7,2,3,4,1,6,5] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 1

[7,2,3,4,5,1,6] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1

[7,2,3,4,5,6,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2

[7,2,3,4,6,1,5] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1

[7,2,3,4,6,5,1] => [[[.,.],[.,[.,[[.,.],.]]]],.] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 2

[7,2,3,5,1,4,6] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1

[7,2,3,5,1,6,4] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 1

[7,2,3,5,4,1,6] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1

[7,2,3,5,4,6,1] => [[[.,.],[.,[[.,.],[.,.]]]],.] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 2

[7,2,3,5,6,1,4] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1

[7,2,3,5,6,4,1] => [[[.,.],[.,[[.,[.,.]],.]]],.] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 2

[7,2,3,6,1,4,5] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1

[7,2,3,6,1,5,4] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 1

[7,2,3,6,4,1,5] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1

[7,2,3,6,4,5,1] => [[[.,.],[.,[[.,.],[.,.]]]],.] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 2

[7,2,3,6,5,1,4] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1

[7,2,3,6,5,4,1] => [[[.,.],[.,[[[.,.],.],.]]],.] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 2

[7,2,4,1,3,5,6] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1

[7,2,4,1,3,6,5] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 1

[7,2,4,1,5,3,6] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[7,2,4,1,5,6,3] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 1

[7,2,4,1,6,3,5] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[7,2,4,1,6,5,3] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1

[7,2,4,3,1,5,6] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1

[7,2,4,3,1,6,5] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1

[7,2,4,3,5,1,6] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[7,2,4,3,5,6,1] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 2

[7,2,4,3,6,1,5] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[7,2,4,3,6,5,1] => [[[.,.],[[.,.],[[.,.],.]]],.] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 2

[7,2,4,5,1,3,6] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1

[7,2,4,5,1,6,3] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 1

[7,2,4,5,3,1,6] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[7,2,4,5,3,6,1] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[7,2,4,5,6,1,3] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1

[7,2,4,5,6,3,1] => [[[.,.],[[.,[.,[.,.]]],.]],.] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 2

[7,2,4,6,1,3,5] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1

[7,2,4,6,1,5,3] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 1

[7,2,4,6,3,1,5] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[7,2,4,6,3,5,1] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[7,2,4,6,5,1,3] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1

[7,2,4,6,5,3,1] => [[[.,.],[[.,[[.,.],.]],.]],.] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 2

[7,2,5,1,3,4,6] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1

[7,2,5,1,3,6,4] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 1

[7,2,5,1,4,3,6] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[7,2,5,1,4,6,3] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 1

[7,2,5,1,6,3,4] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[7,2,5,1,6,4,3] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1

[7,2,5,3,1,4,6] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1

[7,2,5,3,1,6,4] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1

[7,2,5,3,4,1,6] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[7,2,5,3,4,6,1] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 2

[7,2,5,3,6,1,4] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[7,2,5,3,6,4,1] => [[[.,.],[[.,.],[[.,.],.]]],.] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 2

[7,2,5,4,1,3,6] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1

[7,2,5,4,1,6,3] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1

[7,2,5,4,3,1,6] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1

[7,2,5,4,3,6,1] => [[[.,.],[[[.,.],.],[.,.]]],.] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 2

[7,2,5,4,6,1,3] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[7,2,5,4,6,3,1] => [[[.,.],[[[.,.],[.,.]],.]],.] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 2

[7,2,5,6,1,3,4] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1

[7,2,5,6,1,4,3] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 1

[7,2,5,6,3,1,4] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[7,2,5,6,3,4,1] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2

[7,2,5,6,4,1,3] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[7,2,5,6,4,3,1] => [[[.,.],[[[.,[.,.]],.],.]],.] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 2

[7,2,6,1,3,4,5] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1

[7,2,6,1,3,5,4] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 1

[7,2,6,1,4,3,5] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[7,2,6,1,4,5,3] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 1

[7,2,6,1,5,3,4] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[7,2,6,1,5,4,3] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1

[7,2,6,3,1,4,5] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1

[7,2,6,3,1,5,4] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1

[7,2,6,3,4,1,5] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[7,2,6,3,4,5,1] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 2

[7,2,6,3,5,1,4] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[7,2,6,3,5,4,1] => [[[.,.],[[.,.],[[.,.],.]]],.] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 2

[7,2,6,4,1,3,5] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1

[7,2,6,4,1,5,3] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1

[7,2,6,4,3,1,5] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1

[7,2,6,4,3,5,1] => [[[.,.],[[[.,.],.],[.,.]]],.] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 2

[7,2,6,4,5,1,3] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[7,2,6,4,5,3,1] => [[[.,.],[[[.,.],[.,.]],.]],.] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 2

[7,2,6,5,1,3,4] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1

[7,2,6,5,1,4,3] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1

[7,2,6,5,3,1,4] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1

[7,2,6,5,3,4,1] => [[[.,.],[[[.,.],.],[.,.]]],.] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 2

[7,2,6,5,4,1,3] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1

[7,2,6,5,4,3,1] => [[[.,.],[[[[.,.],.],.],.]],.] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 2

[7,3,1,2,4,5,6] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2

[7,3,1,2,4,6,5] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 2

[7,3,1,2,5,4,6] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 2

[7,3,1,2,5,6,4] => [[[.,.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[7,3,1,2,6,4,5] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 2

[7,3,1,2,6,5,4] => [[[.,.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 2

[7,3,1,4,2,5,6] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 2

[7,3,1,4,2,6,5] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 2

[7,3,1,4,5,2,6] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 2

[7,3,1,4,5,6,2] => [[[.,.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[7,3,1,4,6,2,5] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 2

[7,3,1,4,6,5,2] => [[[.,.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 2

[7,3,1,5,2,4,6] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 2

[7,3,1,5,2,6,4] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 2

[7,3,1,5,4,2,6] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 2

[7,3,1,5,4,6,2] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2

[7,3,1,5,6,2,4] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 2

[7,3,1,5,6,4,2] => [[[.,.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2

[7,3,1,6,2,4,5] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 2

[7,3,1,6,2,5,4] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 2

[7,3,1,6,4,2,5] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 2

[7,3,1,6,4,5,2] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2

[7,3,1,6,5,2,4] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 2

[7,3,1,6,5,4,2] => [[[.,.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 2

[7,3,2,1,4,5,6] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3

[7,3,2,1,4,6,5] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 3

[7,3,2,1,5,4,6] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 3

[7,3,2,1,5,6,4] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3

[7,3,2,1,6,4,5] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 3

[7,3,2,1,6,5,4] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 3

[7,3,2,4,1,5,6] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2

[7,3,2,4,1,6,5] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[7,3,2,4,5,1,6] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2

[7,3,2,4,5,6,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 3

[7,3,2,4,6,1,5] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2

[7,3,2,4,6,5,1] => [[[[.,.],.],[.,[[.,.],.]]],.] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 3

[7,3,2,5,1,4,6] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2

[7,3,2,5,1,6,4] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[7,3,2,5,4,1,6] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2

[7,3,2,5,4,6,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 3

[7,3,2,5,6,1,4] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2

[7,3,2,5,6,4,1] => [[[[.,.],.],[[.,[.,.]],.]],.] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[7,3,2,6,1,4,5] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2

[7,3,2,6,1,5,4] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[7,3,2,6,4,1,5] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2

[7,3,2,6,4,5,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 3

[7,3,2,6,5,1,4] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2

[7,3,2,6,5,4,1] => [[[[.,.],.],[[[.,.],.],.]],.] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 3

[7,3,4,1,2,5,6] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1

[7,3,4,1,2,6,5] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 1

[7,3,4,1,5,2,6] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[7,3,4,1,5,6,2] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 1

[7,3,4,1,6,2,5] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[7,3,4,1,6,5,2] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1

[7,3,4,2,1,5,6] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2

[7,3,4,2,1,6,5] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[7,3,4,2,5,1,6] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[7,3,4,2,5,6,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[7,3,4,2,6,1,5] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[7,3,4,2,6,5,1] => [[[[.,.],[.,.]],[[.,.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 2

[7,3,4,5,1,2,6] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1

[7,3,4,5,1,6,2] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 1

[7,3,4,5,2,1,6] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 2

[7,3,4,5,2,6,1] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[7,3,4,5,6,1,2] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1

[7,3,4,5,6,2,1] => [[[[.,.],[.,[.,[.,.]]]],.],.] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3

[7,3,4,6,1,2,5] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1

[7,3,4,6,1,5,2] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 1

[7,3,4,6,2,1,5] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 2

[7,3,4,6,2,5,1] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[7,3,4,6,5,1,2] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1

[7,3,4,6,5,2,1] => [[[[.,.],[.,[[.,.],.]]],.],.] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 3

[7,3,5,1,2,4,6] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1

[7,3,5,1,2,6,4] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 1

[7,3,5,1,4,2,6] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[7,3,5,1,4,6,2] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 1

[7,3,5,1,6,2,4] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[7,3,5,1,6,4,2] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1

[7,3,5,2,1,4,6] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2

[7,3,5,2,1,6,4] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[7,3,5,2,4,1,6] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[7,3,5,2,4,6,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[7,3,5,2,6,1,4] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[7,3,5,2,6,4,1] => [[[[.,.],[.,.]],[[.,.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 2

[7,3,5,4,1,2,6] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1

[7,3,5,4,1,6,2] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1

[7,3,5,4,2,1,6] => [[[[.,.],[[.,.],.]],.],[.,.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 2

[7,3,5,4,2,6,1] => [[[[.,.],[[.,.],.]],[.,.]],.] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[7,3,5,4,6,1,2] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[7,3,5,4,6,2,1] => [[[[.,.],[[.,.],[.,.]]],.],.] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[7,3,5,6,1,2,4] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1

[7,3,5,6,1,4,2] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 1

[7,3,5,6,2,1,4] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 2

[7,3,5,6,2,4,1] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[7,3,5,6,4,1,2] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1

[7,3,5,6,4,2,1] => [[[[.,.],[[.,[.,.]],.]],.],.] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 3

[7,3,6,1,2,4,5] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1

[7,3,6,1,2,5,4] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 1

[7,3,6,1,4,2,5] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[7,3,6,1,4,5,2] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 1

[7,3,6,1,5,2,4] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[7,3,6,1,5,4,2] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1

[7,3,6,2,1,4,5] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2

[7,3,6,2,1,5,4] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[7,3,6,2,4,1,5] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[7,3,6,2,4,5,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[7,3,6,2,5,1,4] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[7,3,6,2,5,4,1] => [[[[.,.],[.,.]],[[.,.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 2

[7,3,6,4,1,2,5] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1

[7,3,6,4,1,5,2] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1

[7,3,6,4,2,1,5] => [[[[.,.],[[.,.],.]],.],[.,.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 2

[7,3,6,4,2,5,1] => [[[[.,.],[[.,.],.]],[.,.]],.] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[7,3,6,4,5,1,2] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1

[7,3,6,4,5,2,1] => [[[[.,.],[[.,.],[.,.]]],.],.] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3

[7,3,6,5,1,2,4] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1

[7,3,6,5,1,4,2] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1

[7,3,6,5,2,1,4] => [[[[.,.],[[.,.],.]],.],[.,.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 2

[7,3,6,5,2,4,1] => [[[[.,.],[[.,.],.]],[.,.]],.] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[7,3,6,5,4,1,2] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1

[7,3,6,5,4,2,1] => [[[[.,.],[[[.,.],.],.]],.],.] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 3

[7,4,1,2,3,5,6] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2

[7,4,1,2,3,6,5] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 2

[7,4,1,2,5,3,6] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 2

[7,4,1,2,5,6,3] => [[[.,.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[7,4,1,2,6,3,5] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 2

[7,4,1,2,6,5,3] => [[[.,.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 2

[7,4,1,3,2,5,6] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 2

[7,4,1,3,2,6,5] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 2

[7,4,1,3,5,2,6] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 2

[7,4,1,3,5,6,2] => [[[.,.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[7,4,1,3,6,2,5] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 2

[7,4,1,3,6,5,2] => [[[.,.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 2

[7,4,1,5,2,3,6] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 2

[7,4,1,5,2,6,3] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 2

[7,4,1,5,3,2,6] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 2

[7,4,1,5,3,6,2] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2

[7,4,1,5,6,2,3] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 2

[7,4,1,5,6,3,2] => [[[.,.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2

[7,4,1,6,2,3,5] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 2

[7,4,1,6,2,5,3] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 2

[7,4,1,6,3,2,5] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 2

[7,4,1,6,3,5,2] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2

[7,4,1,6,5,2,3] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 2

[7,4,1,6,5,3,2] => [[[.,.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 2

[7,4,2,1,3,5,6] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3

[7,4,2,1,3,6,5] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 3

[7,4,2,1,5,3,6] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 3

[7,4,2,1,5,6,3] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3

[7,4,2,1,6,3,5] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 3

[7,4,2,1,6,5,3] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 3

[7,4,2,3,1,5,6] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2

[7,4,2,3,1,6,5] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[7,4,2,3,5,1,6] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2

[7,4,2,3,5,6,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 3

[7,4,2,3,6,1,5] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2

[7,4,2,3,6,5,1] => [[[[.,.],.],[.,[[.,.],.]]],.] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 3

[7,4,2,5,1,3,6] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2

[7,4,2,5,1,6,3] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[7,4,2,5,3,1,6] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2

[7,4,2,5,3,6,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 3

[7,4,2,5,6,1,3] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2

[7,4,2,5,6,3,1] => [[[[.,.],.],[[.,[.,.]],.]],.] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[7,4,2,6,1,3,5] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2

[7,4,2,6,1,5,3] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[7,4,2,6,3,1,5] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2

[7,4,2,6,3,5,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 3

[7,4,2,6,5,1,3] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2

[7,4,2,6,5,3,1] => [[[[.,.],.],[[[.,.],.],.]],.] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 3

[7,4,3,1,2,5,6] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3

[7,4,3,1,2,6,5] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 3

[7,4,3,1,5,2,6] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 3

[7,4,3,1,5,6,2] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3

[7,4,3,1,6,2,5] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 3

[7,4,3,1,6,5,2] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 3

[7,4,3,2,1,5,6] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 4

[7,4,3,2,1,6,5] => [[[[[.,.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 4

[7,4,3,2,5,1,6] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3

[7,4,3,2,5,6,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 4

[7,4,3,2,6,1,5] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3

[7,4,3,2,6,5,1] => [[[[[.,.],.],.],[[.,.],.]],.] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 4

[7,4,3,5,1,2,6] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2

[7,4,3,5,1,6,2] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[7,4,3,5,2,1,6] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3

[7,4,3,5,2,6,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3

[7,4,3,5,6,1,2] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2

[7,4,3,5,6,2,1] => [[[[[.,.],.],[.,[.,.]]],.],.] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 4

[7,4,3,6,1,2,5] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2

[7,4,3,6,1,5,2] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[7,4,3,6,2,1,5] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3

[7,4,3,6,2,5,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3

[7,4,3,6,5,1,2] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2

[7,4,3,6,5,2,1] => [[[[[.,.],.],[[.,.],.]],.],.] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[7,4,5,1,2,3,6] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1

[7,4,5,1,2,6,3] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 1

[7,4,5,1,3,2,6] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[7,4,5,1,3,6,2] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 1

[7,4,5,1,6,2,3] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[7,4,5,1,6,3,2] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1

[7,4,5,2,1,3,6] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2

[7,4,5,2,1,6,3] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[7,4,5,2,3,1,6] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[7,4,5,2,3,6,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[7,4,5,2,6,1,3] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[7,4,5,2,6,3,1] => [[[[.,.],[.,.]],[[.,.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 2

[7,4,5,3,1,2,6] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2

[7,4,5,3,1,6,2] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[7,4,5,3,2,1,6] => [[[[[.,.],[.,.]],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 3

[7,4,5,3,2,6,1] => [[[[[.,.],[.,.]],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3

[7,4,5,3,6,1,2] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[7,4,5,3,6,2,1] => [[[[[.,.],[.,.]],[.,.]],.],.] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[7,4,5,6,1,2,3] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1

[7,4,5,6,1,3,2] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 1

[7,4,5,6,2,1,3] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 2

[7,4,5,6,2,3,1] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2

[7,4,5,6,3,1,2] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 2

[7,4,5,6,3,2,1] => [[[[[.,.],[.,[.,.]]],.],.],.] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4

[7,4,6,1,2,3,5] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1

[7,4,6,1,2,5,3] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 1

[7,4,6,1,3,2,5] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[7,4,6,1,3,5,2] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 1

[7,4,6,1,5,2,3] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[7,4,6,1,5,3,2] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1

[7,4,6,2,1,3,5] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2

[7,4,6,2,1,5,3] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[7,4,6,2,3,1,5] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[7,4,6,2,3,5,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[7,4,6,2,5,1,3] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[7,4,6,2,5,3,1] => [[[[.,.],[.,.]],[[.,.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 2

[7,4,6,3,1,2,5] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2

[7,4,6,3,1,5,2] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[7,4,6,3,2,1,5] => [[[[[.,.],[.,.]],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 3

[7,4,6,3,2,5,1] => [[[[[.,.],[.,.]],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3

[7,4,6,3,5,1,2] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[7,4,6,3,5,2,1] => [[[[[.,.],[.,.]],[.,.]],.],.] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[7,4,6,5,1,2,3] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1

[7,4,6,5,1,3,2] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1

[7,4,6,5,2,1,3] => [[[[.,.],[[.,.],.]],.],[.,.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 2

[7,4,6,5,2,3,1] => [[[[.,.],[[.,.],.]],[.,.]],.] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2

[7,4,6,5,3,1,2] => [[[[.,.],[[.,.],.]],.],[.,.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 2

[7,4,6,5,3,2,1] => [[[[[.,.],[[.,.],.]],.],.],.] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 4

[7,5,1,2,3,4,6] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2

[7,5,1,2,3,6,4] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 2

[7,5,1,2,4,3,6] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 2

[7,5,1,2,4,6,3] => [[[.,.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[7,5,1,2,6,3,4] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 2

[7,5,1,2,6,4,3] => [[[.,.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 2

[7,5,1,3,2,4,6] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 2

[7,5,1,3,2,6,4] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 2

[7,5,1,3,4,2,6] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 2

[7,5,1,3,4,6,2] => [[[.,.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[7,5,1,3,6,2,4] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 2

[7,5,1,3,6,4,2] => [[[.,.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 2

[7,5,1,4,2,3,6] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 2

[7,5,1,4,2,6,3] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 2

[7,5,1,4,3,2,6] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 2

[7,5,1,4,3,6,2] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2

[7,5,1,4,6,2,3] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 2

[7,5,1,4,6,3,2] => [[[.,.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2

[7,5,1,6,2,3,4] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 2

[7,5,1,6,2,4,3] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 2

[7,5,1,6,3,2,4] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 2

[7,5,1,6,3,4,2] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2

[7,5,1,6,4,2,3] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 2

[7,5,1,6,4,3,2] => [[[.,.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 2

[7,5,2,1,3,4,6] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3

[7,5,2,1,3,6,4] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 3

[7,5,2,1,4,3,6] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 3

[7,5,2,1,4,6,3] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3

[7,5,2,1,6,3,4] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 3

[7,5,2,1,6,4,3] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 3

[7,5,2,3,1,4,6] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2

[7,5,2,3,1,6,4] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[7,5,2,3,4,1,6] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2

[7,5,2,3,4,6,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 3

[7,5,2,3,6,1,4] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2

[7,5,2,3,6,4,1] => [[[[.,.],.],[.,[[.,.],.]]],.] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 3

[7,5,2,4,1,3,6] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2

[7,5,2,4,1,6,3] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[7,5,2,4,3,1,6] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2

[7,5,2,4,3,6,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 3

[7,5,2,4,6,1,3] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2

[7,5,2,4,6,3,1] => [[[[.,.],.],[[.,[.,.]],.]],.] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[7,5,2,6,1,3,4] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2

[7,5,2,6,1,4,3] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[7,5,2,6,3,1,4] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2

[7,5,2,6,3,4,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 3

[7,5,2,6,4,1,3] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2

[7,5,2,6,4,3,1] => [[[[.,.],.],[[[.,.],.],.]],.] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 3

[7,5,3,1,2,4,6] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3

[7,5,3,1,2,6,4] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 3

[7,5,3,1,4,2,6] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 3

[7,5,3,1,4,6,2] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3

[7,5,3,1,6,2,4] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 3

[7,5,3,1,6,4,2] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 3

[7,5,3,2,1,4,6] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 4

[7,5,3,2,1,6,4] => [[[[[.,.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 4

[7,5,3,2,4,1,6] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3

[7,5,3,2,4,6,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 4

[7,5,3,2,6,1,4] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3

[7,5,3,2,6,4,1] => [[[[[.,.],.],.],[[.,.],.]],.] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 4

[7,5,3,4,1,2,6] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2

[7,5,3,4,1,6,2] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[7,5,3,4,2,1,6] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3

[7,5,3,4,2,6,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3

[7,5,3,4,6,1,2] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2

[7,5,3,4,6,2,1] => [[[[[.,.],.],[.,[.,.]]],.],.] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 4

[7,5,3,6,1,2,4] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2

[7,5,3,6,1,4,2] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[7,5,3,6,2,1,4] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3

[7,5,3,6,2,4,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3

[7,5,3,6,4,1,2] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2

[7,5,3,6,4,2,1] => [[[[[.,.],.],[[.,.],.]],.],.] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[7,5,4,1,2,3,6] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3

[7,5,4,1,2,6,3] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 3

[7,5,4,1,3,2,6] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 3

[7,5,4,1,3,6,2] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3

[7,5,4,1,6,2,3] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 3

[7,5,4,1,6,3,2] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 3

[7,5,4,2,1,3,6] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 4

[7,5,4,2,1,6,3] => [[[[[.,.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 4

[7,5,4,2,3,1,6] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3

[7,5,4,2,3,6,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 4

[7,5,4,2,6,1,3] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3

[7,5,4,2,6,3,1] => [[[[[.,.],.],.],[[.,.],.]],.] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 4

[7,5,4,3,1,2,6] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 4

[7,5,4,3,1,6,2] => [[[[[.,.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 4

[7,5,4,3,2,1,6] => [[[[[[.,.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 5

[7,5,4,3,2,6,1] => [[[[[[.,.],.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 5

[7,5,4,3,6,1,2] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3

[7,5,4,3,6,2,1] => [[[[[[.,.],.],.],[.,.]],.],.] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 5

[7,5,4,6,1,2,3] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2

[7,5,4,6,1,3,2] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[7,5,4,6,2,1,3] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3

[7,5,4,6,2,3,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3

[7,5,4,6,3,1,2] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3

[7,5,4,6,3,2,1] => [[[[[[.,.],.],[.,.]],.],.],.] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 5

[7,5,6,1,2,3,4] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1

[7,5,6,1,2,4,3] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 1

[7,5,6,1,3,2,4] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[7,5,6,1,3,4,2] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 1

[7,5,6,1,4,2,3] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1

[7,5,6,1,4,3,2] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1

[7,5,6,2,1,3,4] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2

[7,5,6,2,1,4,3] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[7,5,6,2,3,1,4] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[7,5,6,2,3,4,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2

[7,5,6,2,4,1,3] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[7,5,6,2,4,3,1] => [[[[.,.],[.,.]],[[.,.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 2

[7,5,6,3,1,2,4] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2

[7,5,6,3,1,4,2] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[7,5,6,3,2,1,4] => [[[[[.,.],[.,.]],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 3

[7,5,6,3,2,4,1] => [[[[[.,.],[.,.]],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3

[7,5,6,3,4,1,2] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1

[7,5,6,3,4,2,1] => [[[[[.,.],[.,.]],[.,.]],.],.] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3

[7,5,6,4,1,2,3] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2

[7,5,6,4,1,3,2] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2

[7,5,6,4,2,1,3] => [[[[[.,.],[.,.]],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 3

[7,5,6,4,2,3,1] => [[[[[.,.],[.,.]],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3

[7,5,6,4,3,1,2] => [[[[[.,.],[.,.]],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 3

[7,5,6,4,3,2,1] => [[[[[[.,.],[.,.]],.],.],.],.] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5

[7,6,1,2,3,4,5] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2

[7,6,1,2,3,5,4] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 2

[7,6,1,2,4,3,5] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 2

[7,6,1,2,4,5,3] => [[[.,.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2

[7,6,1,2,5,3,4] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 2

[7,6,1,2,5,4,3] => [[[.,.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 2

[7,6,1,3,2,4,5] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 2

[7,6,1,3,2,5,4] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 2

[7,6,1,3,4,2,5] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 2

[7,6,1,3,4,5,2] => [[[.,.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2

[7,6,1,3,5,2,4] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 2

[7,6,1,3,5,4,2] => [[[.,.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 2

[7,6,1,4,2,3,5] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 2

[7,6,1,4,2,5,3] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 2

[7,6,1,4,3,2,5] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 2

[7,6,1,4,3,5,2] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2

[7,6,1,4,5,2,3] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 2

[7,6,1,4,5,3,2] => [[[.,.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2

[7,6,1,5,2,3,4] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 2

[7,6,1,5,2,4,3] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 2

[7,6,1,5,3,2,4] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 2

[7,6,1,5,3,4,2] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2

[7,6,1,5,4,2,3] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 2

[7,6,1,5,4,3,2] => [[[.,.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 2

[7,6,2,1,3,4,5] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3

[7,6,2,1,3,5,4] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 3

[7,6,2,1,4,3,5] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 3

[7,6,2,1,4,5,3] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3

[7,6,2,1,5,3,4] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 3

[7,6,2,1,5,4,3] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 3

[7,6,2,3,1,4,5] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2

[7,6,2,3,1,5,4] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[7,6,2,3,4,1,5] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2

[7,6,2,3,4,5,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 3

[7,6,2,3,5,1,4] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2

[7,6,2,3,5,4,1] => [[[[.,.],.],[.,[[.,.],.]]],.] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 3

[7,6,2,4,1,3,5] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2

[7,6,2,4,1,5,3] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[7,6,2,4,3,1,5] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2

[7,6,2,4,3,5,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 3

[7,6,2,4,5,1,3] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2

[7,6,2,4,5,3,1] => [[[[.,.],.],[[.,[.,.]],.]],.] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3

[7,6,2,5,1,3,4] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2

[7,6,2,5,1,4,3] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[7,6,2,5,3,1,4] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2

[7,6,2,5,3,4,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 3

[7,6,2,5,4,1,3] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2

[7,6,2,5,4,3,1] => [[[[.,.],.],[[[.,.],.],.]],.] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 3

[7,6,3,1,2,4,5] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3

[7,6,3,1,2,5,4] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 3

[7,6,3,1,4,2,5] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 3

[7,6,3,1,4,5,2] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3

[7,6,3,1,5,2,4] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 3

[7,6,3,1,5,4,2] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 3

[7,6,3,2,1,4,5] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 4

[7,6,3,2,1,5,4] => [[[[[.,.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 4

[7,6,3,2,4,1,5] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3

[7,6,3,2,4,5,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 4

[7,6,3,2,5,1,4] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3

[7,6,3,2,5,4,1] => [[[[[.,.],.],.],[[.,.],.]],.] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 4

[7,6,3,4,1,2,5] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2

[7,6,3,4,1,5,2] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[7,6,3,4,2,1,5] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3

[7,6,3,4,2,5,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3

[7,6,3,4,5,1,2] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2

[7,6,3,4,5,2,1] => [[[[[.,.],.],[.,[.,.]]],.],.] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 4

[7,6,3,5,1,2,4] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2

[7,6,3,5,1,4,2] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[7,6,3,5,2,1,4] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3

[7,6,3,5,2,4,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3

[7,6,3,5,4,1,2] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2

[7,6,3,5,4,2,1] => [[[[[.,.],.],[[.,.],.]],.],.] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4

[7,6,4,1,2,3,5] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3

[7,6,4,1,2,5,3] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 3

[7,6,4,1,3,2,5] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 3

[7,6,4,1,3,5,2] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3

[7,6,4,1,5,2,3] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 3

[7,6,4,1,5,3,2] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 3

[7,6,4,2,1,3,5] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 4

[7,6,4,2,1,5,3] => [[[[[.,.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 4

[7,6,4,2,3,1,5] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3

[7,6,4,2,3,5,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 4

[7,6,4,2,5,1,3] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3

[7,6,4,2,5,3,1] => [[[[[.,.],.],.],[[.,.],.]],.] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 4

[7,6,4,3,1,2,5] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 4

[7,6,4,3,1,5,2] => [[[[[.,.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 4

[7,6,4,3,2,1,5] => [[[[[[.,.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 5

[7,6,4,3,2,5,1] => [[[[[[.,.],.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 5

[7,6,4,3,5,1,2] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3

[7,6,4,3,5,2,1] => [[[[[[.,.],.],.],[.,.]],.],.] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 5

[7,6,4,5,1,2,3] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2

[7,6,4,5,1,3,2] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2

[7,6,4,5,2,1,3] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3

[7,6,4,5,2,3,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3

[7,6,4,5,3,1,2] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3

[7,6,4,5,3,2,1] => [[[[[[.,.],.],[.,.]],.],.],.] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 5

[7,6,5,1,2,3,4] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3

[7,6,5,1,2,4,3] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 3

[7,6,5,1,3,2,4] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 3

[7,6,5,1,3,4,2] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3

[7,6,5,1,4,2,3] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 3

[7,6,5,1,4,3,2] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 3

[7,6,5,2,1,3,4] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 4

[7,6,5,2,1,4,3] => [[[[[.,.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 4

[7,6,5,2,3,1,4] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3

[7,6,5,2,3,4,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 4

[7,6,5,2,4,1,3] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3

[7,6,5,2,4,3,1] => [[[[[.,.],.],.],[[.,.],.]],.] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 4

[7,6,5,3,1,2,4] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 4

[7,6,5,3,1,4,2] => [[[[[.,.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 4

[7,6,5,3,2,1,4] => [[[[[[.,.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 5

[7,6,5,3,2,4,1] => [[[[[[.,.],.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 5

[7,6,5,3,4,1,2] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3

[7,6,5,3,4,2,1] => [[[[[[.,.],.],.],[.,.]],.],.] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 5

[7,6,5,4,1,2,3] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 4

[7,6,5,4,1,3,2] => [[[[[.,.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 4

[7,6,5,4,2,1,3] => [[[[[[.,.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 5

[7,6,5,4,2,3,1] => [[[[[[.,.],.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 5

[7,6,5,4,3,1,2] => [[[[[[.,.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 5

[7,6,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],.] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7

[8,7,6,5,4,3,2,1] => [[[[[[[[.,.],.],.],.],.],.],.],.] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 8

[7,8,6,5,4,3,2,1] => [[[[[[[.,[.,.]],.],.],.],.],.],.] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 6

[8,6,7,5,4,3,2,1] => [[[[[[[.,.],[.,.]],.],.],.],.],.] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6

[7,6,8,5,4,3,2,1] => [[[[[[[.,.],[.,.]],.],.],.],.],.] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6

[8,7,5,6,4,3,2,1] => [[[[[[[.,.],.],[.,.]],.],.],.],.] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 6

[7,8,5,6,4,3,2,1] => [[[[[[.,[.,.]],[.,.]],.],.],.],.] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 4

[8,6,5,7,4,3,2,1] => [[[[[[[.,.],.],[.,.]],.],.],.],.] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 6

[8,5,6,7,4,3,2,1] => [[[[[[.,.],[.,[.,.]]],.],.],.],.] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 5

[7,6,5,8,4,3,2,1] => [[[[[[[.,.],.],[.,.]],.],.],.],.] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 6

[6,7,5,8,4,3,2,1] => [[[[[[.,[.,.]],[.,.]],.],.],.],.] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 4

[7,5,6,8,4,3,2,1] => [[[[[[.,.],[.,[.,.]]],.],.],.],.] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 5

[6,5,7,8,4,3,2,1] => [[[[[[.,.],[.,[.,.]]],.],.],.],.] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 5

[8,7,6,4,5,3,2,1] => [[[[[[[.,.],.],.],[.,.]],.],.],.] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 6

[7,8,6,4,5,3,2,1] => [[[[[[.,[.,.]],.],[.,.]],.],.],.] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[8,6,7,4,5,3,2,1] => [[[[[[.,.],[.,.]],[.,.]],.],.],.] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[8,7,5,4,6,3,2,1] => [[[[[[[.,.],.],.],[.,.]],.],.],.] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 6

[8,7,4,5,6,3,2,1] => [[[[[[.,.],.],[.,[.,.]]],.],.],.] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 5

[8,5,6,4,7,3,2,1] => [[[[[[.,.],[.,.]],[.,.]],.],.],.] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[8,6,4,5,7,3,2,1] => [[[[[[.,.],.],[.,[.,.]]],.],.],.] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 5

[8,4,5,6,7,3,2,1] => [[[[[.,.],[.,[.,[.,.]]]],.],.],.] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4

[7,6,5,4,8,3,2,1] => [[[[[[[.,.],.],.],[.,.]],.],.],.] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 6

[6,7,5,4,8,3,2,1] => [[[[[[.,[.,.]],.],[.,.]],.],.],.] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[7,5,6,4,8,3,2,1] => [[[[[[.,.],[.,.]],[.,.]],.],.],.] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[6,5,7,4,8,3,2,1] => [[[[[[.,.],[.,.]],[.,.]],.],.],.] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[7,6,4,5,8,3,2,1] => [[[[[[.,.],.],[.,[.,.]]],.],.],.] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 5

[6,7,4,5,8,3,2,1] => [[[[[.,[.,.]],[.,[.,.]]],.],.],.] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 3

[7,5,4,6,8,3,2,1] => [[[[[[.,.],.],[.,[.,.]]],.],.],.] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 5

[7,4,5,6,8,3,2,1] => [[[[[.,.],[.,[.,[.,.]]]],.],.],.] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4

[6,5,4,7,8,3,2,1] => [[[[[[.,.],.],[.,[.,.]]],.],.],.] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 5

[5,6,4,7,8,3,2,1] => [[[[[.,[.,.]],[.,[.,.]]],.],.],.] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 3

[6,4,5,7,8,3,2,1] => [[[[[.,.],[.,[.,[.,.]]]],.],.],.] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4

[5,4,6,7,8,3,2,1] => [[[[[.,.],[.,[.,[.,.]]]],.],.],.] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4

[8,7,6,5,3,4,2,1] => [[[[[[[.,.],.],.],.],[.,.]],.],.] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 6

[7,8,6,5,3,4,2,1] => [[[[[[.,[.,.]],.],.],[.,.]],.],.] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 4

[8,6,7,5,3,4,2,1] => [[[[[[.,.],[.,.]],.],[.,.]],.],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 4

[7,6,8,5,3,4,2,1] => [[[[[[.,.],[.,.]],.],[.,.]],.],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 4

[8,7,5,6,3,4,2,1] => [[[[[[.,.],.],[.,.]],[.,.]],.],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 4

[7,8,5,6,3,4,2,1] => [[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2

[8,5,6,7,3,4,2,1] => [[[[[.,.],[.,[.,.]]],[.,.]],.],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[7,6,5,8,3,4,2,1] => [[[[[[.,.],.],[.,.]],[.,.]],.],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 4

[6,7,5,8,3,4,2,1] => [[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2

[6,5,7,8,3,4,2,1] => [[[[[.,.],[.,[.,.]]],[.,.]],.],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[8,7,6,4,3,5,2,1] => [[[[[[[.,.],.],.],.],[.,.]],.],.] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 6

[7,8,6,4,3,5,2,1] => [[[[[[.,[.,.]],.],.],[.,.]],.],.] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 4

[7,6,8,4,3,5,2,1] => [[[[[[.,.],[.,.]],.],[.,.]],.],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 4

[8,7,6,3,4,5,2,1] => [[[[[[.,.],.],.],[.,[.,.]]],.],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 5

[7,8,6,3,4,5,2,1] => [[[[[.,[.,.]],.],[.,[.,.]]],.],.] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[8,6,7,3,4,5,2,1] => [[[[[.,.],[.,.]],[.,[.,.]]],.],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3

[7,6,8,3,4,5,2,1] => [[[[[.,.],[.,.]],[.,[.,.]]],.],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3

[8,7,5,4,3,6,2,1] => [[[[[[[.,.],.],.],.],[.,.]],.],.] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 6

[7,8,5,4,3,6,2,1] => [[[[[[.,[.,.]],.],.],[.,.]],.],.] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 4

[8,7,5,3,4,6,2,1] => [[[[[[.,.],.],.],[.,[.,.]]],.],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 5

[7,8,5,3,4,6,2,1] => [[[[[.,[.,.]],.],[.,[.,.]]],.],.] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[8,7,4,3,5,6,2,1] => [[[[[[.,.],.],.],[.,[.,.]]],.],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 5

[8,7,3,4,5,6,2,1] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 4

[7,8,3,4,5,6,2,1] => [[[[.,[.,.]],[.,[.,[.,.]]]],.],.] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 2

[8,6,5,4,3,7,2,1] => [[[[[[[.,.],.],.],.],[.,.]],.],.] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 6

[8,5,4,6,3,7,2,1] => [[[[[[.,.],.],[.,.]],[.,.]],.],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 4

[8,6,4,3,5,7,2,1] => [[[[[[.,.],.],.],[.,[.,.]]],.],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 5

[8,5,3,4,6,7,2,1] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 4

[8,4,3,5,6,7,2,1] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 4

[8,3,4,5,6,7,2,1] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 3

[7,6,5,4,3,8,2,1] => [[[[[[[.,.],.],.],.],[.,.]],.],.] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 6

[6,7,5,4,3,8,2,1] => [[[[[[.,[.,.]],.],.],[.,.]],.],.] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 4

[7,5,6,4,3,8,2,1] => [[[[[[.,.],[.,.]],.],[.,.]],.],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 4

[7,6,4,5,3,8,2,1] => [[[[[[.,.],.],[.,.]],[.,.]],.],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 4

[6,7,4,5,3,8,2,1] => [[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2

[7,5,4,6,3,8,2,1] => [[[[[[.,.],.],[.,.]],[.,.]],.],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 4

[7,4,5,6,3,8,2,1] => [[[[[.,.],[.,[.,.]]],[.,.]],.],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[6,5,4,7,3,8,2,1] => [[[[[[.,.],.],[.,.]],[.,.]],.],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 4

[6,4,5,7,3,8,2,1] => [[[[[.,.],[.,[.,.]]],[.,.]],.],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[5,4,6,7,3,8,2,1] => [[[[[.,.],[.,[.,.]]],[.,.]],.],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[7,6,5,3,4,8,2,1] => [[[[[[.,.],.],.],[.,[.,.]]],.],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 5

[7,6,4,3,5,8,2,1] => [[[[[[.,.],.],.],[.,[.,.]]],.],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 5

[7,6,3,4,5,8,2,1] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 4

[7,5,4,3,6,8,2,1] => [[[[[[.,.],.],.],[.,[.,.]]],.],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 5

[7,5,3,4,6,8,2,1] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 4

[7,3,4,5,6,8,2,1] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 3

[6,5,4,3,7,8,2,1] => [[[[[[.,.],.],.],[.,[.,.]]],.],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 5

[6,5,3,4,7,8,2,1] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 4

[6,3,4,5,7,8,2,1] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 3

[5,4,3,6,7,8,2,1] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 4

[5,3,4,6,7,8,2,1] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 3

[4,3,5,6,7,8,2,1] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 3

[8,7,6,5,4,2,3,1] => [[[[[[[.,.],.],.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 6

[7,8,6,5,4,2,3,1] => [[[[[[.,[.,.]],.],.],.],[.,.]],.] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 4

[8,6,7,5,4,2,3,1] => [[[[[[.,.],[.,.]],.],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 4

[7,6,8,5,4,2,3,1] => [[[[[[.,.],[.,.]],.],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 4

[8,7,5,6,4,2,3,1] => [[[[[[.,.],.],[.,.]],.],[.,.]],.] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 4

[8,6,5,7,4,2,3,1] => [[[[[[.,.],.],[.,.]],.],[.,.]],.] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 4

[8,5,6,7,4,2,3,1] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 3

[7,6,5,8,4,2,3,1] => [[[[[[.,.],.],[.,.]],.],[.,.]],.] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 4

[6,7,5,8,4,2,3,1] => [[[[[.,[.,.]],[.,.]],.],[.,.]],.] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[7,5,6,8,4,2,3,1] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 3

[8,7,6,4,5,2,3,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 4

[8,6,7,4,5,2,3,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[7,6,8,4,5,2,3,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[8,7,4,5,6,2,3,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3

[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

[8,5,6,4,7,2,3,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[8,6,4,5,7,2,3,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3

[8,4,5,6,7,2,3,1] => [[[[.,.],[.,[.,[.,.]]]],[.,.]],.] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2

[7,5,6,4,8,2,3,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,5,7,4,8,2,3,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[7,6,4,5,8,2,3,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3

[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

[8,7,6,5,3,2,4,1] => [[[[[[[.,.],.],.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 6

[7,8,6,5,3,2,4,1] => [[[[[[.,[.,.]],.],.],.],[.,.]],.] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 4

[8,6,7,5,3,2,4,1] => [[[[[[.,.],[.,.]],.],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 4

[7,6,8,5,3,2,4,1] => [[[[[[.,.],[.,.]],.],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 4

[8,7,5,6,3,2,4,1] => [[[[[[.,.],.],[.,.]],.],[.,.]],.] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 4

[8,6,5,7,3,2,4,1] => [[[[[[.,.],.],[.,.]],.],[.,.]],.] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 4

[8,5,6,7,3,2,4,1] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 3

[7,6,5,8,3,2,4,1] => [[[[[[.,.],.],[.,.]],.],[.,.]],.] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 4

[6,7,5,8,3,2,4,1] => [[[[[.,[.,.]],[.,.]],.],[.,.]],.] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[8,7,6,5,2,3,4,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 5

[8,6,7,5,2,3,4,1] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 3

[7,6,8,5,2,3,4,1] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 3

[8,7,5,6,2,3,4,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3

[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

[8,6,5,7,2,3,4,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3

[8,5,6,7,2,3,4,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[7,6,5,8,2,3,4,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3

[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

[6,5,7,8,2,3,4,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[8,7,6,4,3,2,5,1] => [[[[[[[.,.],.],.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 6

[7,6,8,4,3,2,5,1] => [[[[[[.,.],[.,.]],.],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 4

[8,7,6,3,4,2,5,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 4

[7,8,6,3,4,2,5,1] => [[[[[.,[.,.]],.],[.,.]],[.,.]],.] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[8,6,7,3,4,2,5,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[7,6,8,3,4,2,5,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[8,7,6,3,2,4,5,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 5

[7,8,6,3,2,4,5,1] => [[[[[.,[.,.]],.],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 3

[8,6,7,3,2,4,5,1] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 3

[8,7,6,2,3,4,5,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 4

[7,8,6,2,3,4,5,1] => [[[[.,[.,.]],.],[.,[.,[.,.]]]],.] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2

[8,6,7,2,3,4,5,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2

[7,6,8,2,3,4,5,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2

[7,8,5,4,3,2,6,1] => [[[[[[.,[.,.]],.],.],.],[.,.]],.] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 4

[8,7,5,3,4,2,6,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 4

[7,8,5,3,4,2,6,1] => [[[[[.,[.,.]],.],[.,.]],[.,.]],.] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[8,7,4,3,5,2,6,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 4

[7,8,4,3,5,2,6,1] => [[[[[.,[.,.]],.],[.,.]],[.,.]],.] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[8,7,5,4,2,3,6,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 5

[8,7,5,3,2,4,6,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 5

[8,7,4,3,2,5,6,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 5

[7,8,4,3,2,5,6,1] => [[[[[.,[.,.]],.],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 3

[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

[7,8,4,2,3,5,6,1] => [[[[.,[.,.]],.],[.,[.,[.,.]]]],.] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2

[7,8,3,2,4,5,6,1] => [[[[.,[.,.]],.],[.,[.,[.,.]]]],.] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2

[8,7,2,3,4,5,6,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 3

[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

[8,6,5,4,3,2,7,1] => [[[[[[[.,.],.],.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 6

[8,5,4,6,3,2,7,1] => [[[[[[.,.],.],[.,.]],.],[.,.]],.] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 4

[8,5,6,3,4,2,7,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[8,6,4,3,5,2,7,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 4

[8,6,3,4,5,2,7,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3

[8,4,5,3,6,2,7,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[8,4,3,5,6,2,7,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3

[8,6,5,4,2,3,7,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 5

[8,5,6,4,2,3,7,1] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 3

[8,6,5,3,2,4,7,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 5

[8,6,4,2,3,5,7,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 4

[8,6,2,3,4,5,7,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 3

[8,5,4,3,2,6,7,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 5

[8,4,5,3,2,6,7,1] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 3

[8,5,3,4,2,6,7,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3

[8,3,4,5,2,6,7,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[8,5,4,2,3,6,7,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 4

[8,4,3,2,5,6,7,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 4

[8,3,4,2,5,6,7,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2

[8,4,2,3,5,6,7,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 3

[8,3,2,4,5,6,7,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 3

[8,2,3,4,5,6,7,1] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 2

[7,6,5,4,3,2,8,1] => [[[[[[[.,.],.],.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 6

[6,7,5,4,3,2,8,1] => [[[[[[.,[.,.]],.],.],.],[.,.]],.] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 4

[6,5,7,4,3,2,8,1] => [[[[[[.,.],[.,.]],.],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 4

[7,6,4,5,3,2,8,1] => [[[[[[.,.],.],[.,.]],.],[.,.]],.] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 4

[6,7,4,5,3,2,8,1] => [[[[[.,[.,.]],[.,.]],.],[.,.]],.] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[7,4,5,6,3,2,8,1] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 3

[6,4,5,7,3,2,8,1] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 3

[7,6,5,3,4,2,8,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 4

[7,5,6,3,4,2,8,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,5,7,3,4,2,8,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[7,6,4,3,5,2,8,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 4

[7,6,3,4,5,2,8,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3

[7,5,4,3,6,2,8,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 4

[7,4,5,3,6,2,8,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[7,5,3,4,6,2,8,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3

[7,3,4,5,6,2,8,1] => [[[[.,.],[.,[.,[.,.]]]],[.,.]],.] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2

[6,5,4,3,7,2,8,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 4

[6,4,5,3,7,2,8,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,4,6,3,7,2,8,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,5,3,4,7,2,8,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3

[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

[6,4,3,5,7,2,8,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3

[6,3,4,5,7,2,8,1] => [[[[.,.],[.,[.,[.,.]]]],[.,.]],.] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2

[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

[7,6,5,4,2,3,8,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 5

[6,7,5,4,2,3,8,1] => [[[[[.,[.,.]],.],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 3

[7,5,6,4,2,3,8,1] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 3

[6,5,7,4,2,3,8,1] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 3

[7,6,4,5,2,3,8,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3

[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

[7,4,5,6,2,3,8,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[6,5,4,7,2,3,8,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3

[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

[5,4,6,7,2,3,8,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[7,6,5,3,2,4,8,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 5

[6,7,5,3,2,4,8,1] => [[[[[.,[.,.]],.],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 3

[6,5,7,3,2,4,8,1] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 3

[7,6,5,2,3,4,8,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 4

[7,5,6,2,3,4,8,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2

[6,7,4,3,2,5,8,1] => [[[[[.,[.,.]],.],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 3

[7,6,4,2,3,5,8,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 4

[7,6,3,2,4,5,8,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 4

[6,7,3,2,4,5,8,1] => [[[[.,[.,.]],.],[.,[.,[.,.]]]],.] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2

[7,6,2,3,4,5,8,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 3

[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

[7,5,4,3,2,6,8,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 5

[7,4,3,5,2,6,8,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3

[7,5,4,2,3,6,8,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 4

[7,4,5,2,3,6,8,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2

[7,5,3,2,4,6,8,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 4

[7,5,2,3,4,6,8,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 3

[7,4,3,2,5,6,8,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 4

[7,3,2,4,5,6,8,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 3

[7,2,3,4,5,6,8,1] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 2

[6,5,4,3,2,7,8,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 5

[6,5,3,4,2,7,8,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3

[6,3,4,5,2,7,8,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[5,4,3,6,2,7,8,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3

[4,3,5,6,2,7,8,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[6,5,4,2,3,7,8,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 4

[6,4,5,2,3,7,8,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2

[6,5,3,2,4,7,8,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 4

[6,5,2,3,4,7,8,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 3

[6,2,3,4,5,7,8,1] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 2

[5,4,3,2,6,7,8,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 4

[4,5,3,2,6,7,8,1] => [[[[.,[.,.]],.],[.,[.,[.,.]]]],.] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2

[5,3,4,2,6,7,8,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2

[4,3,5,2,6,7,8,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2

[5,4,2,3,6,7,8,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 3

[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

[5,3,2,4,6,7,8,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 3

[5,2,3,4,6,7,8,1] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 2

[4,3,2,5,6,7,8,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 3

[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

[4,2,3,5,6,7,8,1] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 2

[3,2,4,5,6,7,8,1] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 2

[8,7,6,5,4,3,1,2] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6

[7,8,6,5,4,3,1,2] => [[[[[[.,[.,.]],.],.],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 4

[8,6,7,5,4,3,1,2] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 4

[7,6,8,5,4,3,1,2] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 4

[8,7,5,6,4,3,1,2] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 4

[7,8,5,6,4,3,1,2] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2

[8,6,5,7,4,3,1,2] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 4

[7,6,5,8,4,3,1,2] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 4

[6,7,5,8,4,3,1,2] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 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] => 3

[6,5,7,8,4,3,1,2] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 3

[8,7,6,4,5,3,1,2] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 4

[7,8,6,4,5,3,1,2] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 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] => 2

[8,7,5,4,6,3,1,2] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 4

[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

[8,5,6,4,7,3,1,2] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 2

[8,6,4,5,7,3,1,2] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3

[8,5,4,6,7,3,1,2] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3

[7,6,5,4,8,3,1,2] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 4

[7,5,6,4,8,3,1,2] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 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] => 2

[7,6,4,5,8,3,1,2] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3

[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

[6,5,4,7,8,3,1,2] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3

[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

[5,4,6,7,8,3,1,2] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 2

[8,7,6,5,3,4,1,2] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 4

[7,8,6,5,3,4,1,2] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 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] => 2

[8,7,5,6,3,4,1,2] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 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] => 0

[8,6,5,7,3,4,1,2] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 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

[7,6,5,8,3,4,1,2] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 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] => 0

[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

[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

[8,7,6,3,4,5,1,2] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3

[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

[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

[7,8,5,4,3,6,1,2] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2

[8,7,4,5,3,6,1,2] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 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] => 0

[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

[8,7,4,3,5,6,1,2] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3

[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

[8,7,3,4,5,6,1,2] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 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] => 0

[8,6,5,4,3,7,1,2] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 4

[8,5,4,3,6,7,1,2] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3

[8,5,3,4,6,7,1,2] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2

[8,4,3,5,6,7,1,2] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 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

[7,6,5,4,3,8,1,2] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 4

[7,5,6,4,3,8,1,2] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 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] => 0

[5,6,4,7,3,8,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[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

[7,6,5,3,4,8,1,2] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3

[7,6,4,3,5,8,1,2] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3

[7,6,3,4,5,8,1,2] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2

[7,5,4,3,6,8,1,2] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3

[7,5,3,4,6,8,1,2] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 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

[6,5,4,3,7,8,1,2] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3

[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

[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

[5,6,3,4,7,8,1,2] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0

[6,4,3,5,7,8,1,2] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 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

[5,4,3,6,7,8,1,2] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 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] => 0

[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

[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

[8,7,6,5,4,2,1,3] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6

[7,8,6,5,4,2,1,3] => [[[[[[.,[.,.]],.],.],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 4

[8,6,7,5,4,2,1,3] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 4

[7,6,8,5,4,2,1,3] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 4

[8,7,5,6,4,2,1,3] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 4

[7,8,5,6,4,2,1,3] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2

[7,6,5,8,4,2,1,3] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 4

[6,7,5,8,4,2,1,3] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 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] => 3

[6,5,7,8,4,2,1,3] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 3

[8,7,6,4,5,2,1,3] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 4

[7,6,8,4,5,2,1,3] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 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] => 2

[7,6,5,4,8,2,1,3] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 4

[6,7,5,4,8,2,1,3] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 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] => 2

[7,6,4,5,8,2,1,3] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3

[7,5,4,6,8,2,1,3] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3

[7,4,5,6,8,2,1,3] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 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] => 2

[8,7,6,5,4,1,2,3] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 5

[7,8,6,5,4,1,2,3] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 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] => 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

[8,6,5,7,4,1,2,3] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 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] => 2

[7,6,5,8,4,1,2,3] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 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

[7,5,6,8,4,1,2,3] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2

[6,5,7,8,4,1,2,3] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2

[8,7,6,4,5,1,2,3] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 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

[8,7,5,4,6,1,2,3] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 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

[8,7,4,5,6,1,2,3] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[7,8,4,5,6,1,2,3] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[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

[8,6,4,5,7,1,2,3] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[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

[7,6,5,4,8,1,2,3] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 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

[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

[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

[7,6,4,5,8,1,2,3] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[6,7,4,5,8,1,2,3] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[7,5,4,6,8,1,2,3] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[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

[6,5,4,7,8,1,2,3] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[5,6,4,7,8,1,2,3] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[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

[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

[8,7,6,5,3,2,1,4] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6

[7,8,6,5,3,2,1,4] => [[[[[[.,[.,.]],.],.],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 4

[8,6,7,5,3,2,1,4] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 4

[7,6,8,5,3,2,1,4] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 4

[8,7,5,6,3,2,1,4] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 4

[7,8,5,6,3,2,1,4] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2

[8,6,5,7,3,2,1,4] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 4

[8,5,6,7,3,2,1,4] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 3

[7,6,5,8,3,2,1,4] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 4

[6,7,5,8,3,2,1,4] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 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] => 3

[6,5,7,8,3,2,1,4] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 3

[8,7,6,5,2,3,1,4] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 4

[7,8,6,5,2,3,1,4] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 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] => 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] => 2

[8,7,5,6,2,3,1,4] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 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] => 0

[8,6,5,7,2,3,1,4] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 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

[7,6,5,8,2,3,1,4] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 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] => 0

[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

[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

[8,7,6,5,3,1,2,4] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 5

[7,8,6,5,3,1,2,4] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 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] => 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] => 3

[8,7,5,6,3,1,2,4] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 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

[8,6,5,7,3,1,2,4] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3

[7,6,5,8,3,1,2,4] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 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

[7,5,6,8,3,1,2,4] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2

[6,5,7,8,3,1,2,4] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2

[8,7,6,5,2,1,3,4] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 5

[7,8,6,5,2,1,3,4] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 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] => 3

[8,7,5,6,2,1,3,4] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 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

[8,6,5,7,2,1,3,4] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 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] => 2

[7,6,5,8,2,1,3,4] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 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

[7,5,6,8,2,1,3,4] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2

[6,5,7,8,2,1,3,4] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2

[8,7,6,5,1,2,3,4] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4

[7,8,6,5,1,2,3,4] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2

[8,6,7,5,1,2,3,4] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2

[7,6,8,5,1,2,3,4] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2

[8,7,5,6,1,2,3,4] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[7,8,5,6,1,2,3,4] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0

[8,6,5,7,1,2,3,4] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[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

[7,6,5,8,1,2,3,4] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[6,7,5,8,1,2,3,4] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0

[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

[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

[8,7,6,4,3,2,1,5] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6

[7,8,6,4,3,2,1,5] => [[[[[[.,[.,.]],.],.],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 4

[8,6,7,4,3,2,1,5] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 4

[7,6,8,4,3,2,1,5] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 4

[8,7,6,3,4,2,1,5] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 4

[7,8,6,3,4,2,1,5] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2

[8,7,6,4,2,3,1,5] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 4

[8,7,6,3,2,4,1,5] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 4

[8,6,7,3,2,4,1,5] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2

[8,7,6,2,3,4,1,5] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3

[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

[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

[8,7,6,4,3,1,2,5] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 5

[8,7,6,3,4,1,2,5] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 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

[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

[8,7,6,4,2,1,3,5] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 5

[7,8,6,4,2,1,3,5] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 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] => 3

[8,7,6,4,1,2,3,5] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4

[7,8,6,4,1,2,3,5] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2

[7,6,8,4,1,2,3,5] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2

[8,7,6,3,2,1,4,5] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 5

[7,8,6,3,2,1,4,5] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 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] => 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] => 3

[8,7,6,2,3,1,4,5] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 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

[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

[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

[8,7,6,3,1,2,4,5] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4

[7,8,6,3,1,2,4,5] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2

[8,6,7,3,1,2,4,5] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2

[7,6,8,3,1,2,4,5] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2

[8,7,6,2,1,3,4,5] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 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] => 2

[8,6,7,2,1,3,4,5] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2

[8,7,6,1,2,3,4,5] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3

[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

[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

[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

[8,7,5,4,3,2,1,6] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6

[7,8,5,4,3,2,1,6] => [[[[[[.,[.,.]],.],.],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 4

[8,7,4,5,3,2,1,6] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 4

[7,8,4,5,3,2,1,6] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2

[8,7,5,3,4,2,1,6] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 4

[8,7,3,4,5,2,1,6] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3

[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

[8,7,4,5,2,3,1,6] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 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] => 0

[8,7,5,3,2,4,1,6] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 4

[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

[8,7,4,3,2,5,1,6] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 4

[7,8,4,3,2,5,1,6] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2

[8,7,3,4,2,5,1,6] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 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] => 0

[8,7,2,3,4,5,1,6] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 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] => 0

[8,7,5,4,3,1,2,6] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 5

[7,8,5,4,3,1,2,6] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3

[8,7,5,3,4,1,2,6] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3

[8,7,3,4,5,1,2,6] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[7,8,3,4,5,1,2,6] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[7,8,5,4,2,1,3,6] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3

[8,7,5,4,1,2,3,6] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4

[7,8,5,4,1,2,3,6] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2

[7,8,4,5,1,2,3,6] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0

[8,7,5,3,2,1,4,6] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 5

[7,8,5,3,2,1,4,6] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3

[8,7,5,3,1,2,4,6] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4

[7,8,5,3,1,2,4,6] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2

[8,7,5,2,1,3,4,6] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 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] => 2

[8,7,5,1,2,3,4,6] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3

[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

[8,7,4,3,2,1,5,6] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 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] => 3

[8,7,3,4,2,1,5,6] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 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

[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

[8,7,3,2,4,1,5,6] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 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

[8,7,2,3,4,1,5,6] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[7,8,2,3,4,1,5,6] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[7,8,4,3,1,2,5,6] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2

[8,7,3,4,1,2,5,6] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[7,8,3,4,1,2,5,6] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0

[8,7,4,2,1,3,5,6] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 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] => 2

[8,7,4,1,2,3,5,6] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3

[8,7,3,2,1,4,5,6] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 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] => 2

[8,7,2,3,1,4,5,6] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[7,8,2,3,1,4,5,6] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0

[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

[8,7,2,1,3,4,5,6] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3

[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

[8,7,1,2,3,4,5,6] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2

[7,8,1,2,3,4,5,6] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0

[8,6,5,4,3,2,1,7] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 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] => 4

[8,6,4,5,3,2,1,7] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 4

[8,4,5,6,3,2,1,7] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 3

[8,6,5,3,4,2,1,7] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 4

[8,5,6,3,4,2,1,7] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 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] => 2

[8,4,3,5,6,2,1,7] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3

[8,3,4,5,6,2,1,7] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 2

[8,6,5,4,2,3,1,7] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 4

[8,5,6,4,2,3,1,7] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 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

[8,6,5,3,2,4,1,7] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 4

[8,6,5,2,3,4,1,7] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3

[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

[8,6,4,2,3,5,1,7] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3

[8,6,3,2,4,5,1,7] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3

[8,5,4,3,2,6,1,7] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 4

[8,4,3,5,2,6,1,7] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[8,5,4,2,3,6,1,7] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3

[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

[8,5,3,2,4,6,1,7] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3

[8,5,2,3,4,6,1,7] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2

[8,3,2,4,5,6,1,7] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 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

[8,6,5,4,3,1,2,7] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 5

[8,6,4,5,3,1,2,7] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3

[8,6,5,3,4,1,2,7] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3

[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

[8,5,4,3,6,1,2,7] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3

[8,5,3,4,6,1,2,7] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[8,4,3,5,6,1,2,7] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[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

[8,6,5,4,2,1,3,7] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 5

[8,5,6,4,2,1,3,7] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 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] => 2

[8,6,5,4,1,2,3,7] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4

[8,5,6,4,1,2,3,7] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2

[8,6,4,5,1,2,3,7] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[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

[8,6,5,3,2,1,4,7] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 5

[8,5,6,3,2,1,4,7] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 3

[8,6,5,2,3,1,4,7] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 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

[8,5,6,3,1,2,4,7] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2

[8,6,5,2,1,3,4,7] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 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] => 2

[8,6,5,1,2,3,4,7] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3

[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

[8,6,4,3,2,1,5,7] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 5

[8,6,3,4,2,1,5,7] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3

[8,6,4,2,3,1,5,7] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3

[8,6,3,2,4,1,5,7] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3

[8,6,2,3,4,1,5,7] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[8,6,4,3,1,2,5,7] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4

[8,6,3,4,1,2,5,7] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[8,6,4,2,1,3,5,7] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4

[8,6,4,1,2,3,5,7] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3

[8,6,3,2,1,4,5,7] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4

[8,6,1,2,3,4,5,7] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2

[8,5,4,3,2,1,6,7] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 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] => 3

[8,4,3,5,2,1,6,7] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 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] => 2

[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

[8,5,2,3,4,1,6,7] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[8,4,2,3,5,1,6,7] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[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

[8,5,3,4,1,2,6,7] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[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

[8,5,4,2,1,3,6,7] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4

[8,5,4,1,2,3,6,7] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3

[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

[8,5,3,2,1,4,6,7] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4

[8,5,3,1,2,4,6,7] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3

[8,5,2,1,3,4,6,7] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3

[8,5,1,2,3,4,6,7] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2

[8,4,3,2,1,5,6,7] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4

[8,3,4,2,1,5,6,7] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2

[8,4,2,3,1,5,6,7] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[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

[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

[8,4,2,1,3,5,6,7] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3

[8,4,1,2,3,5,6,7] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2

[8,3,2,1,4,5,6,7] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3

[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

[8,3,1,2,4,5,6,7] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2

[8,2,1,3,4,5,6,7] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2

[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

[7,6,5,4,3,2,1,8] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6

[6,7,5,4,3,2,1,8] => [[[[[[.,[.,.]],.],.],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 4

[7,5,6,4,3,2,1,8] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 4

[6,5,7,4,3,2,1,8] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 4

[7,6,4,5,3,2,1,8] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 4

[6,7,4,5,3,2,1,8] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2

[7,5,4,6,3,2,1,8] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 4

[7,4,5,6,3,2,1,8] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 3

[6,5,4,7,3,2,1,8] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 4

[5,6,4,7,3,2,1,8] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 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] => 3

[7,6,5,3,4,2,1,8] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 4

[6,7,5,3,4,2,1,8] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 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] => 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] => 2

[7,6,4,3,5,2,1,8] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 4

[6,7,4,3,5,2,1,8] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2

[7,6,3,4,5,2,1,8] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3

[7,5,4,3,6,2,1,8] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 4

[6,5,4,3,7,2,1,8] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 4

[5,6,4,3,7,2,1,8] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 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] => 2

[5,4,3,6,7,2,1,8] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3

[7,6,5,4,2,3,1,8] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 4

[6,7,5,4,2,3,1,8] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 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] => 2

[7,6,4,5,2,3,1,8] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 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] => 0

[7,5,4,6,2,3,1,8] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[6,5,4,7,2,3,1,8] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 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] => 0

[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

[7,6,5,3,2,4,1,8] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 4

[6,5,7,3,2,4,1,8] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2

[7,6,5,2,3,4,1,8] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3

[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

[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

[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

[6,7,4,3,2,5,1,8] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 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] => 0

[7,6,4,2,3,5,1,8] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3

[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

[7,6,3,2,4,5,1,8] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3

[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

[7,6,2,3,4,5,1,8] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 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] => 0

[7,5,4,3,2,6,1,8] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 4

[7,4,5,3,2,6,1,8] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2

[7,5,3,4,2,6,1,8] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[7,4,3,5,2,6,1,8] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[7,5,3,2,4,6,1,8] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3

[7,4,2,3,5,6,1,8] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 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

[6,5,4,3,2,7,1,8] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 4

[5,6,4,3,2,7,1,8] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 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] => 0

[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

[5,4,3,6,2,7,1,8] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 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] => 0

[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

[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

[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

[6,5,3,2,4,7,1,8] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3

[6,4,2,3,5,7,1,8] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2

[5,4,3,2,6,7,1,8] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3

[4,5,2,3,6,7,1,8] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0

[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

[4,3,2,5,6,7,1,8] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 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] => 0

[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

[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

[7,6,5,4,3,1,2,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 5

[6,7,5,4,3,1,2,8] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 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] => 3

[7,6,4,5,3,1,2,8] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 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] => 2

[7,6,5,3,4,1,2,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 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

[6,7,3,4,5,1,2,8] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[6,5,4,3,7,1,2,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 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] => 0

[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

[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

[7,6,5,4,2,1,3,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 5

[6,5,7,4,2,1,3,8] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 3

[7,6,4,5,2,1,3,8] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3

[7,5,4,6,2,1,3,8] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 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] => 2

[7,6,5,4,1,2,3,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 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

[5,6,4,7,1,2,3,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0

[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

[7,6,5,3,2,1,4,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 5

[7,6,5,2,3,1,4,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3

[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

[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

[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

[7,6,5,2,1,3,4,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 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] => 2

[7,6,5,1,2,3,4,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3

[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

[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

[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

[7,6,4,3,2,1,5,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 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] => 3

[7,6,3,4,2,1,5,8] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 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

[7,6,4,2,3,1,5,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 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

[7,6,3,2,4,1,5,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3

[7,6,2,3,4,1,5,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[6,7,2,3,4,1,5,8] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[7,6,4,3,1,2,5,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4

[7,6,4,2,1,3,5,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4

[7,6,3,2,1,4,5,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4

[6,7,3,2,1,4,5,8] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2

[7,6,2,3,1,4,5,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[6,7,2,3,1,4,5,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0

[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

[7,6,1,2,3,4,5,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2

[6,7,1,2,3,4,5,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0

[7,5,4,3,2,1,6,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 5

[7,4,5,3,2,1,6,8] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 3

[7,4,3,5,2,1,6,8] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 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] => 2

[7,5,4,2,3,1,6,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3

[7,5,3,2,4,1,6,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3

[7,5,2,3,4,1,6,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[7,4,2,3,5,1,6,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[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

[7,5,4,3,1,2,6,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4

[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

[7,5,3,2,1,4,6,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4

[7,5,2,3,1,4,6,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[7,5,3,1,2,4,6,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3

[7,5,1,2,3,4,6,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2

[7,4,3,2,1,5,6,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4

[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

[7,4,3,1,2,5,6,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3

[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

[7,4,1,2,3,5,6,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2

[7,3,2,1,4,5,6,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3

[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

[7,3,1,2,4,5,6,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2

[7,2,1,3,4,5,6,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2

[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

[6,5,4,3,2,1,7,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 5

[5,6,4,3,2,1,7,8] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 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] => 3

[6,5,3,4,2,1,7,8] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 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

[6,3,4,5,2,1,7,8] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2

[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

[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

[6,5,2,3,4,1,7,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[5,6,2,3,4,1,7,8] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[6,4,3,2,5,1,7,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 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

[5,4,3,2,6,1,7,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 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

[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

[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

[4,3,2,5,6,1,7,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[3,4,2,5,6,1,7,8] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[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

[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

[6,5,4,3,1,2,7,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4

[5,6,4,3,1,2,7,8] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2

[5,4,6,3,1,2,7,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2

[5,6,3,4,1,2,7,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0

[6,4,3,5,1,2,7,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[5,4,3,6,1,2,7,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[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

[6,5,4,2,1,3,7,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 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] => 2

[6,4,5,2,1,3,7,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2

[5,4,6,2,1,3,7,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2

[6,5,4,1,2,3,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3

[5,6,3,2,1,4,7,8] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2

[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

[6,5,1,2,3,4,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2

[6,4,3,2,1,5,7,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4

[6,3,4,2,1,5,7,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2

[6,4,3,1,2,5,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3

[6,4,2,1,3,5,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3

[6,4,1,2,3,5,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2

[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

[6,3,1,2,4,5,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2

[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

[5,4,3,2,1,6,7,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4

[4,5,3,2,1,6,7,8] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2

[5,3,4,2,1,6,7,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2

[4,3,5,2,1,6,7,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2

[5,4,2,3,1,6,7,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[4,5,2,3,1,6,7,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0

[5,3,2,4,1,6,7,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[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

[4,3,2,5,1,6,7,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[3,4,2,5,1,6,7,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0

[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

[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

[5,4,3,1,2,6,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3

[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

[5,4,2,1,3,6,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3

[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

[5,4,1,2,3,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2

[4,5,1,2,3,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0

[5,3,2,1,4,6,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3

[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

[5,3,1,2,4,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2

[5,2,1,3,4,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2

[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

[4,3,2,1,5,6,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3

[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

[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

[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

[4,3,1,2,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2

[3,4,1,2,5,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0

[4,2,1,3,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2

[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

[3,2,1,4,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2

[2,3,1,4,5,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0

[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

[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

[6,8,7,5,4,3,2,1] => [[[[[[.,[[.,.],.]],.],.],.],.],.] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 5

[6,5,8,7,4,3,2,1] => [[[[[[.,.],[[.,.],.]],.],.],.],.] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 5

[5,7,6,4,8,3,2,1] => [[[[[.,[[.,.],.]],[.,.]],.],.],.] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 3

[5,4,7,6,8,3,2,1] => [[[[[.,.],[[.,.],[.,.]]],.],.],.] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4

[4,3,8,7,6,5,2,1] => [[[[.,.],[[[[.,.],.],.],.]],.],.] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 3

[4,3,6,7,8,5,2,1] => [[[[.,.],[[.,[.,[.,.]]],.]],.],.] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 3

[5,4,3,8,7,6,2,1] => [[[[[.,.],.],[[[.,.],.],.]],.],.] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 4

[5,4,3,7,8,6,2,1] => [[[[[.,.],.],[[.,[.,.]],.]],.],.] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[4,5,3,7,8,6,2,1] => [[[[.,[.,.]],[[.,[.,.]],.]],.],.] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 2

[4,3,5,7,8,6,2,1] => [[[[.,.],[.,[[.,[.,.]],.]]],.],.] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 3

[6,5,4,3,8,7,2,1] => [[[[[[.,.],.],.],[[.,.],.]],.],.] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 5

[5,6,4,3,8,7,2,1] => [[[[[.,[.,.]],.],[[.,.],.]],.],.] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 3

[4,3,6,5,8,7,2,1] => [[[[.,.],[[.,.],[[.,.],.]]],.],.] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 3

[5,4,3,6,8,7,2,1] => [[[[[.,.],.],[.,[[.,.],.]]],.],.] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[4,5,3,6,8,7,2,1] => [[[[.,[.,.]],[.,[[.,.],.]]],.],.] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 2

[4,3,5,6,8,7,2,1] => [[[[.,.],[.,[.,[[.,.],.]]]],.],.] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 3

[5,7,6,4,3,8,2,1] => [[[[[.,[[.,.],.]],.],[.,.]],.],.] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[5,4,7,6,3,8,2,1] => [[[[[.,.],[[.,.],.]],[.,.]],.],.] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[4,3,7,6,5,8,2,1] => [[[[.,.],[[[.,.],.],[.,.]]],.],.] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 3

[4,3,6,5,7,8,2,1] => [[[[.,.],[[.,.],[.,[.,.]]]],.],.] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 3

[3,2,8,7,6,5,4,1] => [[[.,.],[[[[[.,.],.],.],.],.]],.] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 2

[3,2,6,8,7,5,4,1] => [[[.,.],[[[.,[[.,.],.]],.],.]],.] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 2

[3,2,5,7,8,6,4,1] => [[[.,.],[[.,[[.,[.,.]],.]],.]],.] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 2

[3,2,6,7,5,8,4,1] => [[[.,.],[[[.,[.,.]],[.,.]],.]],.] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 2

[3,2,5,7,6,8,4,1] => [[[.,.],[[.,[[.,.],[.,.]]],.]],.] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 2

[3,2,5,6,7,8,4,1] => [[[.,.],[[.,[.,[.,[.,.]]]],.]],.] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 2

[4,3,2,8,7,6,5,1] => [[[[.,.],.],[[[[.,.],.],.],.]],.] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 3

[4,3,2,7,8,6,5,1] => [[[[.,.],.],[[[.,[.,.]],.],.]],.] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 3

[4,3,2,6,8,7,5,1] => [[[[.,.],.],[[.,[[.,.],.]],.]],.] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 3

[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

[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

[3,2,4,8,7,6,5,1] => [[[.,.],[.,[[[[.,.],.],.],.]]],.] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 2

[3,2,4,7,8,6,5,1] => [[[.,.],[.,[[[.,[.,.]],.],.]]],.] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 2

[5,4,3,2,8,7,6,1] => [[[[[.,.],.],.],[[[.,.],.],.]],.] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 4

[5,4,3,2,7,8,6,1] => [[[[[.,.],.],.],[[.,[.,.]],.]],.] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 4

[4,5,3,2,8,7,6,1] => [[[[.,[.,.]],.],[[[.,.],.],.]],.] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 2

[4,3,5,2,8,7,6,1] => [[[[.,.],[.,.]],[[[.,.],.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 2

[3,2,5,4,7,8,6,1] => [[[.,.],[[.,.],[[.,[.,.]],.]]],.] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 2

[4,3,2,5,8,7,6,1] => [[[[.,.],.],[.,[[[.,.],.],.]]],.] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 3

[4,3,2,5,7,8,6,1] => [[[[.,.],.],[.,[[.,[.,.]],.]]],.] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[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

[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

[3,2,4,5,7,8,6,1] => [[[.,.],[.,[.,[[.,[.,.]],.]]]],.] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 2

[6,5,4,3,2,8,7,1] => [[[[[[.,.],.],.],.],[[.,.],.]],.] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 5

[4,6,5,3,2,8,7,1] => [[[[.,[[.,.],.]],.],[[.,.],.]],.] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 2

[5,4,6,3,2,8,7,1] => [[[[[.,.],[.,.]],.],[[.,.],.]],.] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[4,3,6,5,2,8,7,1] => [[[[.,.],[[.,.],.]],[[.,.],.]],.] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 2

[5,4,3,6,2,8,7,1] => [[[[[.,.],.],[.,.]],[[.,.],.]],.] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[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

[3,2,6,5,4,8,7,1] => [[[.,.],[[[.,.],.],[[.,.],.]]],.] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 2

[4,3,2,6,5,8,7,1] => [[[[.,.],.],[[.,.],[[.,.],.]]],.] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3

[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

[3,2,4,6,5,8,7,1] => [[[.,.],[.,[[.,.],[[.,.],.]]]],.] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 2

[5,4,3,2,6,8,7,1] => [[[[[.,.],.],.],[.,[[.,.],.]]],.] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 4

[3,2,5,4,6,8,7,1] => [[[.,.],[[.,.],[.,[[.,.],.]]]],.] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 2

[4,3,2,5,6,8,7,1] => [[[[.,.],.],[.,[.,[[.,.],.]]]],.] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 3

[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

[3,2,4,5,6,8,7,1] => [[[.,.],[.,[.,[.,[[.,.],.]]]]],.] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 2

[5,7,6,4,3,2,8,1] => [[[[[.,[[.,.],.]],.],.],[.,.]],.] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 3

[4,3,7,6,5,2,8,1] => [[[[.,.],[[[.,.],.],.]],[.,.]],.] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 2

[5,4,3,7,6,2,8,1] => [[[[[.,.],.],[[.,.],.]],[.,.]],.] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 3

[4,3,6,5,7,2,8,1] => [[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[3,2,7,6,5,4,8,1] => [[[.,.],[[[[.,.],.],.],[.,.]]],.] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 2

[3,2,6,7,5,4,8,1] => [[[.,.],[[[.,[.,.]],.],[.,.]]],.] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[3,2,5,7,6,4,8,1] => [[[.,.],[[.,[[.,.],.]],[.,.]]],.] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2

[3,2,6,5,7,4,8,1] => [[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2

[3,2,5,6,7,4,8,1] => [[[.,.],[[.,[.,[.,.]]],[.,.]]],.] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[4,3,2,7,6,5,8,1] => [[[[.,.],.],[[[.,.],.],[.,.]]],.] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 3

[4,3,2,6,7,5,8,1] => [[[[.,.],.],[[.,[.,.]],[.,.]]],.] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 3

[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

[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

[3,2,4,7,6,5,8,1] => [[[.,.],[.,[[[.,.],.],[.,.]]]],.] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 2

[5,4,3,2,7,6,8,1] => [[[[[.,.],.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 4

[4,3,5,2,7,6,8,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[3,2,5,4,7,6,8,1] => [[[.,.],[[.,.],[[.,.],[.,.]]]],.] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 2

[4,3,2,5,7,6,8,1] => [[[[.,.],.],[.,[[.,.],[.,.]]]],.] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 3

[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

[3,2,4,5,7,6,8,1] => [[[.,.],[.,[.,[[.,.],[.,.]]]]],.] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 2

[3,2,5,6,4,7,8,1] => [[[.,.],[[.,[.,.]],[.,[.,.]]]],.] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2

[4,3,2,6,5,7,8,1] => [[[[.,.],.],[[.,.],[.,[.,.]]]],.] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 3

[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

[3,2,5,4,6,7,8,1] => [[[.,.],[[.,.],[.,[.,[.,.]]]]],.] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 2

[2,1,8,7,6,5,4,3] => [[.,.],[[[[[[.,.],.],.],.],.],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1

[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

[2,1,6,8,7,5,4,3] => [[.,.],[[[[.,[[.,.],.]],.],.],.]] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 1

[2,1,7,6,8,5,4,3] => [[.,.],[[[[[.,.],[.,.]],.],.],.]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 1

[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

[2,1,5,8,7,6,4,3] => [[.,.],[[[.,[[[.,.],.],.]],.],.]] => [1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 1

[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

[2,1,6,5,8,7,4,3] => [[.,.],[[[[.,.],[[.,.],.]],.],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 1

[2,1,5,6,8,7,4,3] => [[.,.],[[[.,[.,[[.,.],.]]],.],.]] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 1

[2,1,7,6,5,8,4,3] => [[.,.],[[[[[.,.],.],[.,.]],.],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 1

[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

[2,1,5,7,6,8,4,3] => [[.,.],[[[.,[[.,.],[.,.]]],.],.]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 1

[2,1,6,5,7,8,4,3] => [[.,.],[[[[.,.],[.,[.,.]]],.],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 1

[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

[2,1,4,8,7,6,5,3] => [[.,.],[[.,[[[[.,.],.],.],.]],.]] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 1

[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

[2,1,4,6,8,7,5,3] => [[.,.],[[.,[[.,[[.,.],.]],.]],.]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 1

[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

[2,1,5,4,8,7,6,3] => [[.,.],[[[.,.],[[[.,.],.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 1

[2,1,5,4,7,8,6,3] => [[.,.],[[[.,.],[[.,[.,.]],.]],.]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 1

[2,1,4,5,8,7,6,3] => [[.,.],[[.,[.,[[[.,.],.],.]]],.]] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 1

[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

[2,1,6,5,4,8,7,3] => [[.,.],[[[[.,.],.],[[.,.],.]],.]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 1

[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

[2,1,4,6,5,8,7,3] => [[.,.],[[.,[[.,.],[[.,.],.]]],.]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 1

[2,1,5,4,6,8,7,3] => [[.,.],[[[.,.],[.,[[.,.],.]]],.]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 1

[2,1,4,5,6,8,7,3] => [[.,.],[[.,[.,[.,[[.,.],.]]]],.]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 1

[2,1,7,6,5,4,8,3] => [[.,.],[[[[[.,.],.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 1

[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

[2,1,5,7,6,4,8,3] => [[.,.],[[[.,[[.,.],.]],[.,.]],.]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 1

[2,1,6,5,7,4,8,3] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 1

[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

[2,1,4,7,6,5,8,3] => [[.,.],[[.,[[[.,.],.],[.,.]]],.]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 1

[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

[2,1,5,4,7,6,8,3] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 1

[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

[2,1,5,4,6,7,8,3] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 1

[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

[3,2,1,8,7,6,5,4] => [[[.,.],.],[[[[[.,.],.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2

[3,2,1,7,8,6,5,4] => [[[.,.],.],[[[[.,[.,.]],.],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 2

[3,2,1,6,8,7,5,4] => [[[.,.],.],[[[.,[[.,.],.]],.],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 2

[3,2,1,7,6,8,5,4] => [[[.,.],.],[[[[.,.],[.,.]],.],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 2

[3,2,1,6,7,8,5,4] => [[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 2

[3,2,1,5,8,7,6,4] => [[[.,.],.],[[.,[[[.,.],.],.]],.]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 2

[3,2,1,5,7,8,6,4] => [[[.,.],.],[[.,[[.,[.,.]],.]],.]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 2

[3,2,1,6,5,8,7,4] => [[[.,.],.],[[[.,.],[[.,.],.]],.]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 2

[3,2,1,5,6,8,7,4] => [[[.,.],.],[[.,[.,[[.,.],.]]],.]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 2

[3,2,1,7,6,5,8,4] => [[[.,.],.],[[[[.,.],.],[.,.]],.]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 2

[3,2,1,6,7,5,8,4] => [[[.,.],.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[3,2,1,5,7,6,8,4] => [[[.,.],.],[[.,[[.,.],[.,.]]],.]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 2

[3,2,1,6,5,7,8,4] => [[[.,.],.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[3,2,1,5,6,7,8,4] => [[[.,.],.],[[.,[.,[.,[.,.]]]],.]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[2,3,1,8,7,6,5,4] => [[.,[.,.]],[[[[[.,.],.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 0

[2,3,1,6,8,7,5,4] => [[.,[.,.]],[[[.,[[.,.],.]],.],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 0

[2,3,1,7,6,8,5,4] => [[.,[.,.]],[[[[.,.],[.,.]],.],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 0

[2,3,1,6,7,8,5,4] => [[.,[.,.]],[[[.,[.,[.,.]]],.],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 0

[2,3,1,5,7,8,6,4] => [[.,[.,.]],[[.,[[.,[.,.]],.]],.]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 0

[2,3,1,6,5,8,7,4] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 0

[2,3,1,7,6,5,8,4] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 0

[2,3,1,6,7,5,8,4] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 0

[2,3,1,5,7,6,8,4] => [[.,[.,.]],[[.,[[.,.],[.,.]]],.]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 0

[2,3,1,5,6,7,8,4] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 0

[2,1,3,8,7,6,5,4] => [[.,.],[.,[[[[[.,.],.],.],.],.]]] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 1

[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

[2,1,3,6,8,7,5,4] => [[.,.],[.,[[[.,[[.,.],.]],.],.]]] => [1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 1

[2,1,3,6,5,8,7,4] => [[.,.],[.,[[[.,.],[[.,.],.]],.]]] => [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 1

[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

[4,3,2,1,8,7,6,5] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3

[4,3,2,1,7,8,6,5] => [[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[4,3,2,1,6,8,7,5] => [[[[.,.],.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[4,3,2,1,7,6,8,5] => [[[[.,.],.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 3

[4,3,2,1,6,7,8,5] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 3

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[2,1,4,3,8,7,6,5] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 1

[2,1,4,3,7,8,6,5] => [[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 1

[2,1,4,3,6,8,7,5] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 1

[2,1,4,3,7,6,8,5] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1

[2,1,4,3,6,7,8,5] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 1

[3,2,1,4,8,7,6,5] => [[[.,.],.],[.,[[[[.,.],.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 2

[3,2,1,4,7,8,6,5] => [[[.,.],.],[.,[[[.,[.,.]],.],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 2

[3,2,1,4,6,8,7,5] => [[[.,.],.],[.,[[.,[[.,.],.]],.]]] => [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 2

[3,2,1,4,7,6,8,5] => [[[.,.],.],[.,[[[.,.],[.,.]],.]]] => [1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2

[3,2,1,4,6,7,8,5] => [[[.,.],.],[.,[[.,[.,[.,.]]],.]]] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[2,3,1,4,8,7,6,5] => [[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => 0

[2,3,1,4,7,8,6,5] => [[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 0

[2,3,1,4,7,6,8,5] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 0

[2,3,1,4,6,7,8,5] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 0

[2,1,3,4,8,7,6,5] => [[.,.],[.,[.,[[[[.,.],.],.],.]]]] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1

[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

[2,1,3,4,7,6,8,5] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 1

[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

[5,4,3,2,1,8,7,6] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4

[5,4,3,2,1,7,8,6] => [[[[[.,.],.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 4

[4,5,3,2,1,8,7,6] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 2

[3,5,4,2,1,8,7,6] => [[[.,[[.,.],.]],.],[[[.,.],.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1

[3,5,4,2,1,7,8,6] => [[[.,[[.,.],.]],.],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 1

[4,3,5,2,1,8,7,6] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 2

[3,2,5,4,1,8,7,6] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[3,2,5,4,1,7,8,6] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 1

[4,3,2,5,1,8,7,6] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2

[4,3,2,5,1,7,8,6] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 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] => 0

[3,4,2,5,1,7,8,6] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0

[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

[2,1,5,4,3,8,7,6] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 1

[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

[2,1,3,5,4,8,7,6] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 1

[2,1,3,5,4,7,8,6] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 1

[4,3,2,1,5,8,7,6] => [[[[.,.],.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 3

[4,3,2,1,5,7,8,6] => [[[[.,.],.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 3

[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

[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

[2,1,4,3,5,8,7,6] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 1

[2,1,4,3,5,7,8,6] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 1

[3,2,1,4,5,8,7,6] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 2

[3,2,1,4,5,7,8,6] => [[[.,.],.],[.,[.,[[.,[.,.]],.]]]] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[2,3,1,4,5,7,8,6] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 0

[2,1,3,4,5,8,7,6] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1

[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

[6,5,4,3,2,1,8,7] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5

[5,6,4,3,2,1,8,7] => [[[[[.,[.,.]],.],.],.],[[.,.],.]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 3

[4,6,5,3,2,1,8,7] => [[[[.,[[.,.],.]],.],.],[[.,.],.]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 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] => 3

[4,3,6,5,2,1,8,7] => [[[[.,.],[[.,.],.]],.],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2

[5,4,3,6,2,1,8,7] => [[[[[.,.],.],[.,.]],.],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 3

[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

[4,3,5,6,2,1,8,7] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 2

[3,2,6,5,4,1,8,7] => [[[.,.],[[[.,.],.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 1

[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

[4,3,2,6,5,1,8,7] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 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] => 0

[5,4,3,2,6,1,8,7] => [[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3

[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

[3,2,5,4,6,1,8,7] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[4,3,2,5,6,1,8,7] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 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] => 0

[2,1,6,5,4,3,8,7] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 1

[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

[2,1,4,6,5,3,8,7] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 1

[2,1,5,4,6,3,8,7] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[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

[2,3,1,6,5,4,8,7] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[2,1,3,6,5,4,8,7] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 1

[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

[4,3,2,1,6,5,8,7] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3

[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

[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

[2,1,4,3,6,5,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[2,3,1,4,6,5,8,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 0

[2,1,3,4,6,5,8,7] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 1

[5,4,3,2,1,6,8,7] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 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] => 2

[3,5,4,2,1,6,8,7] => [[[.,[[.,.],.]],.],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => 1

[4,3,5,2,1,6,8,7] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2

[3,2,5,4,1,6,8,7] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 1

[2,1,5,4,3,6,8,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1

[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

[4,3,2,1,5,6,8,7] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3

[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

[2,1,4,3,5,6,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 1

[3,2,1,4,5,6,8,7] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2

[2,3,1,4,5,6,8,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 0

[2,1,3,4,5,6,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1

[5,7,6,4,3,2,1,8] => [[[[[.,[[.,.],.]],.],.],.],[.,.]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 3

[5,4,7,6,3,2,1,8] => [[[[[.,.],[[.,.],.]],.],.],[.,.]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 3

[4,3,7,6,5,2,1,8] => [[[[.,.],[[[.,.],.],.]],.],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 2

[5,4,3,7,6,2,1,8] => [[[[[.,.],.],[[.,.],.]],.],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 3

[4,3,6,5,7,2,1,8] => [[[[.,.],[[.,.],[.,.]]],.],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 2

[3,2,7,6,5,4,1,8] => [[[.,.],[[[[.,.],.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1

[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

[3,2,5,7,6,4,1,8] => [[[.,.],[[.,[[.,.],.]],.]],[.,.]] => [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 1

[3,2,6,5,7,4,1,8] => [[[.,.],[[[.,.],[.,.]],.]],[.,.]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1

[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

[4,3,2,6,7,5,1,8] => [[[[.,.],.],[[.,[.,.]],.]],[.,.]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 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] => 0

[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

[5,4,3,2,7,6,1,8] => [[[[[.,.],.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3

[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

[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

[3,2,5,4,7,6,1,8] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[4,3,2,5,7,6,1,8] => [[[[.,.],.],[.,[[.,.],.]]],[.,.]] => [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 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] => 0

[3,2,6,5,4,7,1,8] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[3,4,2,6,5,7,1,8] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[2,1,7,6,5,4,3,8] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 1

[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

[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

[2,1,5,4,6,7,3,8] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[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

[3,2,1,7,6,5,4,8] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 2

[3,2,1,5,7,6,4,8] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 2

[3,2,1,6,5,7,4,8] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[2,3,1,6,7,5,4,8] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 0

[2,3,1,6,5,7,4,8] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[2,3,1,5,6,7,4,8] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 0

[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

[4,3,2,1,7,6,5,8] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[4,3,2,1,6,7,5,8] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3

[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

[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

[2,1,4,3,6,7,5,8] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[3,2,1,4,7,6,5,8] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 2

[2,3,1,4,6,7,5,8] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 0

[5,4,3,2,1,7,6,8] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4

[4,5,3,2,1,7,6,8] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 2

[3,5,4,2,1,7,6,8] => [[[.,[[.,.],.]],.],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[3,2,5,4,1,7,6,8] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[3,4,2,5,1,7,6,8] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[2,1,5,4,3,7,6,8] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[3,2,1,5,4,7,6,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[2,3,1,5,4,7,6,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[4,3,2,1,5,7,6,8] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3

[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

[3,2,1,4,5,7,6,8] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 2

[2,3,1,4,5,7,6,8] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 0

[2,1,3,4,5,7,6,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1

[4,3,6,5,2,1,7,8] => [[[[.,.],[[.,.],.]],.],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 2

[4,3,2,6,5,1,7,8] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[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

[2,1,4,6,5,3,7,8] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 1

[3,2,1,6,5,4,7,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[3,2,1,5,6,4,7,8] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[2,3,1,6,5,4,7,8] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0

[2,3,1,5,6,4,7,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[4,3,2,1,6,5,7,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[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

[2,1,4,3,6,5,7,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[2,1,3,4,6,5,7,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1

[3,5,4,2,1,6,7,8] => [[[.,[[.,.],.]],.],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1

[3,2,5,4,1,6,7,8] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1

[2,1,5,4,3,6,7,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1

[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

[2,3,1,5,4,6,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0

[2,1,3,5,4,6,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1

[2,1,4,3,5,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1

[2,1,3,4,8,6,7,5] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 1

[2,1,3,5,8,6,7,4] => [[.,.],[.,[[.,[[.,.],[.,.]]],.]]] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 1

[2,1,3,8,5,6,7,4] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 1

[2,1,3,8,5,7,6,4] => [[.,.],[.,[[[.,.],[[.,.],.]],.]]] => [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 1

[2,1,3,8,6,5,7,4] => [[.,.],[.,[[[[.,.],.],[.,.]],.]]] => [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 1

[2,1,3,8,6,7,5,4] => [[.,.],[.,[[[[.,.],[.,.]],.],.]]] => [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 1

[2,1,4,3,8,6,7,5] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1

[2,1,4,5,8,6,7,3] => [[.,.],[[.,[.,[[.,.],[.,.]]]],.]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 1

[2,1,4,8,5,6,7,3] => [[.,.],[[.,[[.,.],[.,[.,.]]]],.]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 1

[2,1,4,8,5,7,6,3] => [[.,.],[[.,[[.,.],[[.,.],.]]],.]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 1

[2,1,4,8,6,5,7,3] => [[.,.],[[.,[[[.,.],.],[.,.]]],.]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 1

[2,1,4,8,6,7,5,3] => [[.,.],[[.,[[[.,.],[.,.]],.]],.]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 1

[2,1,5,4,8,6,7,3] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 1

[2,1,6,4,5,3,8,7] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[2,1,6,4,5,7,8,3] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 1

[2,1,6,4,5,8,7,3] => [[.,.],[[[.,.],[.,[[.,.],.]]],.]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 1

[2,1,8,4,5,6,7,3] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 1

[2,1,8,4,5,7,6,3] => [[.,.],[[[.,.],[.,[[.,.],.]]],.]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 1

[2,1,7,4,6,5,8,3] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 1

[2,1,8,4,6,5,7,3] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 1

[2,1,8,4,6,7,5,3] => [[.,.],[[[.,.],[[.,[.,.]],.]],.]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 1

[2,1,8,4,7,6,5,3] => [[.,.],[[[.,.],[[[.,.],.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 1

[2,1,8,5,4,6,7,3] => [[.,.],[[[[.,.],.],[.,[.,.]]],.]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 1

[2,1,8,5,4,7,6,3] => [[.,.],[[[[.,.],.],[[.,.],.]],.]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 1

[2,1,7,5,6,4,8,3] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 1

[2,1,8,5,6,4,7,3] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 1

[2,1,8,5,6,7,4,3] => [[.,.],[[[[.,.],[.,[.,.]]],.],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 1

[2,1,8,5,7,6,4,3] => [[.,.],[[[[.,.],[[.,.],.]],.],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 1

[2,1,8,6,5,4,7,3] => [[.,.],[[[[[.,.],.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 1

[2,1,8,6,5,7,4,3] => [[.,.],[[[[[.,.],.],[.,.]],.],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 1

[2,1,8,7,5,6,4,3] => [[.,.],[[[[[.,.],.],[.,.]],.],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 1

[2,3,1,7,5,6,4,8] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[2,3,1,8,5,6,7,4] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 0

[2,3,1,8,6,7,5,4] => [[.,[.,.]],[[[[.,.],[.,.]],.],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 0

[3,2,1,4,8,6,7,5] => [[[.,.],.],[.,[[[.,.],[.,.]],.]]] => [1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2

[3,2,1,5,8,6,7,4] => [[[.,.],.],[[.,[[.,.],[.,.]]],.]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 2

[3,2,1,7,5,6,4,8] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[3,2,1,7,5,6,8,4] => [[[.,.],.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[3,2,1,8,5,6,7,4] => [[[.,.],.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[3,2,1,8,5,7,6,4] => [[[.,.],.],[[[.,.],[[.,.],.]],.]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 2

[3,2,1,8,6,5,7,4] => [[[.,.],.],[[[[.,.],.],[.,.]],.]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 2

[3,2,1,8,6,7,5,4] => [[[.,.],.],[[[[.,.],[.,.]],.],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 2

[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

[3,2,4,5,8,6,7,1] => [[[.,.],[.,[.,[[.,.],[.,.]]]]],.] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 2

[3,2,4,7,5,6,8,1] => [[[.,.],[.,[[.,.],[.,[.,.]]]]],.] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 2

[3,2,4,8,5,6,7,1] => [[[.,.],[.,[[.,.],[.,[.,.]]]]],.] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 2

[3,2,4,8,6,7,5,1] => [[[.,.],[.,[[[.,.],[.,.]],.]]],.] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 2

[3,2,5,4,8,6,7,1] => [[[.,.],[[.,.],[[.,.],[.,.]]]],.] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 2

[3,2,6,4,5,1,7,8] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[3,2,6,4,5,1,8,7] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[3,2,7,4,5,6,1,8] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[3,2,8,4,5,6,7,1] => [[[.,.],[[.,.],[.,[.,[.,.]]]]],.] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 2

[3,2,7,4,6,5,1,8] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[3,2,7,4,6,5,8,1] => [[[.,.],[[.,.],[[.,.],[.,.]]]],.] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 2

[3,2,8,4,6,5,7,1] => [[[.,.],[[.,.],[[.,.],[.,.]]]],.] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 2

[3,2,7,5,4,6,1,8] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[3,2,8,5,4,6,7,1] => [[[.,.],[[[.,.],.],[.,[.,.]]]],.] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 2

[3,2,8,5,4,7,6,1] => [[[.,.],[[[.,.],.],[[.,.],.]]],.] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 2

[3,2,7,5,6,4,1,8] => [[[.,.],[[[.,.],[.,.]],.]],[.,.]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1

[3,2,7,5,6,4,8,1] => [[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2

[3,2,8,5,6,4,7,1] => [[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2

[3,2,8,5,7,6,4,1] => [[[.,.],[[[.,.],[[.,.],.]],.]],.] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 2

[3,2,8,6,5,7,4,1] => [[[.,.],[[[[.,.],.],[.,.]],.]],.] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 2

[3,2,8,7,5,6,4,1] => [[[.,.],[[[[.,.],.],[.,.]],.]],.] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[4,2,3,5,6,8,7,1] => [[[.,.],[.,[.,[.,[[.,.],.]]]]],.] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 2

[4,2,3,5,8,7,6,1] => [[[.,.],[.,[.,[[[.,.],.],.]]]],.] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 2

[4,2,3,6,5,8,7,1] => [[[.,.],[.,[[.,.],[[.,.],.]]]],.] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 2

[4,2,3,7,5,6,8,1] => [[[.,.],[.,[[.,.],[.,[.,.]]]]],.] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 2

[4,2,3,8,5,6,7,1] => [[[.,.],[.,[[.,.],[.,[.,.]]]]],.] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 2

[4,2,3,8,5,7,6,1] => [[[.,.],[.,[[.,.],[[.,.],.]]]],.] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 2

[4,2,3,7,6,5,8,1] => [[[.,.],[.,[[[.,.],.],[.,.]]]],.] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 2

[4,2,3,8,7,6,5,1] => [[[.,.],[.,[[[[.,.],.],.],.]]],.] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 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

[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

[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

[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

[5,2,3,4,7,6,1,8] => [[[.,.],[.,[.,[[.,.],.]]]],[.,.]] => [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 1

[5,2,3,4,8,6,7,1] => [[[.,.],[.,[.,[[.,.],[.,.]]]]],.] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 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

[6,2,3,4,5,8,7,1] => [[[.,.],[.,[.,[.,[[.,.],.]]]]],.] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 2

[8,2,3,4,5,7,6,1] => [[[.,.],[.,[.,[.,[[.,.],.]]]]],.] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 2

[7,2,3,4,6,5,1,8] => [[[.,.],[.,[.,[[.,.],.]]]],[.,.]] => [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 1

[8,2,3,4,7,6,5,1] => [[[.,.],[.,[.,[[[.,.],.],.]]]],.] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 2

[6,2,3,5,4,1,7,8] => [[[.,.],[.,[[.,.],.]]],[.,[.,.]]] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 1

[6,2,3,5,4,1,8,7] => [[[.,.],[.,[[.,.],.]]],[[.,.],.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 1

[6,2,3,5,4,7,1,8] => [[[.,.],[.,[[.,.],[.,.]]]],[.,.]] => [1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1

[6,2,3,5,4,7,8,1] => [[[.,.],[.,[[.,.],[.,[.,.]]]]],.] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 2

[7,2,3,5,4,6,1,8] => [[[.,.],[.,[[.,.],[.,.]]]],[.,.]] => [1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1

[8,2,3,5,4,6,7,1] => [[[.,.],[.,[[.,.],[.,[.,.]]]]],.] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 2

[8,2,3,5,4,7,6,1] => [[[.,.],[.,[[.,.],[[.,.],.]]]],.] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 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

[8,2,3,5,6,7,4,1] => [[[.,.],[.,[[.,[.,[.,.]]],.]]],.] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 2

[8,2,3,5,7,6,4,1] => [[[.,.],[.,[[.,[[.,.],.]],.]]],.] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 2

[7,2,3,6,5,4,1,8] => [[[.,.],[.,[[[.,.],.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 1

[8,2,3,6,5,4,7,1] => [[[.,.],[.,[[[.,.],.],[.,.]]]],.] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 2

[8,2,3,7,5,6,4,1] => [[[.,.],[.,[[[.,.],[.,.]],.]]],.] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 2

[8,2,3,7,6,5,4,1] => [[[.,.],[.,[[[[.,.],.],.],.]]],.] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 2

[5,2,4,3,1,6,7,8] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1

[5,2,4,3,1,6,8,7] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 1

[5,2,4,3,1,7,6,8] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[5,2,4,3,1,8,7,6] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[5,2,4,3,6,1,8,7] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[5,2,4,3,6,7,1,8] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[5,2,4,3,7,6,1,8] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[5,2,4,3,7,6,8,1] => [[[.,.],[[.,.],[[.,.],[.,.]]]],.] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 2

[5,2,4,3,8,7,6,1] => [[[.,.],[[.,.],[[[.,.],.],.]]],.] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 2

[6,2,4,3,5,1,8,7] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[7,2,4,3,6,5,1,8] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[7,2,4,3,6,5,8,1] => [[[.,.],[[.,.],[[.,.],[.,.]]]],.] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 2

[8,2,4,3,6,5,7,1] => [[[.,.],[[.,.],[[.,.],[.,.]]]],.] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 2

[8,2,4,3,6,7,5,1] => [[[.,.],[[.,.],[[.,[.,.]],.]]],.] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 2

[8,2,4,3,7,6,5,1] => [[[.,.],[[.,.],[[[.,.],.],.]]],.] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 2

[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

[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

[7,2,4,5,3,6,8,1] => [[[.,.],[[.,[.,.]],[.,[.,.]]]],.] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2

[8,2,4,5,3,7,6,1] => [[[.,.],[[.,[.,.]],[[.,.],.]]],.] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 2

[8,2,4,5,6,7,3,1] => [[[.,.],[[.,[.,[.,[.,.]]]],.]],.] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 2

[8,2,4,5,7,6,3,1] => [[[.,.],[[.,[.,[[.,.],.]]],.]],.] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 2

[7,2,4,6,5,3,1,8] => [[[.,.],[[.,[[.,.],.]],.]],[.,.]] => [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 1

[7,2,4,6,5,3,8,1] => [[[.,.],[[.,[[.,.],.]],[.,.]]],.] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2

[8,2,4,7,5,6,3,1] => [[[.,.],[[.,[[.,.],[.,.]]],.]],.] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 2

[8,2,4,7,6,5,3,1] => [[[.,.],[[.,[[[.,.],.],.]],.]],.] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 2

[6,2,5,4,3,1,8,7] => [[[.,.],[[[.,.],.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 1

[6,2,5,4,3,7,1,8] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[6,2,5,4,3,7,8,1] => [[[.,.],[[[.,.],.],[.,[.,.]]]],.] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 2

[7,2,5,4,3,6,1,8] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[8,2,5,4,3,6,7,1] => [[[.,.],[[[.,.],.],[.,[.,.]]]],.] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 2

[8,2,5,4,3,7,6,1] => [[[.,.],[[[.,.],.],[[.,.],.]]],.] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 2

[7,2,5,4,6,3,8,1] => [[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2

[8,2,5,4,7,6,3,1] => [[[.,.],[[[.,.],[[.,.],.]],.]],.] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 2

[7,2,6,4,5,3,1,8] => [[[.,.],[[[.,.],[.,.]],.]],[.,.]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1

[7,2,6,4,5,3,8,1] => [[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2

[8,2,6,4,5,3,7,1] => [[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2

[8,2,6,4,5,7,3,1] => [[[.,.],[[[.,.],[.,[.,.]]],.]],.] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 2

[8,2,7,4,5,6,3,1] => [[[.,.],[[[.,.],[.,[.,.]]],.]],.] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 2

[8,2,7,4,6,5,3,1] => [[[.,.],[[[.,.],[[.,.],.]],.]],.] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 2

[7,2,6,5,4,3,1,8] => [[[.,.],[[[[.,.],.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1

[7,2,6,5,4,3,8,1] => [[[.,.],[[[[.,.],.],.],[.,.]]],.] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 2

[8,2,6,5,4,3,7,1] => [[[.,.],[[[[.,.],.],.],[.,.]]],.] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 2

[8,2,6,5,4,7,3,1] => [[[.,.],[[[[.,.],.],[.,.]],.]],.] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 2

[8,2,7,5,4,6,3,1] => [[[.,.],[[[[.,.],.],[.,.]],.]],.] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 2

[8,2,7,5,6,4,3,1] => [[[.,.],[[[[.,.],[.,.]],.],.]],.] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 2

[8,2,7,6,5,4,3,1] => [[[.,.],[[[[[.,.],.],.],.],.]],.] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 2

[4,3,2,1,8,6,7,5] => [[[[.,.],.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 3

[4,3,2,7,5,6,8,1] => [[[[.,.],.],[[.,.],[.,[.,.]]]],.] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 3

[4,3,2,8,5,6,7,1] => [[[[.,.],.],[[.,.],[.,[.,.]]]],.] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 3

[4,3,2,8,5,7,6,1] => [[[[.,.],.],[[.,.],[[.,.],.]]],.] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3

[4,3,2,8,6,7,5,1] => [[[[.,.],.],[[[.,.],[.,.]],.]],.] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[5,3,2,4,1,6,8,7] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[5,3,2,4,1,7,6,8] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[5,3,2,4,1,8,7,6] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2

[5,3,2,4,7,6,1,8] => [[[[.,.],.],[.,[[.,.],.]]],[.,.]] => [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 2

[8,3,2,4,6,5,7,1] => [[[[.,.],.],[.,[[.,.],[.,.]]]],.] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 3

[8,3,2,4,6,7,5,1] => [[[[.,.],.],[.,[[.,[.,.]],.]]],.] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[8,3,2,4,7,6,5,1] => [[[[.,.],.],[.,[[[.,.],.],.]]],.] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 3

[6,3,2,5,4,1,7,8] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[6,3,2,5,4,1,8,7] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[6,3,2,5,4,7,1,8] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2

[6,3,2,5,4,7,8,1] => [[[[.,.],.],[[.,.],[.,[.,.]]]],.] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 3

[6,3,2,5,4,8,7,1] => [[[[.,.],.],[[.,.],[[.,.],.]]],.] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3

[7,3,2,5,4,6,1,8] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2

[8,3,2,5,4,7,6,1] => [[[[.,.],.],[[.,.],[[.,.],.]]],.] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3

[7,3,2,5,6,4,8,1] => [[[[.,.],.],[[.,[.,.]],[.,.]]],.] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 3

[8,3,2,5,6,4,7,1] => [[[[.,.],.],[[.,[.,.]],[.,.]]],.] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 3

[8,3,2,5,6,7,4,1] => [[[[.,.],.],[[.,[.,[.,.]]],.]],.] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[8,3,2,5,7,6,4,1] => [[[[.,.],.],[[.,[[.,.],.]],.]],.] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 3

[8,3,2,6,5,7,4,1] => [[[[.,.],.],[[[.,.],[.,.]],.]],.] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[8,3,2,7,5,6,4,1] => [[[[.,.],.],[[[.,.],[.,.]],.]],.] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[8,3,2,7,6,5,4,1] => [[[[.,.],.],[[[[.,.],.],.],.]],.] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 3

[5,3,4,2,1,6,8,7] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2

[5,3,4,2,1,7,8,6] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 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] => 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

[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

[5,3,4,2,7,6,8,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[5,3,4,2,8,6,7,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[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

[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

[7,3,4,2,6,5,8,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[8,3,4,2,6,5,7,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[6,3,4,5,2,1,8,7] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 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] => 2

[8,3,4,5,2,7,6,1] => [[[[.,.],[.,[.,.]]],[[.,.],.]],.] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 2

[8,3,4,5,7,6,2,1] => [[[[.,.],[.,[.,[[.,.],.]]]],.],.] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 3

[8,3,4,7,6,5,2,1] => [[[[.,.],[.,[[[.,.],.],.]]],.],.] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 3

[6,3,5,4,2,1,8,7] => [[[[.,.],[[.,.],.]],.],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2

[6,3,5,4,2,7,1,8] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[6,3,5,4,2,7,8,1] => [[[[.,.],[[.,.],.]],[.,[.,.]]],.] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 2

[6,3,5,4,2,8,7,1] => [[[[.,.],[[.,.],.]],[[.,.],.]],.] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 2

[7,3,5,4,2,6,1,8] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[8,3,5,4,2,6,7,1] => [[[[.,.],[[.,.],.]],[.,[.,.]]],.] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 2

[8,3,5,4,2,7,6,1] => [[[[.,.],[[.,.],.]],[[.,.],.]],.] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 2

[7,3,5,4,6,2,1,8] => [[[[.,.],[[.,.],[.,.]]],.],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 2

[7,3,5,4,6,2,8,1] => [[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[8,3,5,4,6,7,2,1] => [[[[.,.],[[.,.],[.,[.,.]]]],.],.] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 3

[8,3,5,4,7,6,2,1] => [[[[.,.],[[.,.],[[.,.],.]]],.],.] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 3

[7,3,6,4,5,2,1,8] => [[[[.,.],[[.,.],[.,.]]],.],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 2

[7,3,6,4,5,2,8,1] => [[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[8,3,6,4,5,2,7,1] => [[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[8,3,7,4,5,6,2,1] => [[[[.,.],[[.,.],[.,[.,.]]]],.],.] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 3

[8,3,7,4,6,5,2,1] => [[[[.,.],[[.,.],[[.,.],.]]],.],.] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 3

[7,3,6,5,4,2,1,8] => [[[[.,.],[[[.,.],.],.]],.],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 2

[7,3,6,5,4,2,8,1] => [[[[.,.],[[[.,.],.],.]],[.,.]],.] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 2

[8,3,6,5,4,7,2,1] => [[[[.,.],[[[.,.],.],[.,.]]],.],.] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 3

[8,3,7,5,4,6,2,1] => [[[[.,.],[[[.,.],.],[.,.]]],.],.] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 3

[8,3,7,5,6,4,2,1] => [[[[.,.],[[[.,.],[.,.]],.]],.],.] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 3

[8,3,7,6,5,4,2,1] => [[[[.,.],[[[[.,.],.],.],.]],.],.] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 3

[5,4,3,2,8,6,7,1] => [[[[[.,.],.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 4

[6,4,3,2,5,1,8,7] => [[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3

[6,4,3,2,5,8,7,1] => [[[[[.,.],.],.],[.,[[.,.],.]]],.] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 4

[8,4,3,2,5,7,6,1] => [[[[[.,.],.],.],[.,[[.,.],.]]],.] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 4

[7,4,3,2,6,5,1,8] => [[[[[.,.],.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3

[7,4,3,2,6,5,8,1] => [[[[[.,.],.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 4

[8,4,3,2,6,5,7,1] => [[[[[.,.],.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 4

[8,4,3,2,7,6,5,1] => [[[[[.,.],.],.],[[[.,.],.],.]],.] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 4

[6,4,3,5,2,1,8,7] => [[[[[.,.],.],[.,.]],.],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 3

[8,4,3,5,2,7,6,1] => [[[[[.,.],.],[.,.]],[[.,.],.]],.] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[8,4,3,5,7,6,2,1] => [[[[[.,.],.],[.,[[.,.],.]]],.],.] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[7,4,3,6,5,2,1,8] => [[[[[.,.],.],[[.,.],.]],.],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 3

[7,4,3,6,5,2,8,1] => [[[[[.,.],.],[[.,.],.]],[.,.]],.] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 3

[8,4,3,7,5,6,2,1] => [[[[[.,.],.],[[.,.],[.,.]]],.],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 4

[8,4,3,7,6,5,2,1] => [[[[[.,.],.],[[[.,.],.],.]],.],.] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 4

[6,5,3,4,2,1,8,7] => [[[[[.,.],.],[.,.]],.],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 3

[8,5,3,4,2,7,6,1] => [[[[[.,.],.],[.,.]],[[.,.],.]],.] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[8,5,3,4,7,6,2,1] => [[[[[.,.],.],[.,[[.,.],.]]],.],.] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[8,7,3,4,6,5,2,1] => [[[[[.,.],.],[.,[[.,.],.]]],.],.] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[7,6,3,5,4,2,1,8] => [[[[[.,.],.],[[.,.],.]],.],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 3

[7,6,3,5,4,2,8,1] => [[[[[.,.],.],[[.,.],.]],[.,.]],.] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 3

[8,6,3,5,4,2,7,1] => [[[[[.,.],.],[[.,.],.]],[.,.]],.] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 3

[8,6,3,5,4,7,2,1] => [[[[[.,.],.],[[.,.],[.,.]]],.],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 4

[8,7,3,5,4,6,2,1] => [[[[[.,.],.],[[.,.],[.,.]]],.],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 4

[8,7,3,5,6,4,2,1] => [[[[[.,.],.],[[.,[.,.]],.]],.],.] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[8,7,3,6,5,4,2,1] => [[[[[.,.],.],[[[.,.],.],.]],.],.] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 4

[8,5,4,3,2,7,6,1] => [[[[[[.,.],.],.],.],[[.,.],.]],.] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 5

[8,5,4,3,7,6,2,1] => [[[[[[.,.],.],.],[[.,.],.]],.],.] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 5

[8,7,4,3,6,5,2,1] => [[[[[[.,.],.],.],[[.,.],.]],.],.] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 5

[8,7,4,6,5,3,2,1] => [[[[[[.,.],.],[[.,.],.]],.],.],.] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[2,4,1,3,6,5,8,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 0

[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

[2,4,1,6,3,5,8,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0

[2,1,4,3,6,8,5,7] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[2,4,1,3,6,8,5,7] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 0

[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

[2,4,1,6,3,8,5,7] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[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

[2,4,1,6,8,3,5,7] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[2,4,1,3,6,5,7,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 0

[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

[2,4,1,6,3,5,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0

[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

[2,4,1,6,3,7,5,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[2,4,1,3,6,7,8,5] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 0

[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

[2,4,1,6,3,7,8,5] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 0

[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

[2,4,1,6,7,3,8,5] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[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

[2,4,1,6,7,8,3,5] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 0

[2,1,4,3,7,5,8,6] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[2,4,1,3,7,5,8,6] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 0

[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

[2,4,1,7,3,5,8,6] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0

[2,1,4,3,7,8,5,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[2,4,1,3,7,8,5,6] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 0

[2,4,1,7,3,8,5,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[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

[2,4,1,7,8,3,5,6] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[2,4,1,5,3,7,6,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[2,4,1,3,5,7,8,6] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 0

[2,4,1,5,3,7,8,6] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 0

[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

[2,4,1,5,7,3,8,6] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[2,1,4,3,8,5,6,7] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[2,4,1,3,8,5,6,7] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 0

[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

[2,4,1,8,3,5,6,7] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0

[2,1,4,3,5,8,6,7] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 1

[2,4,1,5,3,8,6,7] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[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

[2,4,1,5,8,3,6,7] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[2,4,1,5,3,6,8,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0

[2,4,1,5,6,3,8,7] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[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

[2,4,1,5,6,8,3,7] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 0

[2,4,1,3,5,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0

[2,4,1,5,3,6,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0

[2,4,1,5,6,3,7,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[2,4,1,5,6,7,3,8] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 0

[2,4,1,5,6,7,8,3] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 0

[2,1,5,3,6,4,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[2,5,1,3,6,4,8,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 0

[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

[2,5,1,6,3,4,8,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0

[2,1,5,3,6,8,4,7] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[2,5,1,3,6,8,4,7] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 0

[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

[2,5,1,6,8,3,4,7] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[2,5,1,3,6,4,7,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 0

[2,1,5,3,6,7,4,8] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[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

[2,5,1,6,3,7,4,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[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

[2,5,1,6,7,3,4,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[2,1,5,3,6,7,8,4] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 1

[2,5,1,3,6,7,8,4] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 0

[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

[2,5,1,6,3,7,8,4] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 0

[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

[2,5,1,6,7,3,8,4] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[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

[2,5,1,6,7,8,3,4] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 0

[2,1,5,3,7,4,8,6] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[2,5,1,3,7,4,8,6] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 0

[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

[2,5,1,7,3,4,8,6] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0

[2,1,5,3,7,8,4,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[2,5,1,3,7,8,4,6] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 0

[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

[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

[2,5,1,7,8,3,4,6] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[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

[2,3,1,5,7,8,4,6] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 0

[2,1,5,3,8,4,6,7] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[2,5,1,3,8,4,6,7] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 0

[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

[2,5,1,8,3,4,6,7] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0

[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

[2,1,5,3,4,6,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 1

[2,3,1,5,6,8,4,7] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 0

[2,1,5,3,4,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1

[2,5,1,3,4,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0

[2,1,6,3,7,4,8,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[2,6,1,3,7,4,8,5] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 0

[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

[2,6,1,7,3,4,8,5] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0

[2,1,6,3,7,8,4,5] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[2,6,1,3,7,8,4,5] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 0

[2,6,1,7,3,8,4,5] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[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

[2,6,1,7,8,3,4,5] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[2,6,1,7,3,4,5,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0

[2,6,1,3,4,7,5,8] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 0

[2,3,1,6,4,7,5,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[2,1,6,3,4,7,8,5] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 1

[2,6,1,3,4,7,8,5] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 0

[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

[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

[2,3,1,6,7,8,4,5] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 0

[2,1,6,3,8,4,5,7] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[2,6,1,3,8,4,5,7] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 0

[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

[2,6,1,8,3,4,5,7] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0

[2,1,6,3,4,8,5,7] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 1

[2,6,1,3,4,8,5,7] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 0

[2,1,3,6,4,8,5,7] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 1

[2,3,1,6,4,8,5,7] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[2,3,1,6,8,4,5,7] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[2,1,6,3,4,5,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 1

[2,6,1,3,4,5,8,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 0

[2,1,3,6,4,5,8,7] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 1

[2,6,1,3,4,5,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0

[2,1,3,6,4,5,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1

[2,3,1,6,4,5,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0

[2,1,7,3,8,4,5,6] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[2,7,1,3,8,4,5,6] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 0

[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

[2,7,1,8,3,4,5,6] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0

[2,1,7,3,4,8,5,6] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 1

[2,1,3,7,4,8,5,6] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 1

[2,3,1,7,4,8,5,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[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

[2,3,1,7,8,4,5,6] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[2,1,7,3,4,5,8,6] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 1

[2,7,1,3,4,5,8,6] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 0

[2,3,1,7,4,5,8,6] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0

[2,1,3,4,7,5,8,6] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 1

[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

[2,3,1,4,7,8,5,6] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 0

[2,1,7,3,4,5,6,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1

[2,7,1,3,4,5,6,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0

[2,1,3,4,7,5,6,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1

[2,3,1,4,7,5,6,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 0

[2,1,8,3,4,5,6,7] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1

[2,8,1,3,4,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0

[2,1,3,8,4,5,6,7] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1

[2,3,1,8,4,5,6,7] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0

[2,1,3,4,8,5,6,7] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1

[2,3,1,4,8,5,6,7] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 0

[2,1,3,4,5,8,6,7] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1

[2,3,1,4,5,8,6,7] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 0

[3,1,4,2,6,5,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[3,4,1,2,6,5,8,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 0

[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

[3,4,1,6,2,5,8,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0

[3,1,4,2,6,8,5,7] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[3,4,1,2,6,8,5,7] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 0

[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

[3,4,1,6,2,8,5,7] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[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

[3,4,1,6,8,2,5,7] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[3,4,1,2,6,5,7,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 0

[3,1,4,2,6,7,5,8] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[3,4,1,2,6,7,5,8] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 0

[3,4,1,6,2,7,5,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[3,4,1,6,7,2,5,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[3,1,4,2,6,7,8,5] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 1

[3,4,1,2,6,7,8,5] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 0

[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

[3,4,1,6,2,7,8,5] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 0

[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

[3,4,1,6,7,2,8,5] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[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

[3,4,1,6,7,8,2,5] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 0

[3,1,4,2,7,5,8,6] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[3,4,1,2,7,5,8,6] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 0

[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

[3,1,4,2,7,8,5,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[3,4,1,2,7,8,5,6] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 0

[3,1,4,2,7,5,6,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[3,4,1,2,7,5,6,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 0

[3,4,1,2,5,7,6,8] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 0

[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

[3,4,1,5,2,7,6,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[3,4,1,5,7,2,6,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[3,1,4,2,5,7,8,6] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 1

[3,4,1,2,5,7,8,6] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 0

[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

[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

[3,4,1,5,7,2,8,6] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[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

[3,4,1,5,7,8,2,6] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 0

[3,1,4,2,8,5,6,7] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[3,4,1,2,8,5,6,7] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 0

[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

[3,4,1,8,2,5,6,7] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0

[3,1,4,2,5,8,6,7] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 1

[3,4,1,2,5,8,6,7] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 0

[3,4,1,5,2,8,6,7] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[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

[3,4,1,5,8,2,6,7] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[3,4,1,2,5,6,8,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 0

[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

[3,4,1,5,6,2,8,7] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[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

[3,4,1,5,6,8,2,7] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 0

[3,1,4,2,5,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1

[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

[3,4,1,5,2,6,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0

[3,4,1,5,6,2,7,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[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

[3,4,1,5,6,7,2,8] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 0

[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

[3,4,1,5,6,7,8,2] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 0

[3,1,5,2,6,4,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[3,5,1,2,6,4,8,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 0

[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

[3,5,1,6,2,4,8,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0

[3,1,5,2,6,8,4,7] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[3,5,1,2,6,8,4,7] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 0

[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

[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

[3,5,1,6,8,2,4,7] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[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

[3,5,1,6,2,4,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0

[3,5,1,2,6,7,4,8] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 0

[3,5,1,6,2,7,4,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[3,5,1,6,7,2,4,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[3,1,5,2,6,7,8,4] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 1

[3,5,1,2,6,7,8,4] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 0

[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

[3,5,1,6,2,7,8,4] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 0

[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

[3,5,1,6,7,2,8,4] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[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

[3,5,1,6,7,8,2,4] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 0

[3,1,5,2,7,4,8,6] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[3,5,1,2,7,4,8,6] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 0

[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

[3,1,5,2,7,8,4,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[3,5,1,2,7,8,4,6] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 0

[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

[3,5,1,7,2,8,4,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[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

[3,5,1,7,8,2,4,6] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[3,1,5,2,7,4,6,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[3,5,1,2,7,4,6,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 0

[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

[3,5,1,7,2,4,6,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0

[3,1,5,2,4,7,6,8] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 1

[3,5,1,2,4,7,6,8] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 0

[3,1,2,5,4,7,6,8] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 1

[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

[3,5,1,2,4,7,8,6] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 0

[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

[3,1,5,2,8,4,6,7] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[3,5,1,2,8,4,6,7] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 0

[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

[3,5,1,8,2,4,6,7] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0

[3,1,5,2,4,8,6,7] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 1

[3,5,1,2,4,8,6,7] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 0

[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

[3,5,1,2,4,6,8,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 0

[3,1,2,5,4,6,8,7] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 1

[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

[3,5,1,2,4,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0

[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

[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

[3,1,6,2,7,4,8,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[3,6,1,2,7,4,8,5] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 0

[3,6,1,7,2,4,8,5] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0

[3,6,1,2,7,8,4,5] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 0

[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

[3,6,1,7,2,8,4,5] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[3,6,1,7,8,2,4,5] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[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

[3,1,6,2,4,7,5,8] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 1

[3,6,1,2,4,7,5,8] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 0

[3,1,2,6,4,7,5,8] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 1

[3,1,6,2,4,7,8,5] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 1

[3,6,1,2,4,7,8,5] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 0

[3,1,2,6,4,7,8,5] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 1

[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

[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

[3,6,1,2,8,4,5,7] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 0

[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

[3,6,1,8,2,4,5,7] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0

[3,1,6,2,4,8,5,7] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 1

[3,6,1,2,4,8,5,7] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 0

[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

[3,1,6,2,4,5,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 1

[3,6,1,2,4,5,8,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 0

[3,1,2,6,4,5,8,7] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 1

[3,1,2,4,6,5,8,7] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 1

[3,6,1,2,4,5,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0

[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

[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

[3,1,7,2,8,4,5,6] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[3,7,1,2,8,4,5,6] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 0

[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

[3,7,1,8,2,4,5,6] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0

[3,7,1,2,4,8,5,6] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 0

[3,1,2,7,4,8,5,6] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 1

[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

[3,1,7,2,4,5,8,6] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 1

[3,7,1,2,4,5,8,6] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 0

[3,1,2,4,7,5,8,6] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 1

[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

[3,1,7,2,4,5,6,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1

[3,7,1,2,4,5,6,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0

[3,1,2,7,4,5,6,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1

[3,1,2,4,7,5,6,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1

[3,1,2,4,5,7,6,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1

[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

[3,1,8,2,4,5,6,7] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1

[3,8,1,2,4,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0

[3,1,2,8,4,5,6,7] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1

[3,1,2,4,8,5,6,7] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1

[3,1,2,4,5,8,6,7] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1

[3,1,2,4,5,6,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1

[4,1,5,2,6,3,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[4,5,1,2,6,3,8,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 0

[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

[4,5,1,6,2,3,8,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0

[4,1,5,2,6,8,3,7] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[4,5,1,2,6,8,3,7] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 0

[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

[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

[4,5,1,6,8,2,3,7] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[4,1,5,2,6,3,7,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[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

[4,5,1,6,2,3,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0

[4,5,1,2,6,7,3,8] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 0

[4,5,1,6,2,7,3,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[4,1,5,2,6,7,8,3] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 1

[4,5,1,2,6,7,8,3] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 0

[4,5,1,6,2,7,8,3] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 0

[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

[4,5,1,6,7,2,8,3] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[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

[4,5,1,6,7,8,2,3] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 0

[4,1,5,2,7,3,8,6] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[4,5,1,2,7,3,8,6] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 0

[4,5,1,7,2,3,8,6] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0

[4,1,5,2,7,8,3,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[4,5,1,2,7,8,3,6] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 0

[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

[4,5,1,7,2,8,3,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[4,5,1,7,8,2,3,6] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[4,1,5,2,7,3,6,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[4,5,1,2,7,3,6,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 0

[4,1,5,2,3,7,6,8] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 1

[4,5,1,2,3,7,6,8] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 0

[4,1,2,5,3,7,6,8] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 1

[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

[4,1,5,2,3,7,8,6] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 1

[4,1,2,5,3,7,8,6] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 1

[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

[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

[4,1,5,2,8,3,6,7] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[4,5,1,2,8,3,6,7] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 0

[4,5,1,8,2,3,6,7] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0

[4,1,5,2,3,8,6,7] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 1

[4,5,1,2,3,8,6,7] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 0

[4,1,2,5,3,8,6,7] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 1

[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

[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

[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

[4,1,5,2,3,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1

[4,1,2,5,3,6,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1

[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

[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

[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

[4,1,6,2,7,3,8,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[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

[4,6,1,2,7,8,3,5] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 0

[4,6,1,7,2,8,3,5] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[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

[4,6,1,7,8,2,3,5] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[4,1,6,2,7,3,5,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[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

[4,6,1,7,2,3,5,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0

[4,1,6,2,3,7,5,8] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 1

[4,6,1,2,3,7,5,8] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 0

[4,1,2,6,3,7,5,8] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 1

[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

[4,1,6,2,3,7,8,5] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 1

[4,1,2,6,3,7,8,5] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 1

[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

[4,1,6,2,8,3,5,7] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[4,6,1,2,8,3,5,7] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 0

[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

[4,6,1,8,2,3,5,7] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0

[4,1,6,2,3,8,5,7] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 1

[4,6,1,2,3,8,5,7] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 0

[4,1,2,6,3,8,5,7] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 1

[4,1,6,2,3,5,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 1

[4,6,1,2,3,5,8,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 0

[4,1,2,6,3,5,8,7] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 1

[4,1,2,3,6,5,8,7] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 1

[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

[4,1,6,2,3,5,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1

[4,6,1,2,3,5,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0

[4,1,2,3,6,5,7,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1

[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

[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

[4,1,7,2,8,3,5,6] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[4,7,1,2,8,3,5,6] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 0

[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

[4,7,1,8,2,3,5,6] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0

[4,1,7,2,3,8,5,6] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 1

[4,7,1,2,3,8,5,6] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 0

[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

[4,1,7,2,3,5,8,6] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 1

[4,7,1,2,3,5,8,6] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 0

[4,1,2,7,3,5,8,6] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 1

[4,1,2,3,7,5,8,6] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 1

[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

[4,1,7,2,3,5,6,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1

[4,7,1,2,3,5,6,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0

[4,1,2,7,3,5,6,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1

[4,1,2,3,7,5,6,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1

[4,1,2,3,5,7,6,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1

[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

[4,1,8,2,3,5,6,7] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1

[4,8,1,2,3,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0

[4,1,2,8,3,5,6,7] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1

[4,1,2,3,8,5,6,7] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1

[4,1,2,3,5,8,6,7] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1

[4,1,2,3,5,6,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1

[5,1,6,2,7,3,8,4] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[5,6,1,2,7,3,8,4] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 0

[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

[5,6,1,7,2,3,8,4] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0

[5,6,1,2,7,8,3,4] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 0

[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

[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

[5,6,1,7,8,2,3,4] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[5,1,6,2,7,3,4,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[5,6,1,7,2,3,4,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0

[5,1,6,2,3,7,4,8] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 1

[5,1,2,6,3,7,4,8] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 1

[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

[5,1,6,2,3,7,8,4] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 1

[5,6,1,2,3,7,8,4] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 0

[5,1,2,6,3,7,8,4] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 1

[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

[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

[5,1,6,2,8,3,4,7] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[5,6,1,2,8,3,4,7] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 0

[5,6,1,8,2,3,4,7] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0

[5,1,6,2,3,8,4,7] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 1

[5,6,1,2,3,8,4,7] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 0

[5,1,2,6,3,8,4,7] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 1

[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

[5,1,6,2,3,4,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 1

[5,6,1,2,3,4,8,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 0

[5,1,2,6,3,4,8,7] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 1

[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

[5,1,6,2,3,4,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1

[5,1,2,6,3,4,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1

[5,1,2,3,6,4,7,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1

[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

[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

[5,1,7,2,8,3,4,6] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[5,7,1,2,8,3,4,6] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 0

[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

[5,7,1,8,2,3,4,6] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0

[5,1,7,2,3,8,4,6] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 1

[5,7,1,2,3,8,4,6] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 0

[5,1,2,7,3,8,4,6] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 1

[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

[5,1,7,2,3,4,8,6] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 1

[5,7,1,2,3,4,8,6] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 0

[5,1,2,7,3,4,8,6] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 1

[5,1,2,3,7,4,8,6] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 1

[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

[5,7,1,2,3,4,6,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0

[5,1,2,7,3,4,6,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1

[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

[5,1,8,2,3,4,6,7] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1

[5,8,1,2,3,4,6,7] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0

[5,1,2,8,3,4,6,7] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1

[5,1,2,3,8,4,6,7] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1

[5,1,2,3,4,8,6,7] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1

[5,1,2,3,4,6,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1

[6,1,7,2,8,3,4,5] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[6,7,1,2,8,3,4,5] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 0

[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

[6,7,1,8,2,3,4,5] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0

[6,1,7,2,3,8,4,5] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 1

[6,7,1,2,3,8,4,5] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 0

[6,1,2,7,3,8,4,5] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 1

[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

[6,1,7,2,3,4,8,5] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 1

[6,7,1,2,3,4,8,5] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 0

[6,1,2,7,3,4,8,5] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 1

[6,1,2,3,7,4,8,5] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 1

[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

[6,1,7,2,3,4,5,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1

[6,1,2,7,3,4,5,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1

[6,1,2,3,7,4,5,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1

[6,1,2,3,4,7,5,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1

[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

[6,1,8,2,3,4,5,7] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1

[6,8,1,2,3,4,5,7] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0

[6,1,2,8,3,4,5,7] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1

[6,1,2,3,8,4,5,7] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1

[6,1,2,3,4,8,5,7] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1

[6,1,2,3,4,5,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1

[7,1,8,2,3,4,5,6] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1

[7,1,2,8,3,4,5,6] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1

[7,1,2,3,8,4,5,6] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1

[7,1,2,3,4,8,5,6] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1

[7,1,2,3,4,5,8,6] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1

[5,3,2,6,1,4,8,7] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[7,3,2,5,4,8,1,6] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2

[8,4,5,2,3,7,6,1] => [[[[.,.],[.,.]],[.,[[.,.],.]]],.] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 2

[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

[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

[5,4,6,2,1,3,8,7] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2

[3,6,1,5,4,2,8,7] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[5,6,4,3,1,2,8,7] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => 2

[7,5,4,3,2,8,1,6] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 4

[8,6,4,3,7,2,5,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 4

[7,6,4,3,8,2,1,5] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 4

[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

[5,7,4,3,1,8,2,6] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 2

[3,7,1,5,4,8,2,6] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[2,1,7,5,4,8,3,6] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1

[3,8,1,5,4,7,6,2] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 0

[5,8,4,3,1,7,6,2] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 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

[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

[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

[3,8,1,6,7,4,5,2] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 0

[2,1,8,6,7,4,5,3] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 1

[2,1,7,6,8,4,3,5] => [[.,.],[[[[.,.],[.,.]],.],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 1

[3,7,1,6,8,4,2,5] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 0

[5,4,7,2,1,8,3,6] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2

[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

[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

[8,4,6,2,7,3,5,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[8,3,2,6,7,4,5,1] => [[[[.,.],.],[[.,[.,.]],[.,.]]],.] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 3

[7,3,2,6,8,4,1,5] => [[[[.,.],.],[[.,[.,.]],.]],[.,.]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 2

[6,3,2,7,8,1,4,5] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[5,3,2,7,1,8,4,6] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[4,3,2,1,7,8,5,6] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3

[3,4,1,2,8,7,6,5] => [[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => 0

[5,3,2,8,1,7,6,4] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2

[6,3,2,8,7,1,5,4] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[7,3,2,8,6,5,1,4] => [[[[.,.],.],[[[.,.],.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 2

[8,4,7,2,6,5,3,1] => [[[[.,.],[.,.]],[[[.,.],.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 2

[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

[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

[5,4,8,2,1,7,6,3] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 2

[3,5,1,8,2,7,6,4] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 0

[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

[2,1,6,8,7,3,5,4] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 1

[3,6,1,8,7,2,5,4] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[6,5,8,7,2,1,4,3] => [[[[.,.],[[.,.],.]],.],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2

[7,5,8,6,2,4,1,3] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[8,5,7,6,2,4,3,1] => [[[[.,.],[[.,.],.]],[[.,.],.]],.] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 2

[3,7,1,8,6,5,2,4] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 0

[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

[3,8,1,7,6,5,4,2] => [[.,[.,.]],[[[[[.,.],.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 0

[6,8,7,5,4,1,3,2] => [[[[.,[[.,.],.]],.],.],[[.,.],.]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[3,6,2,5,1,4,7,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0

[4,6,2,5,1,3,7,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0

[4,6,3,5,1,2,7,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0

[5,6,2,4,1,3,7,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0

[3,7,2,5,1,4,6,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0

[4,7,3,5,1,2,6,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0

[3,7,2,6,1,4,5,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0

[4,7,3,6,1,2,5,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0

[5,7,2,6,1,3,4,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0

[6,7,2,5,1,3,4,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0

[4,8,2,5,1,3,6,7] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0

[5,8,2,4,1,3,6,7] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0

[5,8,3,4,1,2,6,7] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0

[5,8,3,6,1,2,4,7] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0

[5,8,4,6,1,2,3,7] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0

[6,8,3,5,1,2,4,7] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0

[3,8,2,7,1,4,5,6] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0

[4,8,2,7,1,3,5,6] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0

[4,8,3,7,1,2,5,6] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0

[5,8,2,7,1,3,4,6] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0

[5,8,3,7,1,2,4,6] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0

[5,8,4,7,1,2,3,6] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0

[6,8,2,7,1,3,4,5] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0

[6,8,3,7,1,2,4,5] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0

[6,8,5,7,1,2,3,4] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0

[7,8,2,4,1,3,5,6] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0

[7,8,2,5,1,3,4,6] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0

[7,8,3,5,1,2,4,6] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0

[7,8,4,6,1,2,3,5] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0

[4,3,2,6,1,5,7,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[5,3,2,6,1,4,7,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[5,4,2,6,1,3,7,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[6,3,2,5,1,4,7,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[6,5,2,4,1,3,7,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[4,3,2,7,1,5,6,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[5,3,2,7,1,4,6,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[6,3,2,7,1,4,5,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[6,4,2,7,1,3,5,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[6,4,3,7,1,2,5,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[6,5,2,7,1,3,4,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[6,5,3,7,1,2,4,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[7,3,2,5,1,4,6,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[7,4,2,5,1,3,6,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[7,3,2,6,1,4,5,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[7,4,2,6,1,3,5,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[7,4,3,6,1,2,5,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[7,5,2,6,1,3,4,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[7,5,3,6,1,2,4,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[4,3,2,8,1,5,6,7] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[5,3,2,8,1,4,6,7] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[6,3,2,8,1,4,5,7] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[6,4,2,8,1,3,5,7] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[6,4,3,8,1,2,5,7] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[6,5,2,8,1,3,4,7] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[6,5,3,8,1,2,4,7] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[7,3,2,8,1,4,5,6] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[7,4,2,8,1,3,5,6] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[7,4,3,8,1,2,5,6] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[7,5,3,8,1,2,4,6] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[7,5,4,8,1,2,3,6] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[7,6,2,8,1,3,4,5] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[8,3,2,5,1,4,6,7] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[8,4,2,5,1,3,6,7] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[8,3,2,6,1,4,5,7] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[8,4,2,6,1,3,5,7] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[8,5,3,6,1,2,4,7] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[8,6,2,4,1,3,5,7] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[8,6,2,5,1,3,4,7] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[8,3,2,7,1,4,5,6] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[8,4,2,7,1,3,5,6] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[8,4,3,7,1,2,5,6] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[8,5,2,7,1,3,4,6] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[8,5,3,7,1,2,4,6] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[8,6,3,7,1,2,4,5] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[8,7,2,4,1,3,5,6] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[8,7,2,5,1,3,4,6] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[8,7,3,5,1,2,4,6] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[8,7,2,6,1,3,4,5] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[8,7,3,6,1,2,4,5] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[8,7,4,6,1,2,3,5] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2

[3,6,2,5,8,1,4,7] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[4,6,3,5,8,1,2,7] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[5,6,2,4,8,1,3,7] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[4,7,2,5,8,1,3,6] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[4,7,3,5,8,1,2,6] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[5,7,2,4,8,1,3,6] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[5,7,3,4,8,1,2,6] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[4,7,3,6,8,1,2,5] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[5,7,2,6,8,1,3,4] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[5,7,4,6,8,1,2,3] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[6,7,3,4,8,1,2,5] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[6,7,3,5,8,1,2,4] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[3,8,2,5,7,1,4,6] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[4,8,3,5,7,1,2,6] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[5,8,2,4,7,1,3,6] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[3,8,2,6,7,1,4,5] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[5,8,2,6,7,1,3,4] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[5,8,3,6,7,1,2,4] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[6,8,2,5,7,1,3,4] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[7,8,2,4,6,1,3,5] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[7,8,3,4,6,1,2,5] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[7,8,2,5,6,1,3,4] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[7,8,3,5,6,1,2,4] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[4,3,2,6,8,1,5,7] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[5,3,2,6,8,1,4,7] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[5,4,2,6,8,1,3,7] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[5,4,3,6,8,1,2,7] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[6,3,2,5,8,1,4,7] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[6,4,3,5,8,1,2,7] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[6,5,2,4,8,1,3,7] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[4,3,2,7,8,1,5,6] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[5,3,2,7,8,1,4,6] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[5,4,2,7,8,1,3,6] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[5,4,3,7,8,1,2,6] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[6,4,2,7,8,1,3,5] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[6,4,3,7,8,1,2,5] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[7,4,2,5,8,1,3,6] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[7,4,3,5,8,1,2,6] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[7,5,2,6,8,1,3,4] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[7,5,3,6,8,1,2,4] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[7,6,2,4,8,1,3,5] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[8,3,2,5,7,1,4,6] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[8,4,2,5,7,1,3,6] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[8,5,2,4,7,1,3,6] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[8,3,2,6,7,1,4,5] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[8,5,2,6,7,1,3,4] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[8,5,3,6,7,1,2,4] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[8,6,2,4,7,1,3,5] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[8,6,2,5,7,1,3,4] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[8,6,3,5,7,1,2,4] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[8,7,2,4,6,1,3,5] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[8,7,3,4,6,1,2,5] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[8,7,2,5,6,1,3,4] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[5,4,3,2,7,1,6,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3

[6,4,3,2,7,1,5,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3

[6,5,3,2,7,1,4,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3

[6,5,4,2,7,1,3,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3

[7,5,3,2,6,1,4,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3

[7,5,4,2,6,1,3,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3

[5,4,3,2,8,1,6,7] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3

[6,5,3,2,8,1,4,7] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3

[6,5,4,3,8,1,2,7] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3

[7,5,3,2,8,1,4,6] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3

[7,5,4,2,8,1,3,6] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3

[7,6,3,2,8,1,4,5] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3

[7,6,4,3,8,1,2,5] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3

[7,6,5,2,8,1,3,4] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3

[8,5,3,2,6,1,4,7] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3

[8,5,4,2,6,1,3,7] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3

[8,6,3,2,5,1,4,7] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3

[8,6,5,2,4,1,3,7] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3

[8,5,3,2,7,1,4,6] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3

[8,6,3,2,7,1,4,5] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3

[8,6,4,3,7,1,2,5] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3

[8,7,3,2,5,1,4,6] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3

[8,7,3,2,6,1,4,5] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3

[8,7,4,2,6,1,3,5] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3

[8,7,4,3,6,1,2,5] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3

[8,7,5,2,6,1,3,4] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3

[8,7,5,3,6,1,2,4] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3

[8,7,6,2,4,1,3,5] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3

[8,7,6,2,5,1,3,4] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3

[8,7,6,3,5,1,2,4] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 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] => 0

[5,8,3,7,2,6,1,4] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[5,8,4,7,2,6,1,3] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[5,8,4,7,3,6,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[6,8,3,7,2,5,1,4] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[6,8,4,7,2,5,1,3] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[6,8,4,7,3,5,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[6,8,5,7,2,4,1,3] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[6,8,5,7,3,4,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[7,8,3,6,2,5,1,4] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[7,8,4,6,2,5,1,3] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[7,8,4,6,3,5,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[7,8,5,6,2,4,1,3] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[5,4,3,8,2,7,1,6] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[6,4,3,8,2,7,1,5] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[6,5,3,8,2,7,1,4] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[6,5,4,8,3,7,1,2] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[7,4,3,8,2,6,1,5] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[7,5,3,8,2,6,1,4] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[7,5,4,8,2,6,1,3] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[7,6,3,8,2,5,1,4] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[7,6,4,8,2,5,1,3] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[7,6,5,8,2,4,1,3] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[8,4,3,7,2,6,1,5] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[8,5,3,7,2,6,1,4] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[8,5,4,7,2,6,1,3] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[8,5,4,7,3,6,1,2] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[8,6,3,7,2,5,1,4] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[8,6,4,7,2,5,1,3] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[8,6,4,7,3,5,1,2] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[8,6,5,7,2,4,1,3] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[8,7,3,6,2,5,1,4] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[8,7,4,6,2,5,1,3] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[8,7,4,6,3,5,1,2] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[8,7,5,6,2,4,1,3] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[6,5,4,3,2,8,1,7] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 4

[7,6,5,4,2,8,1,3] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 4

[8,5,4,3,2,7,1,6] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 4

[8,7,4,3,2,6,1,5] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 4

[8,7,5,3,2,6,1,4] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 4

[8,7,5,4,2,6,1,3] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 4

[8,7,6,3,2,5,1,4] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 4

[8,7,6,4,2,5,1,3] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 4

[8,7,6,5,2,4,1,3] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 4

[8,1,2,3,4,7,5,6] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1

[8,1,2,3,6,4,5,7] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1

[8,1,2,3,7,4,5,6] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1

[7,1,2,3,6,4,8,5] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 1

[5,1,2,3,8,7,4,6] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 1

[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

[4,1,2,8,3,7,5,6] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 1

[8,1,2,5,3,4,6,7] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1

[7,1,2,5,3,4,8,6] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 1

[8,1,2,6,3,4,5,7] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1

[7,1,2,6,3,4,8,5] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 1

[6,1,2,5,3,8,4,7] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 1

[8,1,2,5,3,7,4,6] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 1

[8,1,2,6,3,7,4,5] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 1

[6,1,2,5,3,7,8,4] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 1

[4,1,2,8,6,3,5,7] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 1

[4,1,2,8,7,3,5,6] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 1

[4,1,2,7,6,3,8,5] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 1

[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

[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

[8,1,2,7,6,3,4,5] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 1

[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

[4,1,2,5,8,7,3,6] => [[.,.],[.,[[.,[[.,.],.]],[.,.]]]] => [1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 1

[4,1,2,8,6,7,3,5] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 1

[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

[3,1,8,2,4,7,5,6] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 1

[3,1,8,2,6,4,5,7] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[3,1,8,2,7,4,5,6] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[3,1,7,2,6,4,8,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[3,1,5,2,8,7,4,6] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1

[3,1,8,2,6,7,4,5] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[8,1,4,2,3,5,6,7] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1

[7,1,4,2,3,5,8,6] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 1

[6,1,4,2,3,8,5,7] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 1

[8,1,4,2,3,7,5,6] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 1

[6,1,4,2,3,7,8,5] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 1

[8,1,5,2,3,4,6,7] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1

[7,1,5,2,3,4,8,6] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 1

[8,1,7,2,3,4,5,6] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1

[6,1,5,2,3,8,4,7] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 1

[8,1,5,2,3,7,4,6] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 1

[6,1,8,2,3,7,4,5] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 1

[6,1,5,2,3,7,8,4] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 1

[5,1,4,2,8,3,6,7] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[5,1,4,2,7,3,8,6] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[8,1,4,2,6,3,5,7] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[8,1,4,2,7,3,5,6] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[7,1,4,2,6,3,8,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[8,1,5,2,6,3,4,7] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[8,1,5,2,7,3,4,6] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[7,1,8,2,6,3,4,5] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[7,1,5,2,6,3,8,4] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[5,1,4,2,6,8,3,7] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[5,1,4,2,8,7,3,6] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1

[8,1,4,2,6,7,3,5] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[8,1,5,2,6,7,3,4] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[5,1,4,2,6,7,8,3] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 1

[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

[3,1,8,5,2,4,6,7] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1

[3,1,7,5,2,4,8,6] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1

[3,1,8,6,2,4,5,7] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1

[3,1,7,6,2,4,8,5] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1

[3,1,6,5,2,8,4,7] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[3,1,8,5,2,7,4,6] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[3,1,8,6,2,7,4,5] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[3,1,6,5,2,7,8,4] => [[.,.],[[[.,.],.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 1

[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

[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

[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

[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

[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

[8,1,6,5,2,3,4,7] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1

[7,1,8,5,2,3,4,6] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1

[7,1,8,6,2,3,4,5] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1

[7,1,6,5,2,3,8,4] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1

[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

[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

[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

[8,1,6,5,2,7,3,4] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[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

[3,1,4,8,6,2,5,7] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 1

[3,1,4,8,7,2,5,6] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 1

[3,1,4,7,6,2,8,5] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 1

[3,1,8,5,6,2,4,7] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[3,1,8,5,7,2,4,6] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[3,1,8,7,6,2,4,5] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 1

[3,1,7,5,6,2,8,4] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[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

[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

[8,1,4,7,6,2,3,5] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 1

[8,1,7,5,6,2,3,4] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[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

[3,1,4,5,8,7,2,6] => [[.,.],[[.,[.,[[.,.],.]]],[.,.]]] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 1

[3,1,4,8,6,7,2,5] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 1

[3,1,8,5,6,7,2,4] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[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

[2,8,1,3,4,7,5,6] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 0

[2,8,1,3,6,4,5,7] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 0

[2,8,1,3,7,4,5,6] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 0

[2,7,1,3,6,4,8,5] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 0

[2,5,1,3,8,7,4,6] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 0

[2,8,1,3,6,7,4,5] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 0

[2,4,1,8,3,7,5,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[2,8,1,5,3,4,6,7] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0

[2,7,1,5,3,4,8,6] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0

[2,8,1,6,3,4,5,7] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0

[2,7,1,6,3,4,8,5] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0

[2,6,1,5,3,8,4,7] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[2,8,1,5,3,7,4,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[2,6,1,5,3,7,8,4] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 0

[2,4,1,8,6,3,5,7] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0

[2,4,1,8,7,3,5,6] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0

[2,4,1,7,6,3,8,5] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[2,8,1,5,6,3,4,7] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[2,8,1,5,7,3,4,6] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[2,8,1,7,6,3,4,5] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0

[2,7,1,5,6,3,8,4] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[2,4,1,5,8,7,3,6] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 0

[2,4,1,8,6,7,3,5] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[2,8,1,5,6,7,3,4] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 0

[7,3,1,2,4,5,8,6] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2

[6,3,1,2,4,8,5,7] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 2

[8,3,1,2,4,7,5,6] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 2

[6,3,1,2,4,7,8,5] => [[[.,.],.],[.,[.,[[.,[.,.]],.]]]] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[5,3,1,2,8,4,6,7] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2

[5,3,1,2,7,4,8,6] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2

[8,3,1,2,6,4,5,7] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2

[8,3,1,2,7,4,5,6] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2

[7,3,1,2,6,4,8,5] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2

[5,3,1,2,6,8,4,7] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 2

[5,3,1,2,8,7,4,6] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 2

[8,3,1,2,6,7,4,5] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 2

[5,3,1,2,6,7,8,4] => [[[.,.],.],[.,[[.,[.,[.,.]]],.]]] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[7,4,1,2,3,5,8,6] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2

[6,4,1,2,3,8,5,7] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 2

[8,4,1,2,3,7,5,6] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 2

[6,4,1,2,3,7,8,5] => [[[.,.],.],[.,[.,[[.,[.,.]],.]]]] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[7,6,1,2,3,4,8,5] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2

[5,8,1,2,3,7,4,6] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 0

[8,6,1,2,3,7,4,5] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 2

[5,4,1,2,8,3,6,7] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2

[5,4,1,2,7,3,8,6] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2

[8,4,1,2,6,3,5,7] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2

[8,4,1,2,7,3,5,6] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2

[7,4,1,2,6,3,8,5] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2

[5,8,1,2,6,3,4,7] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 0

[5,8,1,2,7,3,4,6] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 0

[8,7,1,2,6,3,4,5] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2

[5,7,1,2,6,3,8,4] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 0

[5,4,1,2,6,8,3,7] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 2

[5,4,1,2,8,7,3,6] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 2

[8,4,1,2,6,7,3,5] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 2

[5,8,1,2,6,7,3,4] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 0

[5,4,1,2,6,7,8,3] => [[[.,.],.],[.,[[.,[.,[.,.]]],.]]] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[4,3,1,8,2,5,6,7] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2

[4,3,1,7,2,5,8,6] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2

[4,3,1,6,2,8,5,7] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[4,3,1,8,2,7,5,6] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[4,3,1,6,2,7,8,5] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[8,3,1,5,2,4,6,7] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2

[7,3,1,5,2,4,8,6] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2

[8,3,1,6,2,4,5,7] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2

[7,3,1,8,2,4,5,6] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2

[7,3,1,6,2,4,8,5] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2

[6,3,1,5,2,8,4,7] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[8,3,1,5,2,7,4,6] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[8,3,1,6,2,7,4,5] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[6,3,1,5,2,7,8,4] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[8,4,1,5,2,3,6,7] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2

[7,4,1,5,2,3,8,6] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2

[8,4,1,6,2,3,5,7] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2

[7,4,1,8,2,3,5,6] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2

[7,4,1,6,2,3,8,5] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2

[6,8,1,5,2,3,4,7] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0

[8,7,1,5,2,3,4,6] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2

[8,7,1,6,2,3,4,5] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2

[6,7,1,5,2,3,8,4] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0

[6,4,1,5,2,8,3,7] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[8,4,1,5,2,7,3,6] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[8,4,1,6,2,7,3,5] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[6,8,1,5,2,7,3,4] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[6,4,1,5,2,7,8,3] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[4,3,1,5,8,2,6,7] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[4,3,1,5,7,2,8,6] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[4,3,1,8,6,2,5,7] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[4,3,1,8,7,2,5,6] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[4,3,1,7,6,2,8,5] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[8,3,1,5,6,2,4,7] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[8,3,1,5,7,2,4,6] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[8,3,1,7,6,2,4,5] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[7,3,1,5,6,2,8,4] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[8,4,1,5,6,2,3,7] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[8,4,1,5,7,2,3,6] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[8,4,1,7,6,2,3,5] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[7,8,1,5,6,2,3,4] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[7,4,1,5,6,2,8,3] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[4,3,1,5,6,8,2,7] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 2

[4,3,1,5,8,7,2,6] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 2

[4,3,1,8,6,7,2,5] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[8,3,1,5,6,7,2,4] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 2

[8,4,1,5,6,7,2,3] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 2

[4,3,1,5,6,7,8,2] => [[[.,.],.],[[.,[.,[.,[.,.]]]],.]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[7,5,4,1,2,3,8,6] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 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

[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

[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

[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

[6,5,4,1,2,8,3,7] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3

[8,5,4,1,2,7,3,6] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3

[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

[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

[6,5,4,1,2,7,8,3] => [[[[.,.],.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 3

[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

[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

[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

[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

[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

[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

[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

[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

[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

[8,5,4,1,6,2,3,7] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[8,5,4,1,7,2,3,6] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 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

[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

[7,5,4,1,6,2,8,3] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3

[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

[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

[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

[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

[8,5,4,1,6,7,2,3] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 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

[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

[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

[8,3,6,5,1,2,4,7] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1

[7,3,8,5,1,2,4,6] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1

[7,3,8,6,1,2,4,5] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1

[7,3,6,5,1,2,8,4] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 1

[7,6,4,5,1,2,8,3] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[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

[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

[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

[8,3,6,5,1,7,2,4] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[8,6,4,5,1,7,2,3] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[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

[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

[8,3,4,7,6,1,2,5] => [[[.,.],[.,[[.,.],.]]],[.,[.,.]]] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 1

[8,3,7,5,6,1,2,4] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[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

[3,5,2,6,1,4,8,7] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 0

[3,5,2,6,4,1,8,7] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[3,5,2,7,4,8,1,6] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[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

[3,5,1,6,4,2,8,7] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[3,5,1,7,4,8,2,6] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[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

[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

[3,5,1,7,4,8,6,2] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 0

[3,6,1,7,8,4,5,2] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 0

[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

[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

[3,6,1,7,8,4,2,5] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 0

[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

[3,6,2,7,8,4,1,5] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 0

[3,6,2,7,8,1,4,5] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[3,5,2,7,1,8,4,6] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[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

[3,4,1,2,7,8,6,5] => [[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 0

[3,5,2,7,1,8,6,4] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 0

[3,6,2,7,8,1,5,4] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0

[3,6,2,7,8,5,1,4] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 0

[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

[3,5,1,7,2,8,6,4] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 0

[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

[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

[3,6,1,7,8,2,5,4] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[3,6,1,7,8,5,2,4] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 0

[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

[3,6,1,7,8,5,4,2] => [[.,[.,.]],[[[[.,[.,.]],.],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 0

[6,5,8,7,3,4,1,2] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[4,5,3,7,8,6,1,2] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 0

[5,4,3,8,7,6,1,2] => [[[[.,.],.],[[[.,.],.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 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

[6,3,8,4,5,7,1,2] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[5,3,4,8,6,7,1,2] => [[[.,.],[.,[[.,.],[.,.]]]],[.,.]] => [1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1

[4,3,5,6,8,7,1,2] => [[[.,.],[.,[.,[[.,.],.]]]],[.,.]] => [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 1

[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

[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

[5,2,4,8,6,1,7,3] => [[[.,.],[.,[[.,.],.]]],[[.,.],.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 1

[6,2,8,4,5,1,7,3] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[7,8,2,4,5,1,6,3] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0

[7,8,1,4,5,2,3,6] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[6,1,8,4,5,2,3,7] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[5,1,4,8,6,2,3,7] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 1

[4,1,3,2,8,6,5,7] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1

[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

[6,1,8,3,2,5,4,7] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[7,8,1,3,2,5,4,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[7,8,2,3,1,5,6,4] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0

[6,2,8,3,1,5,7,4] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 1

[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

[6,3,8,2,1,7,5,4] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 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] => 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

[5,4,2,8,7,1,6,3] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 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] => 0

[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

[6,5,8,7,1,2,3,4] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1

[5,4,1,8,7,2,3,6] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 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

[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

[5,3,1,8,2,7,4,6] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[4,3,1,2,8,7,5,6] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 2

[4,2,1,3,8,5,7,6] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2

[5,2,1,8,3,4,7,6] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2

[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

[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

[4,3,1,2,6,5,8,7] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2

[5,3,1,6,2,4,8,7] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2

[6,3,1,5,2,4,8,7] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2

[7,3,1,5,2,8,4,6] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[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

[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

[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

[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

[2,1,6,5,3,4,8,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1

[3,6,1,5,2,4,8,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0

[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

[6,5,4,1,2,3,8,7] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3

[7,5,4,1,2,8,3,6] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3

[8,6,4,1,7,2,3,5] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[7,6,4,1,8,2,3,5] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[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

[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

[3,7,1,5,2,8,4,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[2,1,7,5,3,8,4,6] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[2,1,8,5,3,7,4,6] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[3,8,1,5,2,7,4,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[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

[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

[8,7,4,1,6,2,3,5] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[3,8,1,6,7,2,4,5] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[2,1,8,6,7,3,4,5] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[2,1,7,6,8,3,4,5] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[3,7,1,6,8,2,4,5] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[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

[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

[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

[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

[8,3,1,6,7,2,4,5] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[7,3,1,6,8,2,4,5] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[6,3,1,7,8,2,4,5] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[5,3,1,7,2,8,4,6] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[4,3,1,2,7,8,5,6] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 2

[2,1,4,3,8,7,5,6] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1

[3,4,1,2,8,7,5,6] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 0

[6,3,1,8,7,2,4,5] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[7,3,1,8,6,2,4,5] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[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

[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

[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

[3,5,1,8,2,7,4,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[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

[2,1,6,8,7,3,4,5] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 1

[3,6,1,8,7,2,4,5] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0

[7,5,8,6,1,2,3,4] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1

[8,5,7,6,1,2,3,4] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1

[3,7,1,8,6,2,4,5] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0

[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

[2,1,8,7,6,3,4,5] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 1

[3,8,1,7,6,2,4,5] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0

[6,8,7,5,1,2,3,4] => [[[.,[[.,.],.]],.],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1

[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

[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

[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

[5,4,2,7,6,1,3,8] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[5,4,2,7,6,1,8,3] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[5,4,3,7,6,8,1,2] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2

[5,4,3,7,8,6,1,2] => [[[[.,.],.],[[.,[.,.]],.]],[.,.]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 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

[5,4,3,8,6,7,1,2] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2

[5,4,3,6,8,7,1,2] => [[[[.,.],.],[.,[[.,.],.]]],[.,.]] => [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 2

[5,4,2,6,7,1,8,3] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[5,4,2,6,7,1,3,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[5,3,2,6,1,7,4,8] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[5,3,2,6,1,7,8,4] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[5,3,2,6,1,8,7,4] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2

[5,4,2,6,8,1,7,3] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[5,4,2,8,6,1,7,3] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 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

[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

[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

[5,4,2,8,6,1,3,7] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[5,3,2,6,1,8,4,7] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[4,3,2,1,6,8,5,7] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3

[4,3,2,1,8,6,5,7] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[5,3,2,8,1,6,4,7] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[6,3,8,2,1,5,4,7] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2

[7,8,3,2,1,5,4,6] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 2

[7,8,3,2,1,5,6,4] => [[[[.,[.,.]],.],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 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] => 2

[5,3,2,8,1,6,7,4] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[5,4,2,7,8,1,6,3] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[5,3,2,7,1,8,6,4] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2

[5,3,2,7,1,6,8,4] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[5,3,2,7,1,6,4,8] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 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] => 2

[6,3,7,2,1,5,8,4] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 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] => 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

[6,5,7,8,2,1,4,3] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 2

[6,5,8,7,2,1,3,4] => [[[[.,.],[[.,.],.]],.],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 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] => 2

[6,3,7,2,1,4,8,5] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2

[6,3,7,2,1,4,5,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2

[5,3,2,7,1,4,8,6] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[5,4,2,8,7,1,3,6] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[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

[7,8,3,2,1,6,4,5] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 2

[6,3,8,2,1,7,4,5] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2

[5,3,2,8,1,7,4,6] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[4,3,2,1,8,7,5,6] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[4,3,2,1,7,5,8,6] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3

[4,3,2,1,7,5,6,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[4,3,2,1,8,5,7,6] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3

[5,3,2,8,1,4,7,6] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[6,3,8,2,1,4,7,5] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2

[7,8,3,2,1,4,6,5] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => 2

[6,3,8,2,1,4,5,7] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2

[4,3,2,1,8,5,6,7] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[4,3,2,1,5,8,6,7] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3

[7,8,5,6,1,2,4,3] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 0

[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

[7,8,1,4,6,2,5,3] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[6,1,8,4,7,2,5,3] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[7,8,1,3,2,6,5,4] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 0

[7,8,3,4,6,5,1,2] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 0

[7,8,2,4,6,1,5,3] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0

[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

[7,8,1,2,3,6,5,4] => [[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 0

[6,1,8,2,3,7,5,4] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 1

[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

[6,2,8,4,7,1,5,3] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[6,3,8,4,7,5,1,2] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[2,4,1,3,8,7,6,5] => [[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => 0

[5,3,4,8,7,6,1,2] => [[[.,.],[.,[[[.,.],.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 1

[4,2,1,3,8,7,6,5] => [[[.,.],.],[.,[[[[.,.],.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 2

[4,1,2,3,8,7,6,5] => [[.,.],[.,[.,[[[[.,.],.],.],.]]]] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1

[4,3,1,2,8,7,6,5] => [[[.,.],.],[.,[[[[.,.],.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 2

[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

[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

[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

[6,5,8,7,1,2,4,3] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 1

[4,5,1,8,7,2,6,3] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[4,5,3,8,7,6,1,2] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 0

[4,5,2,8,7,1,6,3] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[3,5,2,8,1,7,6,4] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 0

[3,1,2,4,8,7,6,5] => [[.,.],[.,[.,[[[[.,.],.],.],.]]]] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1

[4,3,5,8,7,6,1,2] => [[[.,.],[.,[[[.,.],.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 1

[4,1,3,2,6,5,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[5,1,3,2,6,4,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[6,1,3,2,5,4,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[7,1,3,2,5,4,8,6] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[8,1,3,2,5,4,7,6] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[8,1,4,2,5,3,7,6] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[7,1,4,2,5,3,8,6] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[6,1,4,2,5,3,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[5,1,4,2,6,3,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[2,1,6,3,5,4,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[3,1,6,2,5,4,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[4,1,6,2,5,3,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[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

[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

[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

[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

[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

[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

[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

[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

[4,1,7,2,5,3,8,6] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[3,1,7,2,5,4,8,6] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[2,1,7,3,5,4,8,6] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[2,1,8,3,5,4,7,6] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[3,1,8,2,5,4,7,6] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[4,1,8,2,5,3,7,6] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[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

[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

[7,1,4,3,8,2,6,5] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[8,1,4,3,7,2,6,5] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[8,1,5,3,7,2,6,4] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[7,1,5,3,8,2,6,4] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[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

[5,1,8,2,6,3,7,4] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[4,1,8,2,6,3,7,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[3,1,8,2,6,4,7,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[2,1,8,3,6,4,7,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[2,1,7,3,6,4,8,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[4,1,7,2,6,3,8,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[5,1,7,2,6,3,8,4] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[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

[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

[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

[8,1,5,2,6,3,7,4] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[6,1,5,2,7,3,8,4] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[6,1,4,2,7,3,8,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[8,1,4,2,6,3,7,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[8,1,3,2,6,4,7,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[7,1,3,2,6,4,8,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[6,1,3,2,7,4,8,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[5,1,3,2,7,4,8,6] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[4,1,3,2,7,5,8,6] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[2,1,4,3,8,5,7,6] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[3,1,4,2,8,5,7,6] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[4,1,3,2,8,5,7,6] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[5,1,3,2,8,4,7,6] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[6,1,3,2,8,4,7,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[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

[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

[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

[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

[6,1,4,2,8,3,7,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[5,1,4,2,8,3,7,6] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[4,1,5,2,8,3,7,6] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[3,1,5,2,8,4,7,6] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[2,1,5,3,8,4,7,6] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[2,1,6,3,8,4,7,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[3,1,6,2,8,4,7,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[4,1,6,2,8,3,7,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[5,1,6,2,8,3,7,4] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[6,1,5,2,8,3,7,4] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[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

[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

[6,2,7,3,8,1,5,4] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[6,2,8,3,7,1,5,4] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[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

[5,1,8,3,7,2,6,4] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[4,1,8,3,7,2,6,5] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[3,1,8,4,7,2,6,5] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[2,1,8,4,7,3,6,5] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[2,1,7,4,8,3,6,5] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[3,1,7,4,8,2,6,5] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[4,1,7,3,8,2,6,5] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[5,1,7,3,8,2,6,4] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[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

[8,2,6,3,7,1,5,4] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[7,2,6,3,8,1,5,4] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[3,4,2,6,8,1,5,7] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[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

[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

[5,7,3,8,2,4,1,6] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[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

[7,4,2,5,8,3,6,1] => [[[[.,.],.],[[.,[.,.]],[.,.]]],.] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 3

[7,4,2,5,8,3,1,6] => [[[[.,.],.],[[.,[.,.]],.]],[.,.]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 2

[4,5,2,6,3,8,1,7] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[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

[5,3,1,6,8,2,4,7] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[5,6,2,8,1,3,4,7] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0

[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

[4,5,1,6,3,8,2,7] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[7,4,5,3,8,2,1,6] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 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] => 2

[6,7,4,8,3,2,5,1] => [[[[[.,[.,.]],[.,.]],.],[.,.]],.] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[6,7,4,8,3,2,1,5] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 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

[7,4,5,3,1,8,2,6] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2

[4,7,1,5,8,3,2,6] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 0

[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

[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

[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

[4,5,1,7,8,3,6,2] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 0

[7,4,1,5,8,3,6,2] => [[[.,.],.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 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

[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

[6,7,4,8,3,5,2,1] => [[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 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] => 0

[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

[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

[6,7,2,8,4,5,1,3] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[6,7,2,8,4,1,3,5] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 0

[6,1,7,4,8,3,2,5] => [[.,.],[[[[.,.],[.,.]],.],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 1

[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

[5,6,1,7,3,2,8,4] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[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

[5,6,2,7,3,1,8,4] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[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

[6,1,7,4,2,8,3,5] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[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

[7,5,8,2,1,3,4,6] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2

[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

[4,7,1,5,2,8,3,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[7,4,2,5,1,8,3,6] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[6,7,4,2,1,8,3,5] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 2

[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

[6,7,4,2,8,3,5,1] => [[[[.,[.,.]],.],[[.,.],[.,.]]],.] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => 2

[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

[5,7,3,8,2,6,1,4] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[6,4,7,8,2,5,3,1] => [[[[.,.],[.,[.,.]]],[[.,.],.]],.] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 2

[6,4,7,8,2,1,5,3] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 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

[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

[6,7,2,8,5,1,3,4] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 0

[6,4,1,7,8,2,5,3] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[5,1,6,2,7,8,4,3] => [[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 1

[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

[5,6,2,7,1,8,4,3] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 0

[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

[5,6,1,7,2,8,4,3] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 0

[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

[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

[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

[5,6,1,7,8,4,3,2] => [[.,[.,.]],[[[[.,[.,.]],.],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 0

[8,6,1,3,4,2,5,7] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[8,3,2,5,1,6,4,7] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[8,5,3,6,2,4,1,7] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[5,3,2,7,4,1,8,6] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[7,5,3,8,2,4,6,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3

[7,2,4,5,8,3,6,1] => [[[.,.],[[.,[.,[.,.]]],[.,.]]],.] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 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

[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

[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

[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

[8,5,6,2,1,4,3,7] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2

[8,5,3,6,4,1,2,7] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[8,4,1,5,6,3,2,7] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 2

[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

[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

[7,4,5,8,3,2,6,1] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 3

[4,3,6,7,2,8,5,1] => [[[[.,.],[.,[.,.]]],[[.,.],.]],.] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 2

[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

[4,5,3,7,1,8,2,6] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[4,1,5,3,7,2,8,6] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[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

[7,5,8,2,1,4,6,3] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[7,5,3,8,4,1,6,2] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 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

[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

[6,4,7,8,3,5,2,1] => [[[[[.,.],[.,[.,.]]],[.,.]],.],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[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

[4,6,1,7,8,3,5,2] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 0

[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

[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

[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

[5,3,1,7,8,2,4,6] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[4,5,2,7,8,1,3,6] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[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

[4,2,6,7,8,3,5,1] => [[[.,.],[[.,[.,[.,.]]],[.,.]]],.] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[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

[3,6,2,7,4,8,1,5] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[3,2,1,6,4,7,8,5] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[3,7,4,2,1,5,8,6] => [[[.,[[.,.],.]],.],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => 1

[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

[7,8,4,2,1,3,6,5] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => 2

[7,8,1,3,4,2,6,5] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[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

[6,3,2,7,1,8,5,4] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 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] => 0

[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

[6,4,7,8,5,2,3,1] => [[[[.,.],[[.,[.,.]],.]],[.,.]],.] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 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] => 0

[7,4,5,8,6,2,1,3] => [[[[.,.],[.,[[.,.],.]]],.],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 2

[7,4,1,5,8,6,2,3] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 2

[7,5,3,8,6,1,2,4] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 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] => 2

[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

[6,3,1,7,8,2,5,4] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[4,6,1,7,8,5,2,3] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 0

[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

[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

[5,2,6,7,8,4,3,1] => [[[.,.],[[[.,[.,[.,.]]],.],.]],.] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 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] => 0

[6,4,7,8,5,3,1,2] => [[[[.,.],[[.,[.,.]],.]],.],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 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] => 0

[6,4,3,7,2,5,1,8] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[8,4,3,6,5,1,2,7] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 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] => 0

[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

[4,7,2,6,5,3,1,8] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 0

[8,7,5,4,1,3,2,6] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4

[6,8,5,4,2,1,3,7] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 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] => 0

[3,2,8,6,5,1,4,7] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 1

[4,1,2,6,5,8,7,3] => [[.,.],[.,[[[.,.],[[.,.],.]],.]]] => [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 1

[5,1,6,2,4,8,7,3] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 1

[6,1,5,4,2,8,7,3] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 1

[7,1,5,4,8,2,6,3] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[8,1,5,4,7,6,2,3] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1

[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

[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

[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

[5,1,7,2,8,4,6,3] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1

[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

[3,2,1,7,8,5,6,4] => [[[.,.],.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[3,2,8,7,1,5,4,6] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[4,8,2,7,1,5,3,6] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[5,8,7,2,1,4,3,6] => [[[.,[[.,.],.]],.],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[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

[8,7,6,1,4,3,2,5] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[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

[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

[4,7,2,8,1,3,5,6] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0

[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

[4,6,2,8,3,1,5,7] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 0

[6,5,8,3,2,1,4,7] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 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] => 2

[8,5,7,3,1,4,2,6] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2

[8,4,3,7,1,5,2,6] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[6,4,3,8,2,1,5,7] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3

[4,5,2,3,8,1,6,7] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[3,2,5,4,8,1,6,7] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[4,5,2,3,1,8,7,6] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 0

[6,4,3,1,2,8,7,5] => [[[[.,.],.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 3

[7,4,3,1,8,2,6,5] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3

[8,4,3,1,7,6,2,5] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[8,5,1,3,7,6,2,4] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 2

[7,5,1,3,8,2,6,4] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[6,5,1,3,2,8,7,4] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 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] => 0

[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

[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

[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

[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

[5,7,1,2,8,3,6,4] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 0

[6,7,1,8,2,3,5,4] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0

[7,6,1,8,3,2,5,4] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[8,6,1,7,3,5,2,4] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[8,7,1,6,5,3,2,4] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 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] => 0

[6,8,1,7,2,5,3,4] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[5,8,1,2,7,6,3,4] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 0

[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

[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

[4,1,2,8,7,6,5,3] => [[.,.],[.,[[[[[.,.],.],.],.],.]]] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 1

[5,1,8,2,7,6,4,3] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 1

[6,1,8,7,2,5,4,3] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 1

[7,1,8,6,5,2,4,3] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 1

[8,1,7,6,5,4,2,3] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 1

[3,1,2,6,5,8,7,4] => [[.,.],[.,[[[.,.],[[.,.],.]],.]]] => [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 1

[3,1,6,2,4,8,7,5] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 1

[3,1,5,2,4,8,7,6] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 1

[4,5,1,2,3,8,7,6] => [[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 0

[4,6,1,2,3,8,7,5] => [[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 0

[6,1,5,2,4,8,7,3] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 1

[6,5,1,2,3,8,7,4] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 2

[6,4,1,2,3,8,7,5] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 2

[5,4,1,2,3,8,7,6] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 2

[5,4,1,2,7,3,6,8] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2

[6,4,1,7,2,3,5,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2

[6,4,1,8,2,3,5,7] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2

[7,4,1,2,8,3,6,5] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2

[7,5,1,2,8,3,6,4] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2

[7,1,5,2,8,4,6,3] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1

[8,1,5,2,7,4,6,3] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1

[8,5,1,2,7,3,6,4] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2

[8,4,1,2,7,3,6,5] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2

[8,4,1,7,2,3,5,6] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2

[7,4,1,6,2,3,5,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2

[8,6,1,7,2,3,5,4] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2

[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

[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

[7,6,1,8,2,3,5,4] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2

[4,7,1,2,8,3,6,5] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 0

[3,1,7,2,8,4,6,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[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

[4,1,2,8,7,5,6,3] => [[.,.],[.,[[[[.,.],.],[.,.]],.]]] => [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 1

[3,1,2,8,7,5,6,4] => [[.,.],[.,[[[[.,.],.],[.,.]],.]]] => [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 1

[3,1,8,2,7,4,6,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[3,1,8,7,2,4,5,6] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1

[3,1,7,6,2,4,5,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1

[4,7,1,6,2,3,5,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0

[4,8,1,6,2,3,5,7] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0

[4,8,1,7,2,3,5,6] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0

[4,8,1,2,7,3,6,5] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 0

[5,8,1,2,7,3,6,4] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 0

[5,1,8,2,7,4,6,3] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1

[6,1,8,7,2,4,5,3] => [[.,.],[[[.,.],.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 1

[6,8,1,7,2,3,5,4] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0

[7,8,1,6,2,3,5,4] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0

[7,1,8,6,2,4,5,3] => [[.,.],[[[.,.],.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 1

[8,1,7,6,2,4,5,3] => [[.,.],[[[.,.],.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 1

[8,7,1,6,2,3,5,4] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 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

[3,2,5,4,7,1,8,6] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[4,2,5,3,7,6,8,1] => [[[.,.],[[.,.],[[.,.],[.,.]]]],.] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 2

[4,2,5,3,7,1,8,6] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[4,2,5,3,6,1,8,7] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[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

[3,1,5,4,6,2,8,7] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[4,1,5,3,6,2,8,7] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[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

[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

[4,3,6,2,7,5,8,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[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

[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

[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

[3,1,5,4,7,2,8,6] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[2,1,5,4,7,3,8,6] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[3,1,5,4,7,6,8,2] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 1

[4,1,5,3,7,6,8,2] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 1

[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

[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

[4,3,6,5,7,1,8,2] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[5,3,6,4,7,2,8,1] => [[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[5,3,6,4,7,1,8,2] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[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

[5,1,6,3,7,4,8,2] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 1

[4,1,6,3,7,5,8,2] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 1

[3,1,6,4,7,5,8,2] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 1

[2,1,6,4,7,5,8,3] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 1

[2,1,6,4,7,3,8,5] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[3,1,6,4,7,2,8,5] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[4,1,6,3,7,2,8,5] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[5,1,6,3,7,2,8,4] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[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

[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

[5,3,6,2,7,4,8,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[5,2,6,3,7,4,8,1] => [[[.,.],[[.,.],[[.,.],[.,.]]]],.] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 2

[5,2,6,3,7,1,8,4] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 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

[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

[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

[4,2,6,3,7,1,8,5] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[4,2,6,3,7,5,8,1] => [[[.,.],[[.,.],[[.,.],[.,.]]]],.] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 2

[3,2,6,4,7,5,8,1] => [[[.,.],[[.,.],[[.,.],[.,.]]]],.] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 2

[3,2,6,4,7,1,8,5] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[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

[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

[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

[3,1,4,2,7,6,8,5] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1

[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

[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

[3,2,6,5,7,1,8,4] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[4,2,6,5,7,3,8,1] => [[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2

[4,2,6,5,7,1,8,3] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[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

[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

[4,1,5,2,7,6,8,3] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1

[3,1,5,2,7,6,8,4] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1

[2,1,5,3,7,6,8,4] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1

[2,1,6,3,7,5,8,4] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1

[3,1,6,2,7,5,8,4] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1

[4,1,6,2,7,5,8,3] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1

[5,1,6,2,7,4,8,3] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1

[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

[5,2,6,4,7,1,8,3] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[5,2,6,4,7,3,8,1] => [[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 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] => 2

[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

[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

[5,1,6,4,7,2,8,3] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[4,1,6,5,7,2,8,3] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[3,1,6,5,7,2,8,4] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[2,1,6,5,7,3,8,4] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[3,1,6,5,7,4,8,2] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 1

[4,1,6,5,7,3,8,2] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 1

[5,1,6,4,7,3,8,2] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 1

[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

[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

[8,3,5,2,1,6,4,7] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2

[8,6,3,5,2,4,1,7] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[8,3,7,5,2,4,6,1] => [[[[.,.],[[.,.],.]],[.,[.,.]]],.] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 2

[8,2,4,5,7,3,6,1] => [[[.,.],[[.,[.,[.,.]]],[.,.]]],.] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[8,2,4,6,5,3,1,7] => [[[.,.],[[.,[[.,.],.]],.]],[.,.]] => [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 1

[8,2,5,4,6,1,3,7] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[8,6,3,5,1,4,2,7] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[8,6,1,4,5,3,2,7] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 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

[5,7,4,3,2,1,8,6] => [[[[[.,[.,.]],.],.],.],[[.,.],.]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 3

[8,5,7,4,3,2,6,1] => [[[[[[.,.],[.,.]],.],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 4

[4,7,6,3,2,8,1,5] => [[[[.,[[.,.],.]],.],[.,.]],[.,.]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[5,4,7,3,1,8,2,6] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2

[5,7,4,2,1,3,8,6] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => 2

[8,5,7,4,2,1,6,3] => [[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 3

[8,3,7,5,1,4,6,2] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 1

[8,4,1,7,5,3,6,2] => [[[.,.],.],[[[[.,.],.],[.,.]],.]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 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] => 0

[8,4,7,6,3,5,2,1] => [[[[[.,.],[[.,.],.]],[.,.]],.],.] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[3,1,5,8,6,7,4,2] => [[.,.],[[[.,[[.,.],[.,.]]],.],.]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 1

[4,8,1,6,7,3,5,2] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 0

[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

[3,7,1,6,4,8,2,5] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[2,1,6,5,7,8,3,4] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[4,2,7,6,8,3,1,5] => [[[.,.],[[[.,.],[.,.]],.]],[.,.]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1

[4,2,6,8,7,3,5,1] => [[[.,.],[[.,[[.,.],.]],[.,.]]],.] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2

[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

[3,7,2,6,4,8,1,5] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[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

[5,3,7,2,1,8,4,6] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2

[4,7,3,2,1,5,8,6] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => 2

[8,7,6,1,3,4,2,5] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 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] => 3

[8,3,6,7,2,1,5,4] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 2

[8,7,6,3,5,2,4,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 4

[8,4,1,5,7,2,6,3] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[8,5,3,7,1,6,2,4] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 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] => 2

[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

[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

[4,6,1,8,7,2,5,3] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[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

[8,2,6,5,7,4,1,3] => [[[.,.],[[[.,.],[.,.]],.]],[.,.]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1

[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

[8,2,5,7,6,4,3,1] => [[[.,.],[[[.,[[.,.],.]],.],.]],.] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 2

[8,7,6,3,5,1,4,2] => [[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3

[8,4,7,6,5,1,3,2] => [[[.,.],[[[.,.],.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 1

[8,7,1,5,6,4,3,2] => [[[.,.],.],[[[[.,[.,.]],.],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 2

[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

[6,5,3,1,2,4,8,7] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3

[4,6,3,5,1,2,8,7] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 0

[8,5,3,7,2,1,4,6] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 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] => 0

[8,7,2,4,5,1,3,6] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 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] => 0

[2,6,1,4,5,3,8,7] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[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

[5,6,3,2,1,4,8,7] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => 2

[5,4,3,6,1,2,8,7] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[6,3,1,4,5,2,8,7] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[3,1,6,4,5,2,8,7] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[8,3,7,4,5,1,2,6] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[5,8,7,4,2,6,3,1] => [[[[.,[[.,.],.]],.],[[.,.],.]],.] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 2

[8,1,7,4,2,6,3,5] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[2,1,8,7,5,3,4,6] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 1

[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

[5,6,3,8,1,7,2,4] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[7,6,1,4,5,8,3,2] => [[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 2

[8,5,7,4,1,6,3,2] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 2

[5,1,8,4,7,6,2,3] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1

[4,1,8,3,5,6,7,2] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 1

[8,4,1,3,5,6,7,2] => [[[.,.],.],[[.,[.,[.,[.,.]]]],.]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[7,5,8,4,3,6,1,2] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2

[6,5,3,8,4,1,7,2] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 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

[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

[6,4,3,8,2,1,7,5] => [[[[[.,.],.],[.,.]],.],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 3

[7,3,8,4,2,6,1,5] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[8,3,1,2,5,6,7,4] => [[[.,.],.],[.,[[.,[.,[.,.]]],.]]] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[3,1,8,2,5,6,7,4] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 1

[4,3,8,2,5,6,7,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2

[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

[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

[2,8,1,3,5,6,7,4] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 0

[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

[7,8,2,4,3,6,1,5] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[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

[2,1,8,3,4,6,7,5] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 1

[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

[5,7,3,8,1,4,2,6] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[7,1,8,4,5,3,2,6] => [[.,.],[[[[.,.],[.,.]],.],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 1

[8,7,1,4,3,6,2,5] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[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

[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

[8,6,3,1,4,2,7,5] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3

[7,5,3,8,2,4,1,6] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[4,1,3,2,6,8,7,5] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 1

[7,5,3,6,2,8,1,4] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[8,6,3,5,1,2,7,4] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 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

[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

[5,8,2,4,7,6,1,3] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 0

[8,7,5,4,1,6,2,3] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4

[7,1,6,4,5,8,2,3] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[5,7,3,6,1,8,2,4] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[2,1,7,6,5,8,3,4] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1

[2,1,8,5,3,6,7,4] => [[.,.],[[[.,.],.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 1

[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

[7,8,5,4,2,6,1,3] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2

[8,1,4,2,5,6,7,3] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 1

[4,8,1,2,5,6,7,3] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 0

[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

[2,4,1,8,5,6,7,3] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 0

[4,1,2,8,5,6,7,3] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 1

[8,4,2,1,5,6,7,3] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 3

[7,5,2,4,8,6,1,3] => [[[[.,.],.],[.,[[.,.],.]]],[.,.]] => [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 2

[6,5,3,2,8,1,7,4] => [[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3

[2,1,5,3,8,6,7,4] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1

[6,4,3,5,8,1,7,2] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[7,3,5,4,8,6,1,2] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[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

[4,3,1,8,5,6,7,2] => [[[.,.],.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[3,1,4,8,5,6,7,2] => [[.,.],[[.,[[.,.],[.,[.,.]]]],.]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 1

[6,5,3,7,2,8,4,1] => [[[[[.,.],.],[.,.]],[[.,.],.]],.] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[6,3,7,4,5,8,2,1] => [[[[.,.],[[.,.],[.,[.,.]]]],.],.] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 3

[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

[5,1,7,4,8,6,3,2] => [[.,.],[[[[.,.],[[.,.],.]],.],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 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] => 0

[5,7,1,4,8,6,2,3] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 0

[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

[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

[4,6,3,8,1,2,7,5] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 0

[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

[3,6,2,5,4,8,1,7] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[3,5,2,4,7,1,8,6] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0

[4,2,5,8,3,7,6,1] => [[[.,.],[[.,[.,.]],[[.,.],.]]],.] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 2

[4,2,6,5,3,8,1,7] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[5,4,2,1,6,8,3,7] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3

[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

[4,6,1,5,3,8,2,7] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[5,1,6,4,3,8,2,7] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1

[5,4,3,2,7,1,8,6] => [[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3

[5,4,3,8,2,7,6,1] => [[[[[.,.],.],[.,.]],[[.,.],.]],.] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 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] => 2

[4,3,7,6,2,1,8,5] => [[[[.,.],[[.,.],.]],.],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2

[6,4,3,1,7,2,8,5] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3

[7,5,4,3,1,8,2,6] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4

[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

[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

[6,4,3,8,1,7,5,2] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2

[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

[4,8,3,7,6,5,2,1] => [[[[.,[.,.]],[[[.,.],.],.]],.],.] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 2

[5,3,8,7,6,4,2,1] => [[[[.,.],[[[[.,.],.],.],.]],.],.] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 3

[7,5,3,1,8,6,4,2] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3

[4,6,1,8,7,3,5,2] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 0

[6,8,7,3,1,4,5,2] => [[[.,[[.,.],.]],.],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 1

[6,2,8,7,4,5,1,3] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[7,6,2,8,4,1,3,5] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[7,3,1,6,8,4,2,5] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 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] => 0

[6,1,7,5,3,2,8,4] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 1

[7,6,5,3,2,1,8,4] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5

[6,5,3,2,8,7,4,1] => [[[[[.,.],.],.],[[[.,.],.],.]],.] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 4

[5,2,6,3,8,7,4,1] => [[[.,.],[[.,.],[[[.,.],.],.]]],.] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 2

[5,2,7,6,3,1,8,4] => [[[.,.],[[[.,.],.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 1

[6,5,2,1,7,3,8,4] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3

[5,2,7,4,1,8,3,6] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[4,7,2,6,3,1,8,5] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[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

[4,3,7,8,2,1,5,6] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2

[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

[3,8,2,5,7,1,6,4] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0

[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

[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

[8,7,3,6,2,5,4,1] => [[[[[.,.],.],[.,.]],[[.,.],.]],.] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[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

[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

[4,8,1,5,7,2,6,3] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[5,8,3,7,1,6,2,4] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[8,6,2,7,5,1,3,4] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[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

[6,5,2,8,1,7,4,3] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2

[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

[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

[6,2,8,7,5,4,3,1] => [[[.,.],[[[[[.,.],.],.],.],.]],.] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 2

[7,6,2,1,8,5,4,3] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3

[6,1,7,2,8,5,4,3] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 1

[7,5,1,8,2,6,4,3] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 2

[4,7,1,8,6,2,5,3] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[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

[8,7,4,6,1,5,3,2] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2

[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

[6,8,1,7,5,4,3,2] => [[.,[.,.]],[[[[[.,.],.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 0

[7,1,8,6,5,4,3,2] => [[.,.],[[[[[[.,.],.],.],.],.],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1

[5,4,2,3,7,6,1,8] => [[[[.,.],.],[.,[[.,.],.]]],[.,.]] => [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 2

[6,4,2,7,3,5,1,8] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2

[7,4,2,6,3,5,1,8] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2

[8,4,2,6,3,1,5,7] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[3,2,7,6,4,5,1,8] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[4,7,2,6,3,5,1,8] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[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

[4,8,2,6,3,1,5,7] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 0

[3,2,8,6,4,1,5,7] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 1

[3,2,1,6,4,8,5,7] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[7,1,5,2,8,3,4,6] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[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

[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

[3,2,1,7,8,4,5,6] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[3,2,8,7,1,4,5,6] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1

[5,8,7,2,1,3,4,6] => [[[.,[[.,.],.]],.],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1

[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

[8,5,7,2,1,3,4,6] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2

[6,4,2,8,3,1,5,7] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[5,4,2,3,8,1,6,7] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[3,2,5,4,1,8,6,7] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[4,5,2,3,1,8,6,7] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[5,4,2,3,1,8,6,7] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[6,4,2,1,3,8,5,7] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3

[7,4,2,1,8,3,5,6] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[8,4,2,1,7,3,5,6] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[8,5,1,2,7,3,4,6] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2

[7,5,1,2,8,3,4,6] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2

[6,5,1,2,3,8,4,7] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 2

[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

[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

[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

[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

[7,6,1,8,2,3,4,5] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2

[8,6,1,7,2,3,4,5] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2

[7,8,1,6,2,3,4,5] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0

[6,8,1,7,2,3,4,5] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0

[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

[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

[3,2,1,8,7,4,5,6] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[5,1,8,2,7,3,4,6] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[6,1,8,7,2,3,4,5] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1

[8,1,7,6,2,3,4,5] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1

[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

[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

[8,3,7,5,2,1,4,6] => [[[[.,.],[[.,.],.]],.],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 2

[6,3,7,5,1,8,4,2] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[6,5,2,7,1,8,3,4] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[8,5,2,7,4,1,3,6] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[2,6,1,5,4,3,8,7] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[6,4,3,5,1,2,8,7] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[5,3,1,4,6,2,8,7] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[3,1,4,6,5,2,8,7] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 1

[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

[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

[2,1,8,5,7,3,4,6] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[8,6,3,5,1,7,4,2] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 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

[7,5,4,8,1,6,3,2] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2

[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

[4,1,6,3,8,5,7,2] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 1

[7,4,1,3,5,8,6,2] => [[[.,.],.],[[.,[.,[[.,.],.]]],.]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 2

[6,5,8,4,1,7,3,2] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 2

[8,5,3,7,4,1,6,2] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 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

[7,4,3,8,2,1,6,5] => [[[[[.,.],.],[.,.]],.],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 3

[6,3,7,4,1,8,2,5] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[8,3,1,2,5,7,6,4] => [[[.,.],.],[.,[[.,[[.,.],.]],.]]] => [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 2

[3,1,8,2,7,6,5,4] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 1

[4,3,7,2,6,8,5,1] => [[[[.,.],[.,.]],[[.,[.,.]],.]],.] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 2

[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

[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

[2,8,1,3,6,5,7,4] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 0

[8,7,1,6,3,4,2,5] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[5,3,8,7,4,2,6,1] => [[[[.,.],[[[.,.],.],.]],[.,.]],.] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 2

[4,3,8,7,2,1,6,5] => [[[[.,.],[[.,.],.]],.],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 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

[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

[4,1,3,2,6,7,8,5] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 1

[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

[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

[5,6,2,8,7,4,1,3] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 0

[7,8,5,6,1,4,2,3] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[8,1,6,4,5,7,2,3] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[5,8,3,6,1,7,2,4] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[2,1,8,6,5,7,3,4] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1

[2,1,7,5,3,6,8,4] => [[.,.],[[[.,.],.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 1

[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

[7,1,4,2,5,6,8,3] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 1

[4,6,1,2,8,7,3,5] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 0

[2,4,1,5,8,7,6,3] => [[.,[.,.]],[[.,[[[.,.],.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 0

[4,1,2,5,8,6,7,3] => [[.,.],[.,[[.,[[.,.],[.,.]]],.]]] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 1

[6,4,2,1,5,8,7,3] => [[[[.,.],.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[8,5,2,4,6,1,7,3] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[7,5,3,2,6,8,1,4] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3

[2,1,5,3,6,8,7,4] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 1

[7,3,5,4,6,1,8,2] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[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

[4,3,1,5,7,6,8,2] => [[[.,.],.],[[.,[[.,.],[.,.]]],.]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 2

[3,1,4,5,6,8,7,2] => [[.,.],[[.,[.,[.,[[.,.],.]]]],.]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 1

[4,5,2,6,3,1,8,7] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[6,5,2,1,4,3,8,7] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3

[6,5,2,7,4,8,3,1] => [[[[.,.],.],[[[.,.],[.,.]],.]],.] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[8,5,2,7,4,1,6,3] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[8,3,7,5,2,1,6,4] => [[[[.,.],[[.,.],.]],.],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2

[6,3,7,5,2,8,4,1] => [[[[.,.],[[.,.],.]],[[.,.],.]],.] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 2

[3,1,6,5,4,2,8,7] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 1

[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

[3,6,2,4,1,5,8,7] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 0

[2,6,1,3,5,4,8,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 0

[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

[8,7,2,3,4,1,6,5] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[5,1,7,3,8,4,6,2] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 1

[7,6,1,3,5,8,4,2] => [[[.,.],.],[[.,[[.,[.,.]],.]],.]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 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] => 0

[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

[2,1,8,7,4,3,6,5] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 1

[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

[7,8,1,3,5,2,6,4] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[5,8,7,3,2,6,1,4] => [[[[.,[[.,.],.]],.],[.,.]],[.,.]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[8,1,6,3,2,5,4,7] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[4,8,1,2,7,6,3,5] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 0

[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

[2,1,5,3,8,7,6,4] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 1

[6,5,3,2,8,7,1,4] => [[[[[.,.],.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3

[7,5,2,4,8,1,6,3] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[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

[2,4,1,8,7,6,5,3] => [[.,[.,.]],[[[[[.,.],.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 0

[8,4,2,1,7,5,3,6] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[4,3,1,8,6,7,5,2] => [[[.,.],.],[[[[.,.],[.,.]],.],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 2

[3,1,4,8,6,5,7,2] => [[.,.],[[.,[[[.,.],.],[.,.]]],.]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 1

[7,1,6,5,4,8,2,3] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1

[5,7,1,6,8,2,4,3] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[8,6,2,5,1,7,4,3] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2

[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

[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

[7,5,2,6,3,8,1,4] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2

[4,1,2,3,6,8,7,5] => [[.,.],[.,[.,[[.,[[.,.],.]],.]]]] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 1

[7,5,2,8,3,4,6,1] => [[[[.,.],.],[[.,.],[.,[.,.]]]],.] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 3

[5,6,2,8,4,3,1,7] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 0

[4,7,2,8,1,5,3,6] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[8,7,2,1,4,5,6,3] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 3

[7,1,8,5,4,3,6,2] => [[.,.],[[[[[.,.],.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 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] => 0

[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

[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

[6,5,3,8,4,1,2,7] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[7,5,8,4,3,6,2,1] => [[[[[[.,.],[.,.]],.],[.,.]],.],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 4

[4,1,8,3,6,5,2,7] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1

[8,4,1,3,7,2,6,5] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[3,1,8,2,4,7,6,5] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 1

[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

[6,3,8,4,2,5,7,1] => [[[[.,.],[[.,.],.]],[.,[.,.]]],.] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 2

[7,4,3,8,2,5,1,6] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 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

[6,8,2,4,3,5,1,7] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[4,8,2,3,5,1,6,7] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[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

[2,8,1,3,4,5,7,6] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 0

[7,5,8,6,1,4,2,3] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[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

[6,5,2,7,3,1,4,8] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[6,5,2,8,3,1,7,4] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[6,5,2,8,3,1,4,7] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 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] => 2

[7,5,8,6,1,4,3,2] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 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] => 2

[6,5,2,7,3,1,8,4] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[4,5,2,6,3,1,7,8] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 0

[4,1,2,3,7,6,8,5] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 1

[6,5,2,7,3,4,8,1] => [[[[.,.],.],[[.,.],[.,[.,.]]]],.] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 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

[5,1,2,6,4,8,7,3] => [[.,.],[.,[[[.,.],[[.,.],.]],.]]] => [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 1

[5,1,2,8,6,4,7,3] => [[.,.],[.,[[[[.,.],.],[.,.]],.]]] => [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 1

[5,1,6,8,7,3,4,2] => [[.,.],[[[.,[[.,.],.]],[.,.]],.]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 1

[6,5,2,8,3,7,4,1] => [[[[.,.],.],[[.,.],[[.,.],.]]],.] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3

[4,1,2,3,8,7,5,6] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 1

[4,1,2,3,8,6,5,7] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 1

[4,1,2,3,8,6,7,5] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 1

[4,1,2,3,7,6,5,8] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 1

[4,1,2,3,8,5,7,6] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 1

[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

[6,1,2,8,4,5,7,3] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 1

[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

[6,5,8,2,4,3,7,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[7,5,2,8,3,4,1,6] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2

[6,5,2,8,3,7,1,4] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2

[6,5,2,7,3,4,1,8] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2

[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

[5,1,6,8,7,3,2,4] => [[.,.],[[[.,[[.,.],.]],.],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 1

[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

[4,1,8,3,6,5,7,2] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 1

[4,1,8,3,6,2,7,5] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[3,1,4,8,6,2,7,5] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 1

[3,1,4,8,6,5,2,7] => [[.,.],[[.,[[[.,.],.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 1

[7,1,6,5,8,3,2,4] => [[.,.],[[[[.,.],[.,.]],.],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 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

[4,1,6,5,7,3,2,8] => [[.,.],[[[[.,.],[.,.]],.],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 1

[4,5,2,6,3,7,1,8] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[4,5,2,7,3,8,1,6] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[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

[7,1,6,5,8,3,4,2] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 1

[7,5,2,6,3,8,4,1] => [[[[.,.],.],[[.,.],[[.,.],.]]],.] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3

[4,1,2,3,5,8,7,6] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1

[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

[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

[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

[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

[4,1,2,5,6,8,7,3] => [[.,.],[.,[[.,[.,[[.,.],.]]],.]]] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 1

[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

[7,8,5,6,1,4,3,2] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 0

[7,8,4,2,1,5,3,6] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 2

[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

[6,4,1,2,5,7,3,8] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 2

[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

[6,3,1,4,7,2,5,8] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[7,8,3,4,5,1,6,2] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0

[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

[7,8,3,6,5,4,1,2] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 0

[7,8,2,6,4,1,3,5] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 0

[7,8,1,6,5,4,3,2] => [[.,[.,.]],[[[[[.,.],.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 0

[2,1,8,7,5,4,3,6] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 1

[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

[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

[6,1,2,5,8,7,4,3] => [[.,.],[.,[[[.,[[.,.],.]],.],.]]] => [1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 1

[6,3,1,8,4,2,7,5] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[6,4,2,1,5,3,8,7] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3

[6,4,3,7,5,8,1,2] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2

[4,3,8,7,5,6,1,2] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[3,7,2,8,6,4,1,5] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 0

[3,8,1,7,6,4,5,2] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 0

[2,6,1,4,7,3,5,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[5,1,6,3,4,2,8,7] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[5,7,1,4,2,3,8,6] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0

[5,7,6,4,3,8,1,2] => [[[[.,[[.,.],.]],.],[.,.]],[.,.]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[6,3,4,5,8,7,1,2] => [[[.,.],[.,[.,[[.,.],.]]]],[.,.]] => [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 1

[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

[5,1,4,2,7,6,8,3] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1

[5,7,2,4,1,6,3,8] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[6,7,5,8,1,4,3,2] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 0

[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

[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

[2,1,8,7,6,5,3,4] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 1

[4,3,7,5,6,8,1,2] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[5,3,7,8,2,1,6,4] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 2

[5,2,8,7,1,6,4,3] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[4,1,8,6,2,3,5,7] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1

[6,4,2,7,1,3,8,5] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[7,4,2,5,1,3,8,6] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[8,5,3,6,1,7,2,4] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 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

[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

[3,6,2,7,1,4,8,5] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 0

[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

[6,3,7,4,1,2,8,5] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 1

[4,7,1,5,2,3,8,6] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0

[7,6,4,2,3,8,1,5] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3

[8,6,4,2,3,7,1,5] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3

[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

[6,4,7,5,2,8,1,3] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[7,4,8,5,2,6,1,3] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[5,8,2,6,3,7,1,4] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[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

[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

[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

[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

[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

[8,4,1,6,7,2,3,5] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[7,4,1,6,8,2,3,5] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[6,5,3,7,1,8,2,4] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[6,5,1,2,7,8,3,4] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 2

[5,3,6,4,7,8,1,2] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[6,3,7,4,8,5,1,2] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[4,7,1,5,8,6,2,3] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 0

[7,5,1,2,8,6,3,4] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 2

[7,6,1,8,5,2,3,4] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[8,6,1,7,5,2,3,4] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[5,7,2,8,1,6,3,4] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[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

[4,3,8,7,1,2,5,6] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1

[5,3,8,7,1,2,4,6] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1

[8,3,7,6,1,2,4,5] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1

[8,4,7,6,1,2,3,5] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1

[6,8,4,7,5,1,2,3] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 0

[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

[7,5,3,8,2,1,6,4] => [[[[[.,.],.],[.,.]],.],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 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

[5,7,3,8,1,2,6,4] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 0

[8,7,1,4,5,3,2,6] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 2

[7,1,8,4,2,6,5,3] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 1

[7,5,1,4,8,6,3,2] => [[[.,.],.],[[[.,[[.,.],.]],.],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 2

[6,5,3,1,8,4,7,2] => [[[[.,.],.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 3

[8,6,3,1,2,5,7,4] => [[[[.,.],.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 3

[8,7,1,4,2,6,5,3] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 2

[5,3,2,7,4,6,8,1] => [[[[.,.],.],[[.,.],[.,[.,.]]]],.] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 3

[7,5,3,6,2,4,8,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3

[8,5,3,6,2,7,1,4] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[8,2,6,3,4,7,1,5] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[7,2,6,3,4,5,8,1] => [[[.,.],[[.,.],[.,[.,[.,.]]]]],.] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 2

[6,2,7,3,4,5,8,1] => [[[.,.],[[.,.],[.,[.,[.,.]]]]],.] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 2

[5,4,7,6,2,3,8,1] => [[[[.,.],[[.,.],.]],[.,[.,.]]],.] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 2

[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

[8,6,5,2,3,7,1,4] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3

[8,5,2,1,7,3,4,6] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[7,5,2,1,8,3,4,6] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[5,6,2,3,1,8,4,7] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[5,4,8,6,2,7,1,3] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[6,8,3,5,2,7,1,4] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[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

[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

[2,8,1,7,3,4,5,6] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0

[4,8,1,5,7,2,3,6] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[4,2,8,3,7,1,5,6] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[8,1,2,7,3,4,5,6] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1

[3,6,2,7,1,8,4,5] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[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

[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

[3,2,1,5,8,4,6,7] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[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

[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

[6,5,3,4,8,7,1,2] => [[[[.,.],.],[.,[[.,.],.]]],[.,.]] => [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 2

[5,3,2,8,7,1,4,6] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[5,3,1,8,7,2,4,6] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[8,5,3,7,6,1,2,4] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[6,1,8,3,7,2,4,5] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[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

[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

[6,7,3,8,2,5,1,4] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[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

[4,2,5,8,7,1,3,6] => [[[.,.],[.,[[.,.],.]]],[.,[.,.]]] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 1

[7,2,8,6,1,3,4,5] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1

[2,1,8,7,3,4,5,6] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1

[8,2,7,6,1,3,4,5] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1

[4,1,5,8,7,2,3,6] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 1

[5,4,8,7,6,1,2,3] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 1

[6,8,3,7,5,1,2,4] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 0

[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

[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

[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

[8,1,5,3,7,2,4,6] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[8,1,5,3,6,2,4,7] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[7,5,1,3,6,2,4,8] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[7,5,8,3,6,2,4,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[7,4,8,3,2,6,5,1] => [[[[[.,.],[.,.]],.],[[.,.],.]],.] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[7,4,1,3,2,6,5,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[8,1,4,3,2,6,5,7] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[8,1,4,3,2,7,5,6] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[8,1,4,3,2,7,6,5] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 1

[8,1,5,4,6,7,2,3] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[8,1,5,3,6,2,7,4] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[8,1,4,3,2,6,7,5] => [[.,.],[[[.,.],.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 1

[8,1,4,3,2,5,7,6] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1

[8,1,4,3,2,5,6,7] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1

[7,4,1,3,2,5,6,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2

[7,4,8,3,2,5,6,1] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 3

[6,4,3,8,2,5,7,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3

[6,4,3,1,2,5,8,7] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3

[7,4,1,3,2,5,8,6] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2

[7,4,1,3,2,6,8,5] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[7,5,1,3,6,2,8,4] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[7,5,1,4,6,8,2,3] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 2

[7,5,8,3,6,2,1,4] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 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] => 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] => 2

[6,4,3,8,2,5,1,7] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[6,4,3,7,2,5,8,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3

[5,4,3,2,8,6,1,7] => [[[[[.,.],.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3

[5,4,3,2,8,7,1,6] => [[[[[.,.],.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3

[6,5,3,8,7,2,1,4] => [[[[[.,.],.],[[.,.],.]],.],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 3

[6,5,4,8,7,1,2,3] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[6,5,4,1,7,8,2,3] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3

[6,5,3,1,7,2,8,4] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3

[6,4,3,1,2,7,8,5] => [[[[.,.],.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 3

[5,4,3,2,1,8,6,7] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4

[6,5,3,1,8,2,7,4] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3

[6,5,4,1,8,7,2,3] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[7,5,1,4,8,6,2,3] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 2

[7,4,1,3,2,8,6,5] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 2

[7,4,1,3,2,8,5,6] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[6,4,3,1,2,8,5,7] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3

[6,4,3,1,2,7,5,8] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3

[6,4,3,8,2,7,5,1] => [[[[[.,.],.],[.,.]],[[.,.],.]],.] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[6,5,3,8,7,2,4,1] => [[[[[.,.],.],[[.,.],.]],[.,.]],.] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 3

[6,5,3,1,7,2,4,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[6,5,3,1,8,2,4,7] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[7,5,1,3,8,2,4,6] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[7,6,1,8,3,2,4,5] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[7,6,1,8,4,5,2,3] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 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

[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

[6,5,3,7,8,2,4,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3

[6,4,3,7,2,8,5,1] => [[[[[.,.],.],[.,.]],[[.,.],.]],.] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[6,4,3,7,2,1,5,8] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 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] => 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] => 3

[7,5,8,3,1,2,6,4] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2

[7,5,8,4,1,6,2,3] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2

[6,5,4,8,1,7,2,3] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[6,5,3,8,1,2,7,4] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[5,4,3,2,8,1,7,6] => [[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3

[6,4,3,7,2,1,8,5] => [[[[[.,.],.],[.,.]],.],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 3

[6,5,3,7,1,2,8,4] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[6,5,4,7,1,8,2,3] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[6,5,3,7,8,2,1,4] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3

[6,4,3,7,2,8,1,5] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[5,4,3,2,7,8,1,6] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3

[5,4,3,2,6,8,1,7] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 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

[7,6,1,2,5,8,3,4] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 2

[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

[7,8,1,2,5,4,6,3] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 0

[8,4,1,3,7,6,2,5] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 2

[6,5,2,1,8,7,4,3] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 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] => 0

[4,6,3,7,2,5,1,8] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[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

[4,6,3,8,5,1,7,2] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[4,6,3,8,5,1,2,7] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 0

[4,6,2,7,5,3,1,8] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 0

[4,6,2,8,5,1,7,3] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[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

[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

[4,6,2,8,5,1,3,7] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 0

[4,7,2,8,1,6,3,5] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[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

[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

[4,7,2,8,1,6,5,3] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 0

[4,7,2,8,1,5,6,3] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0

[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

[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

[4,6,2,8,3,1,7,5] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[4,7,3,8,1,6,2,5] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[4,7,3,8,1,6,5,2] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 0

[4,7,3,8,1,5,6,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0

[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

[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

[4,5,2,3,8,1,7,6] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0

[3,2,5,4,8,1,7,6] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[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

[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

[4,7,3,8,1,5,2,6] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[4,7,3,8,1,2,6,5] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 0

[4,7,3,8,1,2,5,6] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0

[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

[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

[7,2,8,5,1,6,4,3] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[7,2,8,5,4,1,6,3] => [[[.,.],[[[.,.],.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 1

[7,2,8,4,5,6,1,3] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[6,2,3,8,5,1,7,4] => [[[.,.],[.,[[.,.],.]]],[[.,.],.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 1

[6,3,2,8,5,1,4,7] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 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] => 2

[7,4,8,5,2,1,3,6] => [[[[.,.],[[.,.],.]],.],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 2

[6,4,8,5,1,3,7,2] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 1

[6,3,7,5,2,1,8,4] => [[[[.,.],[[.,.],.]],.],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2

[4,3,7,5,1,2,8,6] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 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

[3,6,1,7,5,2,8,4] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[3,4,1,2,7,6,8,5] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 0

[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

[6,5,2,7,4,1,8,3] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[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

[5,3,1,8,6,4,7,2] => [[[.,.],.],[[[[.,.],.],[.,.]],.]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 2

[5,6,1,8,7,2,4,3] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[6,3,5,8,2,7,4,1] => [[[[.,.],[.,[.,.]]],[[.,.],.]],.] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 2

[6,5,8,4,2,3,7,1] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 3

[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

[5,2,1,8,7,6,3,4] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 2

[7,1,3,8,4,6,2,5] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 1

[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

[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

[5,3,6,4,1,8,7,2] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[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

[7,3,5,6,8,4,2,1] => [[[[.,.],[[.,[.,[.,.]]],.]],.],.] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 3

[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

[2,6,1,5,8,4,7,3] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 0

[5,7,1,6,3,8,4,2] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 0

[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

[3,1,4,2,7,8,6,5] => [[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 1

[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

[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

[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

[7,2,1,4,3,6,5,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 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

[7,4,3,2,1,6,5,8] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4

[7,6,3,2,5,4,1,8] => [[[[[.,.],.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3

[6,7,3,2,5,4,8,1] => [[[[.,[.,.]],.],[[.,.],[.,.]]],.] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => 2

[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

[7,2,1,5,6,3,4,8] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[7,2,1,6,5,4,3,8] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 2

[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

[7,4,6,5,1,3,2,8] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[6,5,7,4,3,1,8,2] => [[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 3

[6,4,7,5,1,3,8,2] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 1

[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

[6,2,1,7,5,4,8,3] => [[[.,.],.],[[[[.,.],.],[.,.]],.]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 2

[3,2,1,8,5,4,7,6] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[3,2,1,8,6,7,4,5] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[5,2,1,7,6,8,4,3] => [[[.,.],.],[[[[.,.],[.,.]],.],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 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

[5,4,7,6,1,8,3,2] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[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

[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

[5,2,1,6,7,8,3,4] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 2

[6,2,1,5,7,3,8,4] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[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

[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

[6,5,4,7,2,1,8,3] => [[[[[.,.],.],[.,.]],.],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 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] => 0

[5,7,3,2,6,8,4,1] => [[[[.,[.,.]],.],[[.,[.,.]],.]],.] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 2

[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

[6,5,3,2,7,1,8,4] => [[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3

[6,4,3,2,1,7,8,5] => [[[[[.,.],.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 4

[6,2,1,4,3,7,8,5] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[5,2,1,4,3,8,7,6] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 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

[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

[4,7,3,2,8,6,5,1] => [[[[.,[.,.]],.],[[[.,.],.],.]],.] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 2

[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

[4,2,1,5,8,3,7,6] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[4,2,1,6,8,7,3,5] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 2

[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

[4,2,1,7,8,6,5,3] => [[[.,.],.],[[[[.,[.,.]],.],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 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

[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

[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

[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

[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

[7,5,2,1,6,8,4,3] => [[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => 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

[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

[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

[6,7,5,3,1,8,4,2] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 2

[8,4,2,1,6,7,5,3] => [[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[5,3,2,1,7,6,8,4] => [[[[.,.],.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 3

[4,7,1,6,5,8,2,3] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[4,8,2,6,5,7,1,3] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[4,6,1,2,7,5,8,3] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 0

[7,5,1,2,6,8,4,3] => [[[.,.],.],[.,[[[.,[.,.]],.],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 2

[8,4,1,2,6,7,5,3] => [[[.,.],.],[.,[[[.,[.,.]],.],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 2

[5,3,1,2,7,6,8,4] => [[[.,.],.],[.,[[[.,.],[.,.]],.]]] => [1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2

[4,3,1,2,7,6,8,5] => [[[.,.],.],[.,[[[.,.],[.,.]],.]]] => [1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2

[3,5,1,2,7,6,8,4] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 0

[6,7,1,5,8,2,3,4] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[7,6,1,5,8,3,2,4] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 2

[7,1,6,5,8,2,4,3] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[7,5,1,6,8,4,2,3] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 2

[8,4,1,6,7,5,2,3] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 2

[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

[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

[7,6,2,1,5,8,3,4] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3

[8,3,1,5,7,6,2,4] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 2

[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

[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

[7,1,6,4,8,2,5,3] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[8,2,6,4,7,1,5,3] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[6,1,5,2,7,4,8,3] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1

[7,6,2,5,8,3,1,4] => [[[[.,.],.],[[.,[.,.]],.]],[.,.]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 2

[8,3,5,7,6,2,1,4] => [[[[.,.],[.,[[.,.],.]]],.],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 2

[5,2,1,3,7,6,8,4] => [[[.,.],.],[.,[[[.,.],[.,.]],.]]] => [1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2

[7,5,2,6,8,4,1,3] => [[[[.,.],.],[[.,[.,.]],.]],[.,.]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 2

[8,4,2,6,7,5,1,3] => [[[[.,.],.],[[.,[.,.]],.]],[.,.]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 2

[6,1,4,2,7,5,8,3] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1

[8,2,6,5,7,1,4,3] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[8,3,2,5,7,6,1,4] => [[[[.,.],.],[.,[[.,.],.]]],[.,.]] => [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 2

[5,1,3,2,7,6,8,4] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1

[4,1,3,2,7,6,8,5] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1

[4,2,1,3,7,6,8,5] => [[[.,.],.],[.,[[[.,.],[.,.]],.]]] => [1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 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] => 0

[2,5,1,3,7,6,8,4] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 0

[6,8,2,3,5,7,1,4] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0

[6,7,1,3,5,8,2,4] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 0

[8,3,5,7,6,1,2,4] => [[[.,.],[.,[[.,.],.]]],[.,[.,.]]] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 1

[5,1,2,3,7,6,8,4] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 1

[3,1,2,4,7,6,8,5] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 1

[8,1,2,4,3,6,5,7] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 1

[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

[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

[8,1,3,2,4,5,7,6] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 1

[6,3,2,1,4,5,8,7] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3

[7,3,1,4,2,6,8,5] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[7,4,1,5,6,8,2,3] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 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] => 0

[3,5,2,4,8,6,1,7] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 0

[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

[7,4,1,2,3,8,5,6] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 2

[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

[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

[6,5,2,1,8,3,4,7] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[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

[5,6,4,8,1,7,2,3] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[5,6,3,8,1,2,7,4] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 0

[4,2,5,3,7,1,6,8] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[4,3,6,7,2,1,8,5] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 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] => 0

[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

[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

[4,7,1,8,6,5,2,3] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 0

[4,7,1,2,8,6,5,3] => [[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => 0

[7,8,1,6,3,5,2,4] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[7,8,1,3,6,5,2,4] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 0

[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

[4,7,2,8,6,1,5,3] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[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

[7,8,2,3,6,5,1,4] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 0

[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

[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

[6,8,2,7,1,3,5,4] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 0

[6,2,4,8,7,1,5,3] => [[[.,.],[.,[[.,.],.]]],[[.,.],.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 1

[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

[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

[8,5,7,2,1,6,3,4] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2

[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

[8,7,6,2,1,4,3,5] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 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

[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

[8,2,5,4,7,1,6,3] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[8,5,2,7,3,1,6,4] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[8,7,6,2,4,3,1,5] => [[[[[.,.],.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3

[8,7,6,1,2,4,3,5] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3

[8,7,6,1,4,2,3,5] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[8,7,6,4,1,3,2,5] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4

[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

[6,8,7,3,2,5,1,4] => [[[[.,[[.,.],.]],.],[.,.]],[.,.]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[6,8,1,7,3,2,5,4] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[8,5,7,3,1,6,2,4] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2

[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

[8,5,7,3,1,2,6,4] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2

[5,8,4,7,1,2,6,3] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 0

[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

[5,8,4,7,1,6,2,3] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[8,1,2,6,5,7,4,3] => [[.,.],[.,[[[[.,.],[.,.]],.],.]]] => [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 1

[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

[8,5,3,1,7,2,6,4] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3

[8,5,3,7,1,2,6,4] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 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] => 0

[4,6,2,8,1,7,5,3] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 0

[8,5,3,7,2,1,6,4] => [[[[[.,.],.],[.,.]],.],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 3

[8,7,6,3,1,4,2,5] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4

[8,7,6,1,3,2,4,5] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[8,5,3,2,7,1,6,4] => [[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3

[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

[8,5,2,3,7,1,6,4] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[6,3,1,5,4,2,8,7] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[8,3,1,5,2,7,6,4] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 2

[8,5,4,2,1,7,3,6] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4

[8,5,4,2,1,7,6,3] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4

[6,5,4,2,1,3,8,7] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 4

[6,5,4,2,3,1,8,7] => [[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3

[6,3,2,5,1,4,8,7] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[6,5,4,3,1,2,8,7] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 4

[6,5,4,1,3,2,8,7] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3

[8,5,4,1,2,7,6,3] => [[[[.,.],.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 3

[8,7,4,1,6,3,2,5] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[8,7,4,1,6,3,5,2] => [[[[.,.],.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 3

[8,7,4,1,6,5,3,2] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3

[8,5,4,1,3,7,6,2] => [[[[.,.],.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[8,5,4,3,1,7,6,2] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4

[8,3,2,5,1,7,6,4] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2

[2,1,8,5,3,7,6,4] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 1

[8,3,2,5,1,7,4,6] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[8,5,4,3,1,7,2,6] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4

[8,5,4,1,3,7,2,6] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3

[8,7,4,1,6,5,2,3] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[8,7,4,1,6,2,5,3] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3

[8,7,6,5,2,1,4,3] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5

[8,7,4,3,6,2,1,5] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 4

[8,3,2,7,6,4,1,5] => [[[[.,.],.],[[[.,.],.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 2

[2,1,8,7,6,4,3,5] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 1

[2,1,8,7,6,4,5,3] => [[.,.],[[[[[.,.],.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 1

[8,3,2,7,6,4,5,1] => [[[[.,.],.],[[[.,.],.],[.,.]]],.] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 3

[8,7,4,3,6,2,5,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 4

[8,7,6,5,2,4,3,1] => [[[[[[.,.],.],.],.],[[.,.],.]],.] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 5

[8,5,4,2,3,7,6,1] => [[[[[.,.],.],.],[.,[[.,.],.]]],.] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 4

[8,7,4,2,6,5,3,1] => [[[[[.,.],.],.],[[[.,.],.],.]],.] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 4

[8,7,4,2,6,3,5,1] => [[[[[.,.],.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 4

[8,7,4,2,6,3,1,5] => [[[[[.,.],.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3

[8,3,1,7,6,4,2,5] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 2

[8,3,1,7,6,4,5,2] => [[[.,.],.],[[[[.,.],.],[.,.]],.]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 2

[8,3,1,7,6,5,4,2] => [[[.,.],.],[[[[[.,.],.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2

[8,3,1,5,4,7,6,2] => [[[.,.],.],[[[.,.],[[.,.],.]],.]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 2

[8,3,1,5,4,7,2,6] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[8,3,1,7,6,5,2,4] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 2

[8,3,1,7,6,2,5,4] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[8,7,4,2,6,1,5,3] => [[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3

[8,7,4,2,6,5,1,3] => [[[[[.,.],.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3

[8,5,4,2,3,7,1,6] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3

[8,3,2,5,4,7,1,6] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2

[2,1,8,5,4,7,3,6] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1

[8,3,2,7,6,5,1,4] => [[[[.,.],.],[[[.,.],.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 2

[8,7,4,3,6,5,1,2] => [[[[[.,.],.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3

[8,7,6,5,3,1,4,2] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5

[8,7,6,5,1,3,2,4] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4

[8,7,6,5,1,3,4,2] => [[[[[.,.],.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 4

[8,7,6,5,1,4,3,2] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4

[8,7,6,5,4,1,3,2] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5

[8,7,4,3,6,1,5,2] => [[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3

[8,3,2,7,6,1,5,4] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[2,1,8,7,6,3,5,4] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 1

[8,3,2,7,6,1,4,5] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[8,7,6,5,1,4,2,3] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4

[8,7,6,5,1,2,4,3] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 4

[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

[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

[7,4,3,1,8,6,5,2] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3

[7,6,5,1,8,4,3,2] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3

[7,6,4,1,8,5,3,2] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3

[6,4,2,1,8,7,5,3] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3

[5,3,2,1,8,7,6,4] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3

[6,5,1,2,8,4,3,7] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 2

[6,4,1,2,8,5,3,7] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 2

[5,3,1,2,8,6,4,7] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 2

[4,3,1,2,8,6,5,7] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 2

[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

[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

[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

[2,6,1,5,7,8,3,4] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 0

[7,4,1,6,8,5,2,3] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 2

[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

[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

[6,2,1,5,8,7,3,4] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 2

[7,3,1,5,8,6,2,4] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 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

[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

[7,3,1,4,8,6,2,5] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 2

[6,2,1,4,8,7,3,5] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 2

[5,2,1,3,8,7,4,6] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 2

[7,4,1,3,8,5,2,6] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 2

[7,5,1,3,8,4,2,6] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 2

[7,6,1,4,8,3,2,5] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 2

[4,2,1,3,8,7,5,6] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 2

[2,6,1,4,7,8,3,5] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 0

[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

[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

[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

[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

[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

[8,6,7,3,5,2,4,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[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

[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

[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

[4,1,6,3,5,2,8,7] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[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

[5,2,6,3,4,1,8,7] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[5,2,7,3,4,1,8,6] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[5,2,8,6,7,3,4,1] => [[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2

[6,2,8,5,7,3,4,1] => [[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2

[6,2,7,3,4,1,8,5] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[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

[4,1,7,3,5,2,8,6] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[3,1,7,4,5,2,8,6] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[2,1,7,4,5,3,8,6] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[3,1,8,6,7,4,5,2] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 1

[4,1,8,6,7,3,5,2] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 1

[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

[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

[8,5,6,2,7,3,4,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[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

[5,1,8,4,7,3,6,2] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 1

[4,1,8,5,7,3,6,2] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 1

[3,1,8,5,7,4,6,2] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 1

[2,1,8,5,7,4,6,3] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 1

[2,1,7,4,6,3,8,5] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[3,1,7,4,6,2,8,5] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[4,1,7,3,6,2,8,5] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[5,1,7,3,6,2,8,4] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[6,2,7,3,5,1,8,4] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[6,2,8,4,7,3,5,1] => [[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 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] => 2

[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

[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

[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

[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

[8,5,7,3,6,2,4,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[8,5,7,4,6,2,3,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[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

[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

[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

[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

[3,1,4,2,8,6,7,5] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1

[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

[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

[7,4,8,5,6,2,3,1] => [[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[7,3,8,5,6,2,4,1] => [[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 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

[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

[4,1,5,2,8,6,7,3] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1

[3,1,5,2,8,6,7,4] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1

[2,1,6,3,8,5,7,4] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1

[3,1,6,2,8,5,7,4] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1

[4,1,6,2,8,5,7,3] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1

[5,1,6,2,8,4,7,3] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1

[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

[7,3,8,4,6,2,5,1] => [[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[6,2,7,3,8,4,5,1] => [[[.,.],[[.,.],[[.,.],[.,.]]]],.] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 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

[5,1,8,4,6,2,7,3] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[4,1,8,5,6,2,7,3] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[3,1,8,5,6,2,7,4] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[2,1,8,5,6,3,7,4] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[2,1,7,4,8,5,6,3] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 1

[3,1,7,4,8,5,6,2] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 1

[4,1,7,3,8,5,6,2] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 1

[7,3,8,4,5,1,6,2] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[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

[7,3,6,2,8,4,5,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[7,8,5,6,1,3,4,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0

[3,6,1,4,7,2,5,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[4,6,1,2,5,7,3,8] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 0

[7,8,2,4,5,6,1,3] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0

[7,8,1,5,4,6,3,2] => [[.,[.,.]],[[[[.,.],[.,.]],.],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 0

[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

[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

[5,6,1,4,3,2,7,8] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0

[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

[4,6,2,5,3,1,8,7] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[7,5,3,6,2,4,1,8] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 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] => 0

[5,3,6,7,2,1,8,4] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 2

[6,1,7,5,2,4,8,3] => [[.,.],[[[.,.],.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 1

[6,3,1,2,4,5,8,7] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2

[5,2,7,6,1,4,3,8] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[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

[2,7,1,8,5,3,4,6] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0

[3,1,8,5,4,6,7,2] => [[.,.],[[[[.,.],.],[.,[.,.]]],.]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 1

[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

[7,6,5,8,1,3,4,2] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 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

[7,2,1,4,8,3,5,6] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 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] => 0

[5,7,6,4,1,8,3,2] => [[[.,[[.,.],.]],.],[[[.,.],.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1

[6,7,1,5,2,8,3,4] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[6,1,5,2,8,3,4,7] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[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

[7,1,5,3,4,2,8,6] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[7,5,2,4,3,1,6,8] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 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

[6,8,1,3,7,5,4,2] => [[.,[.,.]],[[.,[[[.,.],.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 0

[7,4,2,6,5,1,3,8] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 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] => 2

[7,2,3,5,4,1,6,8] => [[[.,.],[.,[[.,.],.]]],[.,[.,.]]] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 1

[6,8,1,2,3,4,7,5] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 0

[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

[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

[5,2,8,4,6,1,7,3] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[5,2,1,8,6,3,7,4] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[4,2,8,5,7,6,3,1] => [[[.,.],[[[.,.],[[.,.],.]],.]],.] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 2

[4,1,8,6,7,5,3,2] => [[.,.],[[[[[.,.],[.,.]],.],.],.]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 1

[5,3,8,7,6,2,4,1] => [[[[.,.],[[[.,.],.],.]],[.,.]],.] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 2

[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

[5,8,7,4,3,6,1,2] => [[[[.,[[.,.],.]],.],[.,.]],[.,.]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[6,4,8,3,1,7,2,5] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2

[6,4,2,8,7,1,3,5] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[5,8,3,7,1,6,4,2] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 0

[5,8,7,4,1,6,2,3] => [[[.,[[.,.],.]],.],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[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

[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

[6,8,5,2,4,3,7,1] => [[[[.,[.,.]],.],[[.,.],[.,.]]],.] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => 2

[6,8,5,3,1,2,7,4] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => 2

[4,5,1,2,7,6,3,8] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 0

[4,5,1,2,6,8,7,3] => [[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 0

[3,6,2,7,5,1,4,8] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 0

[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

[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

[3,5,2,7,8,1,6,4] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0

[3,1,4,7,5,6,2,8] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 1

[3,1,4,5,8,6,7,2] => [[.,.],[[.,[.,[[.,.],[.,.]]]],.]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 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

[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

[2,1,7,5,8,6,4,3] => [[.,.],[[[[.,.],[[.,.],.]],.],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 1

[4,1,2,7,3,8,6,5] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 1

[6,4,1,7,5,2,3,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[6,1,3,7,5,2,4,8] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 1

[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

[3,7,1,2,5,4,8,6] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 0

[2,4,1,7,8,6,5,3] => [[.,[.,.]],[[[[.,[.,.]],.],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 0

[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

[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

[6,3,7,4,5,1,8,2] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[5,2,1,7,8,3,4,6] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 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] => 0

[5,2,7,3,6,8,1,4] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[5,7,4,6,2,8,1,3] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[5,7,3,4,6,1,8,2] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0

[5,3,8,4,6,1,7,2] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[8,5,2,4,1,6,7,3] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 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

[4,2,8,3,6,7,1,5] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[8,4,1,3,6,2,5,7] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[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

[5,2,8,4,7,1,6,3] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[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

[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

[6,3,1,8,2,4,7,5] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 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

[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

[8,5,4,1,2,6,3,7] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3

[5,1,8,4,2,7,3,6] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[6,8,5,3,1,7,4,2] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 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

[5,6,3,7,1,2,4,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0

[6,3,2,7,8,5,1,4] => [[[[.,.],.],[[.,[.,.]],.]],[.,.]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 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] => 0

[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

[3,8,2,4,6,7,1,5] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0

[4,8,3,5,6,1,7,2] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0

[5,6,2,3,7,8,1,4] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0

[6,8,4,7,1,5,3,2] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 0

[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

[5,4,8,7,2,6,3,1] => [[[[.,.],[[.,.],.]],[[.,.],.]],.] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 2

[5,4,8,7,1,6,3,2] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[5,3,8,7,6,1,2,4] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 1

[4,3,8,7,6,1,2,5] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 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] => 0

[8,3,4,6,5,1,2,7] => [[[.,.],[.,[[.,.],.]]],[.,[.,.]]] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 1

[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

[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

[8,1,3,2,6,5,4,7] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1

[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

[3,4,1,8,7,6,5,2] => [[.,[.,.]],[[[[[.,.],.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 0

[4,3,1,8,7,6,5,2] => [[[.,.],.],[[[[[.,.],.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2

[4,2,1,8,7,6,5,3] => [[[.,.],.],[[[[[.,.],.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 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

[8,3,2,1,6,5,4,7] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[8,4,2,6,1,5,3,7] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[4,2,8,7,1,6,3,5] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[5,2,8,7,1,6,3,4] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[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

[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

[5,3,8,2,7,6,4,1] => [[[[.,.],[.,.]],[[[.,.],.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 2

[6,8,3,2,7,5,4,1] => [[[[.,[.,.]],.],[[[.,.],.],.]],.] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 2

[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

[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

[6,8,2,7,1,5,3,4] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[6,8,7,2,1,4,3,5] => [[[.,[[.,.],.]],.],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[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

[6,8,1,2,7,5,4,3] => [[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => 0

[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

[5,2,8,3,7,6,4,1] => [[[.,.],[[.,.],[[[.,.],.],.]]],.] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 2

[5,1,8,3,7,6,4,2] => [[.,.],[[[.,.],[[[.,.],.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 1

[5,1,8,7,2,6,3,4] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[4,1,8,7,2,6,3,5] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 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] => 0

[8,4,1,6,2,5,3,7] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[8,3,1,2,6,5,4,7] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 2

[3,8,1,2,7,5,4,6] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 0

[3,1,8,2,7,6,4,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1

[3,1,2,8,7,6,5,4] => [[.,.],[.,[[[[[.,.],.],.],.],.]]] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 1

[4,1,3,8,7,6,5,2] => [[.,.],[[.,[[[[.,.],.],.],.]],.]] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 1

[3,1,4,8,7,6,5,2] => [[.,.],[[.,[[[[.,.],.],.],.]],.]] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 1

[2,1,8,3,7,6,4,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1

[2,8,1,3,7,5,4,6] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 0

[8,2,1,3,6,5,4,7] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 2

[8,1,2,3,6,5,4,7] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 1

[3,1,6,2,5,8,4,7] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[3,5,1,8,2,4,7,6] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0

[3,1,6,5,8,2,4,7] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[4,1,2,6,3,8,7,5] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 1

[7,1,5,4,2,8,3,6] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[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

[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

[6,2,1,8,7,3,4,5] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[7,6,2,1,8,3,4,5] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[7,3,1,6,2,8,4,5] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[4,1,2,8,6,3,7,5] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 1

[3,1,8,6,2,4,7,5] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1

[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

[8,3,1,6,2,4,7,5] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2

[7,1,8,3,2,4,6,5] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1

[8,1,5,4,2,7,3,6] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[8,5,3,1,7,2,4,6] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[8,6,2,1,7,3,4,5] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[7,1,8,3,2,6,4,5] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[7,2,1,8,6,3,4,5] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[4,1,7,3,6,5,8,2] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 1

[5,1,8,7,6,2,4,3] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 1

[8,1,7,6,3,4,5,2] => [[.,.],[[[[.,.],.],[.,[.,.]]],.]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 1

[5,7,1,6,2,4,3,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[6,4,1,5,2,7,3,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[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

[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

[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

[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

[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

[7,1,8,6,3,4,5,2] => [[.,.],[[[[.,.],.],[.,[.,.]]],.]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 1

[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

[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

[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

[7,4,1,5,2,6,3,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 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] => 2

[6,3,5,8,2,1,7,4] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 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] => 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

[6,4,5,8,3,7,2,1] => [[[[[.,.],[.,[.,.]]],[.,.]],.],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[5,4,8,6,3,1,7,2] => [[[[.,.],[[.,.],.]],.],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2

[5,4,1,8,2,3,7,6] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2

[5,8,1,6,2,4,3,7] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[8,4,1,5,2,6,3,7] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[6,3,5,8,2,1,4,7] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2

[8,3,5,6,2,1,4,7] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2

[8,3,5,7,2,1,6,4] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 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] => 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] => 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

[7,3,5,8,2,1,6,4] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 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] => 2

[8,7,5,6,1,4,2,3] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[2,6,1,3,8,5,7,4] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 0

[2,7,1,3,6,5,8,4] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 0

[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

[8,4,1,5,2,3,7,6] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2

[7,8,1,6,3,4,2,5] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[6,4,1,8,3,2,7,5] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[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

[8,4,3,6,5,1,7,2] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[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

[8,6,5,4,3,1,7,2] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5

[8,7,5,4,1,6,3,2] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4

[7,8,5,4,1,3,6,2] => [[[[.,[.,.]],.],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 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] => 3

[4,8,2,6,5,1,7,3] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[3,2,8,6,5,1,7,4] => [[[.,.],[[[.,.],.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 1

[3,2,1,7,6,4,5,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[4,1,3,7,6,2,5,8] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 1

[5,1,7,3,6,2,4,8] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[6,1,7,5,3,2,4,8] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 1

[7,1,6,5,2,4,3,8] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[8,1,6,5,2,3,7,4] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1

[8,1,7,2,6,3,5,4] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[7,1,8,2,6,4,3,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1

[6,1,8,2,4,7,3,5] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[5,1,8,3,2,7,4,6] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[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

[3,2,1,8,4,7,5,6] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[3,2,8,7,1,6,5,4] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[4,8,2,7,1,6,5,3] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 0

[5,8,7,2,1,6,4,3] => [[[.,[[.,.],.]],.],[[[.,.],.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1

[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

[8,7,6,1,5,4,3,2] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3

[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

[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

[6,5,8,3,2,1,7,4] => [[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 3

[7,5,8,3,1,4,6,2] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 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] => 2

[8,4,3,7,1,6,5,2] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2

[7,4,3,8,1,5,6,2] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[6,4,3,1,5,2,7,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[7,4,3,1,2,6,5,8] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3

[8,4,3,1,2,5,7,6] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3

[8,5,1,4,2,3,7,6] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2

[7,5,1,4,2,6,3,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[6,5,1,4,3,2,7,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[5,6,1,3,4,2,7,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[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

[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

[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

[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

[5,7,1,3,2,6,4,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[6,7,1,2,4,5,3,8] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 0

[7,6,1,2,5,4,3,8] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 2

[8,6,1,2,5,3,7,4] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2

[8,7,1,2,3,6,5,4] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 2

[7,8,1,2,3,5,6,4] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 0

[6,8,1,2,4,3,7,5] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 0

[5,8,1,3,2,4,7,6] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0

[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

[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

[4,1,3,2,5,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1

[5,1,2,4,3,6,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1

[6,1,2,3,5,4,7,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1

[7,1,2,3,4,6,5,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1

[8,1,2,3,4,5,7,6] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1

[6,7,3,8,5,1,2,4] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 0

[6,7,4,5,1,8,3,2] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 0

[5,4,7,6,8,1,2,3] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[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

[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

[8,1,3,2,5,4,6,7] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 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

[2,4,1,6,8,7,5,3] => [[.,[.,.]],[[[.,[[.,.],.]],.],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 0

[3,4,1,6,7,8,5,2] => [[.,[.,.]],[[[.,[.,[.,.]]],.],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 0

[4,3,1,7,6,8,5,2] => [[[.,.],.],[[[[.,.],[.,.]],.],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 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

[5,3,7,2,6,4,8,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[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

[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

[6,7,2,8,1,5,3,4] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[6,7,1,2,8,4,5,3] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 0

[6,7,1,3,4,8,5,2] => [[.,[.,.]],[[.,[.,[[.,.],.]]],.]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 0

[5,2,7,3,4,6,8,1] => [[[.,.],[[.,.],[.,[.,[.,.]]]]],.] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 2

[5,1,7,3,4,8,6,2] => [[.,.],[[[.,.],[.,[[.,.],.]]],.]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 1

[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

[4,1,8,7,2,3,6,5] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1

[3,8,1,2,7,4,5,6] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 0

[4,1,3,7,5,8,6,2] => [[.,.],[[.,[[.,.],[[.,.],.]]],.]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 1

[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

[2,1,8,3,4,7,6,5] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 1

[8,2,1,3,4,6,5,7] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 2

[4,2,1,6,5,8,7,3] => [[[.,.],.],[[[.,.],[[.,.],.]],.]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 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

[5,2,6,4,1,8,7,3] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[5,2,7,4,8,1,6,3] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[5,2,7,4,8,6,1,3] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[5,7,2,3,8,6,1,4] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 0

[5,7,2,3,8,1,6,4] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0

[5,6,2,3,1,8,7,4] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 0

[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

[5,1,6,4,2,8,7,3] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 1

[5,6,1,3,2,8,7,4] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 0

[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

[5,6,3,2,1,8,7,4] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 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

[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

[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

[6,7,3,8,1,2,5,4] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 0

[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

[5,7,1,3,8,2,6,4] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[5,1,7,4,8,2,6,3] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[5,1,7,4,8,6,2,3] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1

[5,7,1,3,8,6,2,4] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 0

[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

[6,7,3,8,1,5,2,4] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[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

[6,7,1,8,3,5,2,4] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[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

[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

[6,7,1,8,3,2,5,4] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[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

[6,7,2,8,1,3,5,4] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 0

[6,7,2,8,3,1,5,4] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[6,7,2,8,3,5,1,4] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[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

[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

[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

[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

[4,2,1,7,8,5,6,3] => [[[.,.],.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 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

[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

[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

[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

[6,7,2,8,5,3,1,4] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 0

[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

[5,7,1,2,8,6,3,4] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 0

[5,1,7,2,8,6,4,3] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 1

[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

[6,7,1,8,2,5,3,4] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[6,7,1,8,5,2,3,4] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0

[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

[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

[6,7,1,8,5,3,2,4] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 0

[6,3,8,5,2,7,4,1] => [[[[.,.],[[.,.],.]],[[.,.],.]],.] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 2

[6,5,2,8,4,7,3,1] => [[[[.,.],.],[[[.,.],[.,.]],.]],.] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[6,3,4,5,8,7,2,1] => [[[[.,.],[.,[.,[[.,.],.]]]],.],.] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 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] => 0

[5,1,4,8,6,3,7,2] => [[.,.],[[[.,[[.,.],.]],[.,.]],.]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 1

[6,3,8,4,2,7,1,5] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[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

[4,3,8,5,6,7,2,1] => [[[[.,.],[[.,.],[.,[.,.]]]],.],.] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 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] => 0

[6,3,7,5,2,8,1,4] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[6,5,2,7,4,8,1,3] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2

[5,7,1,4,8,3,2,6] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 0

[7,8,3,5,1,4,6,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0

[5,8,1,4,6,7,2,3] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 0

[6,5,8,4,3,7,2,1] => [[[[[[.,.],[.,.]],.],[.,.]],.],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 4

[6,3,7,4,2,8,5,1] => [[[[.,.],[[.,.],.]],[[.,.],.]],.] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 2

[8,7,1,6,2,4,5,3] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[5,3,8,7,4,1,2,6] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 1

[4,3,8,7,1,5,6,2] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 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

[5,6,1,8,7,3,2,4] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 0

[7,5,3,6,4,2,8,1] => [[[[[.,.],.],[[.,.],.]],[.,.]],.] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 3

[6,4,1,5,3,8,2,7] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[8,2,6,3,4,7,5,1] => [[[.,.],[[.,.],[.,[[.,.],.]]]],.] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 2

[7,2,6,3,5,4,8,1] => [[[.,.],[[.,.],[[.,.],[.,.]]]],.] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 2

[6,2,7,4,3,5,8,1] => [[[.,.],[[[.,.],.],[.,[.,.]]]],.] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 2

[6,5,4,3,1,8,2,7] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4

[8,6,5,4,2,7,3,1] => [[[[[[.,.],.],.],.],[[.,.],.]],.] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 5

[6,5,8,4,2,7,3,1] => [[[[[.,.],[.,.]],.],[[.,.],.]],.] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[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

[7,8,5,3,2,6,4,1] => [[[[[.,[.,.]],.],.],[[.,.],.]],.] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 3

[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

[8,7,5,2,6,4,3,1] => [[[[[.,.],.],.],[[[.,.],.],.]],.] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 4

[8,7,1,6,2,5,4,3] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 2

[7,8,1,6,3,2,5,4] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[2,8,1,7,3,5,6,4] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 0

[4,8,1,3,7,2,6,5] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[4,2,8,5,7,3,6,1] => [[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2

[5,1,7,6,8,3,2,4] => [[.,.],[[[[.,.],[.,.]],.],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 1

[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

[7,6,1,8,4,3,2,5] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 2

[8,6,1,7,4,2,5,3] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[8,1,2,7,3,4,6,5] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 1

[7,1,2,8,3,5,4,6] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 1

[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

[4,2,1,5,8,3,6,7] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[5,4,3,1,6,8,2,7] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3

[6,5,4,8,2,7,3,1] => [[[[[.,.],.],[.,.]],[[.,.],.]],.] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[6,5,1,8,7,4,2,3] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 2

[8,6,4,7,5,3,2,1] => [[[[[[.,.],.],[[.,.],.]],.],.],.] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[5,1,8,3,7,6,2,4] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 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

[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

[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

[7,2,8,6,4,3,5,1] => [[[.,.],[[[[.,.],.],.],[.,.]]],.] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 2

[2,1,8,7,5,6,3,4] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1

[8,2,7,6,3,5,4,1] => [[[.,.],[[[.,.],.],[[.,.],.]]],.] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 2

[8,1,7,6,5,2,4,3] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 1

[7,1,8,6,5,3,2,4] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 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] => 0

[6,8,3,7,4,5,1,2] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[5,8,3,7,4,6,1,2] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[4,7,3,8,5,6,1,2] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[4,7,2,8,5,6,1,3] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[4,7,1,8,5,6,2,3] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[3,7,1,8,5,6,2,4] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[3,7,2,8,5,6,1,4] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[5,8,2,7,4,6,1,3] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[6,8,2,7,4,5,1,3] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[7,8,2,6,4,5,1,3] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[7,8,1,6,4,5,2,3] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[6,8,1,7,4,5,2,3] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[5,8,1,7,4,6,2,3] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[4,8,1,7,3,6,2,5] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[5,8,1,7,3,6,2,4] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[6,8,1,7,3,5,2,4] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[7,8,2,6,3,5,1,4] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[6,8,2,7,3,5,1,4] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[5,8,2,7,3,6,1,4] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[4,8,2,7,3,6,1,5] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[3,7,2,8,4,6,1,5] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[3,7,1,8,4,6,2,5] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[6,8,5,7,1,4,2,3] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[2,5,1,8,6,7,3,4] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[2,6,1,8,5,7,3,4] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[6,8,4,7,1,5,2,3] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[7,8,4,6,1,5,2,3] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[7,8,3,6,1,5,2,4] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[6,8,3,7,1,5,2,4] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[4,8,3,7,1,6,2,5] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[2,6,1,8,4,7,3,5] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[3,7,2,6,1,8,4,5] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[3,7,1,6,2,8,4,5] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[4,8,1,6,2,7,3,5] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[5,8,1,6,2,7,3,4] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[7,8,1,5,2,6,3,4] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[7,8,2,5,1,6,3,4] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[6,8,2,5,1,7,3,4] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[5,8,2,6,1,7,3,4] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[4,8,2,6,1,7,3,5] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[6,7,4,8,3,5,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[6,7,4,5,2,8,1,3] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[5,7,4,6,2,3,1,8] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[5,7,4,6,3,8,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[5,7,4,8,3,6,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[6,8,4,5,3,7,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[5,8,4,6,3,7,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[5,6,4,8,3,7,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[5,6,3,7,2,4,1,8] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[5,6,3,7,2,8,1,4] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[5,6,3,8,2,7,1,4] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[5,6,4,8,2,7,1,3] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[5,8,4,6,2,7,1,3] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[6,8,4,5,2,7,1,3] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[7,8,4,5,2,6,1,3] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[6,8,4,5,2,3,1,7] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[5,8,4,6,2,3,1,7] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[5,6,4,8,2,3,1,7] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[5,6,3,8,2,4,1,7] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[5,6,3,4,2,8,1,7] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[4,6,3,5,2,7,1,8] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[4,6,3,5,2,8,1,7] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[4,6,3,8,2,5,1,7] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[4,8,3,6,2,5,1,7] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[5,8,3,6,2,4,1,7] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[6,8,3,5,2,4,1,7] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[7,8,3,5,2,4,1,6] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[7,8,3,5,2,6,1,4] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[5,8,3,6,2,7,1,4] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[4,8,3,6,2,7,1,5] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[4,6,3,8,2,7,1,5] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[4,6,3,7,2,8,1,5] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[4,7,3,6,2,5,1,8] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[4,7,3,6,2,8,1,5] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[4,7,3,8,2,6,1,5] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[5,7,4,8,2,6,1,3] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[5,7,3,6,2,8,1,4] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[5,7,3,6,2,4,1,8] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[6,7,3,5,2,4,1,8] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[6,7,3,5,2,8,1,4] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[6,7,4,8,2,5,1,3] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[6,7,5,8,2,4,1,3] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[6,8,5,7,2,3,1,4] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[6,7,4,8,2,3,1,5] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[6,7,3,8,2,4,1,5] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[6,7,3,4,2,8,1,5] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[5,7,3,4,2,6,1,8] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[5,7,3,4,2,8,1,6] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[5,7,4,8,2,3,1,6] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[5,8,4,7,2,3,1,6] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[6,8,4,7,2,3,1,5] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[7,8,4,6,2,3,1,5] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[7,8,3,6,2,4,1,5] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[6,8,3,7,2,4,1,5] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[5,8,3,7,2,4,1,6] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[4,8,3,7,2,5,1,6] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[4,7,3,8,2,5,1,6] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[4,7,3,5,2,8,1,6] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[4,7,3,5,2,6,1,8] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[4,5,3,7,2,6,1,8] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[4,5,3,7,2,8,1,6] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[4,5,3,8,2,7,1,6] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[4,8,3,5,2,7,1,6] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[5,8,3,4,2,7,1,6] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[6,8,3,4,2,7,1,5] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[7,8,3,4,2,6,1,5] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[6,8,3,4,2,5,1,7] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[5,8,3,4,2,6,1,7] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[4,8,3,5,2,6,1,7] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[4,5,3,8,2,6,1,7] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[4,5,3,6,2,8,1,7] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0

[4,7,5,2,1,8,3,6] => [[[.,[[.,.],.]],.],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[4,8,5,2,1,7,6,3] => [[[.,[[.,.],.]],.],[[[.,.],.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1

[4,6,5,2,1,3,8,7] => [[[.,[[.,.],.]],.],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => 1

[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

[6,4,5,3,1,2,8,7] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2

[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

[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

[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

[8,4,5,3,1,7,6,2] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 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

[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

[8,5,7,6,4,2,1,3] => [[[[[.,.],[[.,.],.]],.],.],[.,.]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 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] => 2

[6,3,2,8,7,4,1,5] => [[[[.,.],.],[[[.,.],.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 2

[2,1,6,8,7,4,3,5] => [[.,.],[[[.,[[.,.],.]],.],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 1

[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

[7,3,2,8,6,4,5,1] => [[[[.,.],.],[[[.,.],.],[.,.]]],.] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 3

[7,6,8,5,2,4,3,1] => [[[[[.,.],[.,.]],.],[[.,.],.]],.] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[6,8,7,5,3,2,4,1] => [[[[[.,[[.,.],.]],.],.],[.,.]],.] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 3

[5,8,4,2,3,7,6,1] => [[[[.,[.,.]],.],[.,[[.,.],.]]],.] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => 2

[7,8,4,2,6,5,3,1] => [[[[.,[.,.]],.],[[[.,.],.],.]],.] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 2

[3,6,1,8,7,4,2,5] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 0

[3,7,1,8,6,4,5,2] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 0

[3,8,1,6,7,5,2,4] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 0

[3,7,1,6,8,2,5,4] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[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

[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

[2,1,8,6,7,5,3,4] => [[.,.],[[[[.,.],[.,.]],.],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 1

[8,3,2,6,7,5,1,4] => [[[[.,.],.],[[.,[.,.]],.]],[.,.]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 2

[8,6,4,3,7,5,1,2] => [[[[[.,.],.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3

[6,7,5,8,1,3,4,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0

[7,6,5,8,1,4,3,2] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2

[8,6,5,7,4,1,3,2] => [[[[[.,.],.],[.,.]],.],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 3

[7,6,4,3,8,1,5,2] => [[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3

[7,3,2,6,8,1,5,4] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[2,1,7,6,8,3,5,4] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[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

[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

[8,1,3,7,4,6,5,2] => [[.,.],[[.,[[.,.],[[.,.],.]]],.]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 1

[5,2,8,7,4,6,1,3] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[6,2,7,5,4,8,3,1] => [[[.,.],[[[[.,.],.],[.,.]],.]],.] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 2

[8,1,3,5,4,7,6,2] => [[.,.],[[.,[[.,.],[[.,.],.]]],.]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 1

[6,1,5,4,3,8,7,2] => [[.,.],[[[[.,.],.],[[.,.],.]],.]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 1

[6,1,8,3,4,5,7,2] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 1

[7,1,5,3,4,8,6,2] => [[.,.],[[[.,.],[.,[[.,.],.]]],.]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 1

[7,1,4,3,5,6,8,2] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 1

[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

[6,3,2,7,5,1,8,4] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 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

[6,5,8,2,4,7,3,1] => [[[[.,.],[.,.]],[[.,[.,.]],.]],.] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 2

[8,5,2,1,4,3,7,6] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3

[6,5,2,8,4,1,3,7] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[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

[3,6,1,8,5,2,4,7] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0

[3,4,1,2,8,6,5,7] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 0

[4,3,1,2,6,8,5,7] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 2

[5,8,1,6,3,2,4,7] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0

[6,3,8,5,2,1,4,7] => [[[[.,.],[[.,.],.]],.],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 2

[8,3,1,5,2,4,7,6] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2

[3,8,2,6,1,5,7,4] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0

[8,5,6,4,2,1,7,3] => [[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 3

[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

[6,1,2,3,8,5,7,4] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 1

[7,1,2,3,6,5,8,4] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 1

[7,2,1,3,8,6,4,5] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 2

[5,2,7,3,1,8,4,6] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[5,8,2,4,1,3,7,6] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 0

[8,7,2,6,3,4,1,5] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2

[4,8,1,6,3,2,7,5] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[3,1,8,6,4,2,7,5] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 1

[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

[4,2,1,3,7,8,5,6] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 2

[2,4,1,3,8,7,5,6] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 0

[8,6,1,3,7,2,4,5] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[2,8,1,3,6,4,7,5] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 0

[6,8,2,3,4,1,5,7] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[5,1,8,3,2,4,6,7] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1

[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

[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

[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

[6,2,1,8,3,4,7,5] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2

[6,2,8,3,5,1,7,4] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[6,2,4,8,5,7,1,3] => [[[.,.],[.,[[.,.],[.,.]]]],[.,.]] => [1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1

[6,2,4,7,5,8,1,3] => [[[.,.],[.,[[.,.],[.,.]]]],[.,.]] => [1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1

[6,2,1,3,7,8,4,5] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 2

[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

[7,6,4,2,3,1,8,5] => [[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3

[5,7,2,3,1,6,8,4] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0

[7,5,4,2,6,8,1,3] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3

[8,2,5,4,6,7,1,3] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[5,2,6,3,1,8,7,4] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[8,2,6,4,3,1,7,5] => [[[.,.],[[[.,.],.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 1

[8,2,7,4,1,3,5,6] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1

[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

[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

[5,1,8,3,2,6,4,7] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[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

[5,3,1,6,7,2,4,8] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[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

[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

[6,3,1,4,2,7,5,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[8,6,3,2,4,1,7,5] => [[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3

[8,5,3,2,6,7,1,4] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3

[4,5,2,6,8,1,7,3] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0

[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

[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

[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

[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

[8,6,1,4,3,2,5,7] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[8,3,1,6,5,2,4,7] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[4,1,5,2,8,7,3,6] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1

[8,1,2,4,6,5,3,7] => [[.,.],[.,[[.,[[.,.],.]],[.,.]]]] => [1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 1

[8,1,2,5,4,6,3,7] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 1

[8,2,6,5,1,3,4,7] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1

[8,3,1,6,2,5,4,7] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[8,1,2,6,4,5,3,7] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 1

[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

[8,1,2,6,5,4,3,7] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 1

[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

[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

[5,7,2,8,1,3,4,6] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0

[5,2,8,7,1,3,4,6] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1

[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

[3,1,2,6,4,8,7,5] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 1

[2,1,7,6,3,4,8,5] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1

[3,1,2,7,4,6,8,5] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 1

[5,1,4,2,7,8,3,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[3,1,2,8,4,6,7,5] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 1

[3,1,2,7,6,4,8,5] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 1

[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

[4,8,7,2,1,3,5,6] => [[[.,[[.,.],.]],.],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1

[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

[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

[2,1,8,6,3,4,7,5] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1

[3,1,7,2,8,6,4,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1

[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

[8,6,3,7,2,1,5,4] => [[[[[.,.],.],[.,.]],.],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 3

[7,6,3,8,2,1,5,4] => [[[[[.,.],.],[.,.]],.],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 3

[8,6,3,7,2,1,4,5] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3

[8,4,3,2,1,6,5,7] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4

[6,4,3,2,1,7,5,8] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4

[6,4,3,2,1,8,5,7] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4

[7,4,3,2,1,8,6,5] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4

[6,4,3,2,1,8,7,5] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4

[8,5,4,2,6,7,1,3] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3

[8,5,3,2,6,1,7,4] => [[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3

[7,5,3,2,6,1,8,4] => [[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3

[7,4,3,2,1,5,8,6] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 4

[6,4,3,2,1,5,8,7] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 4

[5,6,3,4,1,2,8,7] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 0

[8,5,3,7,2,6,4,1] => [[[[[.,.],.],[.,.]],[[.,.],.]],.] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 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] => 3

[7,5,8,4,2,6,1,3] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 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

[6,8,3,7,5,1,4,2] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[5,7,3,8,1,6,2,4] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[3,2,6,4,8,5,1,7] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[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

[3,5,2,4,1,7,6,8] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[4,2,1,5,7,3,6,8] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[4,5,2,3,7,1,6,8] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[4,2,5,3,8,1,6,7] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[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

[3,1,5,4,2,8,6,7] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[4,1,5,3,8,2,6,7] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[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

[4,3,8,5,2,1,6,7] => [[[[.,.],[[.,.],.]],.],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 2

[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

[4,3,2,7,5,1,6,8] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[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

[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

[4,5,1,7,3,2,6,8] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0

[4,5,1,3,7,2,6,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[3,5,1,4,2,7,6,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[2,5,1,4,3,7,8,6] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 0

[5,2,1,4,3,7,8,6] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[5,3,1,4,2,7,6,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[4,3,1,5,7,2,6,8] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[4,3,1,7,5,2,6,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[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

[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

[5,3,6,4,1,2,7,8] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1

[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

[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

[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

[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

[5,3,6,2,1,4,7,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2

[5,6,2,7,1,3,4,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0

[4,5,2,7,3,1,6,8] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 0

[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

[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

[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

[3,5,2,7,4,6,1,8] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[3,7,2,4,8,5,1,6] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 0

[7,2,1,4,6,3,8,5] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[7,3,1,4,6,8,2,5] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 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

[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

[6,3,2,1,5,7,4,8] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3

[6,4,2,1,5,3,7,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 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

[4,2,1,7,5,3,6,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[7,4,1,5,6,2,3,8] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[7,3,1,5,2,6,4,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[7,2,1,5,3,6,8,4] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[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

[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

[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

[5,2,6,4,1,3,7,8] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1

[6,5,2,1,4,7,8,3] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 3

[6,5,3,1,4,7,2,8] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3

[2,3,1,8,5,4,7,6] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[2,4,1,5,8,3,7,6] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[2,3,1,8,6,7,4,5] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[2,5,1,6,7,8,4,3] => [[.,[.,.]],[[[.,[.,[.,.]]],.],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 0

[2,5,1,6,7,4,8,3] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 0

[2,5,1,6,7,4,3,8] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 0

[8,2,5,3,7,1,6,4] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[8,2,4,3,7,1,6,5] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[5,8,2,4,3,7,1,6] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[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

[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

[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

[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

[3,8,2,4,7,1,5,6] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[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

[3,7,1,5,6,8,2,4] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 0

[3,7,1,5,8,2,4,6] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[8,3,2,4,6,1,5,7] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[7,3,2,4,6,1,5,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[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

[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

[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

[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

[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

[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

[6,1,5,8,7,3,2,4] => [[.,.],[[[.,[[.,.],.]],.],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 1

[8,7,3,2,4,6,1,5] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3

[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

[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

[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

[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

[6,5,1,7,8,4,2,3] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 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

[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

[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

[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

[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

[8,3,2,4,7,6,1,5] => [[[[.,.],.],[.,[[.,.],.]]],[.,.]] => [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 2

[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

[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

[6,5,1,7,4,2,3,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[6,5,1,8,4,2,3,7] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[8,4,2,3,7,5,1,6] => [[[[.,.],.],[.,[[.,.],.]]],[.,.]] => [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 2

[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

[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

[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

[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

[7,4,2,3,8,5,1,6] => [[[[.,.],.],[.,[[.,.],.]]],[.,.]] => [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 2

[8,5,1,6,4,2,3,7] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[7,5,1,6,4,2,3,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 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

[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

[7,3,2,4,8,6,1,5] => [[[[.,.],.],[.,[[.,.],.]]],[.,.]] => [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 2

[8,6,1,5,7,3,2,4] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 2

[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

[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

[8,5,1,6,7,4,2,3] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 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

[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

[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

[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

[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

[8,7,5,1,6,4,2,3] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 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

[6,5,7,3,1,8,4,2] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 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] => 0

[4,6,3,7,5,1,8,2] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[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

[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

[5,4,7,8,3,1,6,2] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 2

[4,3,7,5,1,8,6,2] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[6,4,3,8,5,1,7,2] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 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

[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

[5,4,3,6,7,1,8,2] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 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

[5,2,8,4,1,6,7,3] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 1

[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

[2,4,1,7,5,8,6,3] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 0

[2,4,1,7,5,3,8,6] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[5,4,8,2,1,6,3,7] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2

[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

[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

[3,5,2,8,1,6,4,7] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[3,2,1,6,8,5,4,7] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 2

[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

[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

[3,8,2,5,1,6,7,4] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0

[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

[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

[4,3,2,6,7,8,1,5] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2

[4,3,2,6,7,1,5,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 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

[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

[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

[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

[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

[6,3,2,7,1,5,4,8] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[6,3,2,7,1,5,8,4] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[6,3,2,7,8,1,5,4] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[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

[6,5,2,1,7,8,4,3] => [[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[2,1,7,5,3,8,6,4] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 1

[6,2,1,8,5,3,7,4] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[6,3,2,7,1,4,8,5] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[6,3,2,1,4,7,8,5] => [[[[.,.],.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 3

[6,3,2,1,4,7,5,8] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3

[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

[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

[5,8,4,2,1,7,3,6] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 2

[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

[2,4,1,7,3,8,6,5] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 0

[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

[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

[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

[4,3,7,2,1,5,6,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2

[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

[3,5,2,8,1,7,4,6] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[6,3,2,8,1,4,7,5] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[3,2,1,4,7,5,8,6] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2

[5,3,2,1,8,4,6,7] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 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] => 2

[4,3,8,2,1,5,6,7] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2

[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

[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

[8,6,7,2,5,3,4,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[8,2,5,3,4,1,7,6] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[6,2,5,3,4,1,8,7] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[6,1,5,2,4,3,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 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

[6,1,5,3,4,2,8,7] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[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

[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

[8,3,7,5,6,2,4,1] => [[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 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

[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

[8,1,5,3,4,2,7,6] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[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

[2,1,8,4,5,3,7,6] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[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

[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

[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

[8,3,7,5,6,1,4,2] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[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

[8,3,7,4,6,2,5,1] => [[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[8,3,7,4,6,1,5,2] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[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

[8,1,7,3,6,4,5,2] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 1

[8,1,7,5,6,3,4,2] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 1

[8,4,7,5,6,1,3,2] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[2,1,8,4,7,5,6,3] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 1

[8,1,7,3,4,2,6,5] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[8,1,7,3,6,2,5,4] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[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

[8,3,7,2,6,4,5,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[8,2,7,3,6,4,5,1] => [[[.,.],[[.,.],[[.,.],[.,.]]]],.] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 2

[8,2,7,3,6,1,5,4] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 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

[8,1,7,2,4,3,6,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[8,1,3,2,7,4,6,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[2,1,8,3,7,4,6,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[8,1,5,2,4,3,7,6] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[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

[8,2,7,3,4,1,6,5] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[8,2,7,5,6,3,4,1] => [[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2

[8,4,7,5,6,2,3,1] => [[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[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

[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

[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

[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

[4,1,3,2,8,6,7,5] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1

[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

[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

[8,5,7,2,6,3,4,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[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

[8,2,7,5,6,1,4,3] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[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

[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

[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

[2,1,8,6,7,3,5,4] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[2,1,8,3,7,5,6,4] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1

[8,1,3,2,7,5,6,4] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1

[8,1,7,5,6,2,4,3] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[8,1,7,2,6,4,5,3] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1

[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

[8,2,7,4,6,1,5,3] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[8,2,7,4,6,3,5,1] => [[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 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] => 2

[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

[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

[8,1,7,4,6,2,5,3] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[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

[2,1,8,5,7,3,6,4] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[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

[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

[8,1,7,4,6,3,5,2] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 1

[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

[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

[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

[6,5,8,7,3,1,2,4] => [[[[.,.],[[.,.],.]],.],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 2

[6,7,2,8,4,1,5,3] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[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

[2,6,1,8,4,5,7,3] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 0

[6,3,1,8,4,5,7,2] => [[[.,.],.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 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

[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

[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

[7,6,1,8,4,2,5,3] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[5,2,8,7,3,6,1,4] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[7,2,1,8,4,6,5,3] => [[[.,.],.],[[[.,.],[[.,.],.]],.]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 2

[3,2,7,8,4,6,5,1] => [[[.,.],[[.,[.,.]],[[.,.],.]]],.] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 2

[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

[4,2,1,3,8,5,6,7] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2

[7,2,5,8,3,4,6,1] => [[[.,.],[[.,[.,.]],[.,[.,.]]]],.] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2

[6,2,8,5,4,3,1,7] => [[[.,.],[[[[.,.],.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1

[6,4,8,5,2,3,1,7] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 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] => 2

[4,3,1,2,8,5,6,7] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2

[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

[5,7,1,8,3,4,6,2] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 0

[7,5,8,6,3,4,2,1] => [[[[[.,.],[[.,.],.]],[.,.]],.],.] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[4,1,8,3,5,6,2,7] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[3,7,1,8,5,4,6,2] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 0

[7,1,3,8,4,6,5,2] => [[.,.],[[.,[[.,.],[[.,.],.]]],.]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 1

[6,5,8,4,2,3,1,7] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2

[4,1,3,2,8,5,6,7] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[7,3,2,8,5,4,6,1] => [[[[.,.],.],[[[.,.],.],[.,.]]],.] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 3

[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

[6,2,8,4,5,3,1,7] => [[[.,.],[[[.,.],[.,.]],.]],[.,.]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1

[7,2,3,8,5,4,6,1] => [[[.,.],[.,[[[.,.],.],[.,.]]]],.] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 2

[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

[3,2,1,4,8,5,6,7] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2

[5,1,3,2,4,8,6,7] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 1

[2,8,1,5,3,4,7,6] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0

[8,1,5,3,2,4,6,7] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1

[3,8,1,5,2,4,6,7] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0

[3,5,1,4,8,2,6,7] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[5,1,2,7,4,8,3,6] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 1

[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

[2,8,1,5,4,7,3,6] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[2,8,1,4,3,7,6,5] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 0

[6,1,2,8,7,4,3,5] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 1

[6,4,1,2,8,7,3,5] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 2

[7,6,1,4,2,8,3,5] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[7,1,6,2,8,4,3,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1

[6,7,1,4,2,8,3,5] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[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

[7,1,2,8,5,3,4,6] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 1

[6,1,2,8,4,3,7,5] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 1

[6,4,1,2,8,3,7,5] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2

[7,6,1,3,2,4,8,5] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2

[6,7,1,3,2,4,8,5] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0

[5,8,1,3,7,2,4,6] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[2,8,1,7,3,5,4,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[8,6,1,3,2,4,7,5] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2

[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

[2,8,1,7,4,3,6,5] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[7,1,2,8,4,3,6,5] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 1

[2,8,1,7,5,3,4,6] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0

[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

[8,6,1,4,2,7,3,5] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[8,1,6,2,7,4,3,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1

[7,1,2,8,6,4,3,5] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 1

[7,4,1,2,8,6,3,5] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 2

[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

[2,8,1,7,6,4,3,5] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 0

[7,8,3,4,1,6,2,5] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[6,7,3,4,1,8,2,5] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[5,8,3,4,1,7,2,6] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[6,7,3,4,1,5,2,8] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[5,7,3,4,1,6,2,8] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[5,6,2,7,3,4,1,8] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[4,6,2,8,3,5,1,7] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[4,8,3,5,1,6,2,7] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[5,6,2,4,1,7,3,8] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[4,5,1,7,3,8,2,6] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[4,6,2,7,3,8,1,5] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[5,6,2,7,3,8,1,4] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[5,6,2,7,4,8,1,3] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[5,6,3,8,4,7,1,2] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[4,6,2,8,3,7,1,5] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[4,5,1,7,3,6,2,8] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[6,5,3,2,1,4,8,7] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 4

[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

[8,7,3,5,2,4,1,6] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 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

[8,7,2,4,5,3,1,6] => [[[[.,.],.],[[.,[.,.]],.]],[.,.]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 2

[3,6,1,4,5,2,8,7] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[8,3,7,4,5,2,1,6] => [[[[.,.],[[.,.],[.,.]]],.],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 2

[6,3,8,4,5,7,2,1] => [[[[.,.],[[.,.],[.,[.,.]]]],.],.] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 3

[5,8,7,4,3,6,2,1] => [[[[[.,[[.,.],.]],.],[.,.]],.],.] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3

[8,1,7,4,3,6,2,5] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1

[8,7,3,5,1,4,2,6] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[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

[6,8,3,5,1,7,4,2] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 0

[5,1,8,4,7,6,3,2] => [[.,.],[[[[.,.],[[.,.],.]],.],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 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

[4,8,1,3,5,6,7,2] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 0

[5,8,7,4,1,6,3,2] => [[[.,[[.,.],.]],.],[[[.,.],.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1

[5,8,3,6,1,4,7,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0

[4,8,3,6,1,2,7,5] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 0

[3,8,1,2,5,6,7,4] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 0

[8,7,1,4,2,6,3,5] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[8,6,3,1,2,4,7,5] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3

[8,1,7,4,5,2,3,6] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[8,7,2,4,1,6,3,5] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[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

[8,6,3,2,1,4,7,5] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 4

[8,7,3,5,2,1,4,6] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3

[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

[5,8,7,4,2,6,1,3] => [[[[.,[[.,.],.]],.],[.,.]],[.,.]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[6,1,8,4,5,7,2,3] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[6,8,3,5,1,7,2,4] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[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

[5,8,3,6,1,2,7,4] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 0

[4,1,8,2,5,6,7,3] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 1

[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

[5,8,1,4,7,6,2,3] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 0

[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

[4,5,3,8,6,1,7,2] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[3,4,1,8,5,6,7,2] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 0

[8,4,3,7,6,1,5,2] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 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

[5,2,7,3,6,4,8,1] => [[[.,.],[[.,.],[[.,.],[.,.]]]],.] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 2

[8,3,4,7,6,1,5,2] => [[[.,.],[.,[[.,.],.]]],[[.,.],.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 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

[3,1,4,7,6,8,5,2] => [[.,.],[[.,[[[.,.],[.,.]],.]],.]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 1

[4,1,3,7,6,8,5,2] => [[.,.],[[.,[[[.,.],[.,.]],.]],.]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 1

[5,1,7,3,6,8,4,2] => [[.,.],[[[.,.],[[.,[.,.]],.]],.]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 1

[6,7,1,3,5,8,4,2] => [[.,[.,.]],[[.,[[.,[.,.]],.]],.]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 0

[4,8,3,7,6,1,5,2] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[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

[8,1,3,2,7,6,5,4] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 1

[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

[6,7,1,2,8,5,4,3] => [[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => 0

[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

[8,3,2,1,7,6,5,4] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3

[3,4,1,7,6,8,5,2] => [[.,[.,.]],[[[[.,.],[.,.]],.],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 0

[8,4,2,7,1,6,5,3] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 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] => 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] => 0

[5,4,7,6,8,1,3,2] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[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

[8,4,1,7,2,6,5,3] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 2

[4,3,8,7,6,1,5,2] => [[[.,.],[[[.,.],.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 1

[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

[6,7,2,8,1,5,4,3] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 0

[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

[4,2,8,7,1,6,5,3] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[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

[8,3,1,2,7,6,5,4] => [[[.,.],.],[.,[[[[.,.],.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 2

[8,2,1,3,7,6,5,4] => [[[.,.],.],[.,[[[[.,.],.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 2

[2,1,8,3,7,6,5,4] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 1

[4,1,8,7,2,6,5,3] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 1

[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

[6,7,1,8,2,5,4,3] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 0

[4,8,1,7,2,6,5,3] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 0

[3,8,1,2,7,6,5,4] => [[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => 0

[2,8,1,3,7,6,5,4] => [[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => 0

[8,1,2,3,7,6,5,4] => [[.,.],[.,[.,[[[[.,.],.],.],.]]]] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1

[6,7,1,8,4,5,2,3] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[3,7,1,5,8,2,6,4] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[2,7,1,5,8,3,6,4] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[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

[8,1,4,5,7,6,2,3] => [[.,.],[[.,[.,[[.,.],.]]],[.,.]]] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 1

[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

[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

[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

[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

[7,3,1,5,8,2,6,4] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[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

[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

[7,2,1,5,8,3,6,4] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[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

[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

[4,2,5,3,1,8,7,6] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[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

[7,2,1,4,3,8,6,5] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 2

[8,1,2,4,3,7,6,5] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 1

[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

[7,3,1,4,2,8,6,5] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 2

[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

[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

[2,7,1,4,3,8,6,5] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 0

[3,7,1,4,2,8,6,5] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 0

[4,7,1,3,2,8,6,5] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 0

[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

[4,7,1,2,3,8,6,5] => [[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 0

[3,7,1,2,4,8,6,5] => [[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 0

[2,7,1,3,4,8,6,5] => [[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 0

[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

[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

[6,5,2,1,8,3,7,4] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3

[8,1,5,2,7,3,6,4] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[8,1,4,2,3,7,6,5] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 1

[7,4,1,2,3,8,6,5] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 2

[6,4,2,1,3,8,7,5] => [[[[.,.],.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 3

[5,4,2,3,1,8,7,6] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2

[3,5,2,4,1,8,7,6] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 0

[6,3,2,1,4,8,7,5] => [[[[.,.],.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 3

[7,3,1,2,4,8,6,5] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 2

[8,1,3,2,4,7,6,5] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 1

[8,1,2,3,4,7,6,5] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1

[7,2,1,3,4,8,6,5] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 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

[4,2,6,5,3,1,8,7] => [[[.,.],[[[.,.],.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 1

[4,2,6,5,1,8,7,3] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[4,2,6,5,8,1,7,3] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[4,2,6,5,8,1,3,7] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[4,2,6,5,8,3,1,7] => [[[.,.],[[[.,.],[.,.]],.]],[.,.]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1

[2,4,1,6,5,8,3,7] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[2,1,4,6,5,8,3,7] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 1

[2,4,1,6,5,8,7,3] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 0

[4,2,6,5,8,3,7,1] => [[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 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] => 0

[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

[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

[2,4,1,6,8,5,3,7] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 0

[2,4,1,3,6,8,7,5] => [[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 0

[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

[2,4,1,6,8,3,7,5] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[4,6,2,8,5,7,1,3] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[6,2,4,8,7,1,3,5] => [[[.,.],[.,[[.,.],.]]],[.,[.,.]]] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 1

[6,4,2,8,7,5,3,1] => [[[[.,.],.],[[[[.,.],.],.],.]],.] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 3

[2,6,1,4,8,7,5,3] => [[.,[.,.]],[[.,[[[.,.],.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 0

[2,1,6,4,8,7,5,3] => [[.,.],[[[.,.],[[[.,.],.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 1

[2,6,1,4,8,7,3,5] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 0

[6,4,2,8,7,5,1,3] => [[[[.,.],.],[[[.,.],.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 2

[5,2,4,7,3,6,8,1] => [[[.,.],[[.,[.,.]],[.,[.,.]]]],.] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2

[8,1,6,3,7,2,4,5] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[7,1,6,3,8,2,4,5] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[6,1,7,3,4,8,2,5] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[2,1,7,4,5,8,3,6] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 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

[4,3,1,7,5,8,2,6] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[6,8,1,3,7,2,4,5] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[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

[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

[6,7,1,3,8,2,4,5] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[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

[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

[2,6,1,4,5,8,3,7] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 0

[6,5,1,3,4,8,2,7] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 2

[8,5,1,3,7,2,4,6] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[6,4,2,1,5,8,3,7] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 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] => 2

[4,3,2,8,7,1,5,6] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[5,2,4,8,7,1,3,6] => [[[.,.],[.,[[.,.],.]]],[.,[.,.]]] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 1

[6,2,8,3,7,1,4,5] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[5,1,4,8,7,2,3,6] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 1

[4,8,2,5,1,3,7,6] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 0

[4,7,2,5,1,3,8,6] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 0

[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

[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

[8,3,2,1,5,4,6,7] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[8,3,2,1,6,4,5,7] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[8,4,2,5,1,6,3,7] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[8,3,2,1,5,6,4,7] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3

[8,3,2,1,4,6,5,7] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 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

[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

[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

[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

[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

[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

[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

[4,8,2,5,1,7,3,6] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[4,7,2,5,1,8,3,6] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[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

[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

[3,2,1,7,5,8,6,4] => [[[.,.],.],[[[.,.],[[.,.],.]],.]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 2

[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

[4,2,7,6,1,8,3,5] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[4,3,7,6,8,1,2,5] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[4,3,8,6,7,1,2,5] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[4,2,8,6,1,7,3,5] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[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

[3,2,1,8,7,5,6,4] => [[[.,.],.],[[[[.,.],.],[.,.]],.]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 2

[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

[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

[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

[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

[4,2,7,6,1,3,8,5] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 1

[4,2,8,6,1,3,7,5] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 1

[4,2,8,7,1,3,6,5] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 1

[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

[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

[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

[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

[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

[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

[4,7,3,8,5,1,2,6] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 0

[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

[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

[3,2,1,6,8,5,7,4] => [[[.,.],.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[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

[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

[4,3,6,8,7,1,2,5] => [[[.,.],[.,[[.,.],.]]],[.,[.,.]]] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 1

[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

[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

[5,3,6,4,8,7,1,2] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[3,1,8,5,4,2,6,7] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 1

[6,3,7,5,4,8,1,2] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[7,3,8,5,4,6,1,2] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[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

[6,8,3,5,4,7,1,2] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[7,6,3,5,4,8,1,2] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 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

[6,2,1,5,4,8,7,3] => [[[.,.],.],[[[.,.],[[.,.],.]],.]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 2

[4,1,6,2,8,7,5,3] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 1

[7,8,1,2,4,6,5,3] => [[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 0

[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

[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

[4,8,1,5,2,3,7,6] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0

[7,5,1,6,4,3,2,8] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 2

[5,8,1,6,4,3,2,7] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 0

[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

[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

[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

[2,6,1,5,7,3,8,4] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[6,8,1,7,4,3,2,5] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 0

[5,6,1,7,4,3,2,8] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 0

[5,1,7,6,4,3,2,8] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 1

[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

[7,1,8,6,4,3,2,5] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 1

[2,1,7,5,6,3,8,4] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[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

[7,8,1,6,5,3,2,4] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 0

[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

[2,8,1,5,4,6,7,3] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 0

[7,2,1,5,4,6,8,3] => [[[.,.],.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 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

[4,2,1,5,6,3,7,8] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[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

[5,1,6,3,7,8,2,4] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[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

[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

[6,4,1,5,2,3,7,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2

[4,1,7,5,2,3,8,6] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1

[7,2,3,5,4,1,8,6] => [[[.,.],[.,[[.,.],.]]],[[.,.],.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 1

[4,2,6,3,8,1,7,5] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[7,8,2,3,4,1,6,5] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0

[7,8,1,4,6,3,2,5] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 0

[3,1,6,4,7,8,2,5] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[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

[5,1,8,7,4,3,2,6] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 1

[6,5,1,8,4,3,2,7] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 2

[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

[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

[7,8,4,6,1,3,2,5] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[7,8,5,4,1,3,2,6] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 2

[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

[7,6,5,1,4,3,2,8] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 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] => 0

[3,2,7,5,4,1,6,8] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 1

[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

[6,1,2,5,4,7,8,3] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 1

[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

[4,2,8,5,1,3,7,6] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 1

[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

[5,3,6,4,1,7,2,8] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[6,2,1,5,8,3,7,4] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[7,5,4,6,2,8,1,3] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 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

[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

[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

[8,5,6,3,2,7,1,4] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 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

[2,4,1,7,8,5,3,6] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 0

[5,6,3,2,1,8,4,7] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 2

[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

[6,8,4,3,2,1,5,7] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 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] => 2

[7,3,2,8,5,1,6,4] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[8,4,6,3,2,1,7,5] => [[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 3

[8,6,4,3,2,1,7,5] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5

[7,6,4,3,2,1,8,5] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5

[7,8,4,3,2,1,6,5] => [[[[[.,[.,.]],.],.],.],[[.,.],.]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 3

[5,4,7,2,1,8,6,3] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 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] => 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] => 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] => 2

[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

[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

[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

[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

[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

[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

[7,3,5,2,1,8,4,6] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2

[2,4,1,7,8,3,6,5] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[3,7,2,8,6,1,4,5] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 0

[5,3,8,2,1,4,7,6] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2

[4,8,7,3,2,1,5,6] => [[[[.,[[.,.],.]],.],.],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => 2

[4,7,3,2,1,5,6,8] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2

[8,4,7,3,2,1,5,6] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 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] => 2

[7,3,2,8,6,1,4,5] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[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

[7,8,3,5,4,6,1,2] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[8,6,3,7,5,2,4,1] => [[[[[.,.],.],[[.,.],.]],[.,.]],.] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 3

[5,4,1,6,3,2,8,7] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[5,4,1,6,2,3,8,7] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 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] => 0

[5,7,1,6,2,8,4,3] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 0

[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

[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

[2,1,7,6,3,8,5,4] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 1

[2,1,7,6,3,8,4,5] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[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

[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

[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

[7,3,5,4,8,1,2,6] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[6,4,3,5,8,7,2,1] => [[[[[.,.],.],[.,[[.,.],.]]],.],.] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[2,1,4,5,8,7,3,6] => [[.,.],[[.,[.,[[.,.],.]]],[.,.]]] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 1

[6,4,3,5,8,7,1,2] => [[[[.,.],.],[.,[[.,.],.]]],[.,.]] => [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 2

[7,3,5,4,8,1,6,2] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[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

[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

[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

[6,4,1,5,8,7,2,3] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 2

[6,4,1,5,8,7,3,2] => [[[.,.],.],[[[.,[[.,.],.]],.],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 2

[6,4,1,5,8,3,7,2] => [[[.,.],.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[5,7,1,6,3,8,2,4] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[6,4,1,5,8,3,2,7] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 2

[7,4,1,5,8,2,3,6] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[7,4,1,5,8,2,6,3] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[6,3,5,7,8,2,1,4] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 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] => 2

[5,7,3,6,1,8,4,2] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 0

[2,1,4,5,8,6,3,7] => [[.,.],[[.,[.,[[.,.],.]]],[.,.]]] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 1

[7,3,5,4,8,6,2,1] => [[[[.,.],[[.,.],[[.,.],.]]],.],.] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 3

[6,3,5,4,8,2,7,1] => [[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[7,4,3,5,8,2,1,6] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3

[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

[7,4,3,5,8,2,6,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3

[6,3,5,4,8,2,1,7] => [[[[.,.],[[.,.],[.,.]]],.],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 2

[7,8,2,6,1,5,3,4] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[7,8,1,6,2,5,3,4] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[5,8,1,7,2,6,3,4] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[5,8,2,7,1,6,3,4] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[2,8,1,7,5,6,3,4] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[2,8,1,7,4,6,3,5] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[4,8,2,7,1,6,3,5] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[4,8,1,7,2,6,3,5] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[4,8,1,7,5,6,2,3] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[3,8,1,7,5,6,2,4] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[3,8,1,7,4,6,2,5] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[3,8,1,7,2,6,4,5] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[3,8,2,7,1,6,4,5] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[3,8,2,7,4,6,1,5] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[3,8,2,7,5,6,1,4] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[4,8,2,7,5,6,1,3] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[4,8,3,7,5,6,1,2] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[2,8,1,7,3,6,4,5] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[7,5,2,8,6,4,1,3] => [[[[.,.],.],[[[.,.],.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 2

[7,5,1,8,6,2,3,4] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[7,1,8,4,5,2,6,3] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[7,1,8,3,5,6,2,4] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[7,3,8,6,2,5,1,4] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[7,4,2,8,6,1,3,5] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[7,3,1,8,4,2,5,6] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[3,1,5,4,7,8,2,6] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[5,3,1,4,8,2,6,7] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[5,2,4,8,6,1,3,7] => [[[.,.],[.,[[.,.],.]]],[.,[.,.]]] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 1

[5,2,3,8,4,6,7,1] => [[[.,.],[.,[[.,.],[.,[.,.]]]]],.] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 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] => 0

[5,4,3,8,1,2,7,6] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[6,4,2,8,1,3,7,5] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[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

[5,8,1,3,6,2,7,4] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[5,8,1,4,2,6,3,7] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[6,5,1,2,8,7,3,4] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 2

[6,5,3,1,4,2,8,7] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3

[5,3,1,6,4,2,7,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[5,2,6,4,1,7,3,8] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[3,6,2,7,5,1,8,4] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[3,5,2,6,8,1,7,4] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0

[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

[5,3,6,8,4,7,2,1] => [[[[.,.],[[.,[.,.]],[.,.]]],.],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[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

[8,4,2,5,7,3,6,1] => [[[[.,.],.],[[.,[.,.]],[.,.]]],.] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 3

[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

[5,2,6,8,4,3,7,1] => [[[.,.],[[[.,[.,.]],.],[.,.]]],.] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[3,1,6,5,4,8,2,7] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1

[4,1,6,5,8,3,2,7] => [[.,.],[[[[.,.],[.,.]],.],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 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

[8,5,4,7,6,3,2,1] => [[[[[[.,.],.],[[.,.],.]],.],.],.] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[5,7,1,8,4,3,2,6] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 0

[2,7,1,5,4,3,8,6] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[8,2,1,5,4,3,7,6] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[8,4,1,5,7,3,2,6] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 2

[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

[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

[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

[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

[8,3,6,2,4,7,5,1] => [[[[.,.],[.,.]],[.,[[.,.],.]]],.] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 2

[5,7,3,8,4,6,2,1] => [[[[.,[.,.]],[[.,.],[.,.]]],.],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 2

[4,7,3,5,8,6,2,1] => [[[[.,[.,.]],[.,[[.,.],.]]],.],.] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 2

[8,7,2,1,4,3,6,5] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3

[8,7,3,1,4,6,2,5] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3

[8,7,6,3,2,5,4,1] => [[[[[[.,.],.],.],.],[[.,.],.]],.] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 5

[8,7,3,5,1,6,2,4] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[8,7,2,5,1,3,6,4] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[8,2,6,5,1,3,7,4] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 1

[8,4,6,5,7,1,2,3] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 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

[3,6,2,4,8,1,5,7] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[7,3,8,4,5,6,1,2] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[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

[4,2,7,5,1,8,6,3] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[7,8,1,4,2,6,5,3] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 0

[4,1,7,5,3,2,6,8] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 1

[6,5,1,3,4,2,8,7] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[4,8,5,3,1,7,2,6] => [[[.,[[.,.],.]],.],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[7,4,5,3,2,8,1,6] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 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] => 0

[3,6,2,5,8,1,7,4] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0

[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

[7,1,8,6,3,4,2,5] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1

[7,2,1,4,5,6,8,3] => [[[.,.],.],[[.,[.,[.,[.,.]]]],.]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[6,1,3,2,7,5,8,4] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1

[7,6,5,8,1,4,2,3] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[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

[4,1,6,3,8,2,7,5] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[7,8,2,4,6,3,1,5] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 0

[3,2,6,4,7,8,1,5] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[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

[5,3,8,7,1,2,6,4] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 1

[6,5,3,8,2,1,7,4] => [[[[[.,.],.],[.,.]],.],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 3

[7,5,8,4,1,2,3,6] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2

[5,8,7,4,1,3,2,6] => [[[.,[[.,.],.]],.],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[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

[6,8,5,4,3,1,2,7] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3

[6,1,4,2,8,5,7,3] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1

[8,6,5,1,2,4,7,3] => [[[[.,.],.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 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

[6,3,8,5,7,1,2,4] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[8,3,1,5,6,2,7,4] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 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] => 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] => 0

[2,8,1,5,6,3,7,4] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[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

[5,1,8,6,2,7,3,4] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[8,6,1,5,7,2,3,4] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[7,6,5,8,1,2,4,3] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[5,1,7,6,8,4,2,3] => [[.,.],[[[[.,.],[.,.]],.],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 1

[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

[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

[3,2,8,5,7,6,1,4] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[8,2,1,5,7,6,3,4] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 2

[5,2,8,6,1,7,3,4] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[4,2,1,3,6,7,8,5] => [[[.,.],.],[.,[[.,[.,[.,.]]],.]]] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 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

[7,2,6,5,4,1,8,3] => [[[.,.],[[[.,.],.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 1

[6,1,3,5,4,7,8,2] => [[.,.],[[.,[[.,.],[.,[.,.]]]],.]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 1

[6,1,5,3,4,7,8,2] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 1

[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

[8,5,2,6,3,7,1,4] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2

[4,3,1,2,6,7,8,5] => [[[.,.],.],[.,[[.,[.,[.,.]]],.]]] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[8,1,6,5,7,3,2,4] => [[.,.],[[[[.,.],[.,.]],.],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 1

[5,8,1,6,3,7,2,4] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[7,1,4,2,6,5,8,3] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1

[4,1,7,3,5,6,8,2] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 1

[5,7,6,4,1,2,8,3] => [[[.,[[.,.],.]],.],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => 1

[3,8,1,6,5,7,2,4] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[8,1,3,5,7,6,2,4] => [[.,.],[[.,[.,[[.,.],.]]],[.,.]]] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 1

[7,8,5,4,1,6,2,3] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 2

[6,1,5,4,3,7,8,2] => [[.,.],[[[[.,.],.],[.,[.,.]]],.]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 1

[7,5,6,4,2,1,8,3] => [[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 3

[8,3,2,6,5,7,1,4] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 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

[6,1,4,3,5,7,8,2] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 1

[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

[7,2,6,4,5,1,8,3] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[8,2,3,6,5,7,1,4] => [[[.,.],[.,[[.,.],[.,.]]]],[.,.]] => [1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1

[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

[3,6,2,4,7,1,5,8] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[6,8,3,4,5,7,1,2] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0

[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

[6,3,7,5,8,4,1,2] => [[[.,.],[[[.,.],[.,.]],.]],[.,.]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1

[7,3,8,6,4,5,1,2] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[3,2,7,6,5,1,4,8] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 1

[4,8,2,6,1,5,3,7] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[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

[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

[7,8,1,2,5,6,3,4] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 0

[4,1,6,2,5,7,3,8] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[6,1,2,5,8,7,3,4] => [[.,.],[.,[[.,[[.,.],.]],[.,.]]]] => [1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 1

[2,1,8,6,4,7,3,5] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1

[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

[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

[5,1,8,7,2,3,6,4] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1

[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

[3,1,6,4,7,2,5,8] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[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

[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

[6,2,4,3,1,5,7,8] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1

[4,2,8,3,1,7,5,6] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[5,3,7,4,1,6,2,8] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[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

[6,3,1,2,8,4,5,7] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2

[4,2,1,3,6,5,8,7] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2

[2,8,1,4,5,6,3,7] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 0

[7,2,1,5,4,6,3,8] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[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

[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

[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

[7,5,1,6,4,3,8,2] => [[[.,.],.],[[[[.,.],.],[.,.]],.]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 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] => 0

[6,5,1,8,2,7,4,3] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 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] => 0

[7,6,1,8,5,3,2,4] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 2

[5,6,1,7,4,8,2,3] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[3,6,1,5,7,4,2,8] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 0

[3,1,7,5,6,4,8,2] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 1

[5,1,7,6,4,8,3,2] => [[.,.],[[[[[.,.],.],[.,.]],.],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 1

[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

[7,1,8,6,5,4,2,3] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 1

[8,5,3,6,2,7,4,1] => [[[[[.,.],.],[.,.]],[[.,.],.]],.] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[8,1,6,5,7,2,4,3] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[6,1,7,5,3,8,2,4] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1

[2,1,7,5,6,8,3,4] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[5,4,1,7,6,8,2,3] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 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] => 2

[7,8,1,6,2,4,5,3] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 0

[6,8,1,4,7,2,5,3] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[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

[6,7,1,4,8,3,2,5] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 0

[2,7,1,8,4,5,3,6] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[6,1,2,8,4,3,5,7] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 1

[6,5,1,4,3,8,2,7] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[8,5,1,3,7,2,6,4] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[8,4,2,1,7,3,6,5] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3

[7,4,2,1,8,5,3,6] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[6,4,3,1,5,8,2,7] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3

[7,3,8,5,4,6,2,1] => [[[[.,.],[[[.,.],.],[.,.]]],.],.] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 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] => 3

[5,4,3,8,6,7,2,1] => [[[[[.,.],.],[[.,.],[.,.]]],.],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 4

[5,4,2,8,7,3,6,1] => [[[[.,.],.],[[[.,.],.],[.,.]]],.] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 3

[6,2,5,8,7,3,4,1] => [[[.,.],[[.,[[.,.],.]],[.,.]]],.] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2

[3,2,8,5,7,4,6,1] => [[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2

[2,1,8,7,4,6,3,5] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1

[3,1,8,5,7,6,2,4] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1

[6,1,5,8,7,4,2,3] => [[.,.],[[[.,[[.,.],.]],.],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 1

[5,4,1,8,7,6,2,3] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 2

[4,2,1,6,3,5,8,7] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2

[6,2,1,4,3,5,8,7] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2

[6,2,1,4,3,8,5,7] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[8,2,1,4,3,6,5,7] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[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

[2,1,6,4,3,5,8,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1

[2,6,1,4,3,5,8,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0

[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

[6,4,2,1,3,5,8,7] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3

[8,4,2,1,3,6,5,7] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3

[8,4,2,1,6,3,5,7] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[6,4,2,1,8,3,5,7] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[2,6,1,4,3,8,5,7] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[2,1,6,4,3,8,5,7] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[2,1,8,4,3,6,5,7] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[2,8,1,4,3,6,5,7] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[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

[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

[8,6,2,1,4,3,5,7] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[2,8,1,4,6,3,5,7] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[2,6,1,4,8,3,5,7] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[4,6,2,8,1,3,5,7] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0

[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

[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

[4,2,1,6,8,3,5,7] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[4,2,1,6,3,8,5,7] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[4,2,1,3,6,8,5,7] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 2

[2,1,4,3,8,6,5,7] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1

[2,4,1,3,8,6,5,7] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 0

[4,2,1,3,8,6,5,7] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 2

[4,2,1,8,3,6,5,7] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[4,2,1,8,6,3,5,7] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[8,2,1,6,4,3,5,7] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[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

[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

[2,4,1,8,3,6,5,7] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[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

[2,1,4,8,6,3,5,7] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 1

[4,2,8,6,1,3,5,7] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1

[8,4,6,2,1,3,5,7] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2

[2,6,1,8,4,3,5,7] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0

[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

[2,1,8,6,4,3,5,7] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 1

[4,8,6,2,1,3,5,7] => [[[.,[[.,.],.]],.],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1

[6,8,4,2,1,3,5,7] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2

[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

[5,2,4,3,8,1,7,6] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[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

[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

[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

[4,3,7,2,6,5,8,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[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

[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

[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

[5,1,8,3,4,2,7,6] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[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

[2,1,5,4,8,3,7,6] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[5,1,7,6,8,3,4,2] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 1

[4,3,7,6,8,1,5,2] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[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

[4,3,6,5,8,1,7,2] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[6,3,5,4,7,2,8,1] => [[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[6,3,5,4,8,1,7,2] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[7,1,6,3,8,4,5,2] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 1

[7,4,6,5,8,1,3,2] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[2,1,8,4,6,3,7,5] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[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

[8,1,6,3,4,2,7,5] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[8,1,6,3,7,2,5,4] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[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

[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

[7,3,5,2,6,4,8,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[8,2,6,3,5,1,7,4] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 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

[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

[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

[8,2,4,3,6,1,7,5] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[3,2,8,4,6,1,7,5] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[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

[3,2,7,6,8,1,5,4] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[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

[3,2,6,5,8,1,7,4] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[6,5,7,2,4,3,8,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[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

[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

[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

[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

[2,1,7,3,8,5,6,4] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1

[7,1,3,2,8,5,6,4] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1

[7,1,8,5,6,2,4,3] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[7,1,8,2,6,4,5,3] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1

[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

[6,2,7,4,5,3,8,1] => [[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 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] => 2

[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

[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

[2,1,6,5,8,3,7,4] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[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

[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

[6,1,7,4,8,3,5,2] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 1

[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

[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

[4,2,5,3,1,8,6,7] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[4,2,1,8,5,3,6,7] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[5,4,1,3,8,2,6,7] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[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

[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

[4,8,1,5,7,3,6,2] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 0

[8,1,5,3,7,4,6,2] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 1

[6,8,1,7,4,3,5,2] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 0

[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

[6,4,8,7,1,5,2,3] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[7,6,4,1,3,8,2,5] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3

[4,2,1,7,8,5,3,6] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 2

[6,2,4,8,3,7,5,1] => [[[.,.],[[.,[.,.]],[[.,.],.]]],.] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 2

[7,2,6,3,4,1,8,5] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[2,7,1,8,3,5,4,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[2,1,7,3,5,8,4,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[8,7,1,3,6,2,4,5] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[8,2,1,7,3,5,6,4] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[7,8,2,6,3,1,5,4] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[8,7,2,6,3,5,4,1] => [[[[.,.],.],[[.,.],[[.,.],.]]],.] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3

[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

[8,6,1,2,7,5,3,4] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 2

[8,1,6,2,7,4,5,3] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1

[5,2,1,8,6,7,4,3] => [[[.,.],.],[[[[.,.],[.,.]],.],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 2

[7,8,1,6,4,2,5,3] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[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

[7,3,8,6,1,5,2,4] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[8,7,6,1,5,3,4,2] => [[[[.,.],.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 3

[8,7,1,6,4,5,3,2] => [[[.,.],.],[[[[.,.],[.,.]],.],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 2

[8,1,7,5,6,4,3,2] => [[.,.],[[[[[.,.],[.,.]],.],.],.]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 1

[6,3,5,2,1,4,8,7] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2

[6,3,5,7,2,8,4,1] => [[[[.,.],[.,[.,.]]],[[.,.],.]],.] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 2

[8,5,2,7,4,3,1,6] => [[[[.,.],.],[[[.,.],.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 2

[4,5,3,6,1,2,8,7] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 0

[3,5,1,4,6,2,8,7] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[8,3,4,5,7,2,1,6] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 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] => 2

[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

[8,3,4,7,5,1,2,6] => [[[.,.],[.,[[.,.],.]]],[.,[.,.]]] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 1

[8,5,1,4,7,3,2,6] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 2

[8,5,3,7,1,4,2,6] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[2,1,8,5,7,4,3,6] => [[.,.],[[[[.,.],[.,.]],.],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 1

[6,5,3,7,1,8,4,2] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2

[6,5,1,4,7,8,3,2] => [[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 2

[6,3,4,7,5,8,1,2] => [[[.,.],[.,[[.,.],[.,.]]]],[.,.]] => [1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1

[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

[4,7,1,3,5,8,6,2] => [[.,[.,.]],[[.,[.,[[.,.],.]]],.]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 0

[4,8,3,7,1,2,6,5] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 0

[3,8,1,2,5,7,6,4] => [[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 0

[8,7,2,6,4,1,3,5] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[5,3,7,8,2,4,6,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[8,3,6,2,1,4,7,5] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2

[5,3,7,6,2,1,8,4] => [[[[.,.],[[.,.],.]],.],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2

[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

[6,1,7,4,5,8,2,3] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[6,7,3,5,1,8,2,4] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[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

[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

[5,7,3,6,1,2,8,4] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 0

[4,1,7,2,5,6,8,3] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 1

[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

[4,6,1,2,5,8,7,3] => [[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 0

[5,6,1,4,8,2,7,3] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[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

[3,4,1,5,7,6,8,2] => [[.,[.,.]],[[.,[[.,.],[.,.]]],.]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 0

[3,8,2,7,1,6,5,4] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 0

[3,8,2,7,6,1,5,4] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[3,8,2,7,6,5,1,4] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 0

[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

[4,8,7,2,1,6,5,3] => [[[.,[[.,.],.]],.],[[[.,.],.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1

[4,8,7,3,1,6,5,2] => [[[.,[[.,.],.]],.],[[[.,.],.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1

[4,8,7,3,2,1,6,5] => [[[[.,[[.,.],.]],.],.],[[.,.],.]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2

[4,8,7,3,2,6,1,5] => [[[[.,[[.,.],.]],.],[.,.]],[.,.]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[4,8,7,3,2,6,5,1] => [[[[.,[[.,.],.]],.],[[.,.],.]],.] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 2

[7,3,4,2,1,6,5,8] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2

[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

[7,2,1,5,6,4,3,8] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 2

[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

[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

[6,2,1,5,7,4,8,3] => [[[.,.],.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[3,2,1,5,7,4,8,6] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[3,2,1,6,7,8,4,5] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 2

[5,2,1,6,7,8,4,3] => [[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 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

[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

[6,4,5,7,2,1,8,3] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 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] => 2

[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

[6,3,4,2,1,7,8,5] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 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] => 2

[4,2,1,5,7,3,8,6] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 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

[6,8,2,4,5,7,1,3] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0

[7,8,1,4,5,3,6,2] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 0

[4,8,3,6,1,5,7,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0

[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

[5,8,1,4,7,6,3,2] => [[.,[.,.]],[[[.,[[.,.],.]],.],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 0

[7,5,1,8,6,2,4,3] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[7,4,1,8,2,6,3,5] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[7,1,8,4,2,6,3,5] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[6,1,3,8,5,2,4,7] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 1

[7,2,8,4,1,6,5,3] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[7,2,8,3,6,5,1,4] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[7,2,8,3,6,1,5,4] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[7,1,8,2,3,6,5,4] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 1

[5,1,2,3,8,4,7,6] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 1

[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

[2,5,1,3,8,4,7,6] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 0

[5,2,3,8,4,7,1,6] => [[[.,.],[.,[[.,.],[.,.]]]],[.,.]] => [1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1

[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

[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

[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

[6,5,1,2,8,7,4,3] => [[[.,.],.],[.,[[[[.,.],.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 2

[5,3,1,6,4,2,8,7] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[5,1,6,2,8,7,4,3] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 1

[3,6,2,8,7,5,1,4] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 0

[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

[4,3,1,5,8,2,7,6] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[6,3,1,5,4,2,7,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[7,8,3,5,4,1,6,2] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[7,8,2,5,4,6,1,3] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[6,2,1,5,4,7,3,8] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[4,3,7,5,8,6,1,2] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[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

[2,7,1,4,8,3,5,6] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[5,1,6,2,4,8,3,7] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[6,1,3,5,4,8,7,2] => [[.,.],[[.,[[.,.],[[.,.],.]]],.]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 1

[6,1,4,2,8,3,5,7] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[4,7,1,6,2,3,8,5] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0

[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

[3,2,8,5,4,6,1,7] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[4,7,1,2,5,3,8,6] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 0

[6,3,2,1,7,4,8,5] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3

[4,2,1,7,3,5,8,6] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2

[7,3,1,5,4,2,8,6] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[8,4,1,5,2,7,6,3] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 2

[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

[4,7,2,5,3,1,8,6] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[7,5,4,3,2,1,8,6] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5

[5,7,4,3,2,8,1,6] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2

[6,2,7,5,3,8,1,4] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[7,1,8,5,3,6,4,2] => [[.,.],[[[[.,.],.],[[.,.],.]],.]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 1

[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

[8,7,3,1,6,5,4,2] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3

[8,7,2,6,1,5,4,3] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 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] => 0

[7,2,8,5,6,1,4,3] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[6,3,7,5,8,2,1,4] => [[[[.,.],[[.,.],[.,.]]],.],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 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] => 0

[6,5,4,8,3,2,1,7] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 4

[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

[8,4,1,5,7,3,6,2] => [[[.,.],.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[5,4,1,6,8,2,3,7] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[6,3,7,4,8,5,2,1] => [[[[.,.],[[.,.],[[.,.],.]]],.],.] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 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

[6,3,1,8,4,7,5,2] => [[[.,.],.],[[[.,.],[[.,.],.]],.]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 2

[6,5,3,8,7,4,1,2] => [[[[.,.],.],[[[.,.],.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 2

[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

[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

[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

[6,3,7,8,5,2,4,1] => [[[[.,.],[[.,[.,.]],.]],[.,.]],.] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[5,3,8,7,2,1,6,4] => [[[[.,.],[[.,.],.]],.],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2

[8,3,7,6,1,5,4,2] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[8,2,7,6,5,1,4,3] => [[[.,.],[[[.,.],.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 1

[4,3,8,7,6,2,1,5] => [[[[.,.],[[[.,.],.],.]],.],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 2

[4,7,3,8,6,5,1,2] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 0

[7,5,8,6,4,3,2,1] => [[[[[[.,.],[[.,.],.]],.],.],.],.] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 5

[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

[5,1,2,6,4,3,8,7] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 1

[6,1,2,5,4,3,8,7] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 1

[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

[4,1,2,6,5,3,8,7] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 1

[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

[4,1,5,8,7,3,2,6] => [[.,.],[[[.,[[.,.],.]],.],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 1

[4,7,1,8,3,6,2,5] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[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

[5,1,7,4,8,2,3,6] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[7,5,3,8,1,4,2,6] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[2,1,5,8,7,3,4,6] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 1

[5,1,8,4,7,2,3,6] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[4,1,8,7,5,2,3,6] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 1

[4,7,1,6,3,2,8,5] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[6,1,2,3,7,5,8,4] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 1

[7,1,2,3,8,6,5,4] => [[.,.],[.,[.,[[[[.,.],.],.],.]]]] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1

[7,1,2,3,5,8,6,4] => [[.,.],[.,[.,[[.,[[.,.],.]],.]]]] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 1

[6,8,1,4,3,7,2,5] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[8,7,3,2,4,1,6,5] => [[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3

[2,1,7,3,4,8,6,5] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 1

[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

[6,7,1,4,3,8,2,5] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[8,1,2,3,5,7,6,4] => [[.,.],[.,[.,[[.,[[.,.],.]],.]]]] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 1

[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

[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

[7,1,2,3,8,5,6,4] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 1

[8,1,2,3,7,5,6,4] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 1

[8,1,2,3,6,5,7,4] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 1

[7,1,8,5,4,3,2,6] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 1

[7,8,2,6,3,4,1,5] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[6,8,2,7,3,4,1,5] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[6,7,2,8,3,4,1,5] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[7,6,2,8,3,1,4,5] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[8,6,2,7,3,1,4,5] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[8,1,7,5,4,3,2,6] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 1

[8,1,7,4,5,3,2,6] => [[.,.],[[[[.,.],[.,.]],.],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 1

[5,8,3,7,1,4,2,6] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[2,1,7,3,4,6,8,5] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 1

[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

[8,7,2,4,3,6,1,5] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 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

[6,1,2,3,8,7,4,5] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 1

[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

[5,1,2,3,8,7,6,4] => [[.,.],[.,[.,[[[[.,.],.],.],.]]]] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1

[5,1,2,3,8,6,7,4] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 1

[6,1,2,3,5,8,7,4] => [[.,.],[.,[.,[[.,[[.,.],.]],.]]]] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 1

[8,6,2,4,3,1,7,5] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[7,6,3,2,4,8,1,5] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3

[2,1,6,3,4,8,7,5] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 1

[8,6,3,2,4,7,1,5] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3

[7,6,2,4,3,1,8,5] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[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

[5,1,2,3,6,8,7,4] => [[.,.],[.,[.,[[.,[[.,.],.]],.]]]] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 1

[7,1,4,2,6,3,5,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[6,8,1,4,7,2,3,5] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[6,8,1,7,3,5,4,2] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 0

[7,1,3,6,5,4,2,8] => [[.,.],[[.,[[[.,.],.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 1

[7,3,1,6,5,4,2,8] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 2

[7,1,2,3,6,5,4,8] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 1

[6,8,1,2,7,3,5,4] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 0

[5,1,8,2,7,6,3,4] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1

[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

[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

[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

[2,1,6,3,8,5,4,7] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1

[5,3,8,4,1,7,6,2] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[4,2,8,7,6,3,5,1] => [[[.,.],[[[[.,.],.],.],[.,.]]],.] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 2

[4,2,8,7,6,5,3,1] => [[[.,.],[[[[[.,.],.],.],.],.]],.] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 2

[4,1,8,7,6,5,3,2] => [[.,.],[[[[[[.,.],.],.],.],.],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1

[4,3,8,7,6,5,1,2] => [[[.,.],[[[[.,.],.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1

[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

[5,6,2,4,3,1,8,7] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[5,6,1,2,4,3,8,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 0

[3,5,1,8,7,4,6,2] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 0

[3,5,1,8,7,2,6,4] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[3,1,4,8,7,6,2,5] => [[.,.],[[.,[[[.,.],.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 1

[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

[6,8,1,3,7,5,2,4] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 0

[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

[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

[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

[2,8,1,6,7,3,5,4] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[6,8,3,4,1,7,5,2] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 0

[6,8,3,7,4,1,5,2] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[2,8,1,6,7,5,3,4] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 0

[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

[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

[8,5,7,4,2,6,1,3] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 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

[8,5,2,4,7,1,6,3] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 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

[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

[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

[8,7,1,2,4,6,3,5] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 2

[8,7,1,4,6,2,3,5] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[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

[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

[8,5,4,7,1,6,2,3] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[8,5,4,7,1,2,6,3] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[8,5,1,4,7,2,6,3] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[8,5,6,3,1,7,4,2] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 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] => 0

[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

[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

[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

[8,6,4,7,3,1,5,2] => [[[[[.,.],.],[.,.]],.],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 3

[8,4,5,7,3,1,6,2] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 2

[8,4,2,5,7,1,6,3] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 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

[8,7,1,3,4,6,2,5] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 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

[8,7,3,4,5,1,6,2] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[8,7,4,5,2,6,1,3] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[8,7,2,3,4,6,1,5] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2

[8,7,2,3,6,1,4,5] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[4,2,8,5,3,7,1,6] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[5,2,1,8,4,3,7,6] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[6,2,8,4,3,7,5,1] => [[[.,.],[[[.,.],.],[[.,.],.]]],.] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 2

[7,2,8,4,3,1,6,5] => [[[.,.],[[[.,.],.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 1

[7,3,4,8,2,1,6,5] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 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] => 2

[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

[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

[8,1,5,4,3,2,7,6] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 1

[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

[6,4,3,2,8,7,5,1] => [[[[[.,.],.],.],[[[.,.],.],.]],.] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 4

[6,5,3,2,1,7,8,4] => [[[[[.,.],.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 4

[5,6,3,2,7,8,4,1] => [[[[.,[.,.]],.],[[.,[.,.]],.]],.] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 2

[4,1,6,3,2,7,8,5] => [[.,.],[[[.,.],.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 1

[8,1,6,4,3,7,2,5] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1

[8,1,7,4,3,6,5,2] => [[.,.],[[[[.,.],.],[[.,.],.]],.]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 1

[4,1,7,3,2,6,5,8] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 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] => 2

[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

[7,6,3,2,1,5,4,8] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4

[3,1,7,5,6,2,4,8] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[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

[6,5,4,1,7,2,8,3] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3

[7,5,4,6,2,1,8,3] => [[[[[.,.],.],[.,.]],.],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 3

[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

[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

[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

[2,1,4,6,8,7,3,5] => [[.,.],[[.,[.,[[.,.],.]]],[.,.]]] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 1

[4,3,1,6,8,7,2,5] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 2

[5,3,6,8,7,2,4,1] => [[[[.,.],[.,[[.,.],.]]],[.,.]],.] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 2

[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

[7,3,5,8,6,2,1,4] => [[[[.,.],[.,[[.,.],.]]],.],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 2

[7,2,8,5,6,3,1,4] => [[[.,.],[[[.,.],[.,.]],.]],[.,.]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1

[6,2,8,5,1,7,3,4] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[4,2,1,8,6,7,3,5] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[8,1,3,2,6,7,4,5] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[4,2,8,7,6,1,5,3] => [[[.,.],[[[.,.],.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 1

[5,2,8,7,6,4,1,3] => [[[.,.],[[[[.,.],.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1

[7,2,1,8,6,5,4,3] => [[[.,.],.],[[[[[.,.],.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2

[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

[6,3,7,8,5,4,2,1] => [[[[.,.],[[[.,[.,.]],.],.]],.],.] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 3

[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

[4,3,1,7,8,6,5,2] => [[[.,.],.],[[[[.,[.,.]],.],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 2

[8,1,5,7,6,2,4,3] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 1

[5,4,1,7,6,8,3,2] => [[[.,.],.],[[[[.,.],[.,.]],.],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 2

[6,4,7,5,8,3,2,1] => [[[[[.,.],[[.,.],[.,.]]],.],.],.] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4

[7,4,6,5,1,8,3,2] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[7,5,6,4,3,1,8,2] => [[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 3

[6,5,1,7,4,3,8,2] => [[[.,.],.],[[[[.,.],.],[.,.]],.]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 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

[8,1,7,6,5,4,3,2] => [[.,.],[[[[[[.,.],.],.],.],.],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1

[8,6,4,3,1,5,7,2] => [[[[[.,.],.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 4

[8,6,4,1,5,2,7,3] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3

[8,6,5,1,3,2,7,4] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3

[8,6,3,1,7,2,4,5] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[8,7,3,1,5,2,4,6] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[5,3,1,7,2,4,6,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2

[8,7,1,2,4,5,3,6] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 2

[8,6,1,2,4,7,3,5] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 2

[8,5,1,2,6,7,3,4] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 2

[8,5,1,6,4,2,7,3] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[8,5,1,3,6,4,7,2] => [[[.,.],.],[[.,[[.,.],[.,.]]],.]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 2

[8,6,1,5,3,4,7,2] => [[[.,.],.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[8,6,1,5,2,4,7,3] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[8,6,1,2,5,7,3,4] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 2

[8,6,1,2,7,4,3,5] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 2

[8,7,1,2,5,4,3,6] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 2

[5,1,4,2,3,8,6,7] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 1

[5,1,4,2,7,3,6,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[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

[5,8,1,7,3,4,6,2] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 0

[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

[8,4,1,2,7,6,3,5] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 2

[6,1,2,8,7,5,3,4] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 1

[6,1,2,4,8,7,5,3] => [[.,.],[.,[[.,[[[.,.],.],.]],.]]] => [1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 1

[3,1,8,4,6,7,5,2] => [[.,.],[[[.,.],[[.,[.,.]],.]],.]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 1

[3,1,7,6,4,8,5,2] => [[.,.],[[[[.,.],.],[[.,.],.]],.]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 1

[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

[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

[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

[6,1,2,7,4,8,5,3] => [[.,.],[.,[[[.,.],[[.,.],.]],.]]] => [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 1

[3,1,6,4,7,8,5,2] => [[.,.],[[[.,.],[[.,[.,.]],.]],.]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 1

[5,7,1,3,8,4,6,2] => [[.,[.,.]],[[.,[[.,.],[.,.]]],.]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 0

[5,7,1,8,4,2,6,3] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[7,1,5,3,2,8,6,4] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 1

[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

[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

[4,8,7,3,1,5,6,2] => [[[.,[[.,.],.]],.],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 1

[8,1,7,4,5,2,6,3] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[8,1,7,5,3,2,6,4] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 1

[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

[3,1,2,8,4,7,5,6] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 1

[3,1,2,8,6,4,5,7] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 1

[3,1,7,2,6,4,5,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[5,8,1,7,2,4,6,3] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 0

[5,8,1,3,4,7,6,2] => [[.,[.,.]],[[.,[.,[[.,.],.]]],.]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 0

[3,1,8,6,4,7,5,2] => [[.,.],[[[[.,.],.],[[.,.],.]],.]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 1

[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

[6,1,2,8,7,3,5,4] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 1

[7,1,2,8,3,6,5,4] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 1

[7,1,2,8,6,4,5,3] => [[.,.],[.,[[[[.,.],.],[.,.]],.]]] => [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 1

[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

[3,1,8,7,6,4,5,2] => [[.,.],[[[[[.,.],.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 1

[8,1,2,7,4,6,5,3] => [[.,.],[.,[[[.,.],[[.,.],.]],.]]] => [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 1

[8,1,2,7,3,6,5,4] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 1

[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

[7,5,6,3,1,4,2,8] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2

[7,5,8,3,1,4,2,6] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2

[7,8,5,3,1,4,2,6] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 2

[7,8,5,3,1,6,2,4] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 2

[7,8,5,3,1,6,4,2] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 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

[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

[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

[7,5,6,3,1,2,8,4] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2

[7,5,3,6,1,2,8,4] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[7,5,3,1,4,2,6,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[7,5,3,1,6,4,8,2] => [[[[.,.],.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 3

[7,5,3,6,4,1,8,2] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[7,5,3,6,4,8,1,2] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2

[7,5,3,8,4,6,1,2] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2

[7,5,3,8,1,4,6,2] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[7,5,3,1,8,4,6,2] => [[[[.,.],.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 3

[7,5,3,1,8,2,6,4] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3

[7,5,3,1,6,4,2,8] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[7,5,3,1,8,4,2,6] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[7,5,3,1,8,6,2,4] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[7,5,3,8,1,6,4,2] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2

[7,5,3,8,6,1,4,2] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[7,5,3,8,6,4,1,2] => [[[[.,.],.],[[[.,.],.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 2

[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

[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

[7,5,8,3,1,6,4,2] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 2

[7,5,3,6,1,4,2,8] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[7,5,3,8,4,1,2,6] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[7,5,8,6,3,1,2,4] => [[[[.,.],[[.,.],.]],.],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 2

[7,5,8,6,3,1,4,2] => [[[[.,.],[[.,.],.]],.],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2

[7,5,8,6,3,4,1,2] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[7,5,6,8,3,1,4,2] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 2

[7,5,3,4,1,8,2,6] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 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] => 2

[7,5,6,3,1,8,4,2] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 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

[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

[7,5,3,6,1,8,4,2] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2

[7,5,3,1,6,8,2,4] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3

[7,5,3,1,2,8,4,6] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3

[7,5,3,1,2,8,6,4] => [[[[.,.],.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 3

[7,5,3,1,4,8,6,2] => [[[[.,.],.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[7,5,3,4,8,1,6,2] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[7,5,3,4,1,6,8,2] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[7,5,3,1,4,6,8,2] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 3

[3,6,2,5,4,1,8,7] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[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

[5,4,7,3,2,8,6,1] => [[[[[.,.],[.,.]],.],[[.,.],.]],.] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[5,4,8,3,2,7,6,1] => [[[[[.,.],[.,.]],.],[[.,.],.]],.] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[6,4,5,3,2,1,8,7] => [[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 3

[5,3,2,6,4,1,8,7] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[4,8,5,3,2,7,6,1] => [[[[.,[[.,.],.]],.],[[.,.],.]],.] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 2

[5,8,4,3,2,7,6,1] => [[[[[.,[.,.]],.],.],[[.,.],.]],.] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 3

[5,3,2,8,4,7,6,1] => [[[[.,.],.],[[.,.],[[.,.],.]]],.] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3

[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

[5,3,2,7,4,8,6,1] => [[[[.,.],.],[[.,.],[[.,.],.]]],.] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3

[5,7,4,3,2,8,6,1] => [[[[[.,[.,.]],.],.],[[.,.],.]],.] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 3

[4,7,5,3,2,8,6,1] => [[[[.,[[.,.],.]],.],[[.,.],.]],.] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 2

[7,6,4,3,8,5,2,1] => [[[[[[.,.],.],.],[[.,.],.]],.],.] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 5

[7,3,2,6,8,5,4,1] => [[[[.,.],.],[[[.,[.,.]],.],.]],.] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 3

[2,1,8,6,7,5,4,3] => [[.,.],[[[[[.,.],[.,.]],.],.],.]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 1

[8,3,2,6,7,5,4,1] => [[[[.,.],.],[[[.,[.,.]],.],.]],.] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 3

[8,6,4,3,7,5,2,1] => [[[[[[.,.],.],.],[[.,.],.]],.],.] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 5

[8,5,7,6,4,3,2,1] => [[[[[[.,.],[[.,.],.]],.],.],.],.] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 5

[8,4,5,3,2,7,6,1] => [[[[[.,.],[.,.]],.],[[.,.],.]],.] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[8,4,7,3,6,5,2,1] => [[[[[.,.],[.,.]],[[.,.],.]],.],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 3

[8,4,6,3,7,5,2,1] => [[[[[.,.],[.,.]],[[.,.],.]],.],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 3

[7,4,6,3,8,5,2,1] => [[[[[.,.],[.,.]],[[.,.],.]],.],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 3

[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

[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

[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

[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

[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

[6,4,7,3,8,5,2,1] => [[[[[.,.],[.,.]],[[.,.],.]],.],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 3

[6,4,8,3,7,5,2,1] => [[[[[.,.],[.,.]],[[.,.],.]],.],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 3

[7,4,8,3,6,5,2,1] => [[[[[.,.],[.,.]],[[.,.],.]],.],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 3

[7,4,5,3,2,8,6,1] => [[[[[.,.],[.,.]],.],[[.,.],.]],.] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[7,5,4,3,2,8,6,1] => [[[[[[.,.],.],.],.],[[.,.],.]],.] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 5

[7,3,2,5,4,8,6,1] => [[[[.,.],.],[[.,.],[[.,.],.]]],.] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3

[2,1,7,5,4,8,6,3] => [[.,.],[[[[.,.],.],[[.,.],.]],.]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 1

[7,3,2,8,6,5,4,1] => [[[[.,.],.],[[[[.,.],.],.],.]],.] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 3

[7,8,4,3,6,5,2,1] => [[[[[.,[.,.]],.],[[.,.],.]],.],.] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 3

[6,8,5,7,4,3,2,1] => [[[[[[.,[.,.]],[.,.]],.],.],.],.] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 4

[6,8,4,3,7,5,2,1] => [[[[[.,[.,.]],.],[[.,.],.]],.],.] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 3

[6,3,2,8,7,5,4,1] => [[[[.,.],.],[[[[.,.],.],.],.]],.] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 3

[6,3,2,7,8,5,4,1] => [[[[.,.],.],[[[.,[.,.]],.],.]],.] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 3

[6,7,4,3,8,5,2,1] => [[[[[.,[.,.]],.],[[.,.],.]],.],.] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 3

[6,8,1,2,4,5,7,3] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 0

[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

[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

[4,5,2,8,3,1,6,7] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 0

[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

[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

[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

[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

[5,4,8,3,2,1,6,7] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 3

[5,4,3,7,2,6,1,8] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[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

[4,6,3,2,1,8,5,7] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 2

[4,1,7,3,2,5,8,6] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1

[4,3,1,7,8,2,6,5] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[3,5,1,2,7,8,6,4] => [[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 0

[7,5,1,4,8,2,6,3] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[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

[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

[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

[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

[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

[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

[5,3,7,6,4,2,1,8] => [[[[.,.],[[[.,.],.],.]],.],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 2

[6,4,8,7,5,3,1,2] => [[[[.,.],[[[.,.],.],.]],.],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 2

[7,6,4,3,8,5,1,2] => [[[[[.,.],.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3

[7,1,3,2,6,8,5,4] => [[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 1

[6,3,2,1,8,5,4,7] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[6,5,3,2,7,4,1,8] => [[[[[.,.],.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3

[5,2,6,3,7,4,1,8] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[2,1,7,3,8,5,4,6] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1

[5,7,1,8,2,4,6,3] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 0

[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

[2,4,1,7,8,6,3,5] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 0

[4,2,1,7,3,8,5,6] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[6,2,8,4,3,1,5,7] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 1

[7,3,2,1,8,4,5,6] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 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

[7,1,8,2,4,5,6,3] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 1

[8,7,6,1,2,4,5,3] => [[[[.,.],.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 3

[8,3,7,6,2,1,4,5] => [[[[.,.],[[.,.],.]],.],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 2

[3,2,8,7,5,1,4,6] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 1

[8,3,6,5,2,1,4,7] => [[[[.,.],[[.,.],.]],.],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 2

[7,6,3,5,2,4,1,8] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 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

[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

[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

[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

[8,7,1,5,6,2,4,3] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[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

[6,8,3,7,5,4,1,2] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 0

[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

[8,1,2,6,4,3,7,5] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 1

[2,8,1,7,5,4,3,6] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 0

[2,5,1,8,6,4,3,7] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 0

[5,7,2,6,4,3,1,8] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 0

[6,2,7,5,4,3,1,8] => [[[.,.],[[[[.,.],.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1

[2,1,8,6,5,4,3,7] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 1

[7,3,8,6,5,4,1,2] => [[[.,.],[[[[.,.],.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1

[8,1,7,3,2,6,5,4] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 1

[5,1,4,3,2,8,7,6] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 1

[8,6,5,3,2,1,7,4] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5

[8,6,3,2,1,7,4,5] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4

[8,6,5,4,1,7,2,3] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4

[8,6,5,1,7,3,2,4] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[8,6,1,7,4,3,2,5] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 2

[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

[7,4,8,3,1,6,2,5] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2

[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

[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

[5,7,4,3,1,8,6,2] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 2

[4,3,1,8,7,5,2,6] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 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] => 2

[3,1,4,6,8,7,2,5] => [[.,.],[[.,[.,[[.,.],.]]],[.,.]]] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 1

[8,4,1,6,7,5,3,2] => [[[.,.],.],[[[[.,[.,.]],.],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 2

[7,1,6,4,8,5,2,3] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1

[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

[4,2,6,3,8,1,5,7] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[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

[3,6,2,4,7,5,1,8] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 0

[3,6,2,4,1,8,5,7] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[7,3,8,2,1,6,4,5] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2

[7,3,5,2,1,8,6,4] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 2

[8,7,6,4,3,1,5,2] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5

[8,7,6,4,1,5,2,3] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4

[3,8,7,2,1,4,6,5] => [[[.,[[.,.],.]],.],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => 1

[3,8,2,7,1,5,4,6] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[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

[8,5,7,6,1,4,2,3] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[8,6,1,7,3,5,4,2] => [[[.,.],.],[[[.,.],[[.,.],.]],.]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 2

[8,6,1,7,5,4,2,3] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 2

[2,1,5,8,6,4,3,7] => [[.,.],[[[.,[[.,.],.]],.],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 1

[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

[7,1,8,6,3,5,4,2] => [[.,.],[[[[.,.],.],[[.,.],.]],.]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 1

[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

[7,1,6,4,2,3,5,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1

[8,6,2,4,7,3,5,1] => [[[[.,.],.],[[.,[.,.]],[.,.]]],.] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 3

[8,6,2,4,5,7,3,1] => [[[[.,.],.],[[.,[.,[.,.]]],.]],.] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[2,7,1,4,5,8,3,6] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 0

[7,1,6,4,5,2,3,8] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[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

[7,1,4,6,5,8,3,2] => [[.,.],[[[.,[[.,.],[.,.]]],.],.]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 1

[7,1,2,3,8,5,4,6] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 1

[7,1,5,4,3,8,2,6] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1

[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

[7,1,5,4,6,2,8,3] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[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

[7,1,6,5,4,3,2,8] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 1

[8,6,2,5,4,3,7,1] => [[[[.,.],.],[[[.,.],.],[.,.]]],.] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 3

[2,5,1,7,4,3,6,8] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0

[2,5,1,4,7,8,6,3] => [[.,[.,.]],[[.,[[.,[.,.]],.]],.]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 0

[3,5,1,4,8,6,2,7] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 0

[3,6,2,4,7,8,1,5] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0

[5,6,2,4,8,7,1,3] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 0

[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

[6,5,8,7,2,3,1,4] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[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

[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

[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

[4,3,1,7,6,8,2,5] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[3,4,1,7,5,6,8,2] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 0

[3,4,1,5,7,6,2,8] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 0

[8,4,7,2,5,3,6,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[7,6,5,1,3,8,2,4] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3

[7,6,5,1,3,4,8,2] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 3

[7,2,6,4,1,3,8,5] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 1

[6,7,5,2,1,3,8,4] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => 2

[8,4,5,3,7,2,6,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[7,3,8,4,1,5,2,6] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 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

[4,2,8,3,6,1,5,7] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[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

[6,3,5,2,1,7,4,8] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2

[6,8,5,3,1,4,2,7] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 2

[8,4,1,3,7,2,5,6] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[4,7,1,3,8,2,5,6] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[8,7,1,3,6,2,5,4] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[6,8,5,7,3,2,1,4] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2

[6,1,4,3,8,2,5,7] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[8,1,4,3,7,2,5,6] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[8,2,3,4,7,6,1,5] => [[[.,.],[.,[.,[[.,.],.]]]],[.,.]] => [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 1

[4,2,3,8,5,6,1,7] => [[[.,.],[.,[[.,.],[.,.]]]],[.,.]] => [1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1

[8,2,3,7,5,6,1,4] => [[[.,.],[.,[[.,.],[.,.]]]],[.,.]] => [1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1

[7,5,8,6,3,2,1,4] => [[[[[.,.],[[.,.],.]],.],.],[.,.]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 3

[6,5,8,7,3,2,1,4] => [[[[[.,.],[[.,.],.]],.],.],[.,.]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 3

[8,5,7,6,3,2,1,4] => [[[[[.,.],[[.,.],.]],.],.],[.,.]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 3

[6,8,7,5,3,2,1,4] => [[[[[.,[[.,.],.]],.],.],.],[.,.]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 3

[7,8,1,5,4,6,2,3] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[7,8,1,5,2,4,3,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[7,8,5,6,1,3,2,4] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[7,8,1,3,2,6,4,5] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[7,8,1,6,2,4,3,5] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[7,8,1,4,2,6,3,5] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[7,8,1,4,2,5,3,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[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

[4,3,6,5,8,7,1,2] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[7,6,5,4,3,1,8,2] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5

[6,8,5,4,3,2,1,7] => [[[[[[.,[.,.]],.],.],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 4

[7,1,5,4,3,8,6,2] => [[.,.],[[[[.,.],.],[[.,.],.]],.]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 1

[6,8,1,4,3,2,7,5] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[7,6,1,4,3,8,5,2] => [[[.,.],.],[[[.,.],[[.,.],.]],.]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 2

[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

[7,6,5,1,3,8,4,2] => [[[[.,.],.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[6,8,5,4,1,2,7,3] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => 2

[6,8,2,4,3,7,1,5] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[7,5,8,4,3,2,1,6] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 4

[8,4,7,5,2,6,1,3] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[5,4,6,8,2,1,7,3] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 2

[8,4,6,5,2,1,7,3] => [[[[.,.],[[.,.],.]],.],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2

[5,1,8,7,4,2,3,6] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 1

[5,2,3,6,4,1,8,7] => [[[.,.],[.,[[.,.],.]]],[[.,.],.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 1

[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

[5,7,1,2,4,3,8,6] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 0

[4,3,7,6,8,2,5,1] => [[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[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

[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

[6,3,7,2,4,8,5,1] => [[[[.,.],[.,.]],[.,[[.,.],.]]],.] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 2

[7,4,8,6,5,2,1,3] => [[[[.,.],[[[.,.],.],.]],.],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 2

[7,1,8,2,5,4,3,6] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1

[8,4,7,6,2,3,1,5] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 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

[4,2,8,7,3,5,6,1] => [[[.,.],[[[.,.],.],[.,[.,.]]]],.] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 2

[8,1,7,4,2,5,6,3] => [[.,.],[[[.,.],.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 1

[7,4,3,8,2,5,6,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3

[6,4,1,5,8,2,7,3] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[2,1,5,8,7,4,6,3] => [[.,.],[[[.,[[.,.],.]],[.,.]],.]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 1

[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

[7,4,3,2,8,5,6,1] => [[[[[.,.],.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 4

[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

[4,1,7,2,8,5,6,3] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 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] => 0

[7,2,3,4,8,5,6,1] => [[[.,.],[.,[.,[[.,.],[.,.]]]]],.] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 2

[6,1,8,5,2,7,4,3] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 1

[2,1,7,4,5,8,6,3] => [[.,.],[[[.,.],[.,[[.,.],.]]],.]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 1

[2,1,8,3,6,7,5,4] => [[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 1

[8,2,1,6,4,7,5,3] => [[[.,.],.],[[[.,.],[[.,.],.]],.]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 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] => 0

[7,6,2,1,5,8,4,3] => [[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[4,5,2,7,6,1,8,3] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[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

[7,4,8,6,5,2,3,1] => [[[[.,.],[[[.,.],.],.]],[.,.]],.] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 2

[8,1,6,4,7,3,2,5] => [[.,.],[[[[.,.],[.,.]],.],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 1

[7,6,4,1,2,3,8,5] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 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] => 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

[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

[6,1,4,8,7,3,5,2] => [[.,.],[[[.,[[.,.],.]],[.,.]],.]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 1

[7,2,8,4,3,5,6,1] => [[[.,.],[[[.,.],.],[.,[.,.]]]],.] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 2

[8,7,3,4,1,5,6,2] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 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

[3,1,8,7,2,5,6,4] => [[.,.],[[[.,.],.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 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] => 0

[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

[6,4,8,7,1,3,2,5] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[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

[6,8,4,2,1,3,7,5] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => 2

[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

[8,1,2,7,3,5,6,4] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 1

[6,4,1,3,2,8,5,7] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[5,3,8,6,2,1,4,7] => [[[[.,.],[[.,.],.]],.],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 2

[4,3,7,5,1,8,2,6] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 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] => 2

[7,2,5,4,3,8,1,6] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[6,8,1,2,4,5,3,7] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 0

[8,1,6,2,4,5,3,7] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[5,8,1,6,2,3,4,7] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0

[4,1,6,5,8,2,3,7] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[4,3,8,6,2,5,1,7] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[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

[6,3,8,7,4,2,5,1] => [[[[.,.],[[[.,.],.],.]],[.,.]],.] => [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

[8,7,4,3,1,6,2,5] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4

[7,1,5,3,4,8,2,6] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[6,1,8,7,4,3,5,2] => [[.,.],[[[[[.,.],.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 1

[8,5,4,3,1,6,7,2] => [[[[[.,.],.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 4

[4,1,3,8,5,6,7,2] => [[.,.],[[.,[[.,.],[.,[.,.]]]],.]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 1

[6,5,8,4,3,1,7,2] => [[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 3

[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

[4,8,3,2,5,6,7,1] => [[[[.,[.,.]],.],[.,[.,[.,.]]]],.] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2

[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

[2,1,8,3,5,6,7,4] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 1

[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

[7,5,1,8,2,4,3,6] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[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

[5,4,8,2,3,6,7,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2

[5,8,3,6,7,4,1,2] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 0

[2,3,1,6,8,4,7,5] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[2,7,1,4,3,8,5,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[2,4,1,8,6,3,7,5] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[8,4,1,3,6,2,7,5] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[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

[7,3,6,5,8,2,1,4] => [[[[.,.],[[.,.],[.,.]]],.],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 2

[7,6,3,5,8,2,1,4] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3

[3,5,2,8,6,1,7,4] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[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

[8,6,5,4,1,2,7,3] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 4

[2,6,1,8,3,7,5,4] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 0

[4,7,1,6,2,8,5,3] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 0

[6,1,5,3,8,7,2,4] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1

[7,6,1,5,8,2,3,4] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[6,5,2,4,8,1,7,3] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[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

[4,8,2,5,1,6,7,3] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0

[4,2,1,8,5,6,7,3] => [[[.,.],.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[7,2,1,5,8,6,3,4] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 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

[3,1,5,8,6,2,7,4] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 1

[6,3,4,8,5,1,7,2] => [[[.,.],[.,[[.,.],.]]],[[.,.],.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 1

[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

[7,6,1,2,8,3,5,4] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 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] => 2

[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

[6,5,4,8,7,1,3,2] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[6,5,4,8,1,2,7,3] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[7,5,1,6,2,3,8,4] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2

[7,5,1,6,8,2,4,3] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[6,5,4,1,8,2,7,3] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3

[6,5,4,7,1,2,8,3] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[6,5,4,7,8,1,3,2] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[6,5,3,7,1,4,2,8] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[6,5,3,1,8,4,2,7] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[7,5,1,4,8,3,2,6] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 2

[8,1,6,4,7,3,5,2] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 1

[7,5,1,4,8,3,6,2] => [[[.,.],.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[6,5,3,7,1,4,8,2] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[6,4,3,1,5,8,7,2] => [[[[.,.],.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[7,4,1,5,3,8,6,2] => [[[.,.],.],[[[.,.],[[.,.],.]],.]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 2

[8,1,5,4,3,7,6,2] => [[.,.],[[[[.,.],.],[[.,.],.]],.]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 1

[8,1,5,4,3,7,2,6] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1

[7,4,1,5,3,8,2,6] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[7,4,1,5,3,2,6,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[8,1,5,4,3,2,6,7] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 1

[8,1,6,4,2,5,3,7] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[6,5,3,1,2,7,4,8] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3

[6,5,3,8,1,4,2,7] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 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

[8,1,7,2,5,4,3,6] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1

[8,1,7,2,5,4,6,3] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1

[7,6,1,2,5,4,8,3] => [[[.,.],.],[.,[[[.,.],[.,.]],.]]] => [1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2

[6,5,3,8,1,4,7,2] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[6,5,3,1,2,7,8,4] => [[[[.,.],.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 3

[7,5,1,4,2,6,8,3] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[8,1,6,4,2,5,7,3] => [[.,.],[[[.,.],.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 1

[7,4,1,5,3,2,8,6] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[6,4,3,1,5,2,8,7] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3

[6,4,3,1,5,7,2,8] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3

[7,4,1,5,3,6,2,8] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[8,1,5,4,3,6,2,7] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1

[8,1,5,4,3,6,7,2] => [[.,.],[[[[.,.],.],[.,[.,.]]],.]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 1

[7,4,1,5,3,6,8,2] => [[[.,.],.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[6,4,3,1,5,7,8,2] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 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] => 0

[6,7,4,5,1,8,2,3] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[4,5,3,8,6,7,1,2] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[4,8,3,6,5,7,1,2] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[5,6,4,7,1,8,2,3] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[5,6,1,7,3,8,2,4] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[5,6,1,8,2,7,3,4] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[5,6,1,8,4,7,2,3] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[4,8,1,6,5,7,2,3] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[4,5,1,8,6,7,2,3] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[7,8,4,5,1,6,2,3] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[4,8,2,3,1,6,5,7] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[5,6,2,8,1,4,3,7] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[5,6,3,4,1,8,2,7] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[7,8,2,5,3,4,1,6] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[7,8,1,5,3,6,2,4] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[6,7,2,5,3,4,1,8] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[6,7,1,5,3,8,2,4] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[6,7,5,8,1,4,2,3] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[6,7,2,3,1,8,4,5] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[6,7,2,8,1,4,3,5] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[3,4,2,7,5,6,1,8] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[3,4,1,7,5,8,2,6] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[2,3,1,7,5,8,4,6] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[2,3,1,8,4,7,5,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[7,8,2,3,1,6,4,5] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[7,8,2,6,1,4,3,5] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[2,8,1,4,3,7,5,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[3,7,2,5,4,6,1,8] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[4,5,2,7,3,6,1,8] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[4,5,1,8,2,7,3,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[3,4,1,8,2,7,5,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[3,4,1,8,6,7,2,5] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[3,4,2,5,1,8,6,7] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[3,4,2,8,1,6,5,7] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[3,8,2,5,1,6,4,7] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[4,5,2,8,1,6,3,7] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[4,5,3,6,1,8,2,7] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[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

[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

[8,6,3,7,5,1,2,4] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[8,6,1,7,3,2,5,4] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[7,6,1,8,3,5,2,4] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[7,6,1,3,8,5,2,4] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 2

[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

[7,6,2,8,3,5,1,4] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2

[7,6,2,3,8,5,1,4] => [[[[.,.],.],[.,[[.,.],.]]],[.,.]] => [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 2

[8,7,1,5,2,6,3,4] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[8,7,1,5,2,3,6,4] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2

[8,5,2,3,1,7,6,4] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2

[8,6,2,3,7,1,5,4] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[8,6,2,7,3,1,5,4] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 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

[8,7,2,5,1,6,3,4] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[8,7,2,1,4,6,3,5] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3

[8,4,2,1,7,6,3,5] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[8,5,2,7,1,6,3,4] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 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] => 2

[5,8,7,3,1,4,2,6] => [[[.,[[.,.],.]],.],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[5,8,7,3,1,4,6,2] => [[[.,[[.,.],.]],.],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 1

[8,5,7,2,1,4,6,3] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[8,5,2,7,1,3,6,4] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[8,4,2,1,3,7,6,5] => [[[[.,.],.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 3

[8,7,4,1,2,3,6,5] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3

[8,7,4,1,2,6,3,5] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3

[8,4,3,1,7,2,6,5] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3

[8,4,3,1,2,7,6,5] => [[[[.,.],.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 3

[8,6,1,3,7,2,5,4] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[8,5,1,3,2,7,6,4] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 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] => 2

[8,5,7,4,1,2,6,3] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2

[8,1,5,4,2,7,6,3] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 1

[8,1,6,4,7,2,5,3] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[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

[5,8,3,6,4,1,2,7] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 0

[5,2,8,6,4,1,3,7] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 1

[8,4,7,5,1,6,2,3] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[8,4,7,5,1,2,6,3] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 1

[8,4,7,5,1,2,3,6] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1

[8,7,3,5,1,2,6,4] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[8,3,2,6,5,1,4,7] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[4,8,7,3,1,5,2,6] => [[[.,[[.,.],.]],.],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[8,4,7,2,1,5,3,6] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2

[8,3,2,7,1,5,4,6] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[8,3,2,1,7,6,4,5] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[8,7,3,1,4,2,6,5] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3

[8,7,3,1,6,2,4,5] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[8,7,3,1,2,6,4,5] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3

[8,7,3,1,2,4,6,5] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3

[8,3,2,1,4,7,6,5] => [[[[.,.],.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 3

[8,3,2,1,7,4,6,5] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3

[8,3,2,7,1,5,6,4] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[8,4,7,2,1,5,6,3] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[8,7,2,1,6,3,4,5] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[8,7,2,1,3,6,4,5] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3

[8,7,2,1,3,4,6,5] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3

[4,6,3,2,1,5,8,7] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => 2

[6,2,1,5,3,4,8,7] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2

[5,8,1,3,7,6,4,2] => [[.,[.,.]],[[.,[[[.,.],.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 0

[4,7,2,3,6,1,8,5] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0

[4,2,6,8,5,7,3,1] => [[[.,.],[[[.,[.,.]],[.,.]],.]],.] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 2

[6,4,2,7,3,8,5,1] => [[[[.,.],.],[[.,.],[[.,.],.]]],.] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3

[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

[2,1,5,8,7,6,3,4] => [[.,.],[[.,[[[.,.],.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 1

[2,1,4,7,6,3,8,5] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 1

[6,4,7,8,5,3,2,1] => [[[[[.,.],[[.,[.,.]],.]],.],.],.] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 4

[4,1,3,7,6,2,8,5] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 1

[8,5,1,6,3,2,7,4] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[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

[3,2,6,8,4,7,5,1] => [[[.,.],[[.,[.,.]],[[.,.],.]]],.] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 2

[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

[4,2,8,6,7,3,1,5] => [[[.,.],[[[.,.],[.,.]],.]],[.,.]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1

[7,4,3,8,2,1,5,6] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3

[6,4,3,2,7,8,1,5] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3

[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

[3,7,1,4,6,8,5,2] => [[.,[.,.]],[[.,[[.,[.,.]],.]],.]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 0

[7,8,2,5,6,1,4,3] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0

[7,6,8,4,2,5,3,1] => [[[[[.,.],[.,.]],.],[[.,.],.]],.] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[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

[6,5,7,2,8,4,3,1] => [[[[.,.],[.,.]],[[[.,.],.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 2

[6,5,8,2,1,7,3,4] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2

[7,4,3,5,1,6,8,2] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[4,1,6,3,5,8,7,2] => [[.,.],[[[.,.],[.,[[.,.],.]]],.]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 1

[6,2,5,8,4,3,7,1] => [[[.,.],[[[.,[.,.]],.],[.,.]]],.] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[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

[2,1,6,5,8,4,7,3] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 1

[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

[4,1,8,5,6,2,3,7] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[6,2,8,4,3,5,1,7] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[4,8,2,7,6,1,3,5] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 0

[3,1,8,2,7,5,4,6] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1

[3,8,1,2,6,7,4,5] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 0

[5,8,4,3,2,7,1,6] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2

[7,4,8,6,3,2,5,1] => [[[[[.,.],[[.,.],.]],.],[.,.]],.] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 3

[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

[2,1,8,4,3,7,5,6] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[6,3,8,2,4,5,7,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2

[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

[5,8,2,4,3,1,6,7] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 0

[8,2,1,3,4,7,5,6] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 2

[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

[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

[6,7,4,5,1,2,8,3] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 0

[6,7,5,4,1,2,8,3] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => 2

[6,4,7,5,1,2,8,3] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 1

[6,2,1,7,5,3,8,4] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[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

[5,4,8,6,1,7,2,3] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[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

[5,2,1,7,6,8,3,4] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[5,4,7,6,1,8,2,3] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[5,7,4,6,1,8,2,3] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[5,8,4,6,1,7,2,3] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[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

[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

[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

[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

[5,7,4,8,1,6,2,3] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[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

[5,2,1,7,8,6,3,4] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 2

[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

[5,4,8,7,1,6,2,3] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[4,2,7,3,6,5,1,8] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[4,2,6,3,1,5,8,7] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 1

[4,2,7,6,3,5,1,8] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[2,1,3,7,5,4,8,6] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 1

[2,3,1,8,6,5,4,7] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 0

[4,2,8,3,1,6,5,7] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[8,3,2,6,4,1,5,7] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[2,1,3,8,7,5,4,6] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 1

[2,1,3,8,5,4,7,6] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 1

[7,1,8,4,2,3,5,6] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1

[2,1,8,4,3,5,7,6] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1

[4,2,6,3,1,8,5,7] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[5,4,2,8,3,1,6,7] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[4,2,1,8,3,5,7,6] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2

[4,2,1,8,3,7,5,6] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[8,3,2,1,7,4,5,6] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[3,2,8,5,6,1,7,4] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[4,3,1,7,5,2,8,6] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[4,3,8,5,1,6,7,2] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 1

[4,2,3,8,5,1,6,7] => [[[.,.],[.,[[.,.],.]]],[.,[.,.]]] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 1

[3,2,4,8,6,1,5,7] => [[[.,.],[.,[[.,.],.]]],[.,[.,.]]] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 1

[3,2,5,7,6,1,4,8] => [[[.,.],[.,[[.,.],.]]],[.,[.,.]]] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 1

[4,3,8,5,2,6,7,1] => [[[[.,.],[[.,.],.]],[.,[.,.]]],.] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 2

[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

[3,4,1,7,5,6,2,8] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[4,1,7,5,2,8,6,3] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 1

[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

[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

[5,1,8,3,6,7,2,4] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[3,6,1,4,7,8,5,2] => [[.,[.,.]],[[.,[[.,[.,.]],.]],.]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 0

[6,8,1,3,5,7,2,4] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 0

[7,6,1,4,3,8,2,5] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[3,8,1,6,5,4,2,7] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 0

[4,1,3,7,5,8,2,6] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 1

[6,1,7,3,8,4,2,5] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1

[7,1,8,6,3,5,2,4] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1

[3,1,7,6,5,8,4,2] => [[.,.],[[[[[.,.],.],[.,.]],.],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 1

[8,2,7,6,5,3,4,1] => [[[.,.],[[[[.,.],.],.],[.,.]]],.] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 2

[8,4,2,6,7,5,3,1] => [[[[.,.],.],[[[.,[.,.]],.],.]],.] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 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] => 0

[7,4,1,6,8,2,5,3] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[6,1,3,2,7,8,4,5] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[4,7,2,6,8,1,5,3] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0

[8,7,3,6,4,5,2,1] => [[[[[.,.],.],[[.,.],[.,.]]],.],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 4

[3,7,2,4,5,1,6,8] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[3,4,1,7,5,2,6,8] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0

[7,5,8,6,1,2,4,3] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 1

[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

[6,4,1,2,7,5,8,3] => [[[.,.],.],[.,[[[.,.],[.,.]],.]]] => [1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2

[4,1,8,3,6,7,5,2] => [[.,.],[[[.,.],[[.,[.,.]],.]],.]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 1

[8,3,7,4,5,2,6,1] => [[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[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

[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

[5,8,2,6,3,4,1,7] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[4,1,7,5,8,6,2,3] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1

[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

[8,2,7,5,4,3,6,1] => [[[.,.],[[[[.,.],.],.],[.,.]]],.] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 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

[6,5,8,7,1,3,4,2] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 1

[6,1,5,2,8,4,7,3] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1

[4,6,1,8,5,7,2,3] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[4,7,1,2,8,5,6,3] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 0

[7,3,5,8,6,1,2,4] => [[[.,.],[.,[[.,.],.]]],[.,[.,.]]] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 1

[6,8,1,5,7,2,3,4] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[7,1,2,5,8,6,3,4] => [[.,.],[.,[[.,[[.,.],.]],[.,.]]]] => [1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 1

[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

[2,7,1,5,8,6,3,4] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 0

[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

[7,6,8,2,1,3,5,4] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2

[7,4,2,1,6,8,5,3] => [[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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

[6,7,4,3,1,8,5,2] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 2

[7,4,2,6,8,5,1,3] => [[[[.,.],.],[[.,[.,.]],.]],[.,.]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 2

[7,3,2,5,8,6,1,4] => [[[[.,.],.],[.,[[.,.],.]]],[.,.]] => [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 2

[3,1,7,6,8,2,5,4] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[7,4,1,2,6,8,5,3] => [[[.,.],.],[.,[[[.,[.,.]],.],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 2

[7,1,4,2,8,5,6,3] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1

[7,1,8,2,5,4,6,3] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1

[7,3,8,4,6,1,5,2] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[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

[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

[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

[7,6,8,3,1,2,5,4] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2

[7,1,5,8,6,3,2,4] => [[.,.],[[[.,[[.,.],.]],.],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 1

[7,2,5,8,6,3,1,4] => [[[.,.],[[.,[[.,.],.]],.]],[.,.]] => [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 1

[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

[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

[2,7,1,6,8,5,4,3] => [[.,[.,.]],[[[[.,[.,.]],.],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 0

[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

[6,7,1,8,5,4,3,2] => [[.,[.,.]],[[[[[.,.],.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 0

[7,2,1,6,8,5,4,3] => [[[.,.],.],[[[[.,[.,.]],.],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 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] => 3

[5,6,4,8,1,2,7,3] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 0

[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

[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

[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

[4,3,6,7,2,1,5,8] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2

[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

[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

[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

[7,2,1,6,8,4,5,3] => [[[.,.],.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 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

[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

[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

[7,2,1,5,4,8,6,3] => [[[.,.],.],[[[.,.],[[.,.],.]],.]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 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

[7,3,1,5,4,8,2,6] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[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

[5,3,4,2,1,8,6,7] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2

[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

[5,6,3,8,1,4,2,7] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[8,1,7,2,4,5,6,3] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 1

[7,6,1,2,4,5,8,3] => [[[.,.],.],[.,[[.,[.,[.,.]]],.]]] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 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] => 0

[6,5,2,1,3,7,8,4] => [[[[.,.],.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 3

[7,5,1,3,2,6,8,4] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[8,1,6,3,2,5,7,4] => [[.,.],[[[.,.],.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 1

[7,4,1,3,5,2,8,6] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[5,4,2,3,1,6,8,7] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[7,3,1,4,5,6,2,8] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 2

[8,1,4,3,5,6,2,7] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[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

[7,8,4,2,1,6,5,3] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 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] => 2

[6,2,3,4,8,7,1,5] => [[[.,.],[.,[.,[[.,.],.]]]],[.,.]] => [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 1

[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

[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

[6,2,3,8,7,5,1,4] => [[[.,.],[.,[[[.,.],.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 1

[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

[5,2,6,3,8,1,7,4] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[6,4,3,8,7,5,1,2] => [[[[.,.],.],[[[.,.],.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 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

[5,6,1,4,2,3,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0

[5,6,1,4,2,3,8,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0

[5,2,8,3,4,1,7,6] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[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

[5,1,4,3,6,2,8,7] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[5,1,4,3,7,2,8,6] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[5,1,4,3,8,2,7,6] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[5,6,2,4,1,7,8,3] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0

[5,7,2,4,1,8,6,3] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 0

[6,1,4,2,7,8,5,3] => [[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 1

[5,2,7,4,1,6,8,3] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 1

[5,1,6,3,4,2,7,8] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[5,4,7,8,3,2,1,6] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 3

[5,4,8,7,3,2,1,6] => [[[[[.,.],[[.,.],.]],.],.],[.,.]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 3

[5,7,1,3,4,2,6,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[5,1,8,4,2,3,6,7] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1

[5,1,7,4,2,3,6,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1

[5,8,1,3,4,2,6,7] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[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

[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

[4,3,8,7,2,5,1,6] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[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

[6,8,1,2,4,3,5,7] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 0

[4,3,8,2,7,5,6,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[4,3,2,8,1,6,5,7] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[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

[4,1,8,3,7,5,6,2] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 1

[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

[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

[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

[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

[4,3,1,8,2,6,5,7] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[4,3,7,8,5,2,1,6] => [[[[.,.],[[.,[.,.]],.]],.],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 2

[7,6,2,8,3,5,4,1] => [[[[.,.],.],[[.,.],[[.,.],.]]],.] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3

[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

[7,4,1,8,5,2,6,3] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[3,1,2,4,8,6,5,7] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 1

[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

[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

[2,1,3,4,8,6,5,7] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 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

[5,3,8,7,2,4,6,1] => [[[[.,.],[[.,.],.]],[.,[.,.]]],.] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 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

[4,8,1,2,5,6,3,7] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 0

[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

[5,2,1,6,3,8,4,7] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[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

[3,6,1,5,8,4,2,7] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 0

[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

[5,6,4,8,1,3,2,7] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[6,5,4,3,8,2,1,7] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 4

[5,4,3,7,2,8,1,6] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[5,8,4,3,7,2,6,1] => [[[[[.,[.,.]],.],[.,.]],[.,.]],.] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[7,4,6,3,2,8,1,5] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2

[5,7,3,4,1,2,8,6] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 0

[8,5,4,7,6,2,1,3] => [[[[[.,.],.],[[.,.],.]],.],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 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] => 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

[5,3,8,6,7,4,1,2] => [[[.,.],[[[.,.],[.,.]],.]],[.,.]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1

[8,6,2,7,4,1,5,3] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[7,6,2,1,4,3,8,5] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3

[7,6,1,3,4,2,8,5] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[3,2,6,8,5,7,4,1] => [[[.,.],[[[.,[.,.]],[.,.]],.]],.] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 2

[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

[7,5,2,3,1,6,8,4] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[3,1,7,5,2,8,4,6] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[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

[4,2,7,6,3,8,1,5] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[6,4,8,7,2,3,5,1] => [[[[.,.],[[.,.],.]],[.,[.,.]]],.] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 2

[3,2,6,8,7,4,5,1] => [[[.,.],[[.,[[.,.],.]],[.,.]]],.] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2

[3,2,7,4,1,6,8,5] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 1

[6,3,2,1,7,8,4,5] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 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] => 0

[4,2,1,3,7,5,8,6] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2

[8,1,3,7,4,2,6,5] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 1

[8,4,3,7,6,2,1,5] => [[[[[.,.],.],[[.,.],.]],.],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 3

[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

[3,6,2,8,7,1,5,4] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[7,3,2,8,1,6,5,4] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 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

[6,8,2,4,7,1,5,3] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0

[5,2,1,8,7,3,6,4] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[8,2,1,6,3,7,5,4] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 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

[5,8,1,6,7,2,4,3] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[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

[8,7,2,5,6,4,3,1] => [[[[.,.],.],[[[.,[.,.]],.],.]],.] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 3

[8,6,7,5,2,4,3,1] => [[[[[.,.],[.,.]],.],[[.,.],.]],.] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[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

[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

[3,7,1,8,2,6,5,4] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 0

[2,1,7,3,8,6,5,4] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 1

[8,2,1,7,6,5,4,3] => [[[.,.],.],[[[[[.,.],.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2

[8,1,4,7,6,5,3,2] => [[.,.],[[[.,[[[.,.],.],.]],.],.]] => [1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 1

[8,6,7,5,1,4,3,2] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 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] => 3

[5,8,4,3,2,1,6,7] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 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] => 3

[6,5,3,7,2,1,4,8] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3

[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

[5,3,7,6,2,1,4,8] => [[[[.,.],[[.,.],.]],.],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 2

[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

[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

[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

[6,4,2,7,5,1,3,8] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 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

[5,2,7,6,8,1,3,4] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[4,2,7,6,5,1,3,8] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 1

[6,5,4,3,1,7,8,2] => [[[[[.,.],.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 4

[6,4,7,3,1,5,8,2] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 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] => 2

[5,4,3,6,1,8,7,2] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2

[5,3,7,6,1,4,8,2] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 1

[4,3,7,6,1,5,8,2] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 1

[4,8,7,2,1,5,3,6] => [[[.,[[.,.],.]],.],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[5,8,3,2,1,4,7,6] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => 2

[3,8,7,2,1,4,5,6] => [[[.,[[.,.],.]],.],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1

[5,8,2,6,1,4,3,7] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[6,4,2,7,1,5,3,8] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[4,3,2,6,1,5,8,7] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[3,2,7,6,1,4,5,8] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1

[6,5,4,1,8,7,3,2] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 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

[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

[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

[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

[5,3,2,1,6,4,8,7] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 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

[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

[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

[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

[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

[6,4,1,7,5,8,3,2] => [[[.,.],.],[[[[.,.],[.,.]],.],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 2

[5,4,1,6,7,8,3,2] => [[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 2

[6,3,1,7,5,4,8,2] => [[[.,.],.],[[[[.,.],.],[.,.]],.]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 2

[5,3,1,6,7,4,8,2] => [[[.,.],.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[4,3,1,6,5,7,8,2] => [[[.,.],.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[5,2,1,6,7,4,3,8] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 2

[2,8,1,6,5,4,3,7] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 0

[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

[4,1,7,6,5,8,3,2] => [[.,.],[[[[[.,.],.],[.,.]],.],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 1

[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

[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

[8,1,2,3,5,4,6,7] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1

[8,7,3,5,6,2,1,4] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3

[8,7,2,1,3,5,4,6] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3

[8,6,4,1,7,5,3,2] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3

[7,6,4,3,1,8,5,2] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4

[7,4,1,8,5,2,3,6] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[7,1,4,2,8,3,6,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[7,1,8,2,5,3,6,4] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[8,1,7,5,4,2,3,6] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 1

[8,6,3,1,2,5,4,7] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3

[8,1,7,6,3,2,4,5] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 1

[8,2,5,7,6,3,1,4] => [[[.,.],[[.,[[.,.],.]],.]],[.,.]] => [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 1

[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

[7,3,1,8,6,5,4,2] => [[[.,.],.],[[[[[.,.],.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2

[8,7,2,1,6,5,4,3] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3

[8,7,6,3,2,1,5,4] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5

[2,1,8,6,3,7,4,5] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[8,6,1,5,2,7,4,3] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 2

[8,5,1,7,4,2,6,3] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[2,1,7,5,4,3,8,6] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 1

[2,1,8,4,5,3,6,7] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[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

[2,1,8,5,7,6,3,4] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1

[2,1,4,8,5,7,3,6] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 1

[2,1,5,4,6,8,3,7] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[8,5,3,1,6,2,4,7] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[7,5,1,4,6,8,3,2] => [[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 2

[6,4,1,5,2,3,8,7] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2

[8,3,7,5,2,6,1,4] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[5,3,7,4,6,8,1,2] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[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

[5,2,4,8,6,3,1,7] => [[[.,.],[[.,[[.,.],.]],.]],[.,.]] => [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 1

[4,2,6,3,8,5,1,7] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[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

[3,8,2,4,7,5,1,6] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 0

[8,5,2,7,4,6,1,3] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 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

[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

[8,3,2,4,1,7,5,6] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[7,4,2,3,1,8,6,5] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2

[7,2,4,3,1,5,8,6] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 1

[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

[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

[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

[5,6,1,4,3,2,8,7] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[5,7,1,8,3,6,2,4] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[6,8,1,4,5,3,2,7] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 0

[6,7,1,5,4,3,8,2] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 0

[8,7,5,1,3,4,2,6] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3

[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

[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

[5,8,1,6,3,7,4,2] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 0

[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

[7,5,4,8,2,1,3,6] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3

[7,3,6,5,4,1,8,2] => [[[.,.],[[[.,.],.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 1

[8,3,6,4,5,1,2,7] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[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

[6,3,5,4,1,2,8,7] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 1

[8,7,3,6,5,1,4,2] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[4,3,2,5,7,1,8,6] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[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

[3,2,8,4,7,1,6,5] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[8,2,4,7,5,1,6,3] => [[[.,.],[.,[[.,.],.]]],[[.,.],.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 1

[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

[8,3,4,5,7,6,1,2] => [[[.,.],[.,[.,[[.,.],.]]]],[.,.]] => [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 1

[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

[3,5,1,6,8,2,7,4] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[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

[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

[5,1,6,3,8,4,7,2] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 1

[2,5,1,6,8,3,7,4] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[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

[5,7,1,8,6,2,3,4] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0

[6,1,7,5,2,8,3,4] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[5,7,2,8,6,1,3,4] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 0

[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

[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

[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

[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

[6,2,7,5,1,8,3,4] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[6,2,7,5,4,1,8,3] => [[[.,.],[[[.,.],.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 1

[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

[6,7,2,5,3,8,1,4] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[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

[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

[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

[6,3,7,5,1,8,2,4] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[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

[4,1,7,2,6,5,8,3] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1

[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

[6,3,1,7,5,8,2,4] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[6,7,5,4,2,1,8,3] => [[[[[.,[.,.]],.],.],.],[[.,.],.]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 3

[6,3,2,7,5,8,1,4] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 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

[6,2,7,4,5,1,8,3] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[6,2,3,7,5,8,1,4] => [[[.,.],[.,[[.,.],[.,.]]]],[.,.]] => [1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1

[7,5,1,6,3,8,2,4] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 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

[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

[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

[4,6,1,5,8,7,3,2] => [[.,[.,.]],[[[.,[[.,.],.]],.],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 0

[7,5,1,6,2,8,4,3] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 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] => 0

[6,8,5,4,3,2,7,1] => [[[[[[.,[.,.]],.],.],.],[.,.]],.] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 4

[6,8,5,4,3,7,2,1] => [[[[[[.,[.,.]],.],.],[.,.]],.],.] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 4

[5,8,4,3,2,1,7,6] => [[[[[.,[.,.]],.],.],.],[[.,.],.]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 3

[6,5,4,3,1,8,7,2] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4

[8,7,5,4,3,1,6,2] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5

[8,3,4,6,2,1,5,7] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2

[3,5,2,6,8,4,1,7] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 0

[7,5,3,2,8,4,1,6] => [[[[[.,.],.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3

[7,5,3,2,8,4,6,1] => [[[[[.,.],.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 4

[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

[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

[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

[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

[6,4,7,3,2,8,5,1] => [[[[[.,.],[.,.]],.],[[.,.],.]],.] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[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

[5,1,7,3,8,4,2,6] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1

[2,5,1,7,4,3,8,6] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[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

[6,4,3,1,7,8,5,2] => [[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[6,4,1,7,3,8,5,2] => [[[.,.],.],[[[.,.],[[.,.],.]],.]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 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] => 2

[5,1,6,3,7,8,4,2] => [[.,.],[[[.,.],[[.,[.,.]],.]],.]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 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] => 0

[5,6,1,7,8,3,4,2] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 0

[6,7,2,4,1,8,5,3] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 0

[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

[6,4,7,3,1,2,8,5] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2

[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

[5,6,1,3,2,7,8,4] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 0

[5,6,3,2,1,7,8,4] => [[[[.,[.,.]],.],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 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] => 2

[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

[6,3,2,7,1,8,4,5] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[7,5,3,2,1,8,4,6] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4

[7,3,8,4,2,1,5,6] => [[[[.,.],[[.,.],.]],.],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 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

[7,3,8,4,6,2,1,5] => [[[[.,.],[[.,.],[.,.]]],.],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 2

[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

[6,3,7,8,5,2,1,4] => [[[[.,.],[[.,[.,.]],.]],.],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 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

[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

[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

[2,5,1,7,3,8,6,4] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 0

[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

[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

[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

[6,2,1,7,3,8,5,4] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 2

[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

[6,3,1,7,8,5,4,2] => [[[.,.],.],[[[[.,[.,.]],.],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 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

[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

[5,3,2,1,8,4,7,6] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 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

[3,2,6,4,5,8,1,7] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[5,3,2,1,6,8,4,7] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 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

[3,4,1,8,5,2,7,6] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[8,1,4,2,7,3,6,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[8,2,1,7,5,3,4,6] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[5,8,7,4,1,2,6,3] => [[[.,[[.,.],.]],.],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => 1

[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

[4,1,3,5,6,8,7,2] => [[.,.],[[.,[.,[.,[[.,.],.]]]],.]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 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

[3,2,5,6,8,7,1,4] => [[[.,.],[.,[.,[[.,.],.]]]],[.,.]] => [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 1

[2,1,8,5,6,7,3,4] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[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

[3,2,6,4,8,1,7,5] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[8,2,1,6,7,3,4,5] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[4,7,5,3,1,2,8,6] => [[[.,[[.,.],.]],.],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => 1

[7,2,4,8,5,3,1,6] => [[[.,.],[[.,[[.,.],.]],.]],[.,.]] => [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 1

[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

[3,5,2,7,4,1,8,6] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[8,4,2,3,7,1,5,6] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[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

[4,8,2,3,6,7,1,5] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0

[3,5,2,7,6,1,8,4] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[5,8,3,2,1,6,7,4] => [[[[.,[.,.]],.],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 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] => 0

[5,1,4,2,8,7,6,3] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 1

[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

[5,2,6,8,7,1,3,4] => [[[.,.],[.,[[.,.],.]]],[.,[.,.]]] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 1

[6,3,2,1,8,5,7,4] => [[[[.,.],.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 3

[4,2,5,6,8,7,1,3] => [[[.,.],[.,[.,[[.,.],.]]]],[.,.]] => [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 1

[4,2,8,5,6,7,1,3] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[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

[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

[8,6,4,1,3,2,5,7] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[8,1,3,6,5,2,4,7] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 1

[8,1,4,3,6,5,2,7] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1

[3,6,5,2,1,8,7,4] => [[[.,[[.,.],.]],.],[[[.,.],.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1

[8,3,2,4,6,5,1,7] => [[[[.,.],.],[.,[[.,.],.]]],[.,.]] => [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 2

[8,4,2,1,6,5,3,7] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[8,4,1,2,6,5,3,7] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 2

[8,6,4,2,1,5,3,7] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4

[8,3,6,4,1,5,2,7] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[8,2,6,3,4,5,1,7] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[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

[4,7,1,6,5,8,3,2] => [[.,[.,.]],[[[[.,.],[.,.]],.],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 0

[5,4,8,7,6,3,1,2] => [[[[.,.],[[[.,.],.],.]],.],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 2

[4,3,1,5,8,6,7,2] => [[[.,.],.],[[.,[[.,.],[.,.]]],.]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 2

[4,1,3,5,8,6,7,2] => [[.,.],[[.,[.,[[.,.],[.,.]]]],.]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 1

[6,5,3,8,4,7,1,2] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2

[5,4,2,1,6,8,7,3] => [[[[.,.],.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[6,8,4,3,2,7,1,5] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2

[5,1,3,2,8,6,7,4] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1

[5,3,1,2,8,6,7,4] => [[[.,.],.],[.,[[[.,.],[.,.]],.]]] => [1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 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

[5,3,2,1,8,6,7,4] => [[[[.,.],.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 3

[5,2,1,3,6,8,7,4] => [[[.,.],.],[.,[[.,[[.,.],.]],.]]] => [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 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

[8,2,1,3,6,4,7,5] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 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] => 0

[5,4,7,8,3,6,2,1] => [[[[[.,.],[.,[.,.]]],[.,.]],.],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[6,4,3,8,7,2,1,5] => [[[[[.,.],.],[[.,.],.]],.],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 3

[6,3,8,7,4,1,2,5] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 1

[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

[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

[8,4,7,2,1,3,5,6] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2

[8,6,4,2,1,3,7,5] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 4

[8,6,4,1,3,2,7,5] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3

[8,6,4,2,3,1,7,5] => [[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3

[6,1,3,8,5,7,2,4] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 1

[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

[2,8,1,5,4,7,6,3] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 0

[2,1,7,6,4,5,8,3] => [[.,.],[[[[.,.],.],[.,[.,.]]],.]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 1

[3,5,1,7,6,8,2,4] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[5,8,2,6,1,3,7,4] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 0

[6,3,5,8,7,2,1,4] => [[[[.,.],[.,[[.,.],.]]],.],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 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

[4,1,5,2,6,8,7,3] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 1

[4,2,8,5,1,6,7,3] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 1

[4,1,8,5,2,6,7,3] => [[.,.],[[[.,.],.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 1

[2,7,1,8,5,4,6,3] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 0

[5,8,6,2,1,3,7,4] => [[[.,[[.,.],.]],.],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => 1

[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

[4,6,3,5,8,1,7,2] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0

[3,8,1,4,5,6,7,2] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 0

[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

[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

[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

[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

[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

[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

[4,1,6,3,7,8,5,2] => [[.,.],[[[.,.],[[.,[.,.]],.]],.]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 1

[4,1,6,3,8,5,2,7] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1

[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

[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

[4,1,7,3,2,8,6,5] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 1

[4,1,8,3,2,5,6,7] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1

[4,5,2,6,8,1,3,7] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[4,6,2,7,8,5,1,3] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 0

[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

[4,8,2,3,1,5,6,7] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0

[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

[5,1,6,3,8,4,2,7] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1

[5,6,2,3,8,4,1,7] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 0

[5,6,2,7,8,4,1,3] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 0

[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

[5,8,2,3,4,1,6,7] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[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

[6,1,2,3,8,5,4,7] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 1

[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

[6,1,7,3,8,5,4,2] => [[.,.],[[[.,.],[[[.,.],.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 1

[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

[6,1,8,3,4,5,2,7] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[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

[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

[7,1,2,3,4,8,6,5] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1

[7,1,2,8,4,5,6,3] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 1

[7,1,8,3,4,5,6,2] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 1

[6,4,1,8,2,3,7,5] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2

[5,8,1,2,4,3,7,6] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 0

[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

[3,6,2,8,1,5,7,4] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0

[2,6,1,3,8,4,7,5] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 0

[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

[8,2,1,3,7,6,4,5] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 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

[8,2,7,5,3,1,6,4] => [[[.,.],[[[.,.],.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 1

[8,2,6,5,4,7,1,3] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[7,6,5,2,4,8,1,3] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3

[7,8,2,5,3,1,6,4] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[7,1,8,6,3,2,4,5] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 1

[6,8,1,5,3,2,4,7] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0

[6,5,1,2,4,8,3,7] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 2

[7,8,1,6,4,2,3,5] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0

[8,4,1,2,5,6,3,7] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 2

[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

[7,3,2,6,5,1,8,4] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[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

[8,2,7,4,5,6,1,3] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[8,2,3,6,5,1,7,4] => [[[.,.],[.,[[.,.],.]]],[[.,.],.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 1

[7,2,8,6,5,4,1,3] => [[[.,.],[[[[.,.],.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1

[7,2,8,5,4,6,1,3] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[6,3,2,8,5,1,7,4] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 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] => 2

[6,8,5,4,3,1,7,2] => [[[[[.,[.,.]],.],.],.],[[.,.],.]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 3

[5,8,6,4,1,3,7,2] => [[[.,[[.,.],.]],.],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 1

[3,6,1,8,5,2,7,4] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[3,4,1,2,8,6,7,5] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 0

[6,8,3,5,4,1,7,2] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[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

[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

[7,6,3,8,5,2,1,4] => [[[[[.,.],.],[[.,.],.]],.],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 3

[7,2,6,4,8,3,1,5] => [[[.,.],[[[.,.],[.,.]],.]],[.,.]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1

[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

[5,2,8,4,1,7,6,3] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[8,6,3,4,7,2,5,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 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] => 0

[8,3,2,1,5,4,7,6] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3

[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

[2,5,1,8,4,3,7,6] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[6,2,5,4,8,1,3,7] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[4,3,1,6,5,8,2,7] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[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

[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

[7,5,4,2,6,8,3,1] => [[[[[.,.],.],.],[[.,[.,.]],.]],.] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 4

[8,2,6,4,1,7,3,5] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[7,3,8,4,5,2,1,6] => [[[[.,.],[[.,.],[.,.]]],.],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 2

[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

[8,7,2,1,5,3,4,6] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 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] => 0

[8,3,6,4,5,1,7,2] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[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

[6,4,7,2,3,5,8,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2

[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

[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

[6,5,1,8,4,7,3,2] => [[[.,.],.],[[[[.,.],[.,.]],.],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 2

[5,3,1,8,4,7,6,2] => [[[.,.],.],[[[.,.],[[.,.],.]],.]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 2

[8,2,7,4,6,1,3,5] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[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

[6,3,1,4,7,2,8,5] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[8,7,3,6,1,5,2,4] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[7,4,3,6,8,2,5,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3

[7,8,2,5,4,3,1,6] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 0

[8,5,3,7,4,2,6,1] => [[[[[.,.],.],[[.,.],.]],[.,.]],.] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 3

[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

[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

[3,8,1,5,6,2,7,4] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[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

[7,1,5,2,8,6,4,3] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 1

[6,5,4,8,7,2,1,3] => [[[[[.,.],.],[[.,.],.]],.],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 3

[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

[4,7,2,6,5,8,1,3] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[6,8,1,4,2,7,3,5] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[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

[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

[3,2,5,7,6,1,8,4] => [[[.,.],[.,[[.,.],.]]],[[.,.],.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 1

[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

[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

[3,1,4,6,5,7,8,2] => [[.,.],[[.,[[.,.],[.,[.,.]]]],.]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 1

[5,1,3,6,4,8,7,2] => [[.,.],[[.,[[.,.],[[.,.],.]]],.]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 1

[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

[3,1,2,6,5,8,4,7] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 1

[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

[2,3,1,7,5,4,8,6] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[5,2,6,7,3,4,8,1] => [[[.,.],[[.,[.,.]],[.,[.,.]]]],.] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2

[5,2,4,7,6,3,8,1] => [[[.,.],[[.,[[.,.],.]],[.,.]]],.] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2

[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

[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

[2,6,1,4,5,8,7,3] => [[.,[.,.]],[[.,[.,[[.,.],.]]],.]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 0

[5,4,2,7,6,3,8,1] => [[[[.,.],.],[[[.,.],.],[.,.]]],.] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 3

[2,6,1,7,5,8,3,4] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[2,6,1,7,4,8,5,3] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 0

[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

[2,6,1,7,4,8,3,5] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[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

[2,6,1,5,4,8,7,3] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 0

[2,6,1,4,7,8,5,3] => [[.,[.,.]],[[.,[[.,[.,.]],.]],.]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 0

[5,1,2,4,8,6,7,3] => [[.,.],[.,[[.,[[.,.],[.,.]]],.]]] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 1

[5,1,2,4,8,7,3,6] => [[.,.],[.,[[.,[[.,.],.]],[.,.]]]] => [1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 1

[5,1,2,4,8,7,6,3] => [[.,.],[.,[[.,[[[.,.],.],.]],.]]] => [1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 1

[4,3,1,2,8,5,7,6] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2

[2,1,5,3,8,6,4,7] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1

[2,6,1,5,4,8,3,7] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[5,1,2,4,8,6,3,7] => [[.,.],[.,[[.,[[.,.],.]],[.,.]]]] => [1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 1

[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

[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

[5,4,6,3,1,8,7,2] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 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

[5,1,6,2,8,7,3,4] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1

[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

[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

[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

[4,3,1,2,8,6,7,5] => [[[.,.],.],[.,[[[.,.],[.,.]],.]]] => [1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2

[5,1,4,2,8,6,7,3] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1

[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

[2,1,3,6,8,7,4,5] => [[.,.],[.,[[.,[[.,.],.]],[.,.]]]] => [1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 1

[5,4,1,2,8,7,6,3] => [[[.,.],.],[.,[[[[.,.],.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 2

[3,1,6,2,8,7,5,4] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 1

[8,4,7,6,5,3,2,1] => [[[[[.,.],[[[.,.],.],.]],.],.],.] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 4

[8,4,7,5,6,3,2,1] => [[[[[.,.],[[.,.],[.,.]]],.],.],.] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4

[8,5,7,4,6,3,2,1] => [[[[[[.,.],[.,.]],[.,.]],.],.],.] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[8,7,6,3,5,4,2,1] => [[[[[[.,.],.],.],[[.,.],.]],.],.] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 5

[8,6,7,3,5,4,2,1] => [[[[[.,.],[.,.]],[[.,.],.]],.],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 3

[8,5,7,3,6,4,2,1] => [[[[[.,.],[.,.]],[[.,.],.]],.],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 3

[8,1,7,4,6,5,3,2] => [[.,.],[[[[.,.],[[.,.],.]],.],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 1

[8,1,7,3,6,5,4,2] => [[.,.],[[[.,.],[[[.,.],.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 1

[8,2,7,3,6,5,4,1] => [[[.,.],[[.,.],[[[.,.],.],.]]],.] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 2

[8,3,7,2,6,5,4,1] => [[[[.,.],[.,.]],[[[.,.],.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 2

[8,5,7,2,6,4,3,1] => [[[[.,.],[.,.]],[[[.,.],.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 2

[8,6,7,2,5,4,3,1] => [[[[.,.],[.,.]],[[[.,.],.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 2

[8,7,6,2,5,4,3,1] => [[[[[.,.],.],.],[[[.,.],.],.]],.] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 4

[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

[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

[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

[8,1,7,2,6,5,4,3] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 1

[8,7,6,2,5,3,4,1] => [[[[[.,.],.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 4

[8,1,7,6,5,3,4,2] => [[.,.],[[[[[.,.],.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 1

[8,3,7,6,5,2,4,1] => [[[[.,.],[[[.,.],.],.]],[.,.]],.] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 2

[8,4,7,6,5,2,3,1] => [[[[.,.],[[[.,.],.],.]],[.,.]],.] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 2

[8,5,7,6,4,2,3,1] => [[[[[.,.],[[.,.],.]],.],[.,.]],.] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 3

[8,6,7,5,4,1,3,2] => [[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 3

[8,5,7,6,4,1,3,2] => [[[[.,.],[[.,.],.]],.],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2

[8,3,7,6,5,1,4,2] => [[[.,.],[[[.,.],.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 1

[8,7,6,4,5,1,3,2] => [[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3

[8,7,6,2,5,1,4,3] => [[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3

[8,7,6,1,5,2,4,3] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3

[6,8,1,3,2,5,4,7] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[6,8,1,4,2,5,3,7] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[7,8,3,6,1,4,2,5] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[7,8,2,5,3,6,1,4] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[7,8,2,5,1,4,3,6] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[7,8,1,4,3,6,2,5] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[5,8,1,4,3,7,2,6] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[6,8,2,5,1,4,3,7] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[6,8,2,5,3,7,1,4] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[6,8,2,5,4,7,1,3] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[2,5,1,4,3,7,6,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[2,6,1,4,3,7,5,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[2,6,1,5,3,7,4,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[5,8,3,6,4,7,1,2] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[5,8,2,6,4,7,1,3] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[4,8,2,6,3,7,1,5] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[4,8,1,5,3,7,2,6] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[4,8,1,5,2,6,3,7] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[4,8,3,7,1,5,2,6] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[6,8,3,7,1,4,2,5] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[5,8,1,3,2,6,4,7] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[5,8,4,7,1,3,2,6] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[6,8,4,7,1,3,2,5] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[6,8,5,7,1,3,2,4] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[4,7,1,3,2,6,5,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[3,7,1,4,2,6,5,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[3,7,1,5,2,6,4,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[3,7,2,6,1,5,4,8] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[3,7,2,6,5,8,1,4] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[4,7,3,6,5,8,1,2] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[7,6,4,2,8,5,3,1] => [[[[[.,.],.],.],[[[.,.],.],.]],.] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 4

[6,8,4,3,7,2,1,5] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 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

[6,7,3,5,4,8,2,1] => [[[[.,[.,.]],[[.,.],[.,.]]],.],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 2

[7,6,8,3,5,2,4,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[7,6,3,5,8,2,4,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3

[7,6,4,2,5,1,8,3] => [[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3

[7,6,3,8,2,4,1,5] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[6,3,4,8,7,2,5,1] => [[[[.,.],[.,[[.,.],.]]],[.,.]],.] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 2

[6,3,8,4,7,2,1,5] => [[[[.,.],[[.,.],[.,.]]],.],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 2

[6,2,8,4,1,7,5,3] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[6,2,7,4,1,5,3,8] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[6,3,4,7,5,8,2,1] => [[[[.,.],[.,[[.,.],[.,.]]]],.],.] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 3

[6,3,5,7,8,4,2,1] => [[[[.,.],[[.,[.,[.,.]]],.]],.],.] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 3

[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

[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

[5,3,4,8,2,7,6,1] => [[[[.,.],[.,[.,.]]],[[.,.],.]],.] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 2

[6,4,3,5,8,2,1,7] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3

[6,3,5,8,7,2,4,1] => [[[[.,.],[.,[[.,.],.]]],[.,.]],.] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 2

[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

[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

[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

[6,4,5,3,8,2,1,7] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 2

[6,4,8,5,3,7,2,1] => [[[[[.,.],[[.,.],.]],[.,.]],.],.] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[6,4,3,8,5,7,2,1] => [[[[[.,.],.],[[.,.],[.,.]]],.],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 4

[6,4,2,8,5,3,1,7] => [[[[.,.],.],[[[.,.],.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 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

[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

[6,4,2,5,1,7,3,8] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 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

[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

[5,3,6,8,2,1,4,7] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2

[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

[4,6,3,5,7,8,2,1] => [[[[.,[.,.]],[.,[.,[.,.]]]],.],.] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 2

[5,7,4,8,6,3,2,1] => [[[[[.,[.,.]],[[.,.],.]],.],.],.] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 3

[3,2,6,5,1,8,7,4] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[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

[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

[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

[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

[7,4,1,6,2,8,3,5] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[8,4,1,7,2,6,3,5] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[8,1,4,7,5,2,3,6] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 1

[8,1,5,4,7,2,3,6] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[2,1,7,5,8,3,4,6] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[7,1,5,4,8,2,3,6] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[7,1,4,8,5,2,3,6] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 1

[6,4,1,7,2,3,8,5] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2

[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

[8,7,1,6,4,2,3,5] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[8,6,1,7,4,2,3,5] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[7,6,1,8,4,2,3,5] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[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

[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

[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

[8,3,7,5,1,2,4,6] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1

[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

[6,7,1,8,4,2,3,5] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0

[6,8,1,7,4,2,3,5] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0

[7,1,8,5,4,2,3,6] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 1

[7,1,8,4,5,2,3,6] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[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

[7,6,3,1,2,4,8,5] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3

[6,1,2,3,8,7,5,4] => [[.,.],[.,[.,[[[[.,.],.],.],.]]]] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1

[6,8,1,4,2,3,7,5] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0

[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

[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

[6,7,1,4,2,3,8,5] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0

[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

[6,1,2,5,4,8,3,7] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 1

[7,2,1,5,8,3,4,6] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 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] => 0

[5,7,1,6,8,4,3,2] => [[.,[.,.]],[[[[.,[.,.]],.],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 0

[4,8,1,2,5,7,3,6] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 0

[8,3,6,4,7,2,5,1] => [[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[8,2,6,7,5,4,3,1] => [[[.,.],[[[[.,[.,.]],.],.],.]],.] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 2

[3,4,2,7,8,1,6,5] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0

[6,5,8,7,1,4,2,3] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[4,1,7,3,8,5,2,6] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1

[3,6,1,4,5,8,2,7] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 0

[6,1,7,3,5,4,8,2] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 1

[6,8,5,7,1,2,4,3] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 0

[8,2,4,3,7,5,6,1] => [[[.,.],[[.,.],[[.,.],[.,.]]]],.] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 2

[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

[7,2,8,4,1,6,3,5] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[4,8,2,5,7,1,6,3] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0

[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

[5,2,6,4,8,3,1,7] => [[[.,.],[[[.,.],[.,.]],.]],[.,.]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1

[6,7,1,3,4,5,8,2] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 0

[6,3,4,2,8,7,5,1] => [[[[.,.],[.,.]],[[[.,.],.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 2

[4,3,8,7,5,2,6,1] => [[[[.,.],[[[.,.],.],.]],[.,.]],.] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 2

[6,8,7,4,2,3,5,1] => [[[[.,[[.,.],.]],.],[.,[.,.]]],.] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2

[8,6,1,3,5,4,2,7] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 2

[5,3,8,6,1,2,4,7] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1

[6,3,5,4,8,7,2,1] => [[[[.,.],[[.,.],[[.,.],.]]],.],.] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 3

[4,3,8,6,1,5,2,7] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[7,5,2,6,8,1,4,3] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[8,5,2,7,1,4,3,6] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[5,1,7,2,4,3,8,6] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[5,4,1,3,8,6,2,7] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 2

[5,1,8,6,3,4,2,7] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 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

[8,2,3,7,6,4,5,1] => [[[.,.],[.,[[[.,.],.],[.,.]]]],.] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 2

[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

[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

[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

[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

[8,2,1,3,5,6,7,4] => [[[.,.],.],[.,[[.,[.,[.,.]]],.]]] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[6,3,1,4,7,5,8,2] => [[[.,.],.],[[.,[[.,.],[.,.]]],.]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 2

[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

[3,1,7,2,8,5,4,6] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1

[3,6,1,4,7,2,8,5] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[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

[6,2,7,4,5,8,1,3] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[2,1,8,4,5,7,3,6] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[2,1,8,5,4,3,6,7] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 1

[7,4,8,6,2,3,1,5] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[2,7,1,4,6,3,8,5] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[7,1,3,2,8,5,4,6] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1

[5,1,7,4,2,3,8,6] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1

[4,1,8,6,5,3,2,7] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 1

[7,2,8,5,3,6,4,1] => [[[.,.],[[[.,.],.],[[.,.],.]]],.] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 2

[5,2,8,4,3,7,6,1] => [[[.,.],[[[.,.],.],[[.,.],.]]],.] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 2

[8,4,7,5,2,3,6,1] => [[[[.,.],[[.,.],.]],[.,[.,.]]],.] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 2

[7,5,2,8,4,6,1,3] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 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] => 2

[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

[5,2,6,8,3,4,7,1] => [[[.,.],[[.,[.,.]],[.,[.,.]]]],.] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2

[7,6,2,4,5,8,3,1] => [[[[.,.],.],[[.,[.,[.,.]]],.]],.] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[7,6,3,8,4,2,5,1] => [[[[[.,.],.],[[.,.],.]],[.,.]],.] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 3

[7,2,3,6,5,8,4,1] => [[[.,.],[.,[[[.,.],[.,.]],.]]],.] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 2

[6,2,7,5,8,3,1,4] => [[[.,.],[[[.,.],[.,.]],.]],[.,.]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 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

[5,8,1,2,6,4,7,3] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 0

[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

[7,5,1,2,8,4,6,3] => [[[.,.],.],[.,[[[.,.],[.,.]],.]]] => [1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 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] => 2

[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

[6,4,5,8,2,7,3,1] => [[[[.,.],[.,[.,.]]],[[.,.],.]],.] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 2

[5,7,3,6,4,8,2,1] => [[[[.,[.,.]],[[.,.],[.,.]]],.],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 2

[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

[3,5,1,6,4,7,8,2] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 0

[4,6,1,7,5,8,2,3] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[3,1,5,7,6,8,4,2] => [[.,.],[[[.,[[.,.],[.,.]]],.],.]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 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

[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

[5,7,1,2,8,6,4,3] => [[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => 0

[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

[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

[3,2,7,4,6,8,1,5] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[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

[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

[7,6,2,4,5,8,1,3] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2

[6,5,2,3,4,8,1,7] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2

[5,3,1,2,8,4,7,6] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2

[6,5,2,3,7,1,4,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[5,2,1,7,3,4,6,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2

[5,2,1,8,3,4,6,7] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2

[6,3,2,8,4,5,7,1] => [[[[.,.],.],[[.,.],[.,[.,.]]]],.] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 3

[7,3,1,2,8,4,6,5] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2

[6,4,1,3,8,5,7,2] => [[[.,.],.],[[.,[[.,.],[.,.]]],.]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 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

[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

[8,6,2,4,7,1,5,3] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[8,5,2,3,6,1,4,7] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[8,2,1,7,3,4,5,6] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2

[8,6,3,7,2,4,5,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3

[7,1,6,2,3,4,5,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1

[8,2,7,3,4,5,6,1] => [[[.,.],[[.,.],[.,[.,[.,.]]]]],.] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 2

[8,1,6,2,3,4,5,7] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1

[8,1,7,3,4,5,6,2] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 1

[8,6,1,7,2,4,5,3] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[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

[7,2,1,8,3,4,5,6] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2

[7,3,8,2,4,5,6,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2

[7,2,8,3,4,5,6,1] => [[[.,.],[[.,.],[.,[.,[.,.]]]]],.] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 2

[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

[4,7,1,3,8,5,6,2] => [[.,[.,.]],[[.,[[.,.],[.,.]]],.]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 0

[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

[5,3,4,6,8,2,7,1] => [[[[.,.],[.,[.,[.,.]]]],[.,.]],.] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2

[4,6,3,8,7,1,2,5] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 0

[6,4,5,8,7,1,2,3] => [[[.,.],[.,[[.,.],.]]],[.,[.,.]]] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 1

[5,3,4,8,7,1,2,6] => [[[.,.],[.,[[.,.],.]]],[.,[.,.]]] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 1

[3,2,8,7,1,4,6,5] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 1

[3,1,8,7,2,4,6,5] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1

[5,3,7,6,1,2,4,8] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1

[3,8,1,7,2,4,5,6] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0

[6,8,2,3,5,1,4,7] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[6,2,8,7,1,4,5,3] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 1

[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

[8,7,6,1,3,4,5,2] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 3

[3,6,2,4,7,1,8,5] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0

[2,1,6,4,8,5,3,7] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1

[4,1,8,5,3,2,7,6] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 1

[3,6,2,5,7,1,4,8] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[6,1,3,2,8,5,4,7] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1

[5,6,1,2,8,4,3,7] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 0

[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

[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

[3,4,1,6,5,8,7,2] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 0

[3,5,1,2,4,8,7,6] => [[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 0

[3,7,5,2,1,4,6,8] => [[[.,[[.,.],.]],.],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1

[5,2,8,4,7,3,1,6] => [[[.,.],[[[.,.],[.,.]],.]],[.,.]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1

[5,2,7,4,1,3,6,8] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1

[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

[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

[8,4,7,5,2,1,6,3] => [[[[.,.],[[.,.],.]],.],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2

[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

[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

[6,1,4,8,7,3,2,5] => [[.,.],[[[.,[[.,.],.]],.],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 1

[6,4,8,5,7,1,2,3] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[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

[5,4,7,6,3,8,1,2] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[4,6,3,7,5,8,1,2] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[4,1,3,5,8,6,2,7] => [[.,.],[[.,[.,[[.,.],.]]],[.,.]]] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 1

[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

[4,3,8,2,1,6,5,7] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2

[3,1,2,5,7,6,4,8] => [[.,.],[.,[[.,[[.,.],.]],[.,.]]]] => [1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 1

[3,8,1,6,7,5,4,2] => [[.,[.,.]],[[[[.,[.,.]],.],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 0

[3,7,2,6,8,5,1,4] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 0

[7,2,3,8,5,6,1,4] => [[[.,.],[.,[[.,.],[.,.]]]],[.,.]] => [1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1

[8,2,1,7,5,6,4,3] => [[[.,.],.],[[[[.,.],[.,.]],.],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 2

[8,1,3,6,5,7,4,2] => [[.,.],[[.,[[[.,.],[.,.]],.]],.]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 1

[8,2,4,3,6,1,5,7] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[7,8,5,4,3,1,6,2] => [[[[[.,[.,.]],.],.],.],[[.,.],.]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 3

[7,1,6,3,4,2,5,8] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[3,6,1,4,2,7,5,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[3,4,1,8,5,7,6,2] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 0

[8,1,7,6,2,4,3,5] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[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

[8,6,5,4,7,1,3,2] => [[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3

[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

[7,4,1,6,5,8,3,2] => [[[.,.],.],[[[[.,.],[.,.]],.],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 2

[4,1,5,8,7,6,3,2] => [[.,.],[[[.,[[[.,.],.],.]],.],.]] => [1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 1

[4,2,1,5,8,7,3,6] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 2

[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

[3,1,5,7,6,8,2,4] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 1

[8,6,2,5,4,1,7,3] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[3,7,2,6,5,4,1,8] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 0

[7,6,2,5,4,3,1,8] => [[[[.,.],.],[[[.,.],.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 2

[3,2,6,4,7,5,1,8] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[6,2,3,7,5,4,1,8] => [[[.,.],[.,[[[.,.],.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 1

[8,7,2,5,1,6,4,3] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 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] => 0

[7,8,2,5,4,1,6,3] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[4,5,1,3,7,2,8,6] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[6,1,3,7,5,2,8,4] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 1

[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

[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

[7,1,8,2,6,5,4,3] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 1

[3,1,8,6,2,7,5,4] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 1

[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

[5,6,1,8,2,7,4,3] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 0

[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

[3,2,8,6,1,7,5,4] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[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

[5,6,3,8,4,1,7,2] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[7,3,8,5,4,1,6,2] => [[[.,.],[[[.,.],.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 1

[8,3,7,5,1,6,4,2] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[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

[5,6,4,7,8,1,3,2] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0

[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

[7,2,1,6,3,8,5,4] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 2

[2,3,1,7,6,4,8,5] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[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

[3,7,1,6,2,8,5,4] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 0

[7,6,1,2,8,5,4,3] => [[[.,.],.],[.,[[[[.,.],.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 2

[2,7,1,3,8,6,5,4] => [[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => 0

[8,6,1,2,7,5,4,3] => [[[.,.],.],[.,[[[[.,.],.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 2

[8,7,1,2,6,5,4,3] => [[[.,.],.],[.,[[[[.,.],.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 2

[7,8,1,2,6,5,4,3] => [[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => 0

[3,8,1,6,2,7,5,4] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 0

[2,1,3,7,4,8,6,5] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 1

[4,2,7,3,6,8,1,5] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[5,3,6,4,2,8,1,7] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[4,1,5,3,8,2,7,6] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[5,2,6,4,7,3,1,8] => [[[.,.],[[[.,.],[.,.]],.]],[.,.]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1

[7,3,6,4,2,8,1,5] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[7,6,4,5,2,8,1,3] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[5,4,3,1,8,2,7,6] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3

[6,5,4,2,7,3,1,8] => [[[[[.,.],.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3

[5,4,1,7,2,6,3,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[5,4,1,8,3,2,6,7] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[6,5,2,8,3,4,7,1] => [[[[.,.],.],[[.,.],[.,[.,.]]]],.] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 3

[7,4,2,1,8,3,6,5] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3

[6,5,3,4,8,2,7,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3

[6,1,5,3,8,2,7,4] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[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

[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

[8,2,6,4,7,3,1,5] => [[[.,.],[[[.,.],[.,.]],.]],[.,.]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1

[8,6,2,5,7,4,1,3] => [[[[.,.],.],[[.,[.,.]],.]],[.,.]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 2

[8,5,3,2,6,4,1,7] => [[[[[.,.],.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3

[8,3,1,7,2,5,4,6] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[7,5,2,6,4,3,1,8] => [[[[.,.],.],[[[.,.],.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 2

[7,1,6,2,5,4,3,8] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1

[8,1,7,3,5,6,4,2] => [[.,.],[[[.,.],[[.,[.,.]],.]],.]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 1

[8,6,1,7,4,5,2,3] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 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

[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

[7,3,8,4,5,2,6,1] => [[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[7,2,8,5,3,4,6,1] => [[[.,.],[[[.,.],.],[.,[.,.]]]],.] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 2

[6,1,8,4,3,2,5,7] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 1

[6,1,7,4,2,5,3,8] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[2,6,1,7,3,5,4,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[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

[4,3,1,6,8,2,7,5] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[5,7,4,8,3,2,1,6] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 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

[5,2,8,7,3,4,1,6] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[6,4,7,5,3,2,1,8] => [[[[[.,.],[[.,.],.]],.],.],[.,.]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 3

[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

[6,8,2,4,7,5,1,3] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 0

[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

[7,2,8,6,3,5,1,4] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[6,8,1,7,2,5,4,3] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 0

[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

[7,1,8,6,5,2,3,4] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 1

[8,4,7,5,3,2,1,6] => [[[[[.,.],[[.,.],.]],.],.],[.,.]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 3

[8,7,2,5,4,3,1,6] => [[[[.,.],.],[[[.,.],.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 2

[6,8,3,2,5,4,7,1] => [[[[.,[.,.]],.],[[.,.],[.,.]]],.] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => 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

[6,2,1,8,5,4,7,3] => [[[.,.],.],[[[[.,.],.],[.,.]],.]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 2

[5,2,1,8,7,6,4,3] => [[[.,.],.],[[[[[.,.],.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2

[6,5,4,8,2,1,7,3] => [[[[[.,.],.],[.,.]],.],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 3

[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

[5,8,3,2,7,6,4,1] => [[[[.,[.,.]],.],[[[.,.],.],.]],.] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 2

[5,2,1,4,3,6,7,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2

[4,2,1,6,5,3,7,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[4,2,1,5,7,6,3,8] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 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

[2,1,7,3,8,4,6,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[4,1,8,2,7,3,6,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[4,1,7,2,8,3,6,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[7,1,3,2,8,4,6,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[7,1,8,2,4,3,6,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[8,1,7,2,5,3,6,4] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[7,1,5,2,8,3,6,4] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[5,1,7,2,8,3,6,4] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[5,1,8,2,7,3,6,4] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[5,1,8,2,4,3,7,6] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[8,1,6,2,4,3,7,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[6,1,8,2,4,3,7,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[6,1,8,2,5,3,7,4] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[8,1,6,2,5,3,7,4] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[8,1,6,2,7,3,5,4] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[6,1,8,2,7,3,5,4] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[6,1,7,2,8,3,5,4] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[6,1,7,2,5,3,8,4] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[6,1,7,2,4,3,8,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[5,1,6,2,4,3,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[7,1,5,2,4,3,8,6] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[7,1,6,2,4,3,8,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[7,1,6,2,5,3,8,4] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[7,1,6,2,8,3,5,4] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[7,1,8,2,6,3,5,4] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1

[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

[7,5,8,3,2,4,1,6] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 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] => 2

[7,5,4,8,2,3,6,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3

[5,1,7,4,2,6,8,3] => [[.,.],[[[.,.],.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 1

[4,1,6,3,2,5,8,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1

[6,5,4,3,7,1,8,2] => [[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3

[6,5,1,7,3,8,2,4] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[6,3,2,8,5,7,1,4] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2

[6,5,4,3,8,2,7,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 4

[6,5,4,3,8,7,1,2] => [[[[[.,.],.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3

[7,6,3,8,5,4,1,2] => [[[[.,.],.],[[[.,.],.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 2

[5,4,8,2,1,7,3,6] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2

[6,4,2,8,5,1,3,7] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[7,6,4,8,5,1,2,3] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[7,2,8,6,3,1,4,5] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 1

[7,2,8,6,1,5,3,4] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[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

[6,4,1,7,8,2,3,5] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[4,1,5,3,2,8,6,7] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[6,3,1,7,8,5,2,4] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 2

[5,4,3,1,6,7,2,8] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3

[6,5,4,2,7,8,3,1] => [[[[[.,.],.],.],[[.,[.,.]],.]],.] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 4

[4,3,1,5,2,6,8,7] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2

[5,4,2,1,6,7,8,3] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 3

[5,4,3,1,6,7,8,2] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 3

[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

[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

[7,8,1,3,2,4,6,5] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0

[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

[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

[6,2,8,3,1,7,4,5] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[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

[4,3,1,2,7,8,6,5] => [[[.,.],.],[.,[[[.,[.,.]],.],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 2

[5,1,2,7,3,6,4,8] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 1

[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

[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

[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

[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

[4,2,5,7,6,1,8,3] => [[[.,.],[.,[[.,.],.]]],[[.,.],.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 1

[4,5,2,8,6,1,7,3] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[5,3,1,8,2,6,7,4] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[6,1,8,3,2,4,7,5] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1

[4,3,5,7,6,8,1,2] => [[[.,.],[.,[[.,.],[.,.]]]],[.,.]] => [1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1

[4,1,5,7,6,2,3,8] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 1

[4,5,1,8,6,2,3,7] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0

[5,2,1,8,3,6,4,7] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[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

[7,6,5,4,2,1,8,3] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5

[7,6,5,4,8,1,3,2] => [[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3

[7,6,5,8,2,1,4,3] => [[[[[.,.],.],[.,.]],.],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 3

[8,5,4,3,2,1,7,6] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5

[7,6,5,4,1,8,3,2] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4

[7,6,5,2,8,1,4,3] => [[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3

[7,6,5,8,4,1,3,2] => [[[[[.,.],.],[.,.]],.],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 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] => 3

[7,8,6,3,2,1,5,4] => [[[[[.,[.,.]],.],.],.],[[.,.],.]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 3

[8,7,4,3,2,1,6,5] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5

[7,8,1,3,2,4,5,6] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0

[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

[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

[3,5,2,6,1,4,7,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0

[6,2,7,4,5,1,3,8] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[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

[6,1,7,3,2,4,5,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1

[7,3,2,5,4,1,6,8] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[7,3,5,4,2,1,6,8] => [[[[.,.],[[.,.],.]],.],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 2

[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

[7,6,5,2,1,4,3,8] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4

[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

[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

[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

[7,3,2,5,1,6,4,8] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[7,6,5,4,1,3,2,8] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4

[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

[4,3,1,7,2,6,8,5] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[5,6,1,4,7,3,8,2] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 0

[5,3,2,1,7,4,8,6] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3

[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

[3,1,2,5,6,8,7,4] => [[.,.],[.,[[.,[.,[[.,.],.]]],.]]] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 1

[4,3,2,5,6,8,1,7] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2

[3,1,4,6,5,8,2,7] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 1

[3,1,4,6,5,8,7,2] => [[.,.],[[.,[[.,.],[[.,.],.]]],.]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 1

[5,6,1,4,7,2,8,3] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[4,3,1,7,5,6,8,2] => [[[.,.],.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[4,3,1,7,6,5,8,2] => [[[.,.],.],[[[[.,.],.],[.,.]],.]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 2

[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

[5,6,1,2,7,4,8,3] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 0

[6,3,5,2,4,7,8,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2

[5,3,2,1,4,7,8,6] => [[[[.,.],.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 3

[5,3,1,4,2,7,8,6] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[5,3,1,2,4,7,8,6] => [[[.,.],.],[.,[.,[[.,[.,.]],.]]]] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[7,1,5,2,6,8,4,3] => [[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 1

[7,1,5,2,6,8,3,4] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[4,3,2,6,7,1,8,5] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[7,3,2,5,6,8,1,4] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2

[7,1,5,4,6,8,2,3] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[7,3,4,5,8,6,1,2] => [[[.,.],[.,[.,[[.,.],.]]]],[.,.]] => [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 1

[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

[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

[6,3,4,5,8,2,1,7] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 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] => 2

[7,3,4,5,8,6,2,1] => [[[[.,.],[.,[.,[[.,.],.]]]],.],.] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 3

[7,1,5,4,6,8,3,2] => [[.,.],[[[[.,.],[.,[.,.]]],.],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 1

[7,3,2,5,6,8,4,1] => [[[[.,.],.],[[.,[.,[.,.]]],.]],.] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[5,7,4,6,1,8,3,2] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 0

[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

[7,3,4,5,8,2,1,6] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 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] => 2

[7,6,4,2,8,3,5,1] => [[[[[.,.],.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 4

[8,6,4,2,7,5,3,1] => [[[[[.,.],.],.],[[[.,.],.],.]],.] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 4

[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

[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

[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

[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

[6,2,1,7,3,5,4,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[2,1,8,6,3,5,4,7] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[2,1,7,3,5,8,6,4] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 1

[4,2,1,8,3,6,7,5] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[2,1,8,6,3,5,7,4] => [[.,.],[[[.,.],.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 1

[6,2,1,7,3,5,8,4] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[3,2,1,6,4,5,7,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2

[3,2,1,5,7,8,4,6] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 2

[2,1,7,3,6,8,4,5] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[4,3,7,5,6,1,8,2] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[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

[2,6,1,8,3,5,7,4] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 0

[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

[2,1,8,3,5,7,4,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[3,2,1,5,6,8,4,7] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 2

[3,2,1,5,7,4,6,8] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[2,1,7,3,6,4,5,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[2,1,6,3,5,8,4,7] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[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

[8,4,3,6,1,7,5,2] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2

[8,2,1,7,3,5,4,6] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 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] => 0

[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

[5,8,6,3,1,7,4,2] => [[[.,[[.,.],.]],.],[[[.,.],.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1

[6,2,1,7,3,4,8,5] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2

[6,2,1,7,8,3,5,4] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[2,7,1,8,3,5,6,4] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 0

[2,1,8,3,6,4,5,7] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[3,2,1,6,7,4,5,8] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[3,2,1,7,4,5,6,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2

[3,2,1,6,8,4,5,7] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[2,1,8,3,7,4,5,6] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[2,1,8,3,6,7,4,5] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[4,3,8,5,6,1,7,2] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[3,2,1,8,4,5,6,7] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2

[3,8,1,5,7,2,4,6] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[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

[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

[5,3,8,4,7,6,1,2] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[8,7,1,2,5,4,6,3] => [[[.,.],.],[.,[[[.,.],[.,.]],.]]] => [1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 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] => 0

[6,1,2,8,7,4,5,3] => [[.,.],[.,[[[[.,.],.],[.,.]],.]]] => [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 1

[7,1,6,2,8,4,5,3] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1

[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

[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

[8,5,1,7,2,4,6,3] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[5,3,8,7,4,6,1,2] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[6,1,8,2,7,4,5,3] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1

[7,1,6,3,2,5,4,8] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[7,4,2,1,6,5,3,8] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[7,6,1,4,3,5,2,8] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[7,4,1,3,5,2,6,8] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[7,3,1,2,4,6,5,8] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 2

[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

[3,1,7,2,4,6,8,5] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 1

[4,3,2,7,1,5,8,6] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[3,1,2,8,6,5,4,7] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 1

[5,4,8,6,1,2,3,7] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1

[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

[6,4,8,5,3,1,7,2] => [[[[.,.],[[.,.],.]],.],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2

[3,1,2,8,6,4,7,5] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 1

[5,3,2,6,4,8,1,7] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2

[4,1,6,3,5,8,2,7] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[4,1,2,7,6,5,8,3] => [[.,.],[.,[[[[.,.],.],[.,.]],.]]] => [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 1

[2,4,1,6,7,8,5,3] => [[.,[.,.]],[[[.,[.,[.,.]]],.],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 0

[5,3,2,1,4,8,6,7] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3

[5,3,1,4,2,8,6,7] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[7,6,1,3,8,5,4,2] => [[[.,.],.],[[.,[[[.,.],.],.]],.]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 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] => 0

[3,1,6,4,8,2,5,7] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[7,3,2,6,8,5,1,4] => [[[[.,.],.],[[.,[.,.]],.]],[.,.]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 2

[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

[7,5,2,8,4,1,6,3] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 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] => 2

[6,4,2,8,3,5,1,7] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2

[6,3,4,8,2,5,7,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[7,5,4,8,3,6,2,1] => [[[[[[.,.],.],[.,.]],[.,.]],.],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 4

[7,1,5,4,8,3,6,2] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 1

[7,3,2,5,8,4,6,1] => [[[[.,.],.],[[.,[.,.]],[.,.]]],.] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 3

[8,4,6,3,7,2,5,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[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

[8,4,6,2,7,5,3,1] => [[[[.,.],[.,.]],[[[.,.],.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 2

[8,5,6,7,2,4,3,1] => [[[[.,.],[.,[.,.]]],[[.,.],.]],.] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 2

[6,5,7,8,4,1,3,2] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 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

[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

[4,3,2,6,8,5,1,7] => [[[[.,.],.],[[.,[.,.]],.]],[.,.]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 2

[6,5,7,8,3,1,4,2] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 2

[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

[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

[7,4,6,3,8,2,1,5] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 2

[6,3,2,5,4,8,1,7] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 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

[6,4,5,3,2,8,1,7] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 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] => 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

[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

[5,3,2,6,8,4,1,7] => [[[[.,.],.],[[.,[.,.]],.]],[.,.]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 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

[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

[5,3,2,7,8,1,6,4] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[4,3,2,7,8,1,6,5] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 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

[4,2,8,6,1,5,3,7] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[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

[2,7,1,3,5,4,8,6] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 0

[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

[7,2,1,3,5,8,6,4] => [[[.,.],.],[.,[[.,[[.,.],.]],.]]] => [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 2

[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

[8,3,1,6,2,5,7,4] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[4,8,6,2,1,5,7,3] => [[[.,[[.,.],.]],.],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 1

[4,8,3,6,5,1,7,2] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[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

[6,4,7,5,1,8,2,3] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[3,6,1,7,5,8,2,4] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[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

[4,7,3,5,6,1,8,2] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0

[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

[2,6,1,3,5,8,4,7] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 0

[7,3,2,5,6,1,4,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[4,6,2,8,1,5,3,7] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[8,4,1,2,7,5,3,6] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 2

[8,5,1,2,6,3,4,7] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2

[6,2,1,7,8,5,3,4] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 2

[6,7,3,8,4,1,5,2] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[2,7,1,8,5,6,3,4] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[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

[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

[4,2,8,3,7,1,6,5] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[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

[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

[7,6,3,4,8,5,1,2] => [[[[.,.],.],[.,[[.,.],.]]],[.,.]] => [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 2

[7,6,3,5,8,4,1,2] => [[[[.,.],.],[[.,[.,.]],.]],[.,.]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 2

[7,6,3,8,4,5,1,2] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2

[7,2,3,8,5,1,4,6] => [[[.,.],[.,[[.,.],.]]],[.,[.,.]]] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 1

[7,2,3,8,5,1,6,4] => [[[.,.],[.,[[.,.],.]]],[[.,.],.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 1

[7,2,3,8,4,1,5,6] => [[[.,.],[.,[[.,.],.]]],[.,[.,.]]] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 1

[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

[7,8,2,3,6,1,4,5] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[7,8,2,3,6,1,5,4] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0

[4,2,6,3,7,1,5,8] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[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

[7,2,3,8,4,1,6,5] => [[[.,.],[.,[[.,.],.]]],[[.,.],.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 1

[7,6,5,1,2,3,8,4] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3

[7,6,5,1,4,2,8,3] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3

[7,8,5,4,1,2,6,3] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => 2

[7,6,5,1,4,2,3,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[7,6,5,1,2,4,3,8] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3

[7,6,5,1,2,4,8,3] => [[[[.,.],.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 3

[7,6,5,1,3,2,8,4] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3

[7,6,5,1,3,2,4,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[7,6,5,1,3,4,2,8] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 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

[4,2,8,3,6,1,7,5] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[3,6,4,2,1,7,8,5] => [[[.,[[.,.],.]],.],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 1

[3,6,4,2,1,7,5,8] => [[[.,[[.,.],.]],.],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[7,6,5,1,4,3,8,2] => [[[[.,.],.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 3

[7,6,5,1,2,8,4,3] => [[[[.,.],.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 3

[7,6,5,1,2,8,3,4] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3

[7,6,5,1,8,2,4,3] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3

[7,6,5,1,8,2,3,4] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[7,6,5,1,8,3,2,4] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[7,6,5,1,4,8,2,3] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3

[7,8,5,4,1,6,3,2] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 2

[7,6,5,1,4,8,3,2] => [[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[7,6,5,1,8,3,4,2] => [[[[.,.],.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 3

[7,6,5,1,8,4,2,3] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[4,1,7,6,2,8,5,3] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 1

[7,8,6,2,1,3,5,4] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => 2

[4,6,1,5,3,2,8,7] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[3,6,1,4,2,5,8,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0

[8,7,1,6,5,2,4,3] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 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

[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

[8,4,1,6,5,7,3,2] => [[[.,.],.],[[[[.,.],[.,.]],.],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 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

[8,2,6,4,7,3,5,1] => [[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2

[8,7,3,2,1,5,4,6] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4

[2,5,1,8,7,4,6,3] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 0

[3,7,1,8,4,5,6,2] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 0

[6,2,3,8,4,7,5,1] => [[[.,.],[.,[[.,.],[[.,.],.]]]],.] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 2

[8,6,4,3,1,7,2,5] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4

[8,3,7,4,6,1,2,5] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[7,1,3,8,6,4,5,2] => [[.,.],[[.,[[[.,.],.],[.,.]]],.]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 1

[7,4,2,1,8,6,5,3] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3

[7,6,2,5,3,8,1,4] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2

[6,2,1,3,4,8,7,5] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 2

[6,5,4,2,8,3,1,7] => [[[[[.,.],.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3

[5,4,3,1,8,7,2,6] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[6,1,4,3,8,5,2,7] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 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

[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

[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

[6,4,5,8,3,1,2,7] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2

[8,1,3,2,5,6,7,4] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 1

[3,2,8,7,4,5,1,6] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[6,3,8,5,7,4,2,1] => [[[[.,.],[[[.,.],[.,.]],.]],.],.] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 3

[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

[2,1,4,8,7,5,3,6] => [[.,.],[[.,[[[.,.],.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 1

[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

[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

[6,5,3,4,8,1,7,2] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[8,4,3,2,5,1,7,6] => [[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3

[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

[5,1,8,2,6,4,3,7] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1

[7,4,8,6,2,1,3,5] => [[[[.,.],[[.,.],.]],.],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 2

[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

[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

[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

[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

[4,8,1,3,5,7,6,2] => [[.,[.,.]],[[.,[.,[[.,.],.]]],.]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 0

[3,8,1,4,5,6,2,7] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 0

[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

[5,3,8,7,6,1,4,2] => [[[.,.],[[[.,.],.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 1

[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

[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

[7,6,4,8,3,1,5,2] => [[[[[.,.],.],[.,.]],.],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 3

[7,4,8,5,6,1,3,2] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[7,4,2,5,6,3,1,8] => [[[[.,.],.],[[.,[.,.]],.]],[.,.]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 2

[4,2,7,5,6,3,1,8] => [[[.,.],[[[.,.],[.,.]],.]],[.,.]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1

[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

[3,7,2,5,6,4,1,8] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 0

[7,8,3,5,6,1,4,2] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0

[6,2,8,5,1,7,4,3] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[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

[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

[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

[4,1,8,5,6,3,2,7] => [[.,.],[[[[.,.],[.,.]],.],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 1

[6,1,8,5,3,7,4,2] => [[.,.],[[[[.,.],.],[[.,.],.]],.]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 1

[3,8,1,5,2,7,6,4] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 0

[8,2,1,5,3,7,6,4] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 2

[4,1,5,3,6,7,8,2] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 1

[8,1,6,5,3,7,2,4] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1

[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

[3,2,6,4,1,7,8,5] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 1

[7,6,4,3,1,2,8,5] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 4

[8,6,3,5,1,7,2,4] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[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

[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

[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

[8,4,6,5,1,7,2,3] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[7,5,4,6,1,2,8,3] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 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

[3,2,8,7,6,1,4,5] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 1

[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

[8,2,7,5,6,1,3,4] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[7,6,4,2,1,5,8,3] => [[[[[.,.],.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 4

[5,7,4,6,1,3,8,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0

[8,6,4,7,3,1,2,5] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3

[5,2,4,3,7,1,8,6] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[8,6,4,1,3,5,2,7] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3

[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

[7,5,4,1,2,6,8,3] => [[[[.,.],.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 3

[6,8,1,5,4,7,3,2] => [[.,[.,.]],[[[[.,.],[.,.]],.],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 0

[8,2,1,5,6,4,3,7] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 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] => 0

[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

[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

[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

[7,6,4,1,5,2,8,3] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3

[8,6,1,5,4,7,2,3] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 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] => 0

[5,2,1,4,6,7,8,3] => [[[.,.],.],[[.,[.,[.,[.,.]]]],.]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[5,4,1,3,6,7,8,2] => [[[.,.],.],[[.,[.,[.,[.,.]]]],.]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[8,4,1,5,3,7,2,6] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[7,5,4,1,3,2,8,6] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3

[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

[7,1,4,3,5,2,8,6] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[8,1,3,5,4,7,2,6] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 1

[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

[8,3,2,6,1,4,7,5] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 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] => 0

[2,7,1,6,4,8,3,5] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[2,7,1,6,5,3,8,4] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[2,8,1,7,6,5,4,3] => [[.,[.,.]],[[[[[.,.],.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 0

[8,3,2,7,1,6,5,4] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2

[4,1,8,7,3,2,6,5] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 1

[4,1,7,2,8,6,5,3] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 1

[3,7,1,8,6,5,4,2] => [[.,[.,.]],[[[[[.,.],.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 0

[7,3,5,8,2,1,4,6] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2

[7,3,6,2,1,4,5,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2

[7,4,2,8,1,6,5,3] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2

[8,7,5,3,2,1,6,4] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5

[7,5,2,6,3,1,4,8] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[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

[5,1,7,6,3,8,2,4] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1

[5,1,7,6,4,2,8,3] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 1

[5,1,8,7,6,4,3,2] => [[.,.],[[[[[[.,.],.],.],.],.],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1

[8,5,2,1,7,6,4,3] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3

[8,5,2,1,6,3,7,4] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3

[5,1,8,6,3,2,7,4] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 1

[8,4,2,5,7,3,1,6] => [[[[.,.],.],[[.,[.,.]],.]],[.,.]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 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] => 2

[5,4,8,7,3,6,1,2] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 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

[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

[6,5,2,7,1,3,8,4] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[8,6,5,4,2,1,7,3] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5

[6,4,7,3,1,8,2,5] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2

[7,5,8,4,6,3,2,1] => [[[[[[.,.],[.,.]],[.,.]],.],.],.] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4

[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

[7,6,3,8,5,1,4,2] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 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

[7,4,8,6,3,1,5,2] => [[[[.,.],[[.,.],.]],.],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2

[4,2,7,6,5,3,1,8] => [[[.,.],[[[[.,.],.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1

[3,7,2,4,6,5,1,8] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 0

[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

[6,2,8,4,1,5,7,3] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 1

[6,7,4,8,5,1,2,3] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 0

[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

[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

[6,1,4,8,5,3,7,2] => [[.,.],[[[.,[[.,.],.]],[.,.]],.]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 1

[6,1,8,4,3,7,2,5] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1

[3,7,1,4,2,5,8,6] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0

[7,2,1,4,3,5,6,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2

[4,1,5,3,6,8,2,7] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[6,1,8,5,3,2,7,4] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 1

[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

[3,2,6,4,1,8,7,5] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[7,6,4,3,1,8,2,5] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4

[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

[5,4,2,1,7,8,6,3] => [[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[8,2,7,6,5,1,3,4] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 1

[8,6,2,7,1,4,5,3] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[7,6,3,2,1,8,5,4] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4

[8,6,3,7,4,1,2,5] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 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

[8,6,3,1,4,5,7,2] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 3

[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

[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

[8,1,3,2,4,5,6,7] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1

[8,4,1,7,2,3,6,5] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2

[8,2,1,6,5,4,7,3] => [[[.,.],.],[[[[.,.],.],[.,.]],.]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 2

[3,8,1,5,6,4,7,2] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 0

[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

[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

[7,6,4,1,5,2,3,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[8,6,1,5,4,7,3,2] => [[[.,.],.],[[[[.,.],[.,.]],.],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 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] => 0

[5,2,1,4,7,6,3,8] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 2

[5,8,2,3,1,4,6,7] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0

[4,2,1,3,5,8,7,6] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 2

[5,4,1,3,6,2,8,7] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[8,5,4,1,3,6,2,7] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3

[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

[8,1,4,3,5,6,7,2] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 1

[7,1,3,5,4,6,2,8] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 1

[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

[4,1,3,2,5,7,6,8] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 1

[6,8,2,4,5,1,3,7] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[6,8,1,3,5,2,7,4] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[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

[7,5,1,8,2,3,6,4] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2

[5,3,8,4,2,6,7,1] => [[[[.,.],[[.,.],.]],[.,[.,.]]],.] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 2

[4,5,2,7,1,6,8,3] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0

[7,3,1,4,8,5,6,2] => [[[.,.],.],[[.,[[.,.],[.,.]]],.]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 2

[6,4,2,8,7,1,5,3] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 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

[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

[5,3,1,6,7,8,4,2] => [[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 2

[4,1,6,2,7,8,5,3] => [[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 1

[2,1,3,4,8,7,5,6] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 1

[4,8,3,7,6,5,1,2] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 0

[6,3,8,7,5,4,1,2] => [[[.,.],[[[[.,.],.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1

[5,3,8,7,6,4,1,2] => [[[.,.],[[[[.,.],.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1

[5,2,8,7,6,1,4,3] => [[[.,.],[[[.,.],.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 1

[6,2,8,7,5,1,4,3] => [[[.,.],[[[.,.],.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 1

[7,8,2,6,5,1,4,3] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[6,1,8,7,5,4,3,2] => [[.,.],[[[[[[.,.],.],.],.],.],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1

[3,1,8,7,6,5,4,2] => [[.,.],[[[[[[.,.],.],.],.],.],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1

[7,8,2,6,1,5,4,3] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 0

[6,2,8,7,1,5,4,3] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[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

[4,8,2,7,6,1,5,3] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[3,8,7,2,1,6,5,4] => [[[.,[[.,.],.]],.],[[[.,.],.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1

[6,5,8,7,1,4,3,2] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[4,8,1,7,6,5,3,2] => [[.,[.,.]],[[[[[.,.],.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 0

[5,4,1,8,7,6,3,2] => [[[.,.],.],[[[[[.,.],.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 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

[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

[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

[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

[5,3,1,8,7,6,4,2] => [[[.,.],.],[[[[[.,.],.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 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

[6,5,3,1,8,7,4,2] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3

[6,4,3,1,8,7,5,2] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3

[5,4,3,1,8,7,6,2] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3

[7,5,2,1,8,6,4,3] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3

[5,4,2,1,8,7,6,3] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3

[7,3,2,1,8,6,5,4] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3

[6,3,2,1,8,7,5,4] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3

[6,1,4,2,3,5,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 1

[8,6,1,4,2,3,5,7] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 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] => 0

[8,1,4,2,3,6,5,7] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 1

[4,1,8,2,3,6,5,7] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 1

[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

[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

[4,6,2,3,8,1,5,7] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[4,8,2,3,6,1,5,7] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[8,2,3,6,4,1,5,7] => [[[.,.],[.,[[.,.],.]]],[.,[.,.]]] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 1

[8,4,3,6,2,1,5,7] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3

[6,2,3,8,4,1,5,7] => [[[.,.],[.,[[.,.],.]]],[.,[.,.]]] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 1

[8,4,2,3,6,1,5,7] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[6,4,2,3,8,1,5,7] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[6,3,8,4,2,1,5,7] => [[[[.,.],[[.,.],.]],.],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 2

[8,3,6,4,2,1,5,7] => [[[[.,.],[[.,.],.]],.],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 2

[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

[8,3,6,2,1,4,5,7] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2

[6,2,1,3,8,4,5,7] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2

[8,2,1,3,6,4,5,7] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2

[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

[6,2,4,3,8,1,5,7] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[6,4,8,5,3,7,1,2] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[4,2,5,3,6,1,7,8] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[7,1,5,3,6,2,8,4] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[7,8,1,4,2,5,6,3] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 0

[4,8,5,3,1,6,2,7] => [[[.,[[.,.],.]],.],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[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

[6,1,8,7,4,2,3,5] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 1

[7,1,2,4,5,8,6,3] => [[.,.],[.,[[.,[.,[[.,.],.]]],.]]] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 1

[6,1,3,2,5,7,8,4] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 1

[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

[4,6,2,3,7,8,1,5] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0

[4,6,3,7,1,2,8,5] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 0

[4,2,1,3,5,7,8,6] => [[[.,.],.],[.,[.,[[.,[.,.]],.]]]] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[7,3,2,4,5,1,8,6] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[3,8,2,5,4,1,7,6] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[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

[4,2,6,3,8,7,1,5] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[5,8,2,7,4,3,1,6] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 0

[4,3,8,5,1,7,2,6] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[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

[6,4,3,5,2,8,1,7] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[6,5,3,8,4,2,1,7] => [[[[[.,.],.],[[.,.],.]],.],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 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] => 0

[8,2,5,7,3,6,4,1] => [[[.,.],[[.,[.,.]],[[.,.],.]]],.] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 2

[8,2,6,7,5,3,4,1] => [[[.,.],[[[.,[.,.]],.],[.,.]]],.] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[5,4,8,6,2,3,7,1] => [[[[.,.],[[.,.],.]],[.,[.,.]]],.] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 2

[6,4,1,8,2,5,7,3] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[4,1,3,6,5,8,7,2] => [[.,.],[[.,[[.,.],[[.,.],.]]],.]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 1

[2,1,6,3,5,8,7,4] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 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] => 0

[2,4,1,3,5,8,7,6] => [[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 0

[2,6,1,3,5,8,7,4] => [[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 0

[4,6,1,3,5,8,7,2] => [[.,[.,.]],[[.,[.,[[.,.],.]]],.]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 0

[6,1,4,3,5,8,7,2] => [[.,.],[[[.,.],[.,[[.,.],.]]],.]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 1

[6,4,1,3,5,8,7,2] => [[[.,.],.],[[.,[.,[[.,.],.]]],.]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 2

[6,2,1,3,5,8,7,4] => [[[.,.],.],[.,[[.,[[.,.],.]],.]]] => [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 2

[4,2,1,3,6,5,7,8] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2

[4,2,1,6,3,5,7,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2

[6,2,1,8,3,5,7,4] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[6,2,1,3,8,5,7,4] => [[[.,.],.],[.,[[[.,.],[.,.]],.]]] => [1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2

[6,1,4,3,8,5,7,2] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 1

[8,1,4,3,6,5,7,2] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 1

[8,4,1,3,6,5,7,2] => [[[.,.],.],[[.,[[.,.],[.,.]]],.]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 2

[8,2,1,3,6,5,7,4] => [[[.,.],.],[.,[[[.,.],[.,.]],.]]] => [1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2

[8,2,1,6,3,5,7,4] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[8,2,1,4,3,5,7,6] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2

[6,2,1,4,3,5,7,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 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

[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

[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

[8,4,1,6,3,5,7,2] => [[[.,.],.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 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

[6,4,1,8,3,5,7,2] => [[[.,.],.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 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

[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

[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

[4,6,1,8,3,5,7,2] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 0

[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

[4,6,1,3,8,5,7,2] => [[.,[.,.]],[[.,[[.,.],[.,.]]],.]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 0

[2,4,1,8,3,5,7,6] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0

[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

[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

[4,1,3,8,6,5,7,2] => [[.,.],[[.,[[[.,.],.],[.,.]]],.]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 1

[2,1,8,3,6,5,7,4] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1

[2,1,6,4,3,5,7,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1

[2,6,1,4,3,5,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0

[2,8,1,4,3,5,7,6] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0

[2,8,1,6,3,5,7,4] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 0

[4,8,1,3,6,5,7,2] => [[.,[.,.]],[[.,[[.,.],[.,.]]],.]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 0

[4,1,8,6,3,5,7,2] => [[.,.],[[[[.,.],.],[.,[.,.]]],.]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 1

[4,8,1,6,3,5,7,2] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 0

[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

[6,8,1,4,3,5,7,2] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 0

[6,1,8,4,3,5,7,2] => [[.,.],[[[[.,.],.],[.,[.,.]]],.]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 1

[8,1,6,4,3,5,7,2] => [[.,.],[[[[.,.],.],[.,[.,.]]],.]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 1

[8,6,1,4,3,5,7,2] => [[[.,.],.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[8,6,4,1,3,5,7,2] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 3

[8,6,2,1,3,5,7,4] => [[[[.,.],.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 3

[8,4,2,1,3,5,7,6] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3

[7,8,6,5,2,1,4,3] => [[[[[.,[.,.]],.],.],.],[[.,.],.]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 3

[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

[5,6,4,2,8,3,7,1] => [[[[.,[.,.]],.],[[.,.],[.,.]]],.] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => 2

[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

[5,7,1,4,6,3,2,8] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 0

[5,8,1,4,6,3,7,2] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 0

[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

[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

[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

[6,8,1,4,5,3,7,2] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 0

[6,7,1,4,5,3,2,8] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 0

[3,7,1,5,4,6,2,8] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[3,8,1,5,4,6,7,2] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 0

[3,7,1,5,4,6,8,2] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 0

[6,7,1,4,5,3,8,2] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 0

[5,7,1,4,6,3,8,2] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 0

[5,6,4,2,7,3,8,1] => [[[[.,[.,.]],.],[[.,.],[.,.]]],.] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => 2

[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

[5,4,7,2,8,3,6,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[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

[5,8,1,4,6,3,2,7] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 0

[3,8,1,5,4,6,2,7] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[3,6,1,5,4,2,7,8] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0

[3,6,1,5,4,8,2,7] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[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

[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

[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

[3,6,1,5,4,7,8,2] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 0

[3,4,1,2,7,6,5,8] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 0

[3,4,1,2,6,8,7,5] => [[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 0

[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

[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

[5,8,1,4,7,3,2,6] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 0

[7,8,1,4,5,3,2,6] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 0

[3,8,1,5,4,7,2,6] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[3,6,1,5,4,8,7,2] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 0

[3,6,1,5,4,7,2,8] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[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

[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

[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

[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

[6,5,8,7,3,4,2,1] => [[[[[.,.],[[.,.],.]],[.,.]],.],.] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[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

[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

[3,7,1,5,4,2,6,8] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0

[3,8,1,5,4,2,7,6] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[5,8,1,4,7,3,6,2] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 0

[6,8,4,2,7,5,3,1] => [[[[.,[.,.]],.],[[[.,.],.],.]],.] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 2

[6,4,7,2,8,5,3,1] => [[[[.,.],[.,.]],[[[.,.],.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 2

[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

[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

[3,7,1,5,4,8,6,2] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 0

[3,4,1,2,8,5,7,6] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 0

[3,4,1,2,5,8,7,6] => [[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 0

[3,7,1,5,4,2,8,6] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[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

[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

[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

[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

[3,8,1,5,4,2,6,7] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0

[8,7,6,3,5,2,1,4] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 4

[8,7,4,6,3,2,1,5] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 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] => 4

[8,7,6,2,5,4,1,3] => [[[[[.,.],.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3

[8,5,4,7,3,2,1,6] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 4

[8,7,3,6,5,2,1,4] => [[[[[.,.],.],[[.,.],.]],.],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 3

[6,5,8,4,3,2,1,7] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 4

[8,4,7,6,3,2,1,5] => [[[[[.,.],[[.,.],.]],.],.],[.,.]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 3

[5,8,7,4,3,2,1,6] => [[[[[.,[[.,.],.]],.],.],.],[.,.]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 3

[4,5,2,7,3,1,8,6] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[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

[4,1,7,2,5,8,6,3] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 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

[7,3,1,6,8,5,2,4] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 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

[6,5,2,8,1,7,3,4] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[5,4,3,8,7,1,6,2] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[8,5,4,3,7,2,6,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 4

[8,3,7,4,2,6,5,1] => [[[[.,.],[[.,.],.]],[[.,.],.]],.] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 2

[6,3,2,8,4,1,7,5] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[5,4,2,8,3,1,7,6] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[8,3,7,5,2,6,4,1] => [[[[.,.],[[.,.],.]],[[.,.],.]],.] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 2

[8,4,7,6,2,5,3,1] => [[[[.,.],[[.,.],.]],[[.,.],.]],.] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 2

[7,4,8,6,2,1,5,3] => [[[[.,.],[[.,.],.]],.],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2

[7,3,8,5,2,1,6,4] => [[[[.,.],[[.,.],.]],.],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2

[7,3,8,4,2,1,6,5] => [[[[.,.],[[.,.],.]],.],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2

[7,5,4,3,8,2,1,6] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 4

[8,7,4,6,3,5,2,1] => [[[[[[.,.],.],[.,.]],[.,.]],.],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 4

[6,4,7,8,3,1,2,5] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2

[7,3,4,8,2,1,5,6] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2

[7,6,4,8,3,2,1,5] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 4

[7,5,8,6,2,1,4,3] => [[[[.,.],[[.,.],.]],.],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2

[6,5,8,7,3,1,4,2] => [[[[.,.],[[.,.],.]],.],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2

[6,3,2,4,8,1,5,7] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[6,4,8,7,3,1,5,2] => [[[[.,.],[[.,.],.]],.],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2

[8,6,4,7,3,2,5,1] => [[[[[[.,.],.],[.,.]],.],[.,.]],.] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 4

[8,3,4,7,2,5,6,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[8,3,5,7,2,4,6,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[8,4,6,7,2,3,5,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[7,4,6,8,2,1,3,5] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2

[5,4,8,6,2,1,3,7] => [[[[.,.],[[.,.],.]],.],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 2

[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

[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

[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

[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

[7,3,5,4,6,8,1,2] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[6,3,5,4,7,1,8,2] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[6,3,5,4,7,1,2,8] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[3,4,1,5,6,8,7,2] => [[.,[.,.]],[[.,[.,[[.,.],.]]],.]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 0

[3,7,1,6,8,5,2,4] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 0

[2,3,1,8,6,4,7,5] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[2,3,1,8,6,4,5,7] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0

[3,7,1,6,8,5,4,2] => [[.,[.,.]],[[[[.,[.,.]],.],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 0

[6,3,5,4,7,2,1,8] => [[[[.,.],[[.,.],[.,.]]],.],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 2

[7,3,5,4,6,8,2,1] => [[[[.,.],[[.,.],[.,[.,.]]]],.],.] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 3

[6,4,8,5,3,1,2,7] => [[[[.,.],[[.,.],.]],.],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 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] => 3

[6,3,5,8,4,2,7,1] => [[[[.,.],[[.,[.,.]],.]],[.,.]],.] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[7,4,8,5,3,2,1,6] => [[[[[.,.],[[.,.],.]],.],.],[.,.]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 3

[7,4,8,5,3,2,6,1] => [[[[[.,.],[[.,.],.]],.],[.,.]],.] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 3

[6,3,5,8,4,2,1,7] => [[[[.,.],[[.,[.,.]],.]],.],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 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] => 2

[5,2,8,4,6,3,7,1] => [[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2

[6,8,3,4,5,7,2,1] => [[[[.,[.,.]],[.,[.,[.,.]]]],.],.] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 2

[5,4,1,7,8,3,2,6] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 2

[5,4,2,7,8,3,6,1] => [[[[.,.],.],[[.,[.,.]],[.,.]]],.] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 3

[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

[5,1,8,4,6,3,2,7] => [[.,.],[[[[.,.],[.,.]],.],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 1

[8,1,6,4,5,3,2,7] => [[.,.],[[[[.,.],[.,.]],.],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 1

[8,1,3,5,4,6,2,7] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 1

[8,1,6,2,4,3,5,7] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[8,7,1,2,4,3,5,6] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2

[8,7,3,2,4,6,5,1] => [[[[[.,.],.],.],[.,[[.,.],.]]],.] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 4

[8,2,6,3,4,5,7,1] => [[[.,.],[[.,.],[.,[.,[.,.]]]]],.] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 2

[8,7,2,4,5,3,6,1] => [[[[.,.],.],[[.,[.,.]],[.,.]]],.] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 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

[6,8,3,2,4,7,5,1] => [[[[.,[.,.]],.],[.,[[.,.],.]]],.] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => 2

[8,7,1,3,4,5,2,6] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 2

[8,1,6,3,4,5,2,7] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[8,1,2,5,4,3,6,7] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 1

[3,2,8,6,1,5,4,7] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[8,6,1,2,4,3,5,7] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2

[8,7,3,6,4,2,5,1] => [[[[[.,.],.],[[.,.],.]],[.,.]],.] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 3

[8,7,2,4,5,6,3,1] => [[[[.,.],.],[[.,[.,[.,.]]],.]],.] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[5,3,6,2,4,8,7,1] => [[[[.,.],[.,.]],[.,[[.,.],.]]],.] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 2

[3,5,2,8,6,1,4,7] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 0

[3,7,2,5,1,4,8,6] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 0

[5,1,8,6,2,3,4,7] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1

[7,6,3,1,8,2,4,5] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 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

[8,1,3,6,4,7,2,5] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 1

[7,1,3,6,4,8,2,5] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 1

[8,2,1,3,5,7,4,6] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 2

[8,2,6,3,1,4,7,5] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 1

[7,5,4,1,3,8,2,6] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3

[7,3,8,5,4,1,2,6] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 1

[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

[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

[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

[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

[8,6,1,4,7,3,2,5] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 2

[7,5,4,8,1,3,2,6] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[8,5,4,7,1,3,2,6] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[2,3,1,8,5,4,6,7] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0

[8,6,5,1,3,4,2,7] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3

[8,5,1,7,6,3,4,2] => [[[.,.],.],[[[[.,.],.],[.,.]],.]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 2

[3,5,2,6,7,1,8,4] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0

[3,2,8,4,7,5,1,6] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[8,4,7,5,1,3,2,6] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[3,8,1,6,5,2,7,4] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[6,1,2,8,3,4,7,5] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 1

[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

[3,7,2,5,6,1,8,4] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0

[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

[8,3,1,4,7,2,6,5] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[8,3,2,1,5,7,4,6] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3

[7,3,6,4,8,1,2,5] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[8,3,6,4,7,1,2,5] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[6,5,1,7,4,2,8,3] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[7,3,6,4,8,2,1,5] => [[[[.,.],[[.,.],[.,.]]],.],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 2

[6,1,7,3,4,2,8,5] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[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

[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

[5,1,7,4,2,8,6,3] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 1

[4,2,8,6,5,1,7,3] => [[[.,.],[[[.,.],.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 1

[6,4,2,8,5,1,7,3] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[8,6,4,7,1,5,2,3] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[7,6,4,8,1,5,2,3] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[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

[5,1,6,4,2,3,7,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1

[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

[8,6,5,7,1,4,2,3] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[6,7,4,8,1,5,2,3] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[8,3,2,4,7,1,5,6] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[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

[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

[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

[8,6,7,5,1,4,2,3] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2

[7,8,6,5,1,4,2,3] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 2

[3,1,7,5,4,2,8,6] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 1

[2,1,8,5,4,6,3,7] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1

[4,1,8,5,2,3,6,7] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1

[5,4,1,3,6,7,2,8] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 2

[8,4,1,2,6,3,7,5] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2

[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

[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

[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

[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

[7,1,5,3,8,4,2,6] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1

[4,5,1,3,6,8,2,7] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 0

[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

[7,6,3,1,5,4,2,8] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 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

[8,6,2,1,5,3,4,7] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 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

[7,1,3,2,8,6,4,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1

[7,1,6,2,8,3,4,5] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[4,7,1,2,6,3,8,5] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 0

[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

[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

[8,7,2,1,4,5,3,6] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3

[8,7,5,6,1,4,3,2] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 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] => 0

[7,1,6,4,5,8,3,2] => [[.,.],[[[[.,.],[.,[.,.]]],.],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 1

[3,5,1,4,7,6,8,2] => [[.,[.,.]],[[.,[[.,.],[.,.]]],.]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 0

[6,8,5,7,1,4,3,2] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 0

[8,6,5,7,1,4,3,2] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2

[8,5,7,6,1,4,3,2] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[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

[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

[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

[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

[8,3,1,4,5,6,7,2] => [[[.,.],.],[[.,[.,[.,[.,.]]]],.]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[5,3,1,4,8,6,7,2] => [[[.,.],.],[[.,[[.,.],[.,.]]],.]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 2

[7,5,1,6,3,4,8,2] => [[[.,.],.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[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

[5,8,1,6,4,3,7,2] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 0

[5,3,1,8,4,6,7,2] => [[[.,.],.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[8,3,1,5,4,6,7,2] => [[[.,.],.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 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

[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

[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

[4,2,1,5,6,3,8,7] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[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

[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

[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

[7,6,8,5,1,4,3,2] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 2

[6,8,7,5,1,4,3,2] => [[[.,[[.,.],.]],.],[[[.,.],.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1

[3,5,1,7,4,6,8,2] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 0

[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

[7,1,6,5,4,8,3,2] => [[.,.],[[[[[.,.],.],[.,.]],.],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 1

[7,8,6,5,1,4,3,2] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 2

[4,3,1,6,5,8,7,2] => [[[.,.],.],[[[.,.],[[.,.],.]],.]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 2

[5,3,1,2,4,8,7,6] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 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] => 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] => 2

[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

[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

[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

[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

[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

[8,7,4,5,2,1,6,3] => [[[[[.,.],.],[.,.]],.],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 3

[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

[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

[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

[4,8,3,5,6,7,1,2] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0

[4,8,1,5,6,7,2,3] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 0

[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

[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

[5,3,8,4,1,7,2,6] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[4,3,8,2,1,7,5,6] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2

[3,8,1,5,6,7,4,2] => [[.,[.,.]],[[[.,[.,[.,.]]],.],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 0

[3,8,2,5,6,7,1,4] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0

[8,2,1,5,6,7,4,3] => [[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 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

[7,1,4,3,6,2,5,8] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[7,8,4,3,6,2,1,5] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2

[4,3,1,8,5,7,6,2] => [[[.,.],.],[[[.,.],[[.,.],.]],.]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 2

[4,3,1,6,8,7,5,2] => [[[.,.],.],[[[.,[[.,.],.]],.],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 2

[6,3,1,8,2,7,4,5] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 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

[7,5,4,8,6,2,1,3] => [[[[[.,.],.],[[.,.],.]],.],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 3

[7,1,4,8,6,2,3,5] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 1

[7,5,4,1,6,2,3,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[7,6,4,5,8,1,3,2] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 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

[8,3,5,2,1,7,4,6] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2

[8,4,1,5,6,7,3,2] => [[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 2

[8,4,2,5,6,7,1,3] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2

[4,1,8,5,6,7,3,2] => [[.,.],[[[[.,.],[.,[.,.]]],.],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 1

[4,2,1,5,6,7,3,8] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 2

[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

[4,3,7,2,5,6,8,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2

[3,7,1,5,6,2,8,4] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[4,7,1,5,6,8,2,3] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 0

[8,4,2,3,5,7,1,6] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2

[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

[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

[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

[5,3,7,2,4,8,6,1] => [[[[.,.],[.,.]],[.,[[.,.],.]]],.] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 2

[8,7,6,1,4,5,2,3] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3

[8,7,6,1,3,2,5,4] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3

[8,7,4,5,1,6,2,3] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[8,5,6,4,1,7,2,3] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2

[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

[8,3,5,4,2,1,7,6] => [[[[.,.],[[.,.],.]],.],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2

[7,3,5,4,1,8,6,2] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[4,2,1,6,3,7,5,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[4,2,1,6,3,7,8,5] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[4,2,1,3,7,8,6,5] => [[[.,.],.],[.,[[[.,[.,.]],.],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 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] => 0

[4,2,1,8,3,5,6,7] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2

[4,2,1,6,3,8,7,5] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 2

[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

[4,2,1,7,3,6,5,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 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] => 0

[4,2,1,3,5,8,6,7] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 2

[4,8,1,7,3,6,5,2] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 0

[4,2,1,8,3,7,6,5] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 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] => 0

[4,6,3,5,8,7,1,2] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 0

[4,7,5,2,1,3,6,8] => [[[.,[[.,.],.]],.],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1

[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

[7,4,6,5,2,8,1,3] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[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

[5,7,4,6,8,1,3,2] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0

[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

[6,1,8,4,7,5,3,2] => [[.,.],[[[[.,.],[[.,.],.]],.],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 1

[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

[8,4,2,6,1,5,7,3] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[4,8,5,2,1,6,7,3] => [[[.,[[.,.],.]],.],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 1

[5,1,8,4,2,6,3,7] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[6,1,5,2,3,4,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1

[8,3,1,4,6,2,5,7] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[3,1,8,2,5,6,4,7] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[3,5,1,8,2,6,4,7] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[3,5,1,2,8,4,7,6] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 0

[8,2,4,3,6,7,1,5] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[3,2,8,5,7,1,6,4] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[3,6,2,8,5,1,7,4] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[6,2,1,8,4,7,5,3] => [[[.,.],.],[[[.,.],[[.,.],.]],.]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 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

[7,2,5,3,6,8,1,4] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[7,3,1,5,6,2,4,8] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[8,7,2,4,1,6,5,3] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2

[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

[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

[7,1,4,2,3,5,6,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1

[8,2,1,4,7,3,5,6] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[2,1,3,8,4,6,7,5] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 1

[3,1,8,5,2,7,6,4] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 1

[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

[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

[3,1,8,7,2,6,4,5] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[8,3,7,6,1,4,5,2] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 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] => 0

[4,1,7,2,3,6,5,8] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 1

[3,7,1,8,2,6,4,5] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[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

[3,1,6,5,8,2,7,4] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[6,3,5,8,7,1,4,2] => [[[.,.],[.,[[.,.],.]]],[[.,.],.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 1

[7,3,8,5,1,6,4,2] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[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

[7,8,3,6,1,4,5,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0

[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

[8,7,4,6,1,2,5,3] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[7,5,1,2,3,4,8,6] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2

[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

[6,4,1,2,8,5,7,3] => [[[.,.],.],[.,[[[.,.],[.,.]],.]]] => [1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2

[5,7,1,2,3,6,4,8] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 0

[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

[4,8,1,5,2,7,3,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[4,1,2,5,3,8,7,6] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 1

[3,1,4,8,7,5,2,6] => [[.,.],[[.,[[[.,.],.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 1

[4,3,6,8,7,5,1,2] => [[[.,.],[[.,[[.,.],.]],.]],[.,.]] => [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 1

[5,4,1,8,2,7,6,3] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 2

[5,4,1,8,2,7,3,6] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[8,6,7,4,1,2,5,3] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2

[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

[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

[5,6,3,8,7,1,4,2] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[5,4,1,6,8,2,7,3] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 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

[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

[6,5,1,2,3,7,8,4] => [[[.,.],.],[.,[.,[[.,[.,.]],.]]]] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[6,5,1,2,3,4,8,7] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2

[8,6,5,1,2,3,7,4] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3

[6,5,1,2,3,7,4,8] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 2

[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

[7,8,6,4,1,2,5,3] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => 2

[8,6,2,5,3,1,7,4] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[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

[8,7,2,3,1,6,5,4] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 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] => 0

[7,8,2,4,3,1,6,5] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[5,1,4,3,7,2,6,8] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[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

[2,1,4,7,5,3,6,8] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 1

[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

[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

[2,1,8,3,7,5,4,6] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1

[7,1,8,2,5,6,3,4] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[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

[4,5,2,8,1,6,7,3] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0

[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

[3,2,8,5,1,6,7,4] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 1

[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

[8,3,7,4,1,6,5,2] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[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

[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

[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

[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

[8,5,1,3,2,4,7,6] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2

[7,5,1,3,2,6,4,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[2,6,1,4,5,3,7,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[6,7,1,4,2,5,3,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[2,7,1,3,5,6,4,8] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 0

[8,6,1,2,4,3,7,5] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2

[2,8,1,3,4,6,7,5] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 0

[7,8,1,2,5,3,6,4] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 0

[6,5,7,3,8,2,4,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[4,2,6,7,5,8,3,1] => [[[.,.],[[[.,[.,.]],[.,.]],.]],.] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 2

[6,7,5,2,1,8,4,3] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 2

[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

[3,8,2,5,6,1,4,7] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[3,5,2,8,6,4,1,7] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 0

[4,2,5,7,3,8,6,1] => [[[.,.],[[.,[.,.]],[[.,.],.]]],.] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 2

[7,4,2,5,3,8,1,6] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2

[3,1,2,8,5,6,4,7] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 1

[5,2,1,6,8,3,4,7] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[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

[4,5,1,6,8,3,2,7] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 0

[6,4,3,7,8,2,5,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3

[6,4,3,1,7,8,2,5] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3

[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

[7,1,3,5,4,8,2,6] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 1

[7,5,2,8,1,4,3,6] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[5,7,3,8,4,6,1,2] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[4,6,3,7,8,5,2,1] => [[[[.,[.,.]],[[.,[.,.]],.]],.],.] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 2

[5,3,6,7,8,4,2,1] => [[[[.,.],[[.,[.,[.,.]]],.]],.],.] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 3

[4,6,1,7,3,8,5,2] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 0

[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

[6,7,2,4,8,1,5,3] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0

[2,6,1,4,7,3,8,5] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[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

[5,2,3,6,7,8,4,1] => [[[.,.],[.,[[.,[.,[.,.]]],.]]],.] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 2

[6,7,1,3,2,8,4,5] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[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

[5,2,1,7,3,8,4,6] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[6,4,2,7,1,8,3,5] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[4,2,6,3,7,8,1,5] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[4,2,6,3,7,8,5,1] => [[[.,.],[[.,.],[[.,[.,.]],.]]],.] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 2

[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

[3,6,2,7,4,1,8,5] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[6,7,3,2,1,4,8,5] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => 2

[7,1,8,3,4,2,5,6] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[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

[7,2,4,8,6,1,3,5] => [[[.,.],[.,[[.,.],.]]],[.,[.,.]]] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 1

[7,3,4,8,6,2,1,5] => [[[[.,.],[.,[[.,.],.]]],.],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 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] => 2

[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

[4,6,2,7,1,8,5,3] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 0

[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

[5,6,1,2,7,8,4,3] => [[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 0

[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

[6,7,2,8,5,4,1,3] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 0

[3,6,2,7,1,4,5,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0

[4,2,3,8,6,7,1,5] => [[[.,.],[.,[[.,.],[.,.]]]],[.,.]] => [1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1

[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

[6,2,5,4,8,3,7,1] => [[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2

[6,4,3,5,8,2,7,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 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

[3,5,2,4,7,1,6,8] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[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

[4,5,3,7,1,6,2,8] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[7,6,3,8,5,1,2,4] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[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

[4,3,6,5,7,8,1,2] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[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

[5,2,6,4,7,8,3,1] => [[[.,.],[[[.,.],[.,[.,.]]],.]],.] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 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] => 2

[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

[6,4,5,2,3,8,7,1] => [[[[.,.],[.,.]],[.,[[.,.],.]]],.] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 2

[6,4,2,5,3,8,7,1] => [[[[.,.],.],[[.,.],[[.,.],.]]],.] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3

[8,6,4,7,5,2,3,1] => [[[[[.,.],.],[[.,.],.]],[.,.]],.] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 3

[8,6,2,7,4,5,3,1] => [[[[.,.],.],[[[.,.],[.,.]],.]],.] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[6,4,2,5,8,7,3,1] => [[[[.,.],.],[[.,[[.,.],.]],.]],.] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 3

[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

[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

[8,2,4,6,7,5,3,1] => [[[.,.],[[.,[[.,[.,.]],.]],.]],.] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 2

[4,2,6,5,8,7,3,1] => [[[.,.],[[[.,.],[[.,.],.]],.]],.] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 2

[4,2,3,6,8,7,5,1] => [[[.,.],[.,[[.,[[.,.],.]],.]]],.] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 2

[6,4,8,7,2,5,3,1] => [[[[.,.],[[.,.],.]],[[.,.],.]],.] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 2

[6,4,8,7,5,2,3,1] => [[[[.,.],[[[.,.],.],.]],[.,.]],.] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 2

[8,2,6,4,7,5,3,1] => [[[.,.],[[[.,.],[[.,.],.]],.]],.] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 2

[2,1,8,6,4,7,5,3] => [[.,.],[[[[.,.],.],[[.,.],.]],.]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 1

[6,8,7,4,2,5,3,1] => [[[[.,[[.,.],.]],.],[[.,.],.]],.] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 2

[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

[6,2,5,7,4,8,3,1] => [[[.,.],[[[.,[.,.]],[.,.]],.]],.] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 2

[8,5,2,1,4,7,6,3] => [[[[.,.],.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[6,7,3,2,5,8,4,1] => [[[[.,[.,.]],.],[[.,[.,.]],.]],.] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 2

[3,2,6,4,8,1,5,7] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[7,5,1,8,3,4,6,2] => [[[.,.],.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[7,1,6,3,5,8,4,2] => [[.,.],[[[.,.],[[.,[.,.]],.]],.]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 1

[6,3,1,7,8,4,5,2] => [[[.,.],.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[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

[7,3,1,2,5,8,6,4] => [[[.,.],.],[.,[[.,[[.,.],.]],.]]] => [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 2

[6,3,2,8,5,7,4,1] => [[[[.,.],.],[[[.,.],[.,.]],.]],.] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[8,1,6,3,4,5,7,2] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 1

[7,6,5,4,1,2,8,3] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 4

[2,8,1,6,5,7,4,3] => [[.,[.,.]],[[[[.,.],[.,.]],.],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 0

[5,2,3,7,6,1,8,4] => [[[.,.],[.,[[.,.],.]]],[[.,.],.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 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

[5,2,3,7,4,8,6,1] => [[[.,.],[.,[[.,.],[[.,.],.]]]],.] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 2

[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

[7,8,1,5,4,3,6,2] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 0

[7,2,4,8,5,3,6,1] => [[[.,.],[[.,[[.,.],.]],[.,.]]],.] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 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] => 3

[4,8,1,6,3,5,2,7] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[8,3,1,7,4,2,5,6] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[3,1,8,2,4,5,7,6] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 1

[8,1,3,7,6,2,4,5] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 1

[4,3,2,8,5,7,1,6] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2

[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

[3,2,4,7,5,8,6,1] => [[[.,.],[.,[[.,.],[[.,.],.]]]],.] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 2

[4,2,3,8,6,5,1,7] => [[[.,.],[.,[[[.,.],.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 1

[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

[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

[4,5,1,2,8,3,7,6] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 0

[4,6,2,8,1,3,7,5] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 0

[3,6,2,8,4,7,1,5] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[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

[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

[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

[4,2,5,3,8,1,7,6] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[3,2,5,4,8,7,1,6] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[5,1,4,2,3,8,7,6] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 1

[5,4,1,3,2,8,7,6] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 2

[5,4,3,1,2,8,7,6] => [[[[.,.],.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 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] => 0

[4,3,6,8,2,1,7,5] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 2

[5,3,1,4,2,8,7,6] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 2

[5,3,2,1,4,8,7,6] => [[[[.,.],.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 3

[4,3,2,5,8,1,7,6] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[3,2,4,5,8,7,1,6] => [[[.,.],[.,[.,[[.,.],.]]]],[.,.]] => [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 1

[5,2,1,3,4,8,7,6] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 2

[5,1,2,3,4,8,7,6] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1

[8,6,2,5,4,1,3,7] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 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] => 3

[6,7,5,3,8,2,4,1] => [[[[[.,[.,.]],.],[.,.]],[.,.]],.] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[8,2,1,6,3,4,5,7] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2

[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

[8,6,2,1,3,5,4,7] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3

[8,1,2,3,4,6,5,7] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1

[6,2,3,7,8,4,5,1] => [[[.,.],[.,[[.,[.,.]],[.,.]]]],.] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[7,5,8,2,6,3,4,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[7,3,1,6,5,8,4,2] => [[[.,.],.],[[[[.,.],[.,.]],.],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 2

[8,4,7,6,2,1,3,5] => [[[[.,.],[[.,.],.]],.],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 2

[5,3,8,4,7,2,6,1] => [[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[8,1,3,7,6,4,2,5] => [[.,.],[[.,[[[.,.],.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 1

[5,3,1,7,8,6,2,4] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 2

[6,2,8,5,3,1,7,4] => [[[.,.],[[[.,.],.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 1

[8,2,6,4,7,1,3,5] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[3,4,2,8,5,1,7,6] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[8,3,7,4,2,5,6,1] => [[[[.,.],[[.,.],.]],[.,[.,.]]],.] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 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] => 0

[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

[6,8,3,4,1,5,7,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0

[5,1,7,6,2,8,4,3] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 1

[6,8,2,5,7,4,1,3] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 0

[4,2,8,3,1,5,6,7] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 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

[4,2,1,8,7,5,6,3] => [[[.,.],.],[[[[.,.],.],[.,.]],.]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 2

[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

[7,2,8,5,1,4,6,3] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 1

[5,7,4,8,3,6,2,1] => [[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2

[8,4,3,2,5,7,1,6] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3

[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

[3,2,4,7,8,5,6,1] => [[[.,.],[.,[[.,[.,.]],[.,.]]]],.] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[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

[8,2,1,3,4,5,7,6] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2

[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

[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

[4,2,5,3,8,7,6,1] => [[[.,.],[[.,.],[[[.,.],.],.]]],.] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 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] => 0

[3,1,8,6,5,4,2,7] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 1

[5,4,8,7,3,2,6,1] => [[[[[.,.],[[.,.],.]],.],[.,.]],.] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 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] => 2

[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

[5,4,3,7,1,8,2,6] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[7,3,8,5,1,4,2,6] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[5,4,8,7,6,2,1,3] => [[[[.,.],[[[.,.],.],.]],.],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 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] => 0

[4,8,3,6,7,1,5,2] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0

[8,7,5,3,6,4,2,1] => [[[[[[.,.],.],.],[[.,.],.]],.],.] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 5

[4,6,1,3,8,7,5,2] => [[.,[.,.]],[[.,[[[.,.],.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 0

[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

[3,7,1,6,4,2,8,5] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[3,1,2,7,5,6,8,4] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 1

[3,6,1,2,7,5,8,4] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 0

[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

[8,5,2,3,6,7,4,1] => [[[[.,.],.],[.,[[.,[.,.]],.]]],.] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[4,7,2,6,3,8,1,5] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[6,3,2,4,8,7,5,1] => [[[[.,.],.],[.,[[[.,.],.],.]]],.] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 3

[3,7,2,4,6,1,8,5] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0

[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

[6,3,2,8,7,5,1,4] => [[[[.,.],.],[[[.,.],.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 2

[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

[6,4,8,7,2,5,1,3] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[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

[6,2,1,3,8,7,5,4] => [[[.,.],.],[.,[[[[.,.],.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 2

[3,6,1,8,7,5,2,4] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 0

[5,6,1,2,8,7,4,3] => [[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => 0

[7,5,2,8,1,6,4,3] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2

[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

[7,4,8,6,1,2,5,3] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 1

[7,2,1,8,3,6,5,4] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 2

[8,5,4,3,7,2,1,6] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 4

[6,5,4,8,3,2,7,1] => [[[[[[.,.],.],[.,.]],.],[.,.]],.] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 4

[7,3,1,4,8,2,5,6] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[5,7,2,4,6,8,1,3] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0

[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

[4,5,1,2,7,6,8,3] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 0

[5,4,6,8,3,1,2,7] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2

[7,5,8,6,2,1,3,4] => [[[[.,.],[[.,.],.]],.],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 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] => 0

[3,4,2,6,8,7,1,5] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 0

[7,3,8,4,1,2,6,5] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 1

[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

[3,7,1,2,4,6,5,8] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 0

[7,5,6,8,2,1,4,3] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 2

[4,2,1,7,5,8,3,6] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[4,7,1,6,5,2,8,3] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[4,7,3,6,5,1,8,2] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[3,2,4,8,6,7,1,5] => [[[.,.],[.,[[.,.],[.,.]]]],[.,.]] => [1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1

[4,2,6,8,7,3,1,5] => [[[.,.],[[.,[[.,.],.]],.]],[.,.]] => [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 1

[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

[3,8,1,4,2,6,5,7] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[4,2,7,3,6,1,8,5] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[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

[3,8,2,4,1,6,7,5] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0

[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

[4,2,7,5,6,3,8,1] => [[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2

[4,2,7,5,6,1,8,3] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 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

[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

[3,8,1,2,4,6,5,7] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 0

[5,4,2,3,7,6,8,1] => [[[[.,.],.],[.,[[.,.],[.,.]]]],.] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 3

[7,4,3,5,2,8,1,6] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[8,4,3,7,5,1,6,2] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[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

[7,4,6,2,3,5,8,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2

[5,1,7,2,4,6,8,3] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 1

[5,4,1,7,3,6,8,2] => [[[.,.],.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[5,7,6,4,3,1,8,2] => [[[[.,[[.,.],.]],.],.],[[.,.],.]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2

[5,7,6,3,1,4,8,2] => [[[.,[[.,.],.]],.],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 1

[7,5,2,3,4,8,1,6] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2

[8,7,5,3,4,1,6,2] => [[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 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] => 0

[7,6,1,3,4,8,5,2] => [[[.,.],.],[[.,[.,[[.,.],.]]],.]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 2

[3,2,8,6,7,1,4,5] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[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

[7,1,2,8,3,5,6,4] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 1

[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

[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

[7,1,4,5,8,6,2,3] => [[.,.],[[.,[.,[[.,.],.]]],[.,.]]] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 1

[5,7,6,4,2,8,1,3] => [[[[.,[[.,.],.]],.],[.,.]],[.,.]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[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

[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

[5,1,4,3,6,8,7,2] => [[.,.],[[[.,.],[.,[[.,.],.]]],.]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 1

[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

[7,4,8,2,3,6,5,1] => [[[[.,.],[.,.]],[.,[[.,.],.]]],.] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 2

[6,4,7,8,5,2,1,3] => [[[[.,.],[[.,[.,.]],.]],.],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 2

[7,4,3,8,2,6,5,1] => [[[[[.,.],.],[.,.]],[[.,.],.]],.] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[7,6,8,3,2,5,4,1] => [[[[[.,.],[.,.]],.],[[.,.],.]],.] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[8,7,1,3,5,4,6,2] => [[[.,.],.],[[.,[[.,.],[.,.]]],.]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 2

[7,1,8,3,4,2,6,5] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 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] => 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

[4,8,5,2,1,3,6,7] => [[[.,[[.,.],.]],.],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1

[5,8,2,6,3,1,4,7] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 0

[6,8,2,3,7,4,1,5] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 0

[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

[8,1,7,2,4,5,3,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 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

[7,2,1,6,3,5,4,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[2,7,1,6,3,5,4,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[2,7,1,5,4,3,6,8] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0

[7,2,1,5,4,3,6,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[8,1,3,5,4,2,6,7] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 1

[8,1,5,3,4,2,6,7] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[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

[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

[8,1,4,3,5,2,6,7] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[7,2,1,4,5,3,6,8] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[2,7,1,4,5,3,6,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[6,3,2,1,5,4,7,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[7,3,1,4,5,2,6,8] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[7,3,1,5,4,2,6,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[7,3,1,6,2,5,4,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[3,7,1,6,2,5,4,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[3,7,1,4,5,2,6,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[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

[3,5,2,4,1,6,7,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0

[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

[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

[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

[6,5,2,1,3,7,4,8] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3

[7,6,1,2,4,5,3,8] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 2

[6,7,1,2,8,3,5,4] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 0

[6,7,1,2,5,4,3,8] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 0

[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

[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

[4,7,1,3,5,2,6,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[4,7,1,5,3,2,6,8] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0

[5,7,1,4,2,6,3,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[5,7,1,6,2,3,8,4] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0

[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

[4,2,5,3,1,6,7,8] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1

[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

[8,2,7,5,4,1,3,6] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 1

[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

[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

[6,5,1,2,7,8,4,3] => [[[.,.],.],[.,[[[.,[.,.]],.],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 2

[5,7,6,4,1,3,8,2] => [[[.,[[.,.],.]],.],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 1

[7,6,2,4,5,3,8,1] => [[[[.,.],.],[[.,[.,.]],[.,.]]],.] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 3

[6,1,7,5,3,8,4,2] => [[.,.],[[[[.,.],.],[[.,.],.]],.]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 1

[8,6,7,5,3,1,4,2] => [[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 3

[8,5,2,7,1,6,4,3] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2

[7,6,1,5,3,8,4,2] => [[[.,.],.],[[[.,.],[[.,.],.]],.]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 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] => 0

[5,8,6,4,1,2,7,3] => [[[.,[[.,.],.]],.],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => 1

[5,8,7,3,2,6,4,1] => [[[[.,[[.,.],.]],.],[[.,.],.]],.] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 2

[5,8,1,7,2,6,4,3] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 0

[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

[8,1,7,2,5,6,3,4] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[5,8,7,2,1,6,3,4] => [[[.,[[.,.],.]],.],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[4,8,1,5,2,6,7,3] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 0

[6,5,2,7,8,1,4,3] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[7,1,2,8,5,6,3,4] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 1

[8,7,2,1,5,6,3,4] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 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

[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

[7,5,6,2,1,8,4,3] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 2

[8,7,5,2,1,6,4,3] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4

[7,1,3,5,8,6,2,4] => [[.,.],[[.,[.,[[.,.],.]]],[.,.]]] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 1

[5,1,3,4,6,8,7,2] => [[.,.],[[.,[.,[.,[[.,.],.]]]],.]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 1

[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

[5,6,3,4,8,1,7,2] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0

[8,4,3,1,2,6,7,5] => [[[[.,.],.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 3

[8,5,1,6,3,4,7,2] => [[[.,.],.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[5,1,8,6,3,4,7,2] => [[.,.],[[[[.,.],.],[.,[.,.]]],.]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 1

[6,4,5,8,3,2,7,1] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 3

[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

[6,1,8,3,5,2,7,4] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[7,6,8,3,5,2,1,4] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 2

[8,6,1,3,5,2,7,4] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[8,7,1,3,5,6,2,4] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 2

[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

[5,8,2,3,1,6,7,4] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0

[6,8,2,3,5,1,7,4] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0

[7,8,2,3,5,6,1,4] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0

[8,6,5,1,4,3,7,2] => [[[[.,.],.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 3

[4,1,7,6,3,8,2,5] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1

[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

[4,6,1,5,2,3,8,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0

[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

[8,6,1,2,5,3,4,7] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 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

[7,6,5,2,8,3,4,1] => [[[[[.,.],.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 4

[2,1,4,8,7,6,3,5] => [[.,.],[[.,[[[.,.],.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 1

[7,4,6,8,5,3,2,1] => [[[[[.,.],[[.,[.,.]],.]],.],.],.] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 4

[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

[3,2,8,7,5,1,6,4] => [[[.,.],[[[.,.],.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 1

[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

[2,5,1,8,6,7,4,3] => [[.,[.,.]],[[[[.,.],[.,.]],.],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 0

[3,5,1,8,6,7,4,2] => [[.,[.,.]],[[[[.,.],[.,.]],.],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 0

[5,2,3,8,6,7,4,1] => [[[.,.],[.,[[[.,.],[.,.]],.]]],.] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 2

[8,3,5,4,6,7,1,2] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[5,1,3,8,6,7,4,2] => [[.,.],[[.,[[[.,.],[.,.]],.]],.]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 1

[3,2,5,8,6,7,4,1] => [[[.,.],[[.,[[.,.],[.,.]]],.]],.] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 2

[6,2,1,5,3,8,7,4] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 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

[8,1,6,3,5,2,7,4] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[8,7,6,2,5,3,1,4] => [[[[[.,.],.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3

[7,6,2,8,5,1,4,3] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[8,1,3,7,5,2,6,4] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 1

[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

[6,3,8,5,7,4,1,2] => [[[.,.],[[[.,.],[.,.]],.]],[.,.]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1

[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

[2,1,4,8,7,5,6,3] => [[.,.],[[.,[[[.,.],.],[.,.]]],.]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 1

[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

[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

[5,8,3,4,6,7,2,1] => [[[[.,[.,.]],[.,[.,[.,.]]]],.],.] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 2

[8,4,3,2,6,7,1,5] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3

[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

[5,1,8,2,6,7,3,4] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[7,8,5,3,6,4,2,1] => [[[[[.,[.,.]],.],[[.,.],.]],.],.] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 3

[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

[3,8,1,4,6,7,2,5] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 0

[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

[6,2,7,3,8,4,1,5] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[7,4,3,2,8,5,1,6] => [[[[[.,.],.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3

[5,3,2,8,4,6,1,7] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2

[8,4,2,6,5,3,1,7] => [[[[.,.],.],[[[.,.],.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 2

[7,4,2,5,3,1,6,8] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 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

[5,4,8,3,2,6,1,7] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 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

[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

[5,7,4,3,1,2,6,8] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2

[7,3,8,6,4,1,2,5] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 1

[6,1,2,7,3,8,5,4] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 1

[2,1,7,4,3,8,6,5] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 1

[6,1,4,3,8,2,7,5] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[5,1,3,2,8,7,4,6] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1

[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

[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

[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

[8,3,1,6,7,2,5,4] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[7,4,8,6,1,3,2,5] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[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

[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

[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

[7,4,6,2,1,5,3,8] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2

[5,7,2,3,8,1,4,6] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[6,4,7,5,8,1,2,3] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[7,4,8,5,1,6,3,2] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[5,8,3,6,1,7,4,2] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 0

[8,6,4,2,1,7,5,3] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4

[7,4,2,1,5,8,6,3] => [[[[.,.],.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[7,6,4,1,8,5,2,3] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[6,3,1,2,8,4,7,5] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2

[7,5,1,3,2,8,6,4] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 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] => 0

[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

[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

[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

[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

[3,6,1,8,2,4,7,5] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0

[5,4,1,8,7,3,2,6] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 2

[3,5,1,8,7,2,4,6] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0

[4,6,1,8,3,7,2,5] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[4,7,1,2,8,6,3,5] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 0

[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

[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

[8,6,1,7,5,4,3,2] => [[[.,.],.],[[[[[.,.],.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2

[7,1,5,8,6,4,3,2] => [[.,.],[[[[.,[[.,.],.]],.],.],.]] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 1

[5,1,8,7,3,6,4,2] => [[.,.],[[[[.,.],.],[[.,.],.]],.]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 1

[4,1,8,7,6,2,5,3] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 1

[3,1,8,7,6,5,2,4] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 1

[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

[8,6,4,7,2,1,3,5] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 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

[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

[7,4,8,5,2,3,1,6] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[5,8,7,4,1,2,3,6] => [[[.,[[.,.],.]],.],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1

[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

[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

[8,5,1,6,3,7,2,4] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[6,1,3,7,4,8,2,5] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 1

[4,1,7,3,5,8,2,6] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[7,1,6,4,8,2,3,5] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[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

[5,1,7,3,8,2,4,6] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[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

[7,4,8,6,1,2,3,5] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1

[6,5,8,4,1,2,3,7] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2

[8,5,7,4,1,2,3,6] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2

[7,6,4,8,2,1,3,5] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3

[7,6,2,3,8,1,4,5] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[7,4,8,5,1,6,2,3] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[8,6,2,3,1,7,4,5] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[8,6,4,1,2,7,3,5] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3

[7,6,1,3,8,2,4,5] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[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

[5,4,1,8,2,3,6,7] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2

[6,5,1,8,2,3,4,7] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2

[5,7,1,3,8,2,4,6] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[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

[7,1,5,8,6,2,3,4] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 1

[6,1,8,2,7,3,4,5] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[4,1,8,7,2,3,5,6] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1

[5,1,8,7,2,3,4,6] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1

[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

[7,1,4,3,2,5,6,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1

[6,4,2,3,8,5,7,1] => [[[[.,.],.],[.,[[.,.],[.,.]]]],.] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 3

[6,4,2,7,5,8,3,1] => [[[[.,.],.],[[[.,.],[.,.]],.]],.] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 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] => 0

[7,1,4,6,5,2,3,8] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 1

[7,1,4,6,5,8,2,3] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 1

[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

[7,1,4,3,2,5,8,6] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1

[7,1,4,6,5,2,8,3] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 1

[7,1,4,6,5,3,8,2] => [[.,.],[[[.,[[.,.],.]],[.,.]],.]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 1

[7,1,4,6,5,3,2,8] => [[.,.],[[[.,[[.,.],.]],.],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 1

[6,4,2,7,5,3,8,1] => [[[[.,.],.],[[[.,.],.],[.,.]]],.] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 3

[2,4,1,7,5,3,6,8] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0

[3,4,1,7,8,6,2,5] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 0

[6,4,2,3,8,5,1,7] => [[[[.,.],.],[.,[[.,.],.]]],[.,.]] => [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 2

[6,4,2,7,5,8,1,3] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2

[6,4,2,7,5,3,1,8] => [[[[.,.],.],[[[.,.],.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 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] => 3

[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

[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

[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

[5,8,1,6,3,4,2,7] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[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

[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

[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

[5,4,7,3,6,2,8,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[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

[6,4,3,7,5,1,2,8] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[6,4,3,7,5,1,8,2] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[6,2,4,3,1,5,8,7] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 1

[5,8,3,2,1,6,4,7] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 2

[5,8,7,4,3,1,2,6] => [[[[.,[[.,.],.]],.],.],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => 2

[5,4,7,3,6,2,1,8] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 2

[7,4,3,8,5,2,1,6] => [[[[[.,.],.],[[.,.],.]],.],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 3

[3,2,5,8,6,1,4,7] => [[[.,.],[.,[[.,.],.]]],[.,[.,.]]] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 1

[8,4,3,7,5,2,6,1] => [[[[[.,.],.],[[.,.],.]],[.,.]],.] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 3

[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

[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

[5,2,3,8,4,1,6,7] => [[[.,.],[.,[[.,.],.]]],[.,[.,.]]] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 1

[8,6,5,3,7,2,4,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 4

[7,5,4,3,8,2,6,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 4

[6,4,5,3,8,2,7,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[7,4,6,3,8,2,5,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[7,5,6,3,8,2,4,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[8,5,6,3,7,2,4,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[7,4,6,3,5,2,8,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[8,4,6,3,5,2,7,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[8,4,7,3,5,2,6,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[8,5,7,3,4,2,6,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,5,8,3,4,2,7,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[7,5,8,3,4,2,6,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[7,5,8,4,6,2,3,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[7,4,8,3,6,2,5,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[7,4,8,3,5,2,6,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,4,8,3,5,2,7,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,4,7,3,5,2,8,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,4,8,3,7,2,6,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,5,8,3,7,2,4,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,5,8,4,7,2,3,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,4,7,3,8,2,5,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,4,7,3,8,2,6,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,4,6,3,8,2,7,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2

[5,3,6,2,4,7,8,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2

[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

[5,3,7,2,4,6,8,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2

[4,3,1,5,6,8,7,2] => [[[.,.],.],[[.,[.,[[.,.],.]]],.]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 2

[4,2,1,5,8,6,3,7] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 2

[4,2,1,5,8,6,7,3] => [[[.,.],.],[[.,[[.,.],[.,.]]],.]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 2

[4,2,1,5,8,7,6,3] => [[[.,.],.],[[.,[[[.,.],.],.]],.]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 2

[4,3,1,5,7,8,6,2] => [[[.,.],.],[[.,[[.,[.,.]],.]],.]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 2

[4,3,1,7,5,8,6,2] => [[[.,.],.],[[[.,.],[[.,.],.]],.]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 2

[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

[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

[4,3,1,5,7,8,2,6] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 2

[3,2,1,8,5,4,6,7] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[3,2,1,8,5,7,4,6] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[3,2,1,8,7,5,4,6] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 2

[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

[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

[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

[3,2,1,8,5,6,4,7] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[3,2,1,8,6,5,4,7] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 2

[4,3,1,6,7,8,5,2] => [[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 2

[4,2,1,6,8,7,5,3] => [[[.,.],.],[[[.,[[.,.],.]],.],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 2

[4,2,1,6,8,5,7,3] => [[[.,.],.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[4,2,1,6,8,5,3,7] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 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

[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

[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

[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

[4,2,1,6,8,3,7,5] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[4,3,1,6,7,8,2,5] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 2

[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

[4,2,1,7,8,6,3,5] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 2

[3,2,1,8,7,6,4,5] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 2

[3,2,1,8,6,4,7,5] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[3,2,1,8,6,4,5,7] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[3,2,1,8,4,6,5,7] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[3,2,1,8,4,6,7,5] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[3,2,1,8,4,7,6,5] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 2

[3,2,1,8,7,4,6,5] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[4,2,1,7,8,3,6,5] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[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

[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

[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

[4,2,1,7,8,3,5,6] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[3,2,1,8,4,5,7,6] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2

[7,5,2,8,6,3,4,1] => [[[[.,.],.],[[[.,.],.],[.,.]]],.] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 3

[7,4,8,6,2,5,3,1] => [[[[.,.],[[.,.],.]],[[.,.],.]],.] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 2

[7,3,8,6,2,4,5,1] => [[[[.,.],[[.,.],.]],[.,[.,.]]],.] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 2

[7,3,8,5,2,4,6,1] => [[[[.,.],[[.,.],.]],[.,[.,.]]],.] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 2

[7,3,8,4,5,6,2,1] => [[[[.,.],[[.,.],[.,[.,.]]]],.],.] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 3

[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

[6,4,3,8,1,5,2,7] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 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

[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

[5,3,8,2,4,6,7,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2

[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

[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

[6,3,7,2,5,8,4,1] => [[[[.,.],[.,.]],[[.,[.,.]],.]],.] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 2

[5,3,6,8,2,4,7,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[5,3,6,7,8,2,4,1] => [[[[.,.],[.,[.,[.,.]]]],[.,.]],.] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2

[3,6,4,2,1,5,8,7] => [[[.,[[.,.],.]],.],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => 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

[6,3,4,2,1,5,8,7] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2

[5,6,4,2,1,3,8,7] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => 2

[5,8,6,4,2,1,3,7] => [[[[.,[[.,.],.]],.],.],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => 2

[4,2,1,5,7,8,6,3] => [[[.,.],.],[[.,[[.,[.,.]],.]],.]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 2

[4,3,8,5,7,6,2,1] => [[[[.,.],[[.,.],[[.,.],.]]],.],.] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 3

[7,6,2,1,8,4,3,5] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[2,1,8,5,6,4,3,7] => [[.,.],[[[[.,.],[.,.]],.],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 1

[4,2,1,8,5,6,3,7] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[8,4,2,1,5,6,3,7] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3

[6,3,4,2,1,8,5,7] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2

[3,6,4,2,1,8,5,7] => [[[.,[[.,.],.]],.],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[8,5,3,7,6,2,4,1] => [[[[[.,.],.],[[.,.],.]],[.,.]],.] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 3

[7,6,2,4,1,8,5,3] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2

[8,5,4,1,7,6,2,3] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[7,6,2,3,8,5,4,1] => [[[[.,.],.],[.,[[[.,.],.],.]]],.] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 3

[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

[2,1,6,4,3,7,8,5] => [[.,.],[[[.,.],.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 1

[6,4,2,1,3,7,8,5] => [[[[.,.],.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 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] => 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] => 2

[2,6,1,8,4,3,7,5] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[2,6,1,7,5,8,4,3] => [[.,[.,.]],[[[[.,.],[.,.]],.],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 0

[8,4,2,3,7,5,6,1] => [[[[.,.],.],[.,[[.,.],[.,.]]]],.] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 3

[8,5,7,6,2,1,4,3] => [[[[.,.],[[.,.],.]],.],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2

[4,7,6,2,1,3,8,5] => [[[.,[[.,.],.]],.],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => 1

[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

[6,4,7,8,3,2,1,5] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 3

[6,4,3,7,5,2,1,8] => [[[[[.,.],.],[[.,.],.]],.],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 3

[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

[6,3,2,7,5,4,1,8] => [[[[.,.],.],[[[.,.],.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 2

[8,4,2,6,3,1,7,5] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[8,6,5,2,3,1,7,4] => [[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3

[8,7,5,2,1,4,6,3] => [[[[[.,.],.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 4

[7,8,5,2,1,4,6,3] => [[[[.,[.,.]],.],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 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

[4,8,2,6,3,1,7,5] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[3,2,8,6,4,1,7,5] => [[[.,.],[[[.,.],.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 1

[3,2,1,7,5,4,8,6] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[4,1,3,7,5,2,8,6] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 1

[5,1,7,3,4,2,8,6] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[7,1,6,3,2,5,8,4] => [[.,.],[[[.,.],.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 1

[6,1,8,2,4,5,7,3] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 1

[5,1,8,3,2,6,7,4] => [[.,.],[[[.,.],.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 1

[3,2,8,7,1,5,6,4] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 1

[4,8,2,7,1,5,6,3] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0

[5,8,7,2,1,4,6,3] => [[[.,[[.,.],.]],.],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 1

[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

[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

[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

[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

[8,4,2,7,1,5,6,3] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[7,4,2,8,1,5,6,3] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[6,4,2,8,3,1,7,5] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[5,4,2,3,8,1,7,6] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[4,5,2,3,1,6,8,7] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 0

[7,4,2,1,3,6,8,5] => [[[[.,.],.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 3

[8,4,2,1,3,6,7,5] => [[[[.,.],.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 3

[8,5,1,3,2,6,7,4] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[5,6,1,3,4,2,8,7] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[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

[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

[5,7,1,3,2,6,8,4] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 0

[6,7,1,2,4,5,8,3] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 0

[8,6,1,2,4,5,7,3] => [[[.,.],.],[.,[[.,[.,[.,.]]],.]]] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[8,7,1,2,4,5,6,3] => [[[.,.],.],[.,[[.,[.,[.,.]]],.]]] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[7,8,1,2,4,5,6,3] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 0

[5,8,1,3,2,6,7,4] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 0

[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

[4,1,3,2,5,7,8,6] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 1

[5,1,2,4,3,7,8,6] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 1

[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

[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

[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

[4,3,2,8,1,7,6,5] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2

[4,1,8,7,3,2,5,6] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 1

[3,4,2,7,1,6,8,5] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0

[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

[3,7,2,4,8,6,1,5] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 0

[3,2,7,4,8,1,6,5] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[4,7,1,5,8,2,3,6] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[8,6,5,2,7,3,4,1] => [[[[[.,.],.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 4

[7,4,8,5,6,3,2,1] => [[[[[.,.],[[.,.],[.,.]]],.],.],.] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4

[3,1,7,5,4,2,6,8] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 1

[6,3,8,5,4,7,1,2] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[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

[4,8,1,5,2,3,6,7] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0

[7,4,1,5,2,3,6,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2

[5,6,1,8,4,3,2,7] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 0

[5,1,8,6,4,3,2,7] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 1

[5,1,6,3,8,7,2,4] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1

[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

[6,1,8,7,4,3,2,5] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 1

[7,1,2,5,4,8,6,3] => [[.,.],[.,[[[.,.],[[.,.],.]],.]]] => [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 1

[4,1,6,3,7,5,2,8] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1

[4,1,6,3,7,8,2,5] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[3,1,6,4,8,2,7,5] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[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

[4,1,6,3,8,7,2,5] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1

[7,5,1,8,4,3,2,6] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 2

[6,5,1,7,4,3,2,8] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 2

[4,1,8,5,2,3,7,6] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1

[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

[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

[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

[3,5,1,6,2,8,7,4] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 0

[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

[3,5,2,7,8,4,1,6] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 0

[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

[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

[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

[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

[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

[8,5,3,7,2,4,1,6] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 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

[6,3,1,5,8,2,4,7] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[6,5,3,4,2,8,1,7] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[5,2,4,3,8,1,6,7] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[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

[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

[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

[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

[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

[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

[5,3,8,7,2,4,1,6] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[8,7,4,6,2,3,1,5] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[6,4,8,7,2,3,1,5] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[3,1,7,4,2,8,6,5] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 1

[3,2,8,4,1,7,6,5] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[7,6,4,8,2,3,1,5] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[8,6,4,7,2,3,1,5] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[8,2,3,7,4,1,6,5] => [[[.,.],[.,[[.,.],.]]],[[.,.],.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 1

[8,1,6,4,2,3,7,5] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1

[6,3,1,7,4,2,8,5] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[8,5,7,6,2,3,1,4] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[7,5,8,6,2,3,1,4] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[7,1,6,4,2,3,8,5] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1

[3,1,7,6,4,2,8,5] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 1

[6,8,7,5,2,3,1,4] => [[[[.,[[.,.],.]],.],[.,.]],[.,.]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[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

[4,3,6,5,1,8,7,2] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[4,6,3,5,1,8,7,2] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 0

[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

[4,1,6,5,3,8,7,2] => [[.,.],[[[[.,.],.],[[.,.],.]],.]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 1

[4,6,1,5,3,8,7,2] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 0

[4,6,1,5,8,3,7,2] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 0

[4,1,6,5,8,3,7,2] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 1

[4,1,6,5,8,7,3,2] => [[.,.],[[[[.,.],[[.,.],.]],.],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 1

[6,4,3,8,7,1,5,2] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 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

[4,6,1,8,5,7,3,2] => [[.,[.,.]],[[[[.,.],[.,.]],.],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 0

[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

[4,6,1,8,5,3,7,2] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 0

[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

[4,6,3,8,1,5,7,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0

[4,6,3,8,5,7,1,2] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[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

[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

[4,3,1,6,8,5,7,2] => [[[.,.],.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[4,1,3,6,8,7,5,2] => [[.,.],[[.,[[.,[[.,.],.]],.]],.]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 1

[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

[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

[6,5,2,8,7,3,1,4] => [[[[.,.],.],[[[.,.],.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 2

[6,5,2,8,7,1,3,4] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[6,2,5,8,7,1,3,4] => [[[.,.],[.,[[.,.],.]]],[.,[.,.]]] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 1

[6,2,5,8,7,3,1,4] => [[[.,.],[[.,[[.,.],.]],.]],[.,.]] => [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 1

[4,6,3,8,1,7,5,2] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 0

[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

[4,1,6,3,8,7,5,2] => [[.,.],[[[.,.],[[[.,.],.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 1

[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

[4,6,1,8,3,7,5,2] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 0

[6,2,8,5,7,3,1,4] => [[[.,.],[[[.,.],[.,.]],.]],[.,.]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1

[6,2,8,5,7,1,3,4] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[4,2,8,7,5,3,1,6] => [[[.,.],[[[[.,.],.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1

[6,4,1,8,7,5,3,2] => [[[.,.],.],[[[[[.,.],.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2

[6,1,4,8,7,5,3,2] => [[.,.],[[[.,[[[.,.],.],.]],.],.]] => [1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 1

[6,4,1,8,7,3,5,2] => [[[.,.],.],[[[[.,.],.],[.,.]],.]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 2

[4,2,8,7,5,1,3,6] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 1

[2,6,1,3,7,8,5,4] => [[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 0

[6,5,2,4,3,7,1,8] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2

[6,4,2,5,3,7,1,8] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2

[5,4,7,6,2,3,1,8] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[4,6,2,3,7,5,1,8] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 0

[4,7,2,3,6,5,1,8] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 0

[4,7,2,3,5,6,1,8] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0

[5,3,2,7,4,6,1,8] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2

[5,3,2,6,4,7,1,8] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 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] => 0

[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

[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

[4,3,2,6,1,8,5,7] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[6,8,2,3,4,1,7,5] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0

[4,1,8,2,3,5,7,6] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 1

[2,3,1,8,4,5,7,6] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0

[7,3,2,1,4,5,8,6] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3

[7,8,1,4,3,5,2,6] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[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

[6,1,2,3,4,8,7,5] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1

[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

[2,8,1,3,5,4,7,6] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 0

[8,7,1,4,3,5,2,6] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[8,3,2,1,4,5,7,6] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3

[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

[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

[7,4,1,8,3,5,2,6] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[8,4,1,7,3,5,2,6] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[8,4,2,5,3,1,6,7] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[8,5,2,4,3,1,6,7] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[8,3,2,5,4,1,6,7] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[4,3,2,5,1,8,6,7] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[3,5,2,4,1,8,6,7] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[5,1,8,2,7,4,3,6] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1

[5,1,7,2,8,4,3,6] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1

[6,1,2,8,5,3,4,7] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 1

[6,3,2,1,8,4,5,7] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[7,3,2,8,4,5,1,6] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2

[7,1,8,3,5,4,2,6] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1

[7,8,2,3,4,6,1,5] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0

[6,7,1,3,4,8,2,5] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 0

[6,8,1,3,4,7,2,5] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 0

[7,6,2,3,4,1,8,5] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[8,6,2,3,4,1,7,5] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[8,1,7,3,5,4,2,6] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1

[8,3,2,7,4,5,1,6] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2

[6,7,2,3,4,1,8,5] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0

[7,6,2,3,4,8,1,5] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2

[8,6,2,3,4,7,1,5] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2

[6,3,4,8,7,5,1,2] => [[[.,.],[.,[[[.,.],.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 1

[5,8,4,2,1,6,7,3] => [[[[.,[.,.]],.],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 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

[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

[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

[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

[4,8,2,5,1,7,6,3] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 0

[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

[4,8,1,5,2,7,6,3] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 0

[5,8,1,2,4,7,6,3] => [[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 0

[5,2,8,3,6,7,1,4] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[7,8,2,6,5,1,3,4] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 0

[2,8,1,4,5,6,7,3] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 0

[2,1,7,3,6,5,8,4] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1

[3,1,7,2,6,5,8,4] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1

[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

[6,1,2,8,5,7,3,4] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 1

[6,2,1,8,5,7,3,4] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[6,3,1,8,5,7,2,4] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[6,4,2,1,7,5,8,3] => [[[[.,.],.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 3

[6,1,3,8,5,2,7,4] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 1

[7,8,2,6,5,3,1,4] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 0

[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

[7,8,3,6,5,1,2,4] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 0

[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

[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

[2,4,1,5,8,6,3,7] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 0

[4,6,1,2,5,8,3,7] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 0

[7,8,6,5,1,2,4,3] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => 2

[7,4,8,5,3,1,6,2] => [[[[.,.],[[.,.],.]],.],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2

[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

[2,3,1,6,8,5,7,4] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 0

[7,3,2,5,1,4,8,6] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[7,1,4,2,3,6,8,5] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 1

[8,3,1,2,4,7,6,5] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 2

[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

[3,5,2,4,1,7,8,6] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0

[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

[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

[6,1,2,7,5,3,8,4] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 1

[7,3,2,8,6,4,1,5] => [[[[.,.],.],[[[.,.],.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 2

[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

[8,5,2,3,6,1,7,4] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[8,1,6,3,5,7,2,4] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[8,3,2,6,4,7,1,5] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2

[4,2,8,7,3,6,1,5] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[3,2,8,4,7,6,1,5] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[2,1,8,4,3,7,6,5] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 1

[7,1,2,8,6,5,4,3] => [[.,.],[.,[[[[[.,.],.],.],.],.]]] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 1

[7,1,4,8,6,2,5,3] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 1

[7,3,1,8,6,2,5,4] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 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

[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

[7,4,5,8,3,2,1,6] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 3

[3,2,5,8,7,6,1,4] => [[[.,.],[.,[[[.,.],.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 1

[3,2,4,8,7,6,1,5] => [[[.,.],[.,[[[.,.],.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 1

[3,1,5,8,7,2,6,4] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 1

[3,1,4,8,7,2,6,5] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 1

[7,6,1,4,8,2,5,3] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[7,6,1,3,8,2,5,4] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[7,6,3,4,8,2,1,5] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 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

[7,2,5,3,8,6,1,4] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[7,2,1,4,8,6,5,3] => [[[.,.],.],[[.,[[[.,.],.],.]],.]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 2

[7,2,1,3,8,6,5,4] => [[[.,.],.],[.,[[[[.,.],.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 2

[7,2,3,4,8,6,1,5] => [[[.,.],[.,[.,[[.,.],.]]]],[.,.]] => [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 1

[7,3,5,4,8,2,1,6] => [[[[.,.],[[.,.],[.,.]]],.],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 2

[7,6,5,2,3,8,1,4] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3

[7,6,1,4,2,8,5,3] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 2

[7,6,1,2,3,8,5,4] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 2

[7,6,2,4,3,8,1,5] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2

[7,1,5,4,2,8,6,3] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 1

[7,1,5,2,3,8,6,4] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 1

[7,1,2,4,3,8,6,5] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 1

[7,6,1,4,3,2,8,5] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[7,1,5,4,3,2,8,6] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 1

[4,7,1,2,8,5,3,6] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 0

[4,8,1,2,7,5,3,6] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 0

[2,7,1,3,6,8,4,5] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 0

[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

[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

[8,7,4,2,1,5,3,6] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4

[2,7,1,3,6,5,4,8] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 0

[8,4,3,1,5,6,7,2] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 3

[8,5,3,4,1,6,7,2] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[6,4,8,2,1,5,3,7] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2

[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

[6,1,4,2,7,5,3,8] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1

[5,4,3,7,1,6,8,2] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[8,2,7,6,5,4,1,3] => [[[.,.],[[[[.,.],.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1

[7,2,8,6,5,4,3,1] => [[[.,.],[[[[[.,.],.],.],.],.]],.] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 2

[8,7,2,6,5,4,1,3] => [[[[.,.],.],[[[.,.],.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 2

[3,2,8,7,6,5,1,4] => [[[.,.],[[[[.,.],.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1

[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

[7,3,8,6,5,4,2,1] => [[[[.,.],[[[[.,.],.],.],.]],.],.] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 3

[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

[8,6,1,5,3,2,4,7] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[7,8,1,5,3,2,4,6] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0

[8,1,7,5,3,2,4,6] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 1

[8,6,1,4,5,2,3,7] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[8,6,3,1,5,2,4,7] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[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

[8,6,2,1,5,4,3,7] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[8,5,2,6,1,4,3,7] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[8,5,2,1,7,4,3,6] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[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

[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

[8,2,7,5,1,3,4,6] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1

[8,4,1,7,5,2,3,6] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[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

[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

[8,1,7,4,3,2,6,5] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 1

[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

[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

[5,8,1,6,7,2,3,4] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[6,7,2,5,1,8,3,4] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[7,5,1,6,8,2,3,4] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[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

[6,7,3,8,1,2,4,5] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0

[7,5,4,1,8,2,3,6] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[7,6,1,4,8,2,3,5] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[8,1,6,4,7,2,3,5] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[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

[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

[8,3,7,4,1,2,5,6] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1

[8,5,1,7,3,2,4,6] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[6,8,1,7,3,2,4,5] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0

[7,1,8,4,3,6,2,5] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1

[7,3,1,8,6,4,2,5] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 2

[8,3,1,7,4,6,2,5] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[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

[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

[7,3,1,8,5,6,2,4] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[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

[5,8,1,7,3,2,6,4] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[8,4,1,7,3,2,6,5] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[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

[8,2,7,4,1,3,6,5] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 1

[7,4,8,2,1,3,6,5] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2

[7,4,3,8,1,2,6,5] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[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

[7,8,5,2,3,6,4,1] => [[[[.,[.,.]],.],[.,[[.,.],.]]],.] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => 2

[6,8,5,2,3,4,7,1] => [[[[.,[.,.]],.],[.,[.,[.,.]]]],.] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2

[3,5,2,6,8,1,4,7] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[3,5,2,4,6,8,1,7] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0

[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

[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

[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

[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

[4,3,5,7,2,6,8,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[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

[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

[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

[5,7,1,3,4,8,2,6] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 0

[5,7,1,3,4,6,8,2] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 0

[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

[4,6,3,5,1,7,8,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0

[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

[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

[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

[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

[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

[3,5,2,6,1,7,8,4] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0

[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

[5,2,3,6,7,4,8,1] => [[[.,.],[.,[[.,[.,.]],[.,.]]]],.] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[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

[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

[4,2,6,7,3,5,8,1] => [[[.,.],[[.,[.,.]],[.,[.,.]]]],.] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2

[6,3,7,2,4,5,8,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2

[3,7,2,4,8,1,5,6] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[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

[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

[3,7,2,4,6,8,1,5] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0

[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

[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

[6,3,5,7,2,4,8,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[6,2,4,5,7,3,8,1] => [[[.,.],[[.,[.,[.,.]]],[.,.]]],.] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[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

[4,7,1,2,5,6,8,3] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 0

[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

[5,4,2,6,7,3,8,1] => [[[[.,.],.],[[.,[.,.]],[.,.]]],.] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 3

[5,4,2,6,1,7,8,3] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[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

[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

[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

[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

[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

[5,6,4,7,1,3,8,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0

[5,4,6,3,1,7,8,2] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[7,5,3,2,4,8,1,6] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3

[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

[8,5,4,2,1,6,3,7] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4

[8,5,3,4,1,6,2,7] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[8,4,5,3,1,6,2,7] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2

[7,5,4,2,1,8,3,6] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4

[7,5,4,2,1,6,8,3] => [[[[[.,.],.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 4

[7,4,5,3,1,6,8,2] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[7,4,3,5,6,1,8,2] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 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] => 0

[6,7,3,4,1,5,8,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0

[6,7,4,2,1,5,8,3] => [[[[.,[.,.]],.],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[5,6,3,7,8,1,2,4] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[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

[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

[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

[7,6,4,2,1,3,8,5] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 4

[7,6,3,4,1,2,8,5] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[7,6,3,2,4,1,8,5] => [[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3

[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

[6,5,3,2,7,8,1,4] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3

[6,5,3,2,7,4,8,1] => [[[[[.,.],.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 4

[6,4,5,2,7,3,8,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[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

[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

[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

[7,5,6,2,1,3,8,4] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2

[6,7,3,5,1,2,8,4] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 0

[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

[6,5,7,2,1,8,3,4] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2

[6,5,7,2,1,4,8,3] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 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] => 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] => 0

[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

[7,3,5,8,6,1,4,2] => [[[.,.],[.,[[.,.],.]]],[[.,.],.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 1

[7,8,1,5,6,3,4,2] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 0

[7,1,8,5,6,3,4,2] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 1

[7,1,5,8,6,3,4,2] => [[.,.],[[[.,[[.,.],.]],[.,.]],.]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 1

[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

[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

[3,1,7,5,8,6,4,2] => [[.,.],[[[[.,.],[[.,.],.]],.],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 1

[5,1,7,3,8,6,4,2] => [[.,.],[[[.,.],[[[.,.],.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 1

[7,1,5,3,8,6,4,2] => [[.,.],[[[.,.],[[[.,.],.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 1

[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

[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

[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

[5,7,3,8,6,1,4,2] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[3,7,1,8,5,6,4,2] => [[.,[.,.]],[[[[.,.],[.,.]],.],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 0

[5,7,1,8,3,6,4,2] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 0

[5,7,1,8,6,3,4,2] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 0

[7,5,1,8,6,3,4,2] => [[[.,.],.],[[[[.,.],.],[.,.]],.]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 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

[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

[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

[7,5,1,8,3,6,4,2] => [[[.,.],.],[[[.,.],[[.,.],.]],.]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 2

[7,5,1,3,8,6,4,2] => [[[.,.],.],[[.,[[[.,.],.],.]],.]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 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] => 0

[3,7,1,5,8,6,4,2] => [[.,[.,.]],[[[.,[[.,.],.]],.],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 0

[3,5,1,7,8,6,4,2] => [[.,[.,.]],[[[[.,[.,.]],.],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 0

[5,3,1,7,8,6,4,2] => [[[.,.],.],[[[[.,[.,.]],.],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 2

[7,3,1,5,8,6,4,2] => [[[.,.],.],[[[.,[[.,.],.]],.],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 2

[7,3,1,8,5,6,4,2] => [[[.,.],.],[[[[.,.],[.,.]],.],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 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

[7,1,8,3,5,6,4,2] => [[.,.],[[[.,.],[[.,[.,.]],.]],.]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 1

[7,1,3,8,5,6,4,2] => [[.,.],[[.,[[[.,.],[.,.]],.]],.]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 1

[7,1,3,5,8,6,4,2] => [[.,.],[[.,[[.,[[.,.],.]],.]],.]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 1

[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

[5,7,3,4,8,6,1,2] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 0

[5,7,3,4,8,1,6,2] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0

[5,7,3,4,1,8,6,2] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 0

[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

[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

[5,3,7,4,1,2,6,8] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1

[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

[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

[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

[6,1,4,3,5,2,8,7] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[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

[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

[4,7,2,5,8,3,1,6] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 0

[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

[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

[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

[8,7,1,2,5,3,4,6] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2

[5,1,8,2,3,4,7,6] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 1

[5,4,7,6,2,8,1,3] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[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

[8,3,6,5,7,1,4,2] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[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

[2,1,8,4,6,7,3,5] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[3,8,1,5,6,7,2,4] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 0

[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

[8,2,1,7,6,3,5,4] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[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

[7,4,6,3,2,1,8,5] => [[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 3

[4,7,3,2,1,8,6,5] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 2

[6,4,7,5,2,3,8,1] => [[[[.,.],[[.,.],.]],[.,[.,.]]],.] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 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

[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

[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

[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

[4,7,2,6,5,1,8,3] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[6,4,2,1,8,5,7,3] => [[[[.,.],.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 3

[7,2,1,5,6,8,4,3] => [[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 2

[8,7,2,6,4,1,5,3] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[2,1,7,3,6,8,5,4] => [[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 1

[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

[6,4,1,5,7,2,8,3] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 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

[4,2,7,8,6,3,5,1] => [[[.,.],[[[.,[.,.]],.],[.,.]]],.] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[6,1,7,4,3,2,8,5] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 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

[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

[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

[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

[6,8,7,5,3,4,1,2] => [[[[.,[[.,.],.]],.],[.,.]],[.,.]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[4,8,6,3,1,5,7,2] => [[[.,[[.,.],.]],.],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 1

[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

[3,6,2,5,8,7,1,4] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 0

[5,2,8,4,7,6,1,3] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[7,2,4,8,6,5,1,3] => [[[.,.],[.,[[[.,.],.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 1

[6,2,4,8,7,5,1,3] => [[[.,.],[.,[[[.,.],.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 1

[4,2,7,3,8,1,6,5] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[6,1,3,8,7,2,5,4] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 1

[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

[4,1,5,2,8,7,6,3] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 1

[4,1,5,3,2,8,7,6] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 1

[7,4,2,5,1,8,6,3] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2

[4,6,2,7,5,1,8,3] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[3,6,2,5,1,4,8,7] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 0

[5,2,8,4,1,3,7,6] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 1

[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

[6,3,1,7,2,8,5,4] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 2

[7,5,1,2,8,6,4,3] => [[[.,.],.],[.,[[[[.,.],.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 2

[4,5,1,2,8,7,6,3] => [[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => 0

[6,4,1,2,8,7,5,3] => [[[.,.],.],[.,[[[[.,.],.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 2

[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

[8,6,4,7,5,3,1,2] => [[[[[.,.],.],[[.,.],.]],.],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 3

[7,5,2,6,4,1,3,8] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[7,2,6,3,4,1,5,8] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[8,3,7,4,6,5,1,2] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[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

[8,6,5,2,1,4,3,7] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4

[6,8,5,3,2,1,4,7] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 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] => 0

[6,1,3,7,5,8,4,2] => [[.,.],[[.,[[[.,.],[.,.]],.]],.]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 1

[4,1,7,3,6,8,5,2] => [[.,.],[[[.,.],[[.,[.,.]],.]],.]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 1

[8,1,6,4,3,7,5,2] => [[.,.],[[[[.,.],.],[[.,.],.]],.]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 1

[2,1,7,4,8,6,3,5] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1

[2,1,3,8,4,7,5,6] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 1

[8,1,2,7,4,3,6,5] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 1

[5,3,1,6,8,4,7,2] => [[[.,.],.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[6,2,8,7,1,4,3,5] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[8,7,2,1,5,4,3,6] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 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

[3,4,2,7,1,5,6,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0

[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

[5,2,7,3,1,4,6,8] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1

[8,3,7,2,1,5,4,6] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2

[6,5,3,8,2,1,4,7] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 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

[7,6,3,1,8,4,5,2] => [[[[.,.],.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 3

[7,6,2,1,8,5,3,4] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[6,5,1,2,8,3,7,4] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2

[8,6,1,4,3,7,5,2] => [[[.,.],.],[[[.,.],[[.,.],.]],.]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 2

[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

[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

[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

[8,3,1,7,5,4,6,2] => [[[.,.],.],[[[[.,.],.],[.,.]],.]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 2

[8,2,1,7,6,4,3,5] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 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] => 0

[2,4,1,8,5,7,3,6] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[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

[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

[8,7,1,6,5,4,3,2] => [[[.,.],.],[[[[[.,.],.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2

[7,1,8,3,6,5,4,2] => [[.,.],[[[.,.],[[[.,.],.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 1

[4,1,8,7,5,6,3,2] => [[.,.],[[[[[.,.],.],[.,.]],.],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 1

[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

[5,8,2,7,1,6,4,3] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 0

[2,1,6,4,5,8,3,7] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[8,6,3,7,5,2,1,4] => [[[[[.,.],.],[[.,.],.]],.],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 3

[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

[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

[5,6,2,4,1,3,8,7] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 0

[7,6,3,8,5,2,4,1] => [[[[[.,.],.],[[.,.],.]],[.,.]],.] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 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

[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

[8,2,3,4,7,5,1,6] => [[[.,.],[.,[.,[[.,.],.]]]],[.,.]] => [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 1

[7,2,3,4,6,8,5,1] => [[[.,.],[.,[.,[[.,[.,.]],.]]]],.] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 2

[7,8,3,6,5,1,4,2] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[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

[4,8,3,7,5,1,6,2] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[5,2,3,4,7,8,6,1] => [[[.,.],[.,[.,[[.,[.,.]],.]]]],.] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 2

[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

[5,2,3,4,8,7,1,6] => [[[.,.],[.,[.,[[.,.],.]]]],[.,.]] => [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 1

[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

[4,2,8,5,7,6,1,3] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[4,7,3,6,5,8,2,1] => [[[[.,[.,.]],[[.,.],[.,.]]],.],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 2

[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

[8,7,3,6,5,1,2,4] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[8,2,7,5,1,6,3,4] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[4,2,7,5,8,6,3,1] => [[[.,.],[[[.,.],[[.,.],.]],.]],.] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 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] => 0

[5,2,7,8,4,6,3,1] => [[[.,.],[[[.,[.,.]],[.,.]],.]],.] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 2

[5,2,8,3,7,6,1,4] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[8,2,7,3,1,6,4,5] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 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

[6,7,3,8,5,4,2,1] => [[[[.,[.,.]],[[[.,.],.],.]],.],.] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 2

[6,2,3,4,7,5,8,1] => [[[.,.],[.,[.,[[.,.],[.,.]]]]],.] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 2

[6,2,3,4,8,5,1,7] => [[[.,.],[.,[.,[[.,.],.]]]],[.,.]] => [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 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

[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

[6,2,3,4,8,7,5,1] => [[[.,.],[.,[.,[[[.,.],.],.]]]],.] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 2

[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

[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

[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

[8,6,7,4,1,5,3,2] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 2

[7,1,8,4,6,5,2,3] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1

[8,7,1,5,4,6,2,3] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 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

[6,4,8,5,1,7,3,2] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[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

[8,7,1,4,5,6,3,2] => [[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 2

[8,7,4,5,6,1,3,2] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[8,7,5,1,4,6,2,3] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3

[8,7,2,5,1,4,6,3] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[8,7,1,4,2,5,6,3] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[8,7,5,1,2,4,6,3] => [[[[.,.],.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 3

[7,1,8,5,6,2,3,4] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[3,2,8,6,7,5,1,4] => [[[.,.],[[[.,.],[.,.]],.]],[.,.]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1

[4,1,8,6,2,7,5,3] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 1

[8,7,4,1,2,6,5,3] => [[[[.,.],.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 3

[5,7,1,8,2,6,3,4] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[8,7,1,5,2,4,6,3] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[7,1,8,2,4,6,5,3] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 1

[5,7,1,8,2,3,6,4] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0

[7,1,8,2,3,5,6,4] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 1

[8,6,3,7,4,1,5,2] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[4,2,8,6,7,5,1,3] => [[[.,.],[[[.,.],[.,.]],.]],[.,.]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1

[8,4,2,7,5,6,1,3] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2

[4,8,3,6,1,7,5,2] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 0

[8,3,4,7,5,1,6,2] => [[[.,.],[.,[[.,.],.]]],[[.,.],.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 1

[8,3,7,4,5,1,6,2] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[8,7,4,2,5,6,1,3] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3

[8,7,5,1,6,2,3,4] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[8,7,2,4,1,5,6,3] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 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] => 0

[4,2,8,6,7,1,5,3] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[8,7,4,1,2,5,6,3] => [[[[.,.],.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 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

[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

[8,7,2,1,3,5,6,4] => [[[[.,.],.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 3

[8,2,7,3,6,1,4,5] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[8,2,7,4,1,5,6,3] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 1

[8,2,1,7,5,6,3,4] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[8,7,3,1,5,6,2,4] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3

[8,3,1,6,7,5,2,4] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 2

[8,5,2,1,6,7,4,3] => [[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[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

[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

[8,1,3,7,5,6,2,4] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 1

[8,4,1,2,7,5,6,3] => [[[.,.],.],[.,[[[.,.],[.,.]],.]]] => [1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2

[8,1,4,2,6,7,5,3] => [[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 1

[8,1,2,7,3,6,4,5] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 1

[8,1,7,3,6,2,4,5] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[8,1,7,2,6,3,4,5] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[8,1,7,2,3,6,4,5] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 1

[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

[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

[8,7,1,2,3,6,4,5] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 2

[3,1,8,5,7,4,2,6] => [[.,.],[[[[.,.],[.,.]],.],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 1

[8,3,5,7,4,2,6,1] => [[[[.,.],[[.,[.,.]],.]],[.,.]],.] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[8,3,6,2,4,5,7,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2

[8,4,2,7,6,1,3,5] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[4,8,1,7,6,3,2,5] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 0

[4,1,7,6,2,3,5,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1

[3,7,1,8,6,2,5,4] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[3,1,7,6,4,5,2,8] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1

[3,1,7,5,8,4,2,6] => [[.,.],[[[[.,.],[.,.]],.],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 1

[3,1,6,8,7,5,2,4] => [[.,.],[[[.,[[.,.],.]],.],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 1

[6,3,8,7,5,2,4,1] => [[[[.,.],[[[.,.],.],.]],[.,.]],.] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 2

[7,3,5,8,4,2,6,1] => [[[[.,.],[[.,[.,.]],.]],[.,.]],.] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[7,3,6,4,2,8,5,1] => [[[[.,.],[[.,.],.]],[[.,.],.]],.] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 2

[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

[7,4,8,2,1,6,3,5] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2

[8,7,4,6,3,2,5,1] => [[[[[[.,.],.],[.,.]],.],[.,.]],.] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 4

[7,8,5,2,1,4,3,6] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 2

[7,5,2,3,1,4,8,6] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[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

[6,4,2,5,8,3,7,1] => [[[[.,.],.],[[.,[.,.]],[.,.]]],.] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 3

[4,7,1,5,3,8,2,6] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[5,7,1,3,4,6,2,8] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 0

[5,7,1,4,2,3,6,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0

[5,8,1,3,2,4,6,7] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0

[8,4,6,2,1,3,7,5] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2

[5,4,8,7,2,3,6,1] => [[[[.,.],[[.,.],.]],[.,[.,.]]],.] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 2

[5,4,8,7,3,1,2,6] => [[[[.,.],[[.,.],.]],.],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 2

[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

[5,4,6,8,2,3,7,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[5,7,4,2,8,3,6,1] => [[[[.,[.,.]],.],[[.,.],[.,.]]],.] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => 2

[6,4,7,2,1,8,3,5] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2

[6,5,3,4,1,2,8,7] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[6,8,5,4,1,3,2,7] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 2

[6,4,3,7,1,5,2,8] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[6,4,2,8,1,5,7,3] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[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

[7,3,5,6,4,2,1,8] => [[[[.,.],[[.,[.,.]],.]],.],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 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] => 2

[5,3,7,6,8,2,4,1] => [[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[6,3,8,7,2,4,1,5] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[5,3,8,7,2,6,4,1] => [[[[.,.],[[.,.],.]],[[.,.],.]],.] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 2

[5,3,8,6,7,2,4,1] => [[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[5,3,7,8,6,2,4,1] => [[[[.,.],[[.,[.,.]],.]],[.,.]],.] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[6,5,2,4,3,7,8,1] => [[[[.,.],.],[[.,.],[.,[.,.]]]],.] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 3

[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

[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

[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

[3,6,2,5,7,8,1,4] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0

[5,2,7,4,6,8,1,3] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[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

[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

[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

[8,1,4,2,7,5,3,6] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1

[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

[4,5,1,8,2,3,7,6] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0

[4,7,1,8,2,6,3,5] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[7,5,1,2,3,8,6,4] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 2

[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

[6,7,1,3,2,5,4,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[7,8,2,4,3,5,1,6] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[7,8,2,4,1,5,3,6] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[6,7,2,4,3,5,1,8] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[2,4,1,6,5,7,3,8] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[2,5,1,6,4,7,3,8] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[4,5,2,6,1,7,3,8] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[4,5,1,6,3,7,2,8] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[4,5,3,6,1,7,2,8] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[5,6,3,4,1,7,2,8] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[6,7,5,8,1,3,2,4] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[4,5,1,3,2,7,6,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[4,6,1,3,2,7,5,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[3,4,1,6,5,7,2,8] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[4,5,2,3,1,7,6,8] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[3,5,1,6,4,7,2,8] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[3,5,2,6,1,7,4,8] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[3,5,2,6,4,7,1,8] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[3,4,2,6,1,7,5,8] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[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

[4,6,1,7,3,8,2,5] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[5,2,6,7,4,3,8,1] => [[[.,.],[[[.,[.,.]],.],[.,.]]],.] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[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

[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

[4,6,2,7,1,8,3,5] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[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

[2,1,5,6,8,7,3,4] => [[.,.],[[.,[.,[[.,.],.]]],[.,.]]] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 1

[6,2,4,7,5,8,3,1] => [[[.,.],[[.,[[.,.],[.,.]]],.]],.] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 2

[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

[4,6,3,2,1,7,5,8] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 2

[4,3,5,7,6,1,8,2] => [[[.,.],[.,[[.,.],.]]],[[.,.],.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 1

[4,3,2,6,1,7,5,8] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[5,3,2,1,6,4,7,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[5,3,1,6,2,7,4,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[5,1,6,3,2,7,4,8] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[4,6,1,7,5,3,2,8] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 0

[5,1,6,3,7,4,2,8] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1

[5,3,6,4,2,1,7,8] => [[[[.,.],[[.,.],.]],.],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 2

[5,3,2,6,4,1,7,8] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[5,2,1,6,3,7,4,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[5,2,6,3,1,7,4,8] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[4,2,6,3,1,7,8,5] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 1

[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

[3,6,2,7,4,1,5,8] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 0

[2,6,1,3,7,5,4,8] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 0

[5,1,6,2,7,4,3,8] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1

[5,2,6,4,3,1,7,8] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 1

[5,2,1,6,4,3,7,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[5,4,2,1,6,3,7,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[5,4,2,6,3,1,7,8] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[5,4,1,6,2,7,3,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[5,1,6,4,2,7,3,8] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[2,6,1,5,4,3,7,8] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0

[3,1,6,2,5,4,7,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[5,1,6,4,3,2,7,8] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 1

[5,4,1,6,3,2,7,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[5,4,3,1,6,2,7,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[3,8,2,6,5,4,1,7] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 0

[7,3,2,1,5,4,6,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[5,2,7,6,8,4,1,3] => [[[.,.],[[[.,.],[.,.]],.]],[.,.]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1

[7,4,2,1,5,6,3,8] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3

[7,2,8,6,5,1,3,4] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 1

[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

[6,7,1,4,3,2,5,8] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0

[3,4,2,6,7,1,5,8] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[3,7,1,6,5,2,4,8] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0

[8,7,2,5,4,3,6,1] => [[[[.,.],.],[[[.,.],.],[.,.]]],.] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 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] => 0

[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

[4,7,3,5,1,8,6,2] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 0

[8,7,3,6,1,5,4,2] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2

[5,4,2,1,7,8,3,6] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3

[4,7,6,2,1,8,3,5] => [[[.,[[.,.],.]],.],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[8,3,6,2,1,7,5,4] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 2

[8,3,7,6,4,2,1,5] => [[[[.,.],[[[.,.],.],.]],.],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 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] => 0

[8,6,5,1,4,7,3,2] => [[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[8,5,4,1,7,3,6,2] => [[[[.,.],.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 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] => 2

[6,2,7,4,1,8,5,3] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[8,6,3,2,7,5,1,4] => [[[[[.,.],.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3

[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

[3,4,2,8,7,6,1,5] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 0

[5,1,4,3,2,7,8,6] => [[.,.],[[[.,.],.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 1

[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

[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

[5,3,1,7,8,4,2,6] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 2

[4,1,7,6,3,2,8,5] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 1

[8,4,2,7,6,3,1,5] => [[[[.,.],.],[[[.,.],.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 2

[6,3,1,7,5,2,8,4] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[6,2,7,5,3,1,8,4] => [[[.,.],[[[.,.],.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 1

[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

[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

[8,4,7,3,1,6,5,2] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 2

[6,5,2,1,7,4,8,3] => [[[[.,.],.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 3

[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

[5,6,4,8,3,7,2,1] => [[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2

[6,7,1,8,3,4,2,5] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[5,6,2,7,1,8,3,4] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[2,3,1,8,5,6,4,7] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[4,6,2,7,1,5,3,8] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[4,7,1,6,2,5,3,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[4,7,1,5,3,6,2,8] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[4,7,2,3,1,8,5,6] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[5,2,6,8,3,7,4,1] => [[[.,.],[[.,[.,.]],[[.,.],.]]],.] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 2

[3,1,6,8,7,4,5,2] => [[.,.],[[[.,[[.,.],.]],[.,.]],.]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 1

[6,1,4,8,7,2,5,3] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 1

[6,1,8,4,7,3,5,2] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 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] => 2

[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

[6,7,4,2,8,5,3,1] => [[[[.,[.,.]],.],[[[.,.],.],.]],.] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 2

[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

[6,7,4,8,1,5,3,2] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 0

[6,8,5,3,7,2,4,1] => [[[[[.,[.,.]],.],[.,.]],[.,.]],.] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,8,5,2,3,7,4,1] => [[[[.,[.,.]],.],[.,[[.,.],.]]],.] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => 2

[7,5,3,8,2,6,4,1] => [[[[[.,.],.],[.,.]],[[.,.],.]],.] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[7,5,2,3,8,6,4,1] => [[[[.,.],.],[.,[[[.,.],.],.]]],.] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 3

[6,7,3,4,8,5,2,1] => [[[[.,[.,.]],[.,[[.,.],.]]],.],.] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 2

[7,4,2,5,8,6,3,1] => [[[[.,.],.],[[.,[[.,.],.]],.]],.] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 3

[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

[6,3,4,7,8,5,2,1] => [[[[.,.],[.,[[.,[.,.]],.]]],.],.] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 3

[6,1,2,7,4,5,8,3] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 1

[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

[7,8,1,4,6,2,3,5] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[7,8,1,2,3,5,4,6] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 0

[7,8,1,4,5,2,6,3] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[7,8,1,2,3,4,6,5] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 0

[7,8,1,2,3,6,4,5] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 0

[4,2,1,6,5,3,8,7] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[4,2,6,3,5,1,8,7] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[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

[8,6,2,4,3,1,5,7] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[2,1,6,4,8,5,7,3] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 1

[8,4,2,6,3,5,1,7] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2

[4,2,6,3,5,8,7,1] => [[[.,.],[[.,.],[.,[[.,.],.]]]],.] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 2

[6,2,4,3,8,5,7,1] => [[[.,.],[[.,.],[[.,.],[.,.]]]],.] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 2

[8,2,4,3,6,5,1,7] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[6,2,1,8,4,3,7,5] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[6,4,8,5,2,1,7,3] => [[[[.,.],[[.,.],.]],.],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2

[4,2,8,6,5,7,1,3] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[8,2,6,4,5,1,3,7] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[7,2,8,4,3,5,1,6] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[8,4,2,1,5,3,6,7] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[8,5,1,4,2,3,6,7] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2

[8,4,1,5,3,2,6,7] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[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

[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

[7,1,8,4,3,5,2,6] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1

[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

[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

[7,1,8,4,3,5,6,2] => [[.,.],[[[[.,.],.],[.,[.,.]]],.]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 1

[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

[6,7,3,8,4,5,2,1] => [[[[.,[.,.]],[[.,.],[.,.]]],.],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 2

[6,7,1,4,8,3,5,2] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 0

[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

[7,2,1,8,4,5,3,6] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[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

[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

[6,2,7,8,4,3,5,1] => [[[.,.],[[[.,[.,.]],.],[.,.]]],.] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 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] => 0

[6,2,7,8,4,5,3,1] => [[[.,.],[[[.,[.,.]],[.,.]],.]],.] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 2

[7,2,1,8,4,5,6,3] => [[[.,.],.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[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

[6,7,1,2,8,5,3,4] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 0

[3,1,2,7,6,5,8,4] => [[.,.],[.,[[[[.,.],.],[.,.]],.]]] => [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 1

[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

[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

[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

[4,6,1,7,3,2,5,8] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0

[4,6,1,8,3,2,5,7] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0

[4,7,1,8,3,5,2,6] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[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

[4,1,8,7,6,2,3,5] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 1

[4,8,1,7,3,5,2,6] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[4,8,1,6,3,2,5,7] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0

[4,7,1,6,3,2,5,8] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0

[6,1,2,3,7,5,4,8] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 1

[6,8,1,5,3,7,2,4] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[8,7,5,2,4,1,6,3] => [[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3

[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

[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

[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

[8,1,2,3,5,4,7,6] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 1

[7,1,8,4,6,3,2,5] => [[.,.],[[[[.,.],[.,.]],.],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 1

[6,8,2,4,3,1,5,7] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 0

[6,7,2,4,3,1,5,8] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 0

[3,8,1,2,4,5,7,6] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 0

[3,7,1,8,6,4,2,5] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 0

[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

[3,8,1,7,6,4,2,5] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 0

[7,6,2,4,3,1,5,8] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[8,7,2,4,3,5,1,6] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2

[8,1,7,4,6,3,2,5] => [[.,.],[[[[.,.],[.,.]],.],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 1

[8,1,7,6,5,3,2,4] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 1

[8,7,2,5,3,6,1,4] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2

[7,1,2,3,5,4,8,6] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 1

[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

[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

[5,1,2,3,7,6,4,8] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 1

[5,1,2,3,8,6,4,7] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 1

[8,6,5,2,4,7,1,3] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3

[7,6,2,5,3,1,8,4] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 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] => 2

[8,2,3,7,4,5,1,6] => [[[.,.],[.,[[.,.],[.,.]]]],[.,.]] => [1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 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] => 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] => 2

[4,6,2,3,1,5,8,7] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 0

[7,2,3,4,5,8,6,1] => [[[.,.],[.,[.,[.,[[.,.],.]]]]],.] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 2

[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

[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

[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

[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

[4,8,1,5,6,7,3,2] => [[.,[.,.]],[[[.,[.,[.,.]]],.],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 0

[5,8,2,4,6,7,1,3] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0

[6,8,1,3,4,2,7,5] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[5,8,2,4,3,1,7,6] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[2,1,7,6,8,5,3,4] => [[.,.],[[[[.,.],[.,.]],.],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 1

[4,7,2,3,8,5,1,6] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 0

[7,1,3,6,4,8,5,2] => [[.,.],[[.,[[.,.],[[.,.],.]]],.]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 1

[7,6,1,4,8,5,2,3] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 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] => 2

[6,2,3,8,4,5,1,7] => [[[.,.],[.,[[.,.],[.,.]]]],[.,.]] => [1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 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

[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

[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

[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

[3,5,1,8,4,6,7,2] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 0

[3,6,1,8,4,5,2,7] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[4,8,2,3,5,6,1,7] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0

[6,8,2,3,1,4,5,7] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0

[5,2,7,4,8,3,1,6] => [[[.,.],[[[.,.],[.,.]],.]],[.,.]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1

[6,3,2,4,1,8,7,5] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2

[7,2,3,4,8,5,1,6] => [[[.,.],[.,[.,[[.,.],.]]]],[.,.]] => [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 1

[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

[6,3,7,4,8,1,2,5] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[8,3,7,4,2,6,1,5] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[8,4,1,6,3,7,5,2] => [[[.,.],.],[[[.,.],[[.,.],.]],.]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 2

[8,7,4,2,1,6,3,5] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 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

[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

[3,1,8,6,7,5,2,4] => [[.,.],[[[[.,.],[.,.]],.],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 1

[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

[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

[5,2,1,8,7,4,3,6] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 2

[5,2,6,3,8,1,4,7] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[5,2,8,3,4,6,1,7] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[6,2,8,4,3,1,7,5] => [[[.,.],[[[.,.],.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 1

[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

[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

[5,3,8,4,1,2,7,6] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 1

[5,8,4,3,6,2,1,7] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 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] => 0

[3,8,2,5,1,7,6,4] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 0

[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

[8,2,4,3,5,1,7,6] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[8,2,1,4,6,5,7,3] => [[[.,.],.],[[.,[[.,.],[.,.]]],.]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 2

[8,1,3,4,5,7,6,2] => [[.,.],[[.,[.,[.,[[.,.],.]]]],.]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 1

[6,1,5,2,4,7,8,3] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 1

[4,1,8,5,2,7,6,3] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 1

[4,1,8,2,3,7,5,6] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 1

[5,3,8,7,2,1,4,6] => [[[[.,.],[[.,.],.]],.],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 2

[6,7,3,5,1,4,8,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0

[6,4,7,5,8,2,3,1] => [[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[5,4,7,6,2,8,3,1] => [[[[.,.],[[.,.],.]],[[.,.],.]],.] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 2

[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

[6,8,4,5,7,1,3,2] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0

[5,8,4,6,1,7,3,2] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 0

[5,6,1,4,7,8,3,2] => [[.,[.,.]],[[[.,[.,[.,.]]],.],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 0

[5,6,3,7,4,8,2,1] => [[[[.,[.,.]],[[.,.],[.,.]]],.],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 2

[5,3,6,7,4,8,2,1] => [[[[.,.],[[.,[.,.]],[.,.]]],.],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[5,3,2,8,6,7,4,1] => [[[[.,.],.],[[[.,.],[.,.]],.]],.] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[5,4,8,2,6,7,3,1] => [[[[.,.],[.,.]],[[.,[.,.]],.]],.] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 2

[5,4,8,6,2,7,3,1] => [[[[.,.],[[.,.],.]],[[.,.],.]],.] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 2

[6,4,8,5,7,2,3,1] => [[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[7,4,8,5,6,2,1,3] => [[[[.,.],[[.,.],[.,.]]],.],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 2

[5,6,3,8,4,7,2,1] => [[[[.,[.,.]],[[.,.],[.,.]]],.],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 2

[4,6,3,5,8,7,2,1] => [[[[.,[.,.]],[.,[[.,.],.]]],.],.] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 2

[4,6,3,2,8,7,5,1] => [[[[.,[.,.]],.],[[[.,.],.],.]],.] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 2

[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

[5,3,6,8,2,7,4,1] => [[[[.,.],[.,[.,.]]],[[.,.],.]],.] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 2

[4,3,7,2,8,6,5,1] => [[[[.,.],[.,.]],[[[.,.],.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 2

[5,4,7,2,6,8,3,1] => [[[[.,.],[.,.]],[[.,[.,.]],.]],.] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 2

[5,3,2,7,6,8,4,1] => [[[[.,.],.],[[[.,.],[.,.]],.]],.] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[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

[6,3,2,7,5,4,8,1] => [[[[.,.],.],[[[.,.],.],[.,.]]],.] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 3

[6,4,7,2,5,3,8,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[6,2,7,5,1,4,8,3] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 1

[6,3,7,8,4,2,5,1] => [[[[.,.],[[.,[.,.]],.]],[.,.]],.] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[5,3,7,8,4,6,2,1] => [[[[.,.],[[.,[.,.]],[.,.]]],.],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[4,3,7,5,8,6,2,1] => [[[[.,.],[[.,.],[[.,.],.]]],.],.] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 3

[6,3,1,8,7,5,4,2] => [[[.,.],.],[[[[[.,.],.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2

[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

[8,5,4,1,7,6,3,2] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3

[7,2,8,4,5,1,3,6] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 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] => 3

[7,2,8,4,1,5,6,3] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 1

[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

[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

[6,5,4,3,8,1,7,2] => [[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3

[7,3,6,8,5,2,4,1] => [[[[.,.],[[.,[.,.]],.]],[.,.]],.] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[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

[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

[6,1,2,8,3,7,4,5] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 1

[6,1,2,8,5,4,7,3] => [[.,.],[.,[[[[.,.],.],[.,.]],.]]] => [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 1

[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

[6,5,2,1,8,7,3,4] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[6,2,5,3,8,4,7,1] => [[[.,.],[[.,.],[[.,.],[.,.]]]],.] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 2

[6,5,2,3,8,7,1,4] => [[[[.,.],.],[.,[[.,.],.]]],[.,.]] => [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 2

[5,4,1,2,3,8,6,7] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 2

[5,1,4,2,3,7,8,6] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 1

[5,1,6,3,8,2,7,4] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[5,2,7,4,1,6,3,8] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[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

[5,8,3,4,1,6,7,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0

[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

[6,2,3,7,5,1,4,8] => [[[.,.],[.,[[.,.],.]]],[.,[.,.]]] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 1

[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

[8,7,3,2,1,6,5,4] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4

[8,7,6,3,1,5,2,4] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4

[8,5,1,7,2,3,4,6] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 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] => 0

[3,4,1,5,8,2,7,6] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[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

[3,4,1,5,2,8,7,6] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 0

[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

[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

[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

[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

[3,4,1,6,8,7,2,5] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 0

[2,1,3,8,6,7,4,5] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 1

[8,1,3,2,6,7,5,4] => [[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 1

[2,4,1,8,6,7,5,3] => [[.,[.,.]],[[[[.,.],[.,.]],.],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 0

[3,4,1,6,8,7,5,2] => [[.,[.,.]],[[[.,[[.,.],.]],.],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 0

[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

[3,5,1,6,7,8,4,2] => [[.,[.,.]],[[[.,[.,[.,.]]],.],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 0

[3,5,1,6,7,4,8,2] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 0

[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

[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

[3,5,1,6,7,4,2,8] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 0

[6,5,8,7,4,3,1,2] => [[[[[.,.],[[.,.],.]],.],.],[.,.]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 3

[6,4,2,7,8,5,1,3] => [[[[.,.],.],[[.,[.,.]],.]],[.,.]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 2

[6,1,4,8,7,5,2,3] => [[.,.],[[.,[[[.,.],.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 1

[8,1,6,2,4,7,3,5] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[7,6,2,1,4,8,3,5] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3

[6,4,1,7,8,5,2,3] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 2

[7,6,1,2,4,8,3,5] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 2

[7,6,1,3,4,8,2,5] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 2

[8,1,6,3,4,7,2,5] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[7,1,2,5,4,8,3,6] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 1

[2,7,1,5,4,8,3,6] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[7,2,1,5,4,8,3,6] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[3,2,7,5,4,8,1,6] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[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

[3,7,2,5,4,8,1,6] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[3,1,7,5,4,8,2,6] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1

[5,1,8,4,7,3,2,6] => [[.,.],[[[[.,.],[.,.]],.],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 1

[5,8,2,4,7,3,1,6] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 0

[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

[8,7,5,6,2,1,4,3] => [[[[[.,.],.],[.,.]],.],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 3

[8,5,2,4,7,3,1,6] => [[[[.,.],.],[[.,[.,.]],.]],[.,.]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 2

[8,1,5,4,7,3,2,6] => [[.,.],[[[[.,.],[.,.]],.],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 1

[8,6,3,1,4,7,2,5] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3

[8,6,4,2,7,5,1,3] => [[[[[.,.],.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3

[8,6,4,1,7,2,5,3] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3

[5,3,7,4,6,8,2,1] => [[[[.,.],[[.,.],[.,[.,.]]]],.],.] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 3

[4,1,3,2,7,8,5,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[5,7,3,4,6,8,2,1] => [[[[.,[.,.]],[.,[.,[.,.]]]],.],.] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 2

[8,2,5,4,7,3,1,6] => [[[.,.],[[[.,.],[.,.]],.]],[.,.]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1

[7,2,3,5,4,8,1,6] => [[[.,.],[.,[[.,.],[.,.]]]],[.,.]] => [1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1

[3,2,1,4,7,8,5,6] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 2

[8,1,7,6,4,3,5,2] => [[.,.],[[[[[.,.],.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 1

[8,6,4,5,2,7,1,3] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[7,1,8,6,4,3,5,2] => [[.,.],[[[[[.,.],.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 1

[7,4,2,5,1,6,3,8] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[7,3,6,5,2,1,4,8] => [[[[.,.],[[.,.],.]],.],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 2

[8,3,6,5,2,1,7,4] => [[[[.,.],[[.,.],.]],.],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2

[7,3,6,5,2,1,8,4] => [[[[.,.],[[.,.],.]],.],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2

[7,5,8,6,4,2,1,3] => [[[[[.,.],[[.,.],.]],.],.],[.,.]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 3

[5,4,2,8,1,3,7,6] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[5,8,2,6,4,1,3,7] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 0

[6,4,2,5,1,8,3,7] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[6,3,5,2,1,4,7,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2

[6,3,8,5,2,7,1,4] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[6,3,7,5,2,1,4,8] => [[[[.,.],[[.,.],.]],.],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 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] => 2

[8,4,2,5,1,3,7,6] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[7,3,8,5,2,1,4,6] => [[[[.,.],[[.,.],.]],.],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 2

[8,3,5,2,1,4,6,7] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2

[2,7,1,5,8,3,4,6] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[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

[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

[7,4,5,8,6,1,2,3] => [[[.,.],[.,[[.,.],.]]],[.,[.,.]]] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 1

[5,1,8,7,6,2,3,4] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 1

[4,6,1,8,7,5,2,3] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 0

[4,5,1,8,7,2,3,6] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0

[6,4,8,7,1,2,5,3] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 1

[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

[6,5,1,2,7,3,8,4] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2

[6,5,1,8,2,7,3,4] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[6,5,1,8,7,2,3,4] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[6,5,1,7,2,8,3,4] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[6,5,1,7,2,3,8,4] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2

[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

[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

[4,1,7,5,3,6,2,8] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1

[4,1,7,2,3,6,8,5] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 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

[4,5,2,3,1,7,8,6] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0

[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

[5,6,2,7,1,4,8,3] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0

[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

[4,6,2,7,5,1,3,8] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 0

[5,3,2,7,4,8,1,6] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2

[5,1,2,7,6,8,4,3] => [[.,.],[.,[[[[.,.],[.,.]],.],.]]] => [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 1

[5,3,6,4,2,8,7,1] => [[[[.,.],[[.,.],.]],[[.,.],.]],.] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 2

[5,4,2,3,7,8,6,1] => [[[[.,.],.],[.,[[.,[.,.]],.]]],.] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[4,1,8,2,5,7,3,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[6,2,3,8,4,1,7,5] => [[[.,.],[.,[[.,.],.]]],[[.,.],.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 1

[6,2,1,4,7,8,3,5] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 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

[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

[5,1,7,4,2,6,3,8] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[6,8,5,2,1,7,3,4] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 2

[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

[6,8,4,3,1,5,7,2] => [[[[.,[.,.]],.],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 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] => 2

[5,1,7,3,2,4,6,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1

[5,2,1,8,3,6,7,4] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 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

[4,2,1,8,5,7,3,6] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[6,3,2,1,7,4,5,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[6,4,2,1,7,5,3,8] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[7,5,2,1,8,6,3,4] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[5,3,2,7,6,1,4,8] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[5,3,2,8,6,1,4,7] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[6,3,2,8,7,1,4,5] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[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

[4,3,8,7,2,1,5,6] => [[[[.,.],[[.,.],.]],.],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 2

[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

[5,4,1,7,2,8,6,3] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 2

[6,5,3,1,7,8,4,2] => [[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[5,4,2,1,6,7,3,8] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3

[6,4,2,1,7,8,5,3] => [[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[5,3,2,1,6,7,8,4] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 3

[8,6,1,4,5,7,2,3] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 2

[5,2,8,3,7,4,6,1] => [[[.,.],[[.,.],[[.,.],[.,.]]]],.] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 2

[6,2,8,5,4,7,3,1] => [[[.,.],[[[[.,.],.],[.,.]],.]],.] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 2

[6,5,3,8,4,7,2,1] => [[[[[.,.],.],[[.,.],[.,.]]],.],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 4

[6,2,8,3,7,4,1,5] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[6,4,3,7,1,2,8,5] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[6,4,3,8,1,2,7,5] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[7,6,3,8,4,2,1,5] => [[[[[.,.],.],[[.,.],.]],.],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 3

[7,5,3,8,4,2,6,1] => [[[[[.,.],.],[[.,.],.]],[.,.]],.] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 3

[6,4,2,7,3,1,5,8] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[5,4,1,6,3,8,7,2] => [[[.,.],.],[[[.,.],[[.,.],.]],.]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 2

[6,5,1,7,8,2,3,4] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[6,3,1,7,8,4,2,5] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 2

[6,1,5,4,3,2,8,7] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 1

[8,7,6,1,3,5,2,4] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3

[8,1,6,5,7,3,4,2] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 1

[8,4,1,5,7,6,2,3] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 2

[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

[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

[8,1,3,7,4,2,5,6] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 1

[4,3,8,7,5,2,1,6] => [[[[.,.],[[[.,.],.],.]],.],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 2

[6,7,1,8,5,3,4,2] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 0

[6,5,2,7,1,4,8,3] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 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

[7,5,2,1,3,8,4,6] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3

[8,4,7,6,3,1,5,2] => [[[[.,.],[[.,.],.]],.],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2

[7,4,1,5,6,3,8,2] => [[[.,.],.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[5,4,1,7,6,2,8,3] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 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

[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

[8,6,2,5,7,1,4,3] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[5,8,4,3,2,6,7,1] => [[[[[.,[.,.]],.],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 3

[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

[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

[2,3,1,7,8,6,4,5] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 0

[5,4,1,2,8,6,7,3] => [[[.,.],.],[.,[[[.,.],[.,.]],.]]] => [1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2

[8,4,5,2,1,6,7,3] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 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

[5,1,3,2,7,8,4,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[7,6,2,8,4,3,1,5] => [[[[.,.],.],[[[.,.],.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 2

[5,2,8,6,3,4,7,1] => [[[.,.],[[[.,.],.],[.,[.,.]]]],.] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 2

[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

[6,5,1,8,4,3,7,2] => [[[.,.],.],[[[[.,.],.],[.,.]],.]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 2

[6,3,8,4,2,1,7,5] => [[[[.,.],[[.,.],.]],.],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2

[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

[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

[5,1,8,3,4,6,7,2] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 1

[4,8,7,2,1,6,3,5] => [[[.,[[.,.],.]],.],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[2,8,1,6,3,4,7,5] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0

[8,3,4,2,1,6,5,7] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2

[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

[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

[8,6,1,3,5,2,4,7] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[8,5,1,2,6,4,3,7] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 2

[5,8,4,6,1,3,2,7] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[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

[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

[7,4,1,8,3,2,5,6] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[6,2,1,7,8,4,5,3] => [[[.,.],.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[7,6,3,1,5,4,8,2] => [[[[.,.],.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 3

[5,6,1,7,4,2,8,3] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[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

[6,4,7,8,2,1,3,5] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2

[6,7,3,8,4,1,2,5] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 0

[7,5,8,4,1,3,2,6] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2

[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

[4,8,1,2,3,5,7,6] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 0

[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

[7,6,8,5,1,3,2,4] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2

[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

[8,7,6,4,1,2,5,3] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 4

[6,7,1,3,5,2,8,4] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[5,7,2,3,6,8,1,4] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0

[8,5,3,2,7,6,1,4] => [[[[[.,.],.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3

[2,5,1,3,6,8,7,4] => [[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 0

[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

[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

[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

[6,7,2,5,1,8,4,3] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 0

[3,6,1,2,5,8,4,7] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 0

[3,6,1,5,8,2,4,7] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[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

[2,5,1,8,4,7,3,6] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[2,7,1,4,3,6,8,5] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 0

[8,2,1,5,7,3,4,6] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[2,4,1,3,8,6,7,5] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 0

[8,4,3,7,1,2,6,5] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[3,1,6,8,7,2,4,5] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 1

[7,2,1,6,8,3,4,5] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[3,1,7,6,8,2,4,5] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[4,1,7,2,6,8,3,5] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[5,1,7,2,3,6,8,4] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 1

[7,2,1,6,3,5,8,4] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[2,6,1,7,3,5,8,4] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 0

[7,1,2,5,3,6,8,4] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 1

[5,4,1,2,7,8,3,6] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 2

[8,1,3,2,4,6,7,5] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 1

[7,3,1,2,4,6,8,5] => [[[.,.],.],[.,[.,[[.,[.,.]],.]]]] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[4,1,3,8,7,2,6,5] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 1

[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

[3,1,7,2,8,5,6,4] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1

[8,4,1,7,3,6,2,5] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 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] => 0

[6,2,3,8,7,1,5,4] => [[[.,.],[.,[[.,.],.]]],[[.,.],.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 1

[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

[5,1,8,7,4,2,6,3] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 1

[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

[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

[5,1,7,4,8,3,6,2] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 1

[4,1,8,7,5,3,6,2] => [[.,.],[[[[[.,.],.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 1

[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

[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

[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

[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

[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

[6,5,1,4,2,3,8,7] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2

[8,6,1,7,2,5,4,3] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 2

[8,7,6,1,2,3,5,4] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3

[5,4,3,1,6,2,8,7] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3

[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

[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

[2,1,8,7,3,6,4,5] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[5,2,1,8,7,3,4,6] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[6,5,2,7,4,3,8,1] => [[[[.,.],.],[[[.,.],.],[.,.]]],.] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 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

[8,7,5,1,2,6,4,3] => [[[[.,.],.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 3

[8,4,3,2,7,1,6,5] => [[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3

[7,1,6,2,3,8,5,4] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 1

[4,8,1,3,2,7,5,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[3,8,1,4,7,5,2,6] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 0

[6,3,8,7,4,5,1,2] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[6,1,4,8,5,2,3,7] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 1

[8,5,7,4,6,2,1,3] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 2

[8,7,4,6,2,1,5,3] => [[[[[.,.],.],[.,.]],.],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 3

[7,6,1,3,5,2,8,4] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[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

[8,2,6,5,3,1,7,4] => [[[.,.],[[[.,.],.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 1

[2,1,8,6,4,3,7,5] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 1

[2,1,7,6,5,3,8,4] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 1

[7,2,5,4,6,1,8,3] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[2,4,1,7,6,8,5,3] => [[.,[.,.]],[[[[.,.],[.,.]],.],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 0

[3,4,1,7,8,5,6,2] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 0

[7,5,4,3,1,8,6,2] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4

[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

[8,4,2,5,6,1,7,3] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[6,3,5,4,1,7,8,2] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 1

[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

[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

[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

[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

[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

[5,4,2,1,3,7,8,6] => [[[[.,.],.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 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

[6,3,2,1,7,8,5,4] => [[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[8,6,5,1,3,2,4,7] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 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] => 3

[8,6,1,2,5,4,3,7] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 2

[5,8,6,4,1,3,2,7] => [[[.,[[.,.],.]],.],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[8,3,6,4,5,2,1,7] => [[[[.,.],[[.,.],[.,.]]],.],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 2

[6,8,5,7,4,2,3,1] => [[[[[.,[.,.]],[.,.]],.],[.,.]],.] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[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

[7,3,8,4,1,2,5,6] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1

[4,8,1,2,7,3,5,6] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 0

[6,8,1,2,7,4,5,3] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 0

[8,5,4,7,1,6,3,2] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2

[6,4,8,7,5,1,2,3] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 1

[5,7,1,8,4,6,2,3] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[6,3,8,7,2,1,4,5] => [[[[.,.],[[.,.],.]],.],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 2

[5,4,7,8,2,6,3,1] => [[[[.,.],[.,[.,.]]],[[.,.],.]],.] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 2

[6,8,3,4,1,2,7,5] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 0

[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

[4,5,3,2,8,6,7,1] => [[[[.,[.,.]],.],[[.,.],[.,.]]],.] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => 2

[5,8,2,3,7,6,1,4] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 0

[7,6,4,8,5,2,1,3] => [[[[[.,.],.],[[.,.],.]],.],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 3

[7,5,3,2,8,6,1,4] => [[[[[.,.],.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3

[2,5,1,3,8,6,7,4] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 0

[4,5,1,2,8,6,7,3] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 0

[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

[8,3,5,4,1,6,7,2] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 1

[7,3,4,8,5,6,1,2] => [[[.,.],[.,[[.,.],[.,.]]]],[.,.]] => [1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1

[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

[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

[7,4,3,1,2,8,5,6] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3

[8,4,7,6,2,1,5,3] => [[[[.,.],[[.,.],.]],.],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2

[8,4,6,5,7,1,3,2] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[7,2,1,4,5,8,3,6] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 2

[7,4,1,6,3,5,8,2] => [[[.,.],.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[4,7,5,2,1,3,8,6] => [[[.,[[.,.],.]],.],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => 1

[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

[8,6,2,3,7,1,4,5] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[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

[7,6,1,5,4,8,3,2] => [[[.,.],.],[[[[.,.],[.,.]],.],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 2

[4,7,3,2,1,8,5,6] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 2

[3,1,7,2,5,8,4,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[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

[5,8,6,4,2,3,1,7] => [[[[.,[[.,.],.]],.],[.,.]],[.,.]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[3,8,1,2,5,7,4,6] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 0

[6,8,5,4,2,7,3,1] => [[[[[.,[.,.]],.],.],[[.,.],.]],.] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 3

[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

[6,5,3,7,8,4,1,2] => [[[[.,.],.],[[.,[.,.]],.]],[.,.]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 2

[4,1,3,8,7,5,6,2] => [[.,.],[[.,[[[.,.],.],[.,.]]],.]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 1

[6,2,7,4,8,1,3,5] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[8,4,5,2,1,6,3,7] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2

[4,3,2,6,8,1,7,5] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[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

[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

[5,1,3,8,4,2,7,6] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 1

[6,2,8,7,3,5,4,1] => [[[.,.],[[[.,.],.],[[.,.],.]]],.] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 2

[7,1,8,4,3,6,5,2] => [[.,.],[[[[.,.],.],[[.,.],.]],.]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 1

[3,1,6,8,7,4,2,5] => [[.,.],[[[.,[[.,.],.]],.],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 1

[7,4,6,8,2,1,5,3] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 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] => 3

[8,5,1,3,7,4,6,2] => [[[.,.],.],[[.,[[.,.],[.,.]]],.]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 2

[3,8,2,7,1,5,6,4] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0

[5,8,2,3,6,4,1,7] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 0

[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

[7,5,1,8,4,2,6,3] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[2,1,6,5,4,8,3,7] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 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

[2,1,7,4,3,5,8,6] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1

[7,5,2,8,4,6,3,1] => [[[[.,.],.],[[[.,.],[.,.]],.]],.] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[8,6,2,3,5,7,1,4] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 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] => 0

[7,6,3,8,1,5,4,2] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2

[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

[6,1,8,2,3,5,4,7] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 1

[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

[8,4,3,1,7,5,2,6] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[7,3,1,4,6,8,5,2] => [[[.,.],.],[[.,[[.,[.,.]],.]],.]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 2

[7,3,8,5,2,6,4,1] => [[[[.,.],[[.,.],.]],[[.,.],.]],.] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 2

[4,3,8,7,1,6,5,2] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[4,7,1,8,5,2,6,3] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[5,3,2,4,7,8,6,1] => [[[[.,.],.],[.,[[.,[.,.]],.]]],.] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 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

[5,2,4,3,6,8,1,7] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[4,2,7,5,8,3,6,1] => [[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 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

[6,8,2,5,4,3,1,7] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 0

[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

[5,7,2,8,3,6,1,4] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[5,1,3,6,4,2,8,7] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 1

[5,1,8,7,4,6,2,3] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1

[6,8,3,7,5,4,2,1] => [[[[.,[.,.]],[[[.,.],.],.]],.],.] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 2

[6,1,3,4,7,5,8,2] => [[.,.],[[.,[.,[[.,.],[.,.]]]],.]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 1

[6,3,2,1,4,8,5,7] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3

[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

[6,2,1,4,8,7,5,3] => [[[.,.],.],[[.,[[[.,.],.],.]],.]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 2

[6,2,8,3,5,7,4,1] => [[[.,.],[[.,.],[[.,[.,.]],.]]],.] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 2

[5,2,1,3,6,4,8,7] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2

[7,1,8,3,5,4,6,2] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 1

[7,1,2,4,8,5,6,3] => [[.,.],[.,[[.,[[.,.],[.,.]]],.]]] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 1

[7,1,3,2,4,8,6,5] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 1

[7,2,1,3,4,5,8,6] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2

[8,7,3,5,4,2,1,6] => [[[[[.,.],.],[[.,.],.]],.],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 3

[8,4,6,5,3,2,1,7] => [[[[[.,.],[[.,.],.]],.],.],[.,.]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 3

[5,1,6,4,3,2,8,7] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 1

[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

[6,2,1,7,5,8,3,4] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[6,3,8,7,5,2,1,4] => [[[[.,.],[[[.,.],.],.]],.],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 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

[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

[7,6,1,8,5,4,3,2] => [[[.,.],.],[[[[[.,.],.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 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

[6,5,8,7,4,1,3,2] => [[[[.,.],[[.,.],.]],.],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 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

[8,7,2,5,6,1,4,3] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[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

[6,7,4,2,1,3,8,5] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => 2

[6,4,3,8,5,7,1,2] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2

[7,4,3,6,2,1,5,8] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3

[7,2,5,3,4,1,6,8] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[8,3,7,4,5,6,1,2] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[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

[7,1,3,2,8,4,5,6] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[2,1,7,4,8,3,5,6] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[5,2,8,6,1,3,4,7] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1

[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

[4,2,7,3,1,5,6,8] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1

[8,3,7,2,1,4,5,6] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2

[6,5,2,4,7,1,3,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[6,5,7,4,1,8,2,3] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2

[7,6,4,5,1,8,2,3] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[8,6,4,1,3,7,2,5] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3

[6,4,3,1,8,2,5,7] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[7,4,1,2,8,3,5,6] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2

[4,8,1,3,5,7,2,6] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 0

[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

[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

[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

[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

[8,3,1,7,2,4,5,6] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2

[2,8,1,4,7,3,5,6] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[3,1,8,5,4,7,6,2] => [[.,.],[[[[.,.],.],[[.,.],.]],.]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 1

[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

[4,1,5,3,8,7,6,2] => [[.,.],[[[.,.],[[[.,.],.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 1

[4,5,1,8,2,7,6,3] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 0

[4,8,5,3,1,7,6,2] => [[[.,[[.,.],.]],.],[[[.,.],.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1

[4,5,2,8,1,7,6,3] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 0

[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

[5,6,2,7,8,1,4,3] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0

[4,6,2,8,7,1,5,3] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[4,6,2,8,7,5,1,3] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 0

[5,6,2,7,4,1,8,3] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[5,6,1,7,8,2,4,3] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[5,6,1,7,2,4,8,3] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 0

[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

[4,1,6,8,7,3,5,2] => [[.,.],[[[.,[[.,.],.]],[.,.]],.]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 1

[3,1,8,6,7,5,4,2] => [[.,.],[[[[[.,.],[.,.]],.],.],.]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 1

[4,1,6,8,7,5,3,2] => [[.,.],[[[[.,[[.,.],.]],.],.],.]] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 1

[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

[5,6,1,7,8,4,2,3] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 0

[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

[7,4,1,6,3,8,5,2] => [[[.,.],.],[[[.,.],[[.,.],.]],.]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 2

[7,6,3,1,5,8,4,2] => [[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[6,4,2,5,7,3,1,8] => [[[[.,.],.],[[.,[.,.]],.]],[.,.]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 2

[4,2,5,7,6,3,1,8] => [[[.,.],[[.,[[.,.],.]],.]],[.,.]] => [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 1

[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

[4,1,5,8,6,3,2,7] => [[.,.],[[[.,[[.,.],.]],.],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 1

[3,2,7,6,1,8,5,4] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[8,6,5,1,2,7,4,3] => [[[[.,.],.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 3

[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

[8,5,4,1,3,2,7,6] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 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

[4,7,1,8,2,5,3,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[6,4,1,8,5,3,7,2] => [[[.,.],.],[[[[.,.],.],[.,.]],.]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 2

[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

[3,2,5,4,7,8,1,6] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[5,2,4,3,7,8,1,6] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[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

[3,1,7,6,5,8,2,4] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1

[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

[3,2,1,7,6,8,4,5] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[3,2,8,6,4,7,1,5] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[7,8,4,6,3,2,1,5] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2

[8,2,5,3,6,7,1,4] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[4,7,5,3,1,8,6,2] => [[[.,[[.,.],.]],.],[[[.,.],.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1

[4,5,3,6,8,1,7,2] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0

[3,5,2,6,1,8,7,4] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 0

[8,4,6,5,7,2,1,3] => [[[[.,.],[[.,.],[.,.]]],.],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 2

[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

[5,4,2,6,8,7,1,3] => [[[[.,.],.],[.,[[.,.],.]]],[.,.]] => [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 2

[6,5,1,4,3,2,8,7] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[7,5,4,2,3,8,1,6] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3

[7,8,1,3,5,6,2,4] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 0

[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

[3,1,7,5,8,2,6,4] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[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

[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

[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

[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

[4,6,2,5,1,3,8,7] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 0

[6,4,2,5,1,3,8,7] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[8,6,1,7,3,2,4,5] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[6,8,2,7,3,1,4,5] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 0

[6,8,2,3,7,1,4,5] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[8,6,2,7,4,5,1,3] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2

[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

[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

[5,2,8,3,7,1,4,6] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[5,2,8,4,6,1,3,7] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[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

[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

[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

[5,1,8,3,7,2,4,6] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[5,1,8,4,6,2,3,7] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[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

[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

[2,1,5,4,8,3,6,7] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[3,1,8,4,2,5,6,7] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1

[3,8,4,2,1,5,6,7] => [[[.,[[.,.],.]],.],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1

[3,4,2,8,1,5,6,7] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0

[2,1,4,8,5,3,6,7] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 1

[3,2,8,4,1,5,6,7] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1

[4,1,7,5,6,2,8,3] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[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

[5,7,4,3,8,2,6,1] => [[[[[.,[.,.]],.],[.,.]],[.,.]],.] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[6,1,7,5,2,8,4,3] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 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] => 2

[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

[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

[3,8,4,2,1,6,7,5] => [[[.,[[.,.],.]],.],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 1

[5,7,4,3,8,2,1,6] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 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] => 0

[6,7,5,8,1,2,4,3] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 0

[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

[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

[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

[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

[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

[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

[6,7,4,8,1,3,5,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0

[6,3,1,4,8,2,5,7] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[6,7,4,8,1,3,2,5] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[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

[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

[6,7,4,8,1,2,3,5] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0

[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

[5,1,7,3,4,8,2,6] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[8,7,2,3,6,5,4,1] => [[[[.,.],.],[.,[[[.,.],.],.]]],.] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 3

[3,8,1,7,5,2,6,4] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[4,8,1,6,7,2,5,3] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[2,1,3,8,4,6,5,7] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 1

[8,2,1,7,4,3,6,5] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[8,3,1,5,7,2,6,4] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[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

[8,4,5,7,6,3,2,1] => [[[[[.,.],[.,[[.,.],.]]],.],.],.] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 4

[4,3,8,6,5,7,2,1] => [[[[.,.],[[[.,.],.],[.,.]]],.],.] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 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

[5,2,7,8,6,3,4,1] => [[[.,.],[[[.,[.,.]],.],[.,.]]],.] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[4,2,8,6,7,3,5,1] => [[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2

[3,2,8,7,5,4,6,1] => [[[.,.],[[[[.,.],.],.],[.,.]]],.] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 2

[3,1,8,7,5,6,2,4] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1

[4,1,8,6,7,5,2,3] => [[.,.],[[[[.,.],[.,.]],.],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 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

[6,7,1,8,5,4,2,3] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 0

[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

[7,8,1,4,5,6,3,2] => [[.,[.,.]],[[[.,[.,[.,.]]],.],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 0

[7,8,4,5,1,6,3,2] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 0

[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

[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

[7,4,2,8,1,5,3,6] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[6,1,7,5,8,4,3,2] => [[.,.],[[[[[.,.],[.,.]],.],.],.]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 1

[6,2,1,8,4,5,3,7] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[3,1,8,4,5,6,7,2] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 1

[2,1,4,8,6,5,3,7] => [[.,.],[[.,[[[.,.],.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 1

[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

[3,6,2,8,5,1,4,7] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 0

[4,1,2,8,7,5,3,6] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 1

[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

[7,2,1,8,5,3,4,6] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[7,1,6,5,8,4,3,2] => [[.,.],[[[[[.,.],[.,.]],.],.],.]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 1

[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

[6,7,3,8,5,4,1,2] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 0

[7,1,2,8,4,5,3,6] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 1

[7,6,1,5,8,4,3,2] => [[[.,.],.],[[[[.,[.,.]],.],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 2

[7,1,6,5,3,2,4,8] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 1

[8,7,4,2,5,3,6,1] => [[[[[.,.],.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 4

[7,1,6,4,2,5,3,8] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[7,1,5,3,6,4,2,8] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1

[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

[5,3,6,4,2,7,1,8] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[7,4,2,8,6,3,5,1] => [[[[.,.],.],[[[.,.],.],[.,.]]],.] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 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

[6,1,5,3,8,7,4,2] => [[.,.],[[[.,.],[[[.,.],.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 1

[2,3,1,8,7,5,4,6] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 0

[5,3,8,7,4,2,1,6] => [[[[.,.],[[[.,.],.],.]],.],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 2

[7,4,2,1,8,6,3,5] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[8,6,3,5,7,4,2,1] => [[[[[.,.],.],[[.,[.,.]],.]],.],.] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[6,3,8,5,2,1,7,4] => [[[[.,.],[[.,.],.]],.],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2

[8,6,3,7,4,2,1,5] => [[[[[.,.],.],[[.,.],.]],.],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 3

[5,1,8,6,3,7,4,2] => [[.,.],[[[[.,.],.],[[.,.],.]],.]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 1

[6,3,7,4,1,8,5,2] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[8,5,2,6,3,7,4,1] => [[[[.,.],.],[[.,.],[[.,.],.]]],.] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3

[6,1,8,7,4,2,5,3] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 1

[8,6,3,7,4,2,5,1] => [[[[[.,.],.],[[.,.],.]],[.,.]],.] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 3

[8,6,3,2,4,7,5,1] => [[[[[.,.],.],.],[.,[[.,.],.]]],.] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 4

[7,5,1,8,6,3,2,4] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 2

[6,1,8,7,5,3,2,4] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 1

[4,3,2,8,7,6,1,5] => [[[[.,.],.],[[[.,.],.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 2

[7,5,8,6,3,2,4,1] => [[[[[.,.],[[.,.],.]],.],[.,.]],.] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 3

[8,6,3,1,7,4,2,5] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[8,7,4,2,5,3,1,6] => [[[[[.,.],.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3

[5,3,1,8,7,4,2,6] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 2

[4,1,8,7,5,3,2,6] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 1

[4,1,8,6,3,2,7,5] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 1

[7,4,2,8,6,3,1,5] => [[[[.,.],.],[[[.,.],.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 2

[6,3,1,8,5,2,7,4] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[8,5,2,6,3,1,7,4] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[7,4,8,5,2,6,3,1] => [[[[.,.],[[.,.],.]],[[.,.],.]],.] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 2

[8,5,2,7,4,6,3,1] => [[[[.,.],.],[[[.,.],[.,.]],.]],.] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 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] => 2

[6,3,1,7,4,8,5,2] => [[[.,.],.],[[[.,.],[[.,.],.]],.]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 2

[8,6,3,1,5,7,4,2] => [[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[4,1,7,5,8,6,3,2] => [[.,.],[[[[.,.],[[.,.],.]],.],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 1

[2,3,1,7,5,8,6,4] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 0

[7,4,8,5,2,1,6,3] => [[[[.,.],[[.,.],.]],.],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2

[8,5,2,1,7,4,6,3] => [[[[.,.],.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 3

[4,1,8,5,7,3,2,6] => [[.,.],[[[[.,.],[.,.]],.],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 1

[5,1,7,4,8,3,2,6] => [[.,.],[[[[.,.],[.,.]],.],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 1

[4,6,2,7,3,1,8,5] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[6,2,8,4,1,7,3,5] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[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

[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

[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

[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

[4,5,3,8,1,2,7,6] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 0

[6,4,3,8,1,7,2,5] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[7,4,3,8,1,6,2,5] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[6,5,3,8,7,1,2,4] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[5,6,3,8,7,1,2,4] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 0

[4,6,3,8,1,7,2,5] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[5,7,3,8,6,1,2,4] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 0

[5,3,6,8,7,1,2,4] => [[[.,.],[.,[[.,.],.]]],[.,[.,.]]] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 1

[6,3,5,8,7,1,2,4] => [[[.,.],[.,[[.,.],.]]],[.,[.,.]]] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 1

[7,2,8,5,6,1,3,4] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[5,2,8,6,7,1,3,4] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[5,2,8,7,6,1,3,4] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 1

[6,2,8,7,5,1,3,4] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 1

[7,4,6,5,8,1,2,3] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[6,3,8,7,5,1,2,4] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 1

[5,4,8,7,1,3,2,6] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[5,4,2,7,6,8,1,3] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2

[4,2,1,8,7,3,5,6] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[5,1,6,3,2,8,7,4] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 1

[4,6,1,8,7,3,2,5] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 0

[8,7,2,3,5,4,1,6] => [[[[.,.],.],[.,[[.,.],.]]],[.,.]] => [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 2

[5,3,1,4,8,7,2,6] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 2

[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

[3,4,2,8,6,1,5,7] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 0

[8,1,4,2,3,6,7,5] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 1

[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

[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

[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

[2,7,1,6,5,4,8,3] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 0

[7,3,2,6,1,8,5,4] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 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

[5,3,1,8,4,6,2,7] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 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] => 0

[8,4,1,6,3,2,5,7] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[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

[3,1,7,4,8,5,2,6] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1

[7,4,1,6,3,2,8,5] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[7,3,1,4,5,2,8,6] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[6,1,4,8,5,3,2,7] => [[.,.],[[[.,[[.,.],.]],.],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 1

[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

[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

[7,5,2,3,8,6,1,4] => [[[[.,.],.],[.,[[.,.],.]]],[.,.]] => [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 2

[8,6,2,4,1,3,7,5] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 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] => 2

[8,4,5,7,6,1,3,2] => [[[.,.],[.,[[.,.],.]]],[[.,.],.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 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] => 3

[4,2,7,6,1,5,8,3] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 1

[8,3,1,4,5,7,6,2] => [[[.,.],.],[[.,[.,[[.,.],.]]],.]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 2

[3,5,1,6,8,4,7,2] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 0

[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

[5,8,4,7,3,2,6,1] => [[[[[.,[.,.]],[.,.]],.],[.,.]],.] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2

[7,2,6,5,8,4,1,3] => [[[.,.],[[[.,.],[.,.]],.]],[.,.]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1

[8,3,2,5,1,6,7,4] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 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

[7,4,1,8,3,2,6,5] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[8,3,7,4,2,1,6,5] => [[[[.,.],[[.,.],.]],.],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 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

[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

[8,2,7,3,4,6,5,1] => [[[.,.],[[.,.],[.,[[.,.],.]]]],.] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 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] => 2

[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

[6,1,3,2,4,8,7,5] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 1

[8,7,4,2,3,6,1,5] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3

[8,7,1,5,4,2,3,6] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 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] => 0

[8,7,2,5,4,1,3,6] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[8,7,2,5,3,1,4,6] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[5,2,8,7,1,4,3,6] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[7,1,8,6,2,4,3,5] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[8,1,6,2,7,5,3,4] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1

[7,1,6,2,8,5,3,4] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1

[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

[7,2,4,3,5,1,8,6] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[5,1,7,2,3,8,6,4] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 1

[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

[7,6,3,1,4,8,2,5] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3

[6,1,8,2,7,5,3,4] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1

[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

[7,2,6,4,3,8,1,5] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[5,1,7,4,3,8,2,6] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1

[5,3,1,7,4,8,2,6] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[7,4,8,2,1,5,3,6] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2

[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

[8,2,7,5,1,6,4,3] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[6,1,7,3,2,8,5,4] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 1

[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

[6,2,1,5,3,8,4,7] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[5,3,1,6,2,8,4,7] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[6,1,5,2,8,4,3,7] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1

[7,4,3,8,1,5,2,6] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[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

[6,1,5,3,2,8,4,7] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[6,3,2,8,4,1,5,7] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[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

[7,1,6,3,4,2,8,5] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[8,5,1,3,7,4,2,6] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 2

[8,6,1,3,7,5,2,4] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 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] => 0

[7,1,3,8,4,2,6,5] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 1

[5,6,2,7,1,3,8,4] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 0

[5,6,2,8,1,3,7,4] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 0

[6,1,8,3,7,5,2,4] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1

[7,4,2,1,5,8,3,6] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3

[7,4,1,5,8,3,2,6] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 2

[7,3,2,6,4,8,1,5] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2

[6,4,2,7,3,8,1,5] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2

[5,1,8,3,7,4,2,6] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1

[7,4,8,3,1,5,2,6] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2

[5,2,1,7,4,8,3,6] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[6,1,8,4,5,2,7,3] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[7,1,6,4,5,2,8,3] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[3,5,2,7,1,6,8,4] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0

[3,5,1,7,2,6,8,4] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 0

[3,6,1,5,7,8,4,2] => [[.,[.,.]],[[[.,[.,[.,.]]],.],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 0

[6,1,3,7,4,8,5,2] => [[.,.],[[.,[[.,.],[[.,.],.]]],.]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 1

[3,2,1,7,4,8,5,6] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[4,1,5,2,7,6,3,8] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1

[2,5,1,3,7,6,4,8] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 0

[2,5,1,4,3,8,6,7] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[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

[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

[3,7,4,2,1,8,5,6] => [[[.,[[.,.],.]],.],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[7,2,5,3,1,8,6,4] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[7,5,1,4,2,8,6,3] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 2

[7,5,4,1,3,8,6,2] => [[[[.,.],.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[5,3,2,1,7,6,4,8] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[6,3,2,8,1,5,7,4] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[7,4,3,2,8,1,6,5] => [[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3

[7,6,2,4,8,3,5,1] => [[[[.,.],.],[[.,[.,.]],[.,.]]],.] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 3

[7,3,6,4,8,1,5,2] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[8,6,2,3,7,5,4,1] => [[[[.,.],.],[.,[[[.,.],.],.]]],.] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 3

[8,6,3,2,7,5,4,1] => [[[[[.,.],.],.],[[[.,.],.],.]],.] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 4

[8,3,2,7,1,6,4,5] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 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

[8,5,7,4,3,6,2,1] => [[[[[[.,.],[.,.]],.],[.,.]],.],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 4

[8,5,7,2,4,6,3,1] => [[[[.,.],[.,.]],[[.,[.,.]],.]],.] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 2

[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

[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

[7,6,4,8,3,2,5,1] => [[[[[[.,.],.],[.,.]],.],[.,.]],.] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 4

[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

[6,5,8,4,1,3,7,2] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 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] => 3

[4,3,7,2,1,6,5,8] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 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] => 0

[5,7,1,4,8,2,6,3] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[3,5,1,8,4,2,7,6] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[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

[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

[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

[5,3,1,8,6,4,2,7] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 2

[3,1,8,4,7,5,2,6] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1

[4,2,8,7,3,5,1,6] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[4,8,1,7,6,2,3,5] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0

[6,8,1,4,7,5,2,3] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 0

[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

[7,1,8,6,2,5,3,4] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[3,8,7,2,1,6,4,5] => [[[.,[[.,.],.]],.],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[6,8,1,7,5,2,4,3] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[7,3,8,6,5,1,2,4] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 1

[5,8,6,4,3,2,1,7] => [[[[[.,[[.,.],.]],.],.],.],[.,.]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 3

[8,7,3,6,4,2,1,5] => [[[[[.,.],.],[[.,.],.]],.],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 3

[5,2,6,3,4,7,1,8] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[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

[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

[2,7,1,6,8,3,5,4] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[5,2,8,7,6,4,3,1] => [[[.,.],[[[[[.,.],.],.],.],.]],.] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 2

[8,2,7,6,1,5,4,3] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[8,4,1,7,6,5,3,2] => [[[.,.],.],[[[[[.,.],.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 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

[6,5,7,3,8,4,2,1] => [[[[[.,.],[.,.]],[[.,.],.]],.],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 3

[3,2,7,4,5,8,1,6] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 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] => 0

[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

[6,3,4,7,8,2,5,1] => [[[[.,.],[.,[.,[.,.]]]],[.,.]],.] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2

[5,3,7,4,8,6,1,2] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[8,3,6,4,1,7,2,5] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[5,4,3,1,7,8,2,6] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3

[6,1,7,5,8,3,4,2] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 1

[7,5,6,4,1,3,8,2] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[4,1,3,7,6,5,8,2] => [[.,.],[[.,[[[.,.],.],[.,.]]],.]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 1

[3,4,1,7,5,8,6,2] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 0

[8,5,7,4,3,1,6,2] => [[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 3

[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

[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

[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

[8,1,7,4,2,3,6,5] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1

[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

[5,4,7,2,3,6,8,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2

[6,3,2,1,8,4,7,5] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3

[6,4,1,3,2,7,8,5] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[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

[6,7,1,5,8,2,4,3] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[7,8,1,5,3,2,6,4] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[6,5,7,3,8,2,1,4] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 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

[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

[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

[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

[4,2,3,8,6,1,5,7] => [[[.,.],[.,[[.,.],.]]],[.,[.,.]]] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 1

[6,4,1,2,8,3,5,7] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2

[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

[2,1,5,3,8,7,4,6] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1

[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

[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

[4,1,8,2,7,3,5,6] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[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

[6,2,8,3,7,5,1,4] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[4,2,8,3,7,5,6,1] => [[[.,.],[[.,.],[[.,.],[.,.]]]],.] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 2

[7,3,4,8,6,5,1,2] => [[[.,.],[.,[[[.,.],.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 1

[5,3,4,8,7,2,6,1] => [[[[.,.],[.,[[.,.],.]]],[.,.]],.] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 2

[4,3,5,8,7,2,6,1] => [[[[.,.],[.,[[.,.],.]]],[.,.]],.] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 2

[4,6,3,8,5,7,2,1] => [[[[.,[.,.]],[[.,.],[.,.]]],.],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 2

[7,5,3,8,6,2,4,1] => [[[[[.,.],.],[[.,.],.]],[.,.]],.] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 3

[7,4,3,8,6,2,5,1] => [[[[[.,.],.],[[.,.],.]],[.,.]],.] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 3

[4,5,3,8,6,7,2,1] => [[[[.,[.,.]],[[.,.],[.,.]]],.],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 2

[7,4,6,5,8,3,2,1] => [[[[[.,.],[[.,.],[.,.]]],.],.],.] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4

[6,3,7,8,4,5,2,1] => [[[[.,.],[[.,[.,.]],[.,.]]],.],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[4,3,7,8,5,6,2,1] => [[[[.,.],[[.,[.,.]],[.,.]]],.],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[5,2,8,6,4,7,3,1] => [[[.,.],[[[[.,.],.],[.,.]],.]],.] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 2

[4,2,8,6,5,7,3,1] => [[[.,.],[[[[.,.],.],[.,.]],.]],.] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 2

[3,2,8,6,7,4,5,1] => [[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2

[7,2,8,6,3,4,5,1] => [[[.,.],[[[.,.],.],[.,[.,.]]]],.] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 2

[6,2,8,4,5,7,3,1] => [[[.,.],[[[.,.],[.,[.,.]]],.]],.] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 2

[5,2,8,4,6,7,3,1] => [[[.,.],[[[.,.],[.,[.,.]]],.]],.] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 2

[4,2,8,5,6,7,3,1] => [[[.,.],[[[.,.],[.,[.,.]]],.]],.] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 2

[4,3,6,8,5,7,2,1] => [[[[.,.],[[.,[.,.]],[.,.]]],.],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[7,3,5,8,6,2,4,1] => [[[[.,.],[.,[[.,.],.]]],[.,.]],.] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 2

[5,7,4,6,8,3,2,1] => [[[[[.,[.,.]],[.,[.,.]]],.],.],.] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 3

[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

[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

[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

[3,7,1,2,5,8,6,4] => [[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 0

[7,5,1,3,4,8,6,2] => [[[.,.],.],[[.,[.,[[.,.],.]]],.]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 2

[7,5,1,2,4,8,6,3] => [[[.,.],.],[.,[[.,[[.,.],.]],.]]] => [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 2

[6,4,2,3,7,1,5,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[7,6,3,8,1,2,5,4] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[7,4,2,3,8,1,6,5] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[8,2,6,3,7,1,4,5] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[8,6,1,2,7,4,5,3] => [[[.,.],.],[.,[[[.,.],[.,.]],.]]] => [1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2

[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

[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

[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

[8,6,2,7,1,3,5,4] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[7,6,4,8,1,3,5,2] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[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

[3,7,2,4,8,1,6,5] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0

[4,6,3,8,1,2,5,7] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0

[4,6,3,7,1,2,5,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0

[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

[5,1,2,8,6,3,4,7] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 1

[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

[6,1,8,5,2,3,4,7] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1

[6,1,7,5,2,3,4,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1

[6,8,1,3,7,4,5,2] => [[.,[.,.]],[[.,[[.,.],[.,.]]],.]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 0

[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

[6,8,2,7,1,4,5,3] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0

[7,1,8,6,2,3,5,4] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1

[5,8,6,4,1,2,3,7] => [[[.,[[.,.],.]],.],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1

[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

[7,8,1,2,6,5,3,4] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 0

[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

[5,1,7,3,6,4,8,2] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 1

[6,2,1,5,7,4,3,8] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 2

[5,1,2,4,7,6,8,3] => [[.,.],[.,[[.,[[.,.],[.,.]]],.]]] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 1

[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

[4,8,1,2,6,7,3,5] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 0

[3,1,2,4,6,8,7,5] => [[.,.],[.,[.,[[.,[[.,.],.]],.]]]] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 1

[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

[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

[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

[8,6,1,4,2,3,7,5] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2

[3,6,1,4,2,8,7,5] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 0

[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

[6,1,7,4,3,8,2,5] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1

[7,4,1,3,8,2,6,5] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[4,8,2,3,1,5,7,6] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 0

[4,8,6,2,1,3,7,5] => [[[.,[[.,.],.]],.],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => 1

[4,7,1,3,8,2,6,5] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[8,7,1,3,4,2,6,5] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[6,4,1,3,7,2,8,5] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[8,1,4,3,6,2,7,5] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[4,2,3,8,5,7,1,6] => [[[.,.],[.,[[.,.],[.,.]]]],[.,.]] => [1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1

[5,8,2,6,4,3,1,7] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 0

[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

[4,2,3,5,8,7,1,6] => [[[.,.],[.,[.,[[.,.],.]]]],[.,.]] => [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 1

[8,2,3,5,4,7,1,6] => [[[.,.],[.,[[.,.],[.,.]]]],[.,.]] => [1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1

[6,1,8,3,4,2,7,5] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[6,3,1,4,2,8,7,5] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 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

[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

[5,1,4,8,6,3,2,7] => [[.,.],[[[.,[[.,.],.]],.],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 1

[5,3,1,8,4,7,2,6] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[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

[6,3,1,2,5,7,4,8] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 2

[7,1,4,2,6,5,3,8] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1

[7,3,6,4,5,8,2,1] => [[[[.,.],[[.,.],[.,[.,.]]]],.],.] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 3

[8,7,2,4,5,1,6,3] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[7,1,5,4,8,6,3,2] => [[.,.],[[[[.,.],[[.,.],.]],.],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 1

[2,1,8,7,5,3,6,4] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 1

[5,8,3,7,4,1,6,2] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[5,7,1,4,8,6,3,2] => [[.,[.,.]],[[[.,[[.,.],.]],.],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 0

[5,3,7,4,8,6,2,1] => [[[[.,.],[[.,.],[[.,.],.]]],.],.] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 3

[6,5,3,7,4,8,2,1] => [[[[[.,.],.],[[.,.],[.,.]]],.],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 4

[7,5,8,4,1,6,3,2] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 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] => 0

[5,6,3,8,1,4,7,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0

[8,5,1,7,2,6,4,3] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 2

[8,7,1,4,5,2,6,3] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[7,6,3,1,5,2,8,4] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3

[7,5,1,8,2,6,3,4] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[8,7,3,1,5,4,2,6] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[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

[5,4,2,6,1,3,8,7] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[3,2,6,5,1,4,8,7] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 1

[6,8,2,7,4,3,1,5] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 0

[6,8,2,3,7,5,1,4] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 0

[7,6,2,5,4,8,1,3] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2

[4,2,7,3,1,8,5,6] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[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

[5,2,7,3,8,6,1,4] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[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

[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

[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

[4,8,3,2,1,7,6,5] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 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

[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

[5,1,7,4,6,8,3,2] => [[.,.],[[[[.,.],[.,[.,.]]],.],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 1

[7,6,4,8,1,5,3,2] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2

[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

[2,1,7,6,4,8,3,5] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1

[2,1,5,4,8,7,3,6] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1

[5,4,8,7,2,6,1,3] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[3,4,1,8,6,2,7,5] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[3,2,8,7,5,4,1,6] => [[[.,.],[[[[.,.],.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1

[7,3,6,5,2,8,4,1] => [[[[.,.],[[.,.],.]],[[.,.],.]],.] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 2

[8,7,5,3,1,4,2,6] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4

[7,1,5,3,8,4,6,2] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 1

[2,1,8,7,4,3,5,6] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 1

[8,6,7,5,1,3,2,4] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2

[8,5,2,6,1,7,3,4] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[5,4,2,6,8,3,7,1] => [[[[.,.],.],[[.,[.,.]],[.,.]]],.] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 3

[6,5,2,8,1,4,3,7] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[4,8,1,2,5,3,6,7] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 0

[8,1,2,4,3,5,6,7] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1

[5,8,4,7,6,3,2,1] => [[[[[.,[.,.]],[[.,.],.]],.],.],.] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 3

[6,8,5,4,7,3,2,1] => [[[[[[.,[.,.]],.],[.,.]],.],.],.] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4

[7,5,8,4,6,3,1,2] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 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

[3,5,2,4,7,6,1,8] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 0

[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

[3,5,2,7,6,4,1,8] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 0

[5,3,7,6,2,4,1,8] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[5,3,7,6,1,2,8,4] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 1

[5,3,7,6,1,4,2,8] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[5,3,7,6,4,1,2,8] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 1

[3,5,2,7,6,1,4,8] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 0

[5,3,7,6,4,1,8,2] => [[[.,.],[[[.,.],.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 1

[3,5,2,7,1,6,4,8] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[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

[3,5,2,7,1,4,6,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0

[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

[3,5,2,7,4,1,6,8] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 0

[3,2,5,4,7,1,6,8] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[5,7,6,3,1,8,4,2] => [[[.,[[.,.],.]],.],[[[.,.],.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1

[5,7,6,3,1,8,2,4] => [[[.,[[.,.],.]],.],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[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

[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

[3,5,2,7,1,4,8,6] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 0

[3,7,5,2,1,8,6,4] => [[[.,[[.,.],.]],.],[[[.,.],.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1

[3,7,2,5,1,8,6,4] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 0

[3,2,7,5,1,8,6,4] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[3,2,7,5,1,8,4,6] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[3,7,2,5,1,8,4,6] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[3,7,5,2,1,8,4,6] => [[[.,[[.,.],.]],.],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[2,1,7,5,8,4,6,3] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 1

[5,8,3,4,1,7,6,2] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 0

[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

[3,2,7,6,1,5,4,8] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[3,2,8,7,6,1,5,4] => [[[.,.],[[[.,.],.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 1

[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

[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

[5,8,2,4,1,6,3,7] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[8,4,2,6,5,1,3,7] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[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

[8,3,2,5,6,1,4,7] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[3,2,8,6,7,1,5,4] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[3,2,6,8,7,1,5,4] => [[[.,.],[.,[[.,.],.]]],[[.,.],.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 1

[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

[8,7,3,2,5,6,1,4] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 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

[8,4,2,7,5,1,3,6] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[7,4,2,8,5,1,3,6] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[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

[3,2,8,5,7,1,4,6] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[2,5,1,8,7,4,3,6] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 0

[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

[8,3,5,4,1,6,2,7] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[8,6,3,4,1,5,2,7] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[5,4,7,6,8,2,3,1] => [[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[4,1,8,2,3,7,6,5] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 1

[2,1,8,5,3,4,7,6] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1

[5,2,4,6,8,7,3,1] => [[[.,.],[[.,[.,[[.,.],.]]],.]],.] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 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] => 0

[5,4,2,6,7,8,1,3] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2

[6,4,2,7,3,5,8,1] => [[[[.,.],.],[[.,.],[.,[.,.]]]],.] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 3

[7,4,1,8,3,5,6,2] => [[[.,.],.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[6,5,4,8,7,3,1,2] => [[[[[.,.],.],[[.,.],.]],.],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 3

[8,7,4,2,1,3,6,5] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 4

[8,7,1,3,2,5,6,4] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 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] => 0

[7,4,3,2,6,8,5,1] => [[[[[.,.],.],.],[[.,[.,.]],.]],.] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 4

[8,3,7,2,1,5,6,4] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 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] => 2

[8,3,1,6,7,4,2,5] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 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

[8,2,7,3,4,1,5,6] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[7,1,6,3,5,8,2,4] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[3,5,1,6,8,7,2,4] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 0

[5,7,6,2,1,3,8,4] => [[[.,[[.,.],.]],.],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => 1

[4,1,7,5,2,6,8,3] => [[.,.],[[[.,.],.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 1

[7,6,2,4,5,1,8,3] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[7,3,4,2,5,8,6,1] => [[[[.,.],[.,.]],[.,[[.,.],.]]],.] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 2

[8,7,4,2,5,1,6,3] => [[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3

[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

[5,2,4,8,6,7,1,3] => [[[.,.],[.,[[.,.],[.,.]]]],[.,.]] => [1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1

[8,5,6,2,1,3,7,4] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2

[4,2,1,5,6,7,8,3] => [[[.,.],.],[[.,[.,[.,[.,.]]]],.]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[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

[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

[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

[5,7,3,2,1,4,6,8] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2

[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

[3,7,2,5,4,1,6,8] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 0

[5,1,3,2,4,7,6,8] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 1

[5,1,3,2,7,4,6,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[7,1,3,2,5,4,6,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[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

[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

[3,2,7,5,1,4,6,8] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1

[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

[5,3,2,7,4,1,6,8] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[5,3,2,4,7,1,6,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[5,3,2,1,4,7,6,8] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3

[5,3,2,1,7,4,6,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[7,3,1,2,5,4,6,8] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2

[5,3,1,2,7,4,6,8] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2

[5,3,1,2,4,7,6,8] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 2

[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

[7,3,1,5,2,4,6,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2

[7,5,1,3,2,4,6,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2

[5,7,1,3,2,4,6,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0

[3,7,1,5,2,4,6,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0

[3,7,1,2,5,4,6,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 0

[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

[3,2,1,7,5,4,6,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[3,1,2,7,5,4,6,8] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 1

[3,1,7,2,5,4,6,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[3,1,7,5,2,4,6,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1

[7,1,5,3,2,4,6,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1

[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

[2,8,1,4,7,6,5,3] => [[.,[.,.]],[[.,[[[.,.],.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 0

[7,5,3,4,2,8,1,6] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[8,5,3,6,2,4,7,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3

[8,5,6,3,7,4,2,1] => [[[[[.,.],[.,.]],[[.,.],.]],.],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 3

[8,5,6,2,7,4,3,1] => [[[[.,.],[.,.]],[[[.,.],.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 2

[8,7,6,3,4,1,5,2] => [[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3

[3,5,1,4,8,2,7,6] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[2,5,1,4,8,7,3,6] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 0

[7,6,1,4,5,3,8,2] => [[[.,.],.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[7,6,5,8,2,4,3,1] => [[[[[.,.],.],[.,.]],[[.,.],.]],.] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[7,6,5,8,3,1,4,2] => [[[[[.,.],.],[.,.]],.],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 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

[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

[7,2,6,5,3,8,1,4] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[7,2,3,5,4,8,6,1] => [[[.,.],[.,[[.,.],[[.,.],.]]]],.] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 2

[7,6,1,3,4,5,8,2] => [[[.,.],.],[[.,[.,[.,[.,.]]]],.]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[7,1,3,2,4,8,5,6] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 1

[7,6,1,5,4,3,8,2] => [[[.,.],.],[[[[.,.],.],[.,.]],.]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 2

[7,6,5,8,1,3,2,4] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[4,2,1,5,3,7,8,6] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[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

[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

[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

[5,3,1,4,2,6,7,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2

[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

[4,6,2,7,1,3,5,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0

[5,1,4,2,3,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1

[3,6,1,7,2,5,8,4] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 0

[5,1,4,3,2,6,7,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1

[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

[2,1,4,8,6,3,7,5] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 1

[8,6,2,4,7,5,1,3] => [[[[.,.],.],[.,[[.,.],.]]],[.,.]] => [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 2

[8,4,2,6,7,3,1,5] => [[[[.,.],.],[[.,[.,.]],.]],[.,.]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 2

[6,2,3,8,7,4,1,5] => [[[.,.],[.,[[[.,.],.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 1

[5,8,1,4,3,6,2,7] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[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

[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

[4,3,5,7,2,1,6,8] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2

[4,2,8,3,5,7,1,6] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[4,3,8,6,5,7,1,2] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[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

[5,1,8,3,6,4,7,2] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 1

[6,7,4,8,5,1,3,2] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[6,4,8,3,1,7,5,2] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 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

[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

[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

[6,5,3,8,2,7,4,1] => [[[[[.,.],.],[.,.]],[[.,.],.]],.] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 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

[7,6,3,1,4,2,5,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[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

[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

[4,2,5,3,1,7,8,6] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 1

[4,2,8,7,6,3,1,5] => [[[.,.],[[[[.,.],.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1

[4,2,7,6,3,1,5,8] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 1

[6,3,1,7,5,2,4,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[6,3,1,8,7,5,2,4] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 2

[8,6,3,1,7,5,2,4] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[4,2,7,6,3,1,8,5] => [[[.,.],[[[.,.],.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 1

[7,6,3,1,8,4,2,5] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[7,6,4,2,1,8,3,5] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4

[8,3,5,7,6,4,2,1] => [[[[.,.],[[.,[[.,.],.]],.]],.],.] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 3

[8,4,2,5,7,6,3,1] => [[[[.,.],.],[[.,[[.,.],.]],.]],.] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 3

[7,5,2,4,8,6,3,1] => [[[[.,.],.],[[.,[[.,.],.]],.]],.] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 3

[8,7,5,2,4,6,3,1] => [[[[[.,.],.],.],[[.,[.,.]],.]],.] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 4

[7,5,2,4,6,3,1,8] => [[[[.,.],.],[[.,[.,.]],.]],[.,.]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 2

[5,2,8,6,3,7,4,1] => [[[.,.],[[[.,.],.],[[.,.],.]]],.] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 2

[8,4,7,5,2,6,3,1] => [[[[.,.],[[.,.],.]],[[.,.],.]],.] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 2

[8,3,6,4,7,5,2,1] => [[[[.,.],[[.,.],[[.,.],.]]],.],.] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 3

[7,5,2,1,8,3,6,4] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3

[7,5,2,6,3,1,8,4] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[5,2,7,4,1,8,6,3] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[5,2,8,7,4,1,6,3] => [[[.,.],[[[.,.],.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 1

[8,7,4,1,5,2,6,3] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3

[7,4,1,5,2,8,6,3] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 2

[7,6,3,1,4,2,8,5] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3

[7,5,2,8,6,3,1,4] => [[[[.,.],.],[[[.,.],.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 2

[8,7,5,2,6,3,1,4] => [[[[[.,.],.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3

[7,5,2,1,3,6,4,8] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3

[8,7,5,2,1,3,6,4] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 4

[7,5,2,1,3,8,6,4] => [[[[.,.],.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 3

[8,6,4,7,5,2,1,3] => [[[[[.,.],.],[[.,.],.]],.],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 3

[6,4,8,7,5,2,1,3] => [[[[.,.],[[[.,.],.],.]],.],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 2

[6,4,7,5,2,1,3,8] => [[[[.,.],[[.,.],.]],.],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 2

[6,3,1,4,7,5,2,8] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 2

[6,3,1,4,8,7,5,2] => [[[.,.],.],[[.,[[[.,.],.],.]],.]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 2

[8,6,3,1,4,7,5,2] => [[[[.,.],.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[8,5,7,6,3,1,4,2] => [[[[.,.],[[.,.],.]],.],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2

[7,5,2,1,6,4,8,3] => [[[[.,.],.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 3

[6,3,8,7,4,1,5,2] => [[[.,.],[[[.,.],.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 1

[6,3,7,4,1,5,2,8] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[7,4,1,6,3,5,2,8] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[7,4,1,8,6,3,5,2] => [[[.,.],.],[[[[.,.],.],[.,.]],.]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 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] => 2

[6,4,7,5,2,1,8,3] => [[[[.,.],[[.,.],.]],.],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2

[8,6,3,5,2,7,4,1] => [[[[[.,.],.],[.,.]],[[.,.],.]],.] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[6,3,5,2,8,7,4,1] => [[[[.,.],[.,.]],[[[.,.],.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 2

[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

[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

[4,2,6,3,5,7,1,8] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[6,1,3,7,4,2,5,8] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 1

[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

[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

[8,6,2,7,1,5,4,3] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 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] => 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

[7,5,2,8,6,1,4,3] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[8,4,6,5,3,1,7,2] => [[[[.,.],[[.,.],.]],.],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 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

[7,8,1,2,4,3,6,5] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 0

[8,4,1,6,2,3,7,5] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2

[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

[8,1,4,3,5,7,6,2] => [[.,.],[[[.,.],[.,[[.,.],.]]],.]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 1

[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

[8,7,1,3,6,5,4,2] => [[[.,.],.],[[.,[[[.,.],.],.]],.]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 2

[8,1,5,4,7,2,6,3] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[6,3,5,8,7,4,1,2] => [[[.,.],[[.,[[.,.],.]],.]],[.,.]] => [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 1

[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

[8,1,7,6,3,5,4,2] => [[.,.],[[[[.,.],.],[[.,.],.]],.]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 1

[4,2,6,8,7,1,5,3] => [[[.,.],[.,[[.,.],.]]],[[.,.],.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 1

[5,1,8,4,2,7,6,3] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 1

[3,6,1,8,2,7,5,4] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 0

[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

[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

[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

[4,7,1,3,6,8,2,5] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 0

[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

[8,7,2,4,6,5,3,1] => [[[[.,.],.],[[.,[[.,.],.]],.]],.] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 3

[8,7,2,5,4,6,1,3] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2

[8,7,3,2,1,5,6,4] => [[[[[.,.],.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 4

[8,7,6,1,4,5,3,2] => [[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[4,8,1,2,3,7,5,6] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 0

[7,1,3,4,8,6,5,2] => [[.,.],[[.,[.,[[[.,.],.],.]]],.]] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 1

[7,6,1,3,8,4,2,5] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 2

[7,2,3,4,8,6,5,1] => [[[.,.],[.,[.,[[[.,.],.],.]]]],.] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 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

[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

[7,3,8,6,1,4,2,5] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[7,2,8,6,3,4,1,5] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[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

[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

[7,2,3,8,5,6,4,1] => [[[.,.],[.,[[[.,.],[.,.]],.]]],.] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 2

[7,6,1,3,5,8,2,4] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 2

[7,1,3,2,5,6,8,4] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 1

[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

[7,6,1,8,5,4,2,3] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 2

[4,1,6,5,8,2,7,3] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[3,1,6,5,8,4,7,2] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 1

[3,2,6,5,8,4,7,1] => [[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2

[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

[5,2,6,4,8,3,7,1] => [[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2

[5,1,6,4,8,3,7,2] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 1

[5,1,6,4,8,2,7,3] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[5,2,6,4,8,1,7,3] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[4,3,7,5,8,1,6,2] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[4,3,7,5,8,2,6,1] => [[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[5,3,7,4,8,2,6,1] => [[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[5,3,7,4,8,1,6,2] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[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

[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

[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

[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

[5,4,8,2,6,3,7,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[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

[4,1,7,5,2,3,6,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1

[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

[6,8,3,2,1,4,7,5] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => 2

[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

[7,5,8,4,3,1,6,2] => [[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 3

[6,8,2,4,1,3,7,5] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 0

[6,1,2,7,5,8,4,3] => [[.,.],[.,[[[[.,.],[.,.]],.],.]]] => [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 1

[4,2,7,3,8,5,6,1] => [[[.,.],[[.,.],[[.,.],[.,.]]]],.] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 2

[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

[6,8,5,3,4,7,2,1] => [[[[[.,[.,.]],.],[.,[.,.]]],.],.] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[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

[8,3,4,7,6,2,5,1] => [[[[.,.],[.,[[.,.],.]]],[.,.]],.] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 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] => 0

[6,8,5,4,2,3,7,1] => [[[[[.,[.,.]],.],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 3

[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

[8,1,3,2,5,6,4,7] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[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

[6,5,3,8,4,2,7,1] => [[[[[.,.],.],[[.,.],.]],[.,.]],.] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 3

[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

[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

[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

[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

[3,2,7,5,8,6,1,4] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[7,4,3,8,6,2,1,5] => [[[[[.,.],.],[[.,.],.]],.],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 3

[3,2,7,6,1,8,4,5] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 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

[4,3,6,2,1,8,5,7] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2

[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

[5,8,4,2,3,6,7,1] => [[[[.,[.,.]],.],[.,[.,[.,.]]]],.] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2

[8,4,5,3,2,1,7,6] => [[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 3

[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

[6,4,8,3,2,7,1,5] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 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

[6,4,7,3,8,2,1,5] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 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] => 3

[8,4,3,7,2,1,5,6] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3

[5,1,2,7,3,6,8,4] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 1

[5,1,2,8,3,6,7,4] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 1

[5,6,3,4,8,7,2,1] => [[[[.,[.,.]],[.,[[.,.],.]]],.],.] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 2

[6,5,3,4,8,7,2,1] => [[[[[.,.],.],[.,[[.,.],.]]],.],.] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[4,1,2,8,3,6,7,5] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 1

[4,1,2,7,3,6,8,5] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 1

[7,5,3,8,4,6,2,1] => [[[[[.,.],.],[[.,.],[.,.]]],.],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 4

[8,5,3,7,4,6,2,1] => [[[[[.,.],.],[[.,.],[.,.]]],.],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 4

[5,8,1,2,3,4,7,6] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 0

[7,1,2,8,3,6,4,5] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 1

[6,1,8,2,3,5,7,4] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 1

[6,1,7,2,3,5,8,4] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 1

[4,3,8,7,5,6,2,1] => [[[[.,.],[[[.,.],.],[.,.]]],.],.] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 3

[7,1,6,2,3,5,8,4] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 1

[8,1,6,2,3,5,7,4] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 1

[8,1,7,2,3,5,6,4] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 1

[5,8,3,7,4,6,2,1] => [[[[.,[.,.]],[[.,.],[.,.]]],.],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 2

[8,7,1,2,3,4,6,5] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2

[8,6,1,2,3,4,7,5] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2

[8,1,6,2,3,5,4,7] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 1

[4,2,5,8,7,3,6,1] => [[[.,.],[[.,[[.,.],.]],[.,.]]],.] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2

[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

[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

[2,4,1,8,5,6,3,7] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[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

[4,5,1,6,7,3,8,2] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 0

[8,5,3,1,7,4,2,6] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[4,2,8,7,1,5,3,6] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[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

[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

[6,7,1,2,3,5,8,4] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 0

[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

[3,1,4,8,5,6,2,7] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 1

[8,3,1,4,5,7,2,6] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 2

[8,6,2,3,5,1,4,7] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[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

[8,2,3,7,5,4,1,6] => [[[.,.],[.,[[[.,.],.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 1

[8,2,6,3,5,4,1,7] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[8,6,1,5,2,4,3,7] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[8,6,2,4,1,5,3,7] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[8,4,1,6,5,3,2,7] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 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

[8,3,2,6,5,4,1,7] => [[[[.,.],.],[[[.,.],.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 2

[8,3,2,5,7,4,1,6] => [[[[.,.],.],[[.,[.,.]],.]],[.,.]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 2

[8,3,1,7,5,4,2,6] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 2

[8,2,7,4,1,5,3,6] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[6,1,3,8,7,5,4,2] => [[.,.],[[.,[[[[.,.],.],.],.]],.]] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 1

[3,6,1,8,7,5,4,2] => [[.,[.,.]],[[[[[.,.],.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 0

[3,8,1,5,7,6,4,2] => [[.,[.,.]],[[[.,[[.,.],.]],.],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 0

[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

[8,1,3,5,7,6,4,2] => [[.,.],[[.,[[.,[[.,.],.]],.]],.]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 1

[4,1,8,5,7,6,3,2] => [[.,.],[[[[.,.],[[.,.],.]],.],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 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

[8,1,7,3,4,6,2,5] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[8,3,1,7,2,6,5,4] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 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

[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

[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

[8,1,7,2,6,4,3,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1

[8,1,7,5,2,4,3,6] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[8,2,3,7,4,6,1,5] => [[[.,.],[.,[[.,.],[.,.]]]],[.,.]] => [1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1

[8,2,4,3,7,6,1,5] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[8,2,7,3,5,1,4,6] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[8,2,7,4,3,1,5,6] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 1

[8,2,7,3,1,5,6,4] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 1

[8,2,1,5,7,6,4,3] => [[[.,.],.],[[[.,[[.,.],.]],.],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 2

[6,2,1,8,7,5,4,3] => [[[.,.],.],[[[[[.,.],.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2

[6,1,8,2,7,5,4,3] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 1

[8,1,7,3,5,2,6,4] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[8,1,5,2,7,6,4,3] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 1

[8,1,7,2,4,6,5,3] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 1

[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

[4,2,8,3,7,6,5,1] => [[[.,.],[[.,.],[[[.,.],.],.]]],.] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 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

[5,1,8,7,2,6,4,3] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 1

[5,8,1,3,7,6,2,4] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 0

[8,2,5,4,1,7,6,3] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[5,1,4,8,7,6,3,2] => [[.,.],[[[.,[[[.,.],.],.]],.],.]] => [1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 1

[8,1,4,3,7,6,5,2] => [[.,.],[[[.,.],[[[.,.],.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 1

[4,8,1,3,7,6,5,2] => [[.,[.,.]],[[.,[[[.,.],.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 0

[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

[5,8,6,3,2,1,7,4] => [[[[.,[[.,.],.]],.],.],[[.,.],.]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2

[5,7,6,3,2,4,1,8] => [[[[.,[[.,.],.]],.],[.,.]],[.,.]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[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

[5,7,1,3,2,8,6,4] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 0

[5,8,1,3,2,7,4,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[8,5,1,3,2,4,6,7] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2

[7,5,8,2,1,4,3,6] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2

[6,7,1,2,5,4,8,3] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 0

[6,8,1,2,5,7,4,3] => [[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 0

[8,1,6,4,2,3,5,7] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1

[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

[7,4,1,2,6,8,3,5] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 2

[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

[7,3,5,4,2,1,8,6] => [[[[.,.],[[.,.],.]],.],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2

[7,3,2,8,5,6,1,4] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2

[6,7,4,2,1,8,5,3] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 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] => 2

[5,4,2,1,7,3,6,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[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

[6,5,8,2,3,7,4,1] => [[[[.,.],[.,.]],[.,[[.,.],.]]],.] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 2

[4,1,2,8,5,3,6,7] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 1

[2,7,1,5,8,4,3,6] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 0

[7,1,2,6,3,5,4,8] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 1

[7,2,6,3,4,5,1,8] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 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

[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

[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

[3,2,6,4,7,8,5,1] => [[[.,.],[[.,.],[[.,[.,.]],.]]],.] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 2

[4,2,7,5,8,3,1,6] => [[[.,.],[[[.,.],[.,.]],.]],[.,.]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1

[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

[5,2,1,4,7,8,3,6] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 2

[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

[6,1,3,8,5,4,7,2] => [[.,.],[[.,[[[.,.],.],[.,.]]],.]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 1

[4,7,2,3,1,6,8,5] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0

[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

[7,4,6,2,8,3,5,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[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

[4,3,8,2,6,7,5,1] => [[[[.,.],[.,.]],[[.,[.,.]],.]],.] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 2

[5,1,8,6,4,7,2,3] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1

[4,1,8,5,6,3,7,2] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 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

[6,7,2,3,1,5,8,4] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0

[7,5,2,3,8,1,6,4] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[7,5,2,3,8,4,1,6] => [[[[.,.],.],[.,[[.,.],.]]],[.,.]] => [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 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] => 0

[8,1,7,5,2,3,4,6] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1

[8,6,3,1,4,2,5,7] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[4,5,1,6,2,8,7,3] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 0

[4,8,3,6,1,7,2,5] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[6,2,7,8,3,4,5,1] => [[[.,.],[[.,[.,.]],[.,[.,.]]]],.] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2

[2,1,7,5,8,6,3,4] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1

[4,7,3,8,6,5,2,1] => [[[[.,[.,.]],[[[.,.],.],.]],.],.] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 2

[7,3,8,4,6,5,1,2] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[7,4,3,6,5,8,1,2] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2

[4,2,7,6,5,8,3,1] => [[[.,.],[[[[.,.],.],[.,.]],.]],.] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 2

[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

[6,4,7,2,5,8,3,1] => [[[[.,.],[.,.]],[[.,[.,.]],.]],.] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 2

[6,3,8,7,5,1,4,2] => [[[.,.],[[[.,.],.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 1

[5,3,6,4,1,2,8,7] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 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

[5,2,4,8,7,6,1,3] => [[[.,.],[.,[[[.,.],.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 1

[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

[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

[5,1,8,2,4,3,6,7] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[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

[3,6,2,4,8,7,1,5] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 0

[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

[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

[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

[6,8,1,3,5,4,7,2] => [[.,[.,.]],[[.,[[.,.],[.,.]]],.]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 0

[8,1,6,3,5,4,7,2] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 1

[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

[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

[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

[2,7,1,8,4,3,5,6] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0

[6,7,1,8,3,2,4,5] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0

[6,7,2,8,1,3,4,5] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0

[5,1,6,8,7,2,3,4] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 1

[7,4,6,8,5,3,1,2] => [[[[.,.],[[.,[.,.]],.]],.],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 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] => 0

[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

[3,1,2,4,8,5,7,6] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 1

[7,1,5,4,8,3,2,6] => [[.,.],[[[[.,.],[.,.]],.],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 1

[6,4,1,7,5,3,2,8] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 2

[7,2,5,4,8,1,6,3] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[7,2,3,8,6,1,5,4] => [[[.,.],[.,[[.,.],.]]],[[.,.],.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 1

[7,3,2,5,8,1,6,4] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[5,3,8,4,1,2,6,7] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1

[5,2,8,4,1,6,3,7] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[7,6,5,2,1,8,4,3] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4

[5,1,8,7,4,3,6,2] => [[.,.],[[[[[.,.],.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 1

[5,7,1,3,2,4,8,6] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0

[4,2,7,6,3,5,8,1] => [[[.,.],[[[.,.],.],[.,[.,.]]]],.] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 2

[8,4,7,6,3,5,1,2] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[8,1,7,4,2,3,5,6] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1

[6,5,1,3,8,7,4,2] => [[[.,.],.],[[.,[[[.,.],.],.]],.]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 2

[6,1,8,5,3,7,2,4] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1

[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

[8,6,5,1,7,4,3,2] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3

[7,6,4,1,3,5,8,2] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 3

[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

[5,6,2,7,4,3,1,8] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 0

[8,6,2,7,4,1,3,5] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[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

[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

[5,7,2,6,1,8,4,3] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 0

[5,7,2,6,1,3,8,4] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 0

[5,8,2,6,1,4,7,3] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0

[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

[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

[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

[4,1,8,7,5,6,2,3] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1

[6,4,1,3,8,7,5,2] => [[[.,.],.],[[.,[[[.,.],.],.]],.]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 2

[2,1,7,4,6,8,3,5] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[8,6,4,2,7,3,5,1] => [[[[[.,.],.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 4

[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

[2,1,8,3,5,7,6,4] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 1

[2,8,1,3,6,7,5,4] => [[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 0

[7,2,4,8,6,1,5,3] => [[[.,.],[.,[[.,.],.]]],[[.,.],.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 1

[6,4,3,2,8,1,7,5] => [[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3

[6,2,4,3,8,1,7,5] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[5,8,4,3,1,6,7,2] => [[[[.,[.,.]],.],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 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

[6,3,7,2,5,4,8,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[5,4,7,3,2,6,8,1] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 3

[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

[6,8,3,2,1,7,4,5] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 2

[4,8,1,7,5,3,2,6] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 0

[5,4,3,7,2,8,6,1] => [[[[[.,.],.],[.,.]],[[.,.],.]],.] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[6,3,8,4,1,7,2,5] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[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

[8,2,6,4,3,5,1,7] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[5,4,2,8,6,3,7,1] => [[[[.,.],.],[[[.,.],.],[.,.]]],.] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 3

[6,5,3,2,4,1,8,7] => [[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3

[6,5,8,7,3,2,4,1] => [[[[[.,.],[[.,.],.]],.],[.,.]],.] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 3

[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

[8,3,1,6,5,7,4,2] => [[[.,.],.],[[[[.,.],[.,.]],.],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 2

[8,5,6,7,3,1,4,2] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 2

[8,7,5,3,2,6,4,1] => [[[[[[.,.],.],.],.],[[.,.],.]],.] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 5

[8,5,3,1,4,6,7,2] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 3

[8,5,1,6,4,3,7,2] => [[[.,.],.],[[[[.,.],.],[.,.]],.]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 2

[6,1,4,3,7,8,2,5] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[6,1,2,7,5,8,3,4] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 1

[6,5,1,2,8,4,7,3] => [[[.,.],.],[.,[[[.,.],[.,.]],.]]] => [1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2

[2,1,8,7,5,4,6,3] => [[.,.],[[[[[.,.],.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 1

[7,8,3,4,1,6,5,2] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 0

[8,7,3,4,2,6,5,1] => [[[[[.,.],.],[.,.]],[[.,.],.]],.] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[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

[4,7,2,8,6,3,1,5] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 0

[6,4,7,5,2,8,3,1] => [[[[.,.],[[.,.],.]],[[.,.],.]],.] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 2

[7,5,1,3,6,4,8,2] => [[[.,.],.],[[.,[[.,.],[.,.]]],.]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 2

[6,5,2,3,7,8,4,1] => [[[[.,.],.],[.,[[.,[.,.]],.]]],.] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[7,2,6,3,1,5,8,4] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 1

[4,6,3,8,7,5,1,2] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 0

[7,8,2,4,1,6,5,3] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 0

[2,1,6,8,7,5,3,4] => [[.,.],[[[.,[[.,.],.]],.],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 1

[2,6,1,8,7,5,3,4] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 0

[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

[3,1,8,2,5,7,6,4] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 1

[2,8,1,4,5,7,6,3] => [[.,[.,.]],[[.,[.,[[.,.],.]]],.]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 0

[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

[3,1,6,8,7,2,5,4] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 1

[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

[8,1,4,7,6,3,2,5] => [[.,.],[[[.,[[.,.],.]],.],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 1

[8,3,1,6,4,7,2,5] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[5,3,8,6,2,7,1,4] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[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

[8,4,6,3,1,2,5,7] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2

[6,8,1,4,5,2,3,7] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[2,1,6,5,3,8,4,7] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[5,7,4,8,1,2,3,6] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0

[8,2,1,5,3,7,4,6] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[8,7,1,5,6,2,3,4] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[3,7,1,6,2,4,8,5] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0

[5,1,2,7,6,8,3,4] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 1

[6,1,7,2,5,8,3,4] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[7,5,1,2,6,8,3,4] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 2

[6,1,5,2,7,8,3,4] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[8,3,1,4,2,5,7,6] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2

[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

[5,1,2,6,8,7,3,4] => [[.,.],[.,[[.,[[.,.],.]],[.,.]]]] => [1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 1

[8,1,5,7,6,2,3,4] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 1

[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

[8,3,1,2,7,6,4,5] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 2

[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

[7,8,6,3,1,5,2,4] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 2

[7,8,1,3,4,5,2,6] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 0

[7,1,8,2,4,6,3,5] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[7,6,8,4,1,5,3,2] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 2

[7,3,2,8,1,5,4,6] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 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] => 2

[7,6,5,3,8,4,1,2] => [[[[[.,.],.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3

[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

[3,1,2,7,6,8,5,4] => [[.,.],[.,[[[[.,.],[.,.]],.],.]]] => [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 1

[6,3,2,8,4,5,1,7] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2

[6,1,8,3,5,4,2,7] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1

[4,8,2,5,3,7,1,6] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[4,1,8,6,5,3,7,2] => [[.,.],[[[[[.,.],.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 1

[5,3,2,8,6,4,7,1] => [[[[.,.],.],[[[.,.],.],[.,.]]],.] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 3

[6,8,1,2,7,4,3,5] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 0

[7,5,2,3,4,8,6,1] => [[[[.,.],.],[.,[.,[[.,.],.]]]],.] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 3

[7,3,5,4,2,8,6,1] => [[[[.,.],[[.,.],.]],[[.,.],.]],.] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 2

[5,6,1,3,2,4,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0

[2,5,1,3,7,8,6,4] => [[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 0

[4,3,7,2,1,8,6,5] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 2

[4,6,2,3,1,5,7,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0

[3,1,6,4,7,5,2,8] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1

[3,6,2,7,5,4,1,8] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 0

[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

[3,1,5,4,7,8,6,2] => [[.,.],[[[.,.],[[.,[.,.]],.]],.]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 1

[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

[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

[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

[6,1,4,7,5,3,8,2] => [[.,.],[[[.,[[.,.],.]],[.,.]],.]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 1

[8,7,4,3,1,5,6,2] => [[[[[.,.],.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 4

[8,7,1,4,3,5,6,2] => [[[.,.],.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[6,1,8,4,7,3,2,5] => [[.,.],[[[[.,.],[.,.]],.],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 1

[4,7,3,6,1,2,8,5] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 0

[5,2,1,7,4,3,8,6] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[7,6,8,2,5,3,4,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[6,4,1,7,5,2,8,3] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[8,6,2,1,5,7,4,3] => [[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[6,1,3,7,5,8,2,4] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 1

[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

[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

[6,1,8,5,3,4,7,2] => [[.,.],[[[[.,.],.],[.,[.,.]]],.]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 1

[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

[6,4,1,8,7,2,5,3] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 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

[7,4,6,8,5,2,3,1] => [[[[.,.],[[.,[.,.]],.]],[.,.]],.] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[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

[4,2,6,8,7,1,3,5] => [[[.,.],[.,[[.,.],.]]],[.,[.,.]]] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 1

[4,5,3,8,1,7,2,6] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[6,5,4,8,1,3,7,2] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[7,6,4,8,5,1,3,2] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[6,3,7,5,2,4,8,1] => [[[[.,.],[[.,.],.]],[.,[.,.]]],.] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 2

[8,1,2,7,4,5,3,6] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 1

[6,1,7,4,5,3,8,2] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 1

[8,2,7,3,1,5,4,6] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[8,1,3,7,5,6,4,2] => [[.,.],[[.,[[[.,.],[.,.]],.]],.]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 1

[4,1,6,5,7,8,2,3] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[6,1,3,7,4,2,8,5] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 1

[6,7,2,4,1,3,8,5] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 0

[8,5,3,4,2,7,1,6] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[7,6,8,3,5,4,2,1] => [[[[[.,.],[.,.]],[[.,.],.]],.],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 3

[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

[8,7,2,4,6,1,5,3] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 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] => 3

[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

[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

[5,3,7,6,8,4,1,2] => [[[.,.],[[[.,.],[.,.]],.]],[.,.]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1

[7,5,3,2,8,6,4,1] => [[[[[.,.],.],.],[[[.,.],.],.]],.] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 4

[5,4,8,6,7,2,3,1] => [[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[5,4,8,6,3,1,2,7] => [[[[.,.],[[.,.],.]],.],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 2

[5,4,8,7,2,1,3,6] => [[[[.,.],[[.,.],.]],.],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 2

[5,3,6,4,8,2,7,1] => [[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[5,3,7,4,6,2,8,1] => [[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[8,2,6,3,7,4,5,1] => [[[.,.],[[.,.],[[.,.],[.,.]]]],.] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 2

[8,2,4,7,3,5,6,1] => [[[.,.],[[.,[.,.]],[.,[.,.]]]],.] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2

[8,2,6,5,7,3,4,1] => [[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2

[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

[5,4,6,2,8,3,7,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[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

[5,2,1,6,3,8,7,4] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 2

[6,3,2,8,5,4,1,7] => [[[[.,.],.],[[[.,.],.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 2

[4,3,1,5,2,8,6,7] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[8,5,4,1,3,2,6,7] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 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

[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

[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

[4,1,6,3,5,2,7,8] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[4,2,1,8,6,3,7,5] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[3,1,7,2,5,6,4,8] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[3,7,2,4,1,6,5,8] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[7,3,2,1,6,4,5,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[8,5,2,6,1,3,7,4] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[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

[7,1,2,5,4,6,3,8] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 1

[2,4,1,6,5,3,7,8] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0

[4,1,2,7,5,6,3,8] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 1

[7,1,2,6,5,4,3,8] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 1

[8,2,1,5,6,3,7,4] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[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

[3,1,6,5,4,2,7,8] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 1

[3,1,4,6,5,2,7,8] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 1

[2,1,8,6,3,7,5,4] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 1

[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

[7,6,3,2,8,5,1,4] => [[[[[.,.],.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3

[5,6,3,8,7,4,1,2] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 0

[5,2,6,8,7,4,1,3] => [[[.,.],[[.,[[.,.],.]],.]],[.,.]] => [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 1

[4,3,8,5,7,2,6,1] => [[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[6,3,8,5,4,1,2,7] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 1

[6,3,8,4,5,1,2,7] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[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

[5,4,1,3,2,8,6,7] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[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

[5,2,1,4,3,8,6,7] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[4,2,7,3,8,5,1,6] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[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

[4,3,7,2,8,5,6,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[5,3,1,2,4,8,6,7] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 2

[5,4,3,1,2,8,6,7] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3

[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

[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

[5,1,7,3,4,6,8,2] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 1

[5,8,7,4,3,1,6,2] => [[[[.,[[.,.],.]],.],.],[[.,.],.]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2

[6,8,1,3,4,5,7,2] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 0

[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

[6,3,7,4,1,2,5,8] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1

[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

[3,7,2,8,6,5,1,4] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 0

[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

[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

[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

[4,8,1,6,7,3,2,5] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 0

[4,8,1,3,5,6,2,7] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 0

[5,3,7,8,4,2,6,1] => [[[[.,.],[[.,[.,.]],.]],[.,.]],.] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[6,3,7,8,2,4,5,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[8,5,2,4,3,1,7,6] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[7,5,4,2,3,1,8,6] => [[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3

[2,5,1,4,3,8,7,6] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 0

[4,8,1,3,2,6,5,7] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[8,3,1,4,2,6,5,7] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[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

[8,6,3,1,5,4,2,7] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[8,6,4,1,5,3,2,7] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[8,6,5,4,1,3,2,7] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4

[5,3,8,7,4,6,2,1] => [[[[.,.],[[[.,.],.],[.,.]]],.],.] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 3

[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

[4,8,5,3,1,2,7,6] => [[[.,[[.,.],.]],.],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => 1

[6,8,7,3,1,5,4,2] => [[[.,[[.,.],.]],.],[[[.,.],.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1

[6,8,5,4,1,3,7,2] => [[[[.,[.,.]],.],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[8,5,4,7,2,1,3,6] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3

[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

[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

[5,8,4,6,1,2,7,3] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 0

[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

[5,7,2,8,4,6,1,3] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[6,7,3,2,4,8,5,1] => [[[[.,[.,.]],.],[.,[[.,.],.]]],.] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => 2

[7,2,8,6,4,5,1,3] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[8,7,2,6,5,1,3,4] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[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

[7,6,3,5,2,8,4,1] => [[[[[.,.],.],[.,.]],[[.,.],.]],.] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[6,2,7,4,8,5,3,1] => [[[.,.],[[[.,.],[[.,.],.]],.]],.] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 2

[8,6,5,1,7,2,4,3] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 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

[5,1,6,3,4,8,2,7] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[3,5,2,6,4,8,1,7] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[3,5,2,4,8,1,7,6] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0

[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

[4,6,3,8,7,5,2,1] => [[[[.,[.,.]],[[[.,.],.],.]],.],.] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 2

[6,3,8,7,5,4,2,1] => [[[[.,.],[[[[.,.],.],.],.]],.],.] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 3

[6,8,4,2,1,7,5,3] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 2

[5,2,6,4,3,8,1,7] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[6,5,3,1,4,8,2,7] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3

[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

[3,8,1,7,6,2,5,4] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[8,1,7,6,4,2,5,3] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 1

[7,2,6,3,8,5,4,1] => [[[.,.],[[.,.],[[[.,.],.],.]]],.] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 2

[7,3,8,6,4,1,5,2] => [[[.,.],[[[.,.],.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 1

[6,1,5,2,4,8,3,7] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[8,7,1,3,6,5,2,4] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 2

[5,2,4,7,3,8,6,1] => [[[.,.],[[.,[.,.]],[[.,.],.]]],.] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 2

[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

[3,7,2,8,1,5,4,6] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[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

[7,2,1,5,8,4,3,6] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 2

[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

[6,1,5,4,3,8,2,7] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1

[2,1,5,8,6,3,7,4] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 1

[6,3,2,5,8,1,7,4] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[5,3,2,8,6,1,7,4] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 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] => 0

[5,3,8,6,1,4,7,2] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 1

[8,3,5,7,2,6,4,1] => [[[[.,.],[.,[.,.]]],[[.,.],.]],.] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 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

[4,3,6,8,5,2,7,1] => [[[[.,.],[[.,[.,.]],.]],[.,.]],.] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[8,5,4,7,2,6,3,1] => [[[[[.,.],.],[.,.]],[[.,.],.]],.] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[5,6,2,4,7,1,8,3] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0

[6,5,7,4,1,3,8,2] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[4,1,6,3,5,7,8,2] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 1

[4,3,6,2,5,7,8,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2

[4,6,1,2,5,7,8,3] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 0

[2,4,1,6,5,7,8,3] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 0

[7,5,4,2,6,1,8,3] => [[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3

[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

[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

[5,3,6,4,8,2,1,7] => [[[[.,.],[[.,.],[.,.]]],.],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 2

[7,3,2,5,4,1,8,6] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[7,3,2,5,1,8,6,4] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 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

[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

[7,5,2,8,4,3,1,6] => [[[[.,.],.],[[[.,.],.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 2

[7,3,2,4,1,8,6,5] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2

[8,4,3,2,7,5,1,6] => [[[[[.,.],.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3

[4,3,7,5,8,2,1,6] => [[[[.,.],[[.,.],[.,.]]],.],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 2

[4,3,7,5,2,6,1,8] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[8,4,5,3,7,2,1,6] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 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

[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

[8,7,5,6,1,3,4,2] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[3,2,6,4,1,8,5,7] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[5,4,8,6,2,3,1,7] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[5,2,4,7,6,8,3,1] => [[[.,.],[[.,[[.,.],[.,.]]],.]],.] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 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] => 0

[8,5,7,6,3,2,4,1] => [[[[[.,.],[[.,.],.]],.],[.,.]],.] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 3

[6,4,1,8,7,3,2,5] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 2

[8,3,2,7,4,6,5,1] => [[[[.,.],.],[[.,.],[[.,.],.]]],.] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3

[7,5,8,4,1,3,6,2] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[7,1,6,2,3,8,4,5] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 1

[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

[5,1,3,8,7,2,6,4] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 1

[8,7,1,6,2,5,3,4] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[7,1,5,2,4,8,3,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[7,2,5,4,1,3,8,6] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 1

[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

[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

[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

[4,5,2,6,7,3,1,8] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 0

[8,1,7,5,3,6,2,4] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1

[5,2,8,3,6,1,4,7] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[5,2,6,3,1,7,8,4] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 1

[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

[5,6,3,7,1,4,8,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0

[5,3,2,1,8,6,4,7] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[6,5,8,3,7,2,1,4] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 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] => 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] => 2

[5,4,3,8,2,1,7,6] => [[[[[.,.],.],[.,.]],.],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 3

[6,4,8,3,2,1,7,5] => [[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 3

[5,4,3,8,2,1,6,7] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3

[6,4,2,3,5,1,8,7] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 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

[5,2,3,8,6,4,7,1] => [[[.,.],[.,[[[.,.],.],[.,.]]]],.] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 2

[5,2,3,7,4,8,1,6] => [[[.,.],[.,[[.,.],[.,.]]]],[.,.]] => [1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1

[8,6,3,2,5,4,7,1] => [[[[[.,.],.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 4

[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

[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

[2,1,8,6,4,5,7,3] => [[.,.],[[[[.,.],.],[.,[.,.]]],.]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 1

[4,8,2,5,7,3,1,6] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 0

[5,8,2,3,4,7,1,6] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0

[6,3,4,7,8,2,1,5] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 2

[8,5,4,7,1,3,6,2] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[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

[8,1,5,2,3,7,6,4] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 1

[6,4,2,3,7,8,5,1] => [[[[.,.],.],[.,[[.,[.,.]],.]]],.] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[8,4,2,3,6,7,1,5] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 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] => 0

[3,5,1,8,4,6,2,7] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[4,2,1,5,6,8,3,7] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 2

[4,1,2,6,5,8,3,7] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 1

[4,1,8,3,2,6,7,5] => [[.,.],[[[.,.],.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 1

[4,2,7,5,8,1,3,6] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[4,6,2,7,8,3,1,5] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 0

[4,6,1,3,8,2,5,7] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[4,3,6,2,1,8,7,5] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 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

[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

[7,5,4,1,6,3,2,8] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[7,5,4,8,6,3,1,2] => [[[[[.,.],.],[[.,.],.]],.],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 3

[8,3,7,4,1,6,2,5] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[8,5,4,1,6,3,2,7] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[8,2,1,5,6,7,3,4] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 2

[6,3,1,8,4,7,2,5] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[7,1,4,8,6,3,2,5] => [[.,.],[[[.,[[.,.],.]],.],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 1

[4,1,8,5,6,7,2,3] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[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

[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

[6,3,7,4,8,2,1,5] => [[[[.,.],[[.,.],[.,.]]],.],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 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

[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

[5,3,7,4,8,2,1,6] => [[[[.,.],[[.,.],[.,.]]],.],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 2

[5,3,8,4,1,6,2,7] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[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

[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

[7,3,8,4,1,6,2,5] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[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

[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

[8,3,1,2,5,7,4,6] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 2

[8,1,4,2,6,5,3,7] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1

[5,1,3,7,4,8,2,6] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 1

[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

[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

[4,5,2,3,8,6,1,7] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 0

[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

[4,8,1,3,7,5,2,6] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 0

[5,3,1,4,7,2,8,6] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[7,2,8,4,3,6,5,1] => [[[.,.],[[[.,.],.],[[.,.],.]]],.] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 2

[7,2,8,5,6,3,4,1] => [[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2

[7,6,3,8,5,4,2,1] => [[[[[.,.],.],[[[.,.],.],.]],.],.] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 4

[6,2,8,7,5,4,1,3] => [[[.,.],[[[[.,.],.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1

[6,2,8,4,3,7,1,5] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[5,2,8,4,3,1,7,6] => [[[.,.],[[[.,.],.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 1

[3,6,2,7,1,5,4,8] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[4,2,6,5,7,8,1,3] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[3,2,5,7,6,8,1,4] => [[[.,.],[.,[[.,.],[.,.]]]],[.,.]] => [1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1

[3,2,4,6,8,7,1,5] => [[[.,.],[.,[.,[[.,.],.]]]],[.,.]] => [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 1

[5,3,2,6,8,4,7,1] => [[[[.,.],.],[[.,[.,.]],[.,.]]],.] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 3

[3,1,8,6,4,7,2,5] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1

[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

[5,3,2,8,7,6,4,1] => [[[[.,.],.],[[[[.,.],.],.],.]],.] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 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

[6,5,4,8,3,7,2,1] => [[[[[[.,.],.],[.,.]],[.,.]],.],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 4

[4,3,8,7,2,6,5,1] => [[[[.,.],[[.,.],.]],[[.,.],.]],.] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 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] => 2

[7,6,4,8,1,2,5,3] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[7,5,4,8,3,2,6,1] => [[[[[[.,.],.],[.,.]],.],[.,.]],.] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 4

[4,3,1,5,6,2,8,7] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[4,1,5,8,6,7,2,3] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 1

[4,3,7,6,1,2,8,5] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 1

[4,3,7,5,6,2,8,1] => [[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 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] => 0

[2,1,5,8,6,7,4,3] => [[.,.],[[[.,[[.,.],[.,.]]],.],.]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 1

[4,7,1,5,6,2,8,3] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[5,3,8,6,4,7,2,1] => [[[[.,.],[[[.,.],.],[.,.]]],.],.] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 3

[6,4,1,5,7,8,3,2] => [[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 2

[6,4,1,7,3,2,8,5] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[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

[6,5,4,7,1,3,8,2] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[2,1,6,5,3,7,8,4] => [[.,.],[[[.,.],.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 1

[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

[4,1,2,7,5,8,3,6] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 1

[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

[5,6,4,3,1,8,2,7] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 2

[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

[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

[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

[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

[4,1,7,5,8,3,6,2] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 1

[6,7,1,3,8,4,5,2] => [[.,[.,.]],[[.,[[.,.],[.,.]]],.]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 0

[6,1,7,4,2,8,5,3] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 1

[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

[6,7,3,2,1,8,4,5] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 2

[6,7,3,2,8,4,5,1] => [[[[.,[.,.]],.],[[.,.],[.,.]]],.] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => 2

[2,7,1,8,4,6,3,5] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[6,7,1,8,4,5,3,2] => [[.,[.,.]],[[[[.,.],[.,.]],.],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 0

[8,3,7,6,1,2,5,4] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 1

[8,7,3,4,6,2,5,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3

[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

[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

[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

[8,7,3,5,6,2,4,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3

[8,7,4,6,5,2,3,1] => [[[[[.,.],.],[[.,.],.]],[.,.]],.] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 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

[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

[8,3,5,7,6,1,4,2] => [[[.,.],[.,[[.,.],.]]],[[.,.],.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 1

[8,7,3,6,2,1,5,4] => [[[[[.,.],.],[.,.]],.],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 3

[8,7,3,4,6,2,1,5] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3

[8,7,4,6,5,2,1,3] => [[[[[.,.],.],[[.,.],.]],.],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 3

[8,6,5,2,7,4,3,1] => [[[[[.,.],.],.],[[[.,.],.],.]],.] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 4

[8,4,3,7,6,5,1,2] => [[[[.,.],.],[[[.,.],.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 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] => 2

[8,5,7,6,4,1,2,3] => [[[[.,.],[[.,.],.]],.],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 2

[8,4,2,7,5,1,6,3] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 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] => 2

[8,4,7,6,5,1,2,3] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 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] => 2

[8,5,2,6,7,4,1,3] => [[[[.,.],.],[[.,[.,.]],.]],[.,.]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 2

[8,5,3,7,6,4,1,2] => [[[[.,.],.],[[[.,.],.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 2

[8,6,2,5,7,3,1,4] => [[[[.,.],.],[[.,[.,.]],.]],[.,.]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 2

[8,6,2,4,7,3,1,5] => [[[[.,.],.],[[.,[.,.]],.]],[.,.]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 2

[8,5,2,3,7,4,1,6] => [[[[.,.],.],[.,[[.,.],.]]],[.,.]] => [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 2

[8,5,3,2,7,6,4,1] => [[[[[.,.],.],.],[[[.,.],.],.]],.] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 4

[8,6,1,5,4,3,2,7] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 2

[7,8,3,2,5,4,6,1] => [[[[.,[.,.]],.],[[.,.],[.,.]]],.] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => 2

[7,2,1,6,4,8,5,3] => [[[.,.],.],[[[.,.],[[.,.],.]],.]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 2

[3,1,8,7,6,4,2,5] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 1

[3,1,8,7,5,4,2,6] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 1

[3,1,7,6,5,4,2,8] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 1

[4,7,1,6,5,3,2,8] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 0

[4,8,1,6,5,3,2,7] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 0

[8,4,1,7,6,3,2,5] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 2

[5,4,1,8,6,3,2,7] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 2

[5,4,1,7,6,3,2,8] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 2

[6,4,1,8,5,3,2,7] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 2

[8,4,1,7,5,3,2,6] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 2

[7,4,1,6,5,3,2,8] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 2

[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

[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

[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

[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

[8,7,5,1,4,3,2,6] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[8,6,5,1,4,3,2,7] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[3,1,6,4,5,8,7,2] => [[.,.],[[[.,.],[.,[[.,.],.]]],.]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 1

[3,1,6,4,5,8,2,7] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[7,6,3,8,4,5,2,1] => [[[[[.,.],.],[[.,.],[.,.]]],.],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 4

[8,2,7,6,1,4,3,5] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[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

[5,6,3,8,4,1,2,7] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 0

[8,2,7,6,1,4,5,3] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 1

[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

[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

[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

[8,7,5,3,1,6,4,2] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 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

[5,8,3,7,6,4,1,2] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 0

[6,5,1,7,2,4,8,3] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[8,1,2,7,5,4,3,6] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 1

[6,5,1,8,3,7,2,4] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[7,8,1,5,4,2,3,6] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0

[6,8,1,7,5,4,2,3] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 0

[7,6,3,1,2,8,5,4] => [[[[.,.],.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 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

[3,1,2,7,5,4,8,6] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 1

[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

[8,6,1,7,5,2,4,3] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[7,6,4,1,8,3,2,5] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[8,4,1,6,5,2,7,3] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[4,2,1,5,7,8,3,6] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 2

[5,4,1,6,7,8,2,3] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 2

[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

[4,1,5,3,7,8,2,6] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[8,1,4,6,5,2,7,3] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 1

[7,1,5,4,6,3,2,8] => [[.,.],[[[[.,.],[.,.]],.],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 1

[8,2,1,6,7,5,4,3] => [[[.,.],.],[[[[.,[.,.]],.],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 2

[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

[8,6,4,1,5,7,3,2] => [[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[5,2,4,3,7,1,6,8] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[6,1,5,4,8,3,2,7] => [[.,.],[[[[.,.],[.,.]],.],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 1

[3,2,1,7,5,8,4,6] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[4,5,1,3,7,8,2,6] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 0

[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

[7,6,4,3,1,5,2,8] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4

[7,5,4,6,1,3,2,8] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[8,4,6,5,1,2,7,3] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 1

[8,6,5,7,2,1,4,3] => [[[[[.,.],.],[.,.]],.],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 3

[7,5,4,2,6,3,8,1] => [[[[[.,.],.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 4

[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

[4,3,7,8,6,2,5,1] => [[[[.,.],[[.,[.,.]],.]],[.,.]],.] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[3,8,1,7,5,2,4,6] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0

[8,2,4,6,3,7,5,1] => [[[.,.],[[.,[.,.]],[[.,.],.]]],.] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 2

[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

[8,2,1,4,5,6,7,3] => [[[.,.],.],[[.,[.,[.,[.,.]]]],.]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[7,3,1,2,5,6,4,8] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 2

[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

[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

[7,2,1,3,6,8,4,5] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 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

[7,3,8,2,6,5,4,1] => [[[[.,.],[.,.]],[[[.,.],.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 2

[7,1,3,8,6,5,4,2] => [[.,.],[[.,[[[[.,.],.],.],.]],.]] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 1

[8,1,3,7,6,5,4,2] => [[.,.],[[.,[[[[.,.],.],.],.]],.]] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 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] => 0

[7,3,8,6,1,5,4,2] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[3,5,1,7,8,2,6,4] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[5,4,7,8,2,1,6,3] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 2

[6,3,8,7,1,5,4,2] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[8,6,4,7,1,5,3,2] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 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

[5,6,4,8,3,2,1,7] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 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

[5,7,4,2,6,3,8,1] => [[[[.,[.,.]],.],[[.,.],[.,.]]],.] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => 2

[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

[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

[4,5,1,6,7,8,3,2] => [[.,[.,.]],[[[.,[.,[.,.]]],.],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 0

[4,5,2,6,1,3,8,7] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 0

[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

[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

[6,7,1,2,4,8,5,3] => [[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 0

[7,8,1,3,4,5,6,2] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 0

[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

[7,1,2,6,3,8,5,4] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 1

[8,1,2,6,3,7,5,4] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 1

[8,1,2,7,6,3,5,4] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 1

[4,8,7,3,1,6,2,5] => [[[.,[[.,.],.]],.],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[7,4,3,1,6,2,8,5] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3

[7,4,3,1,8,6,2,5] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 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

[6,1,2,7,4,3,8,5] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 1

[5,1,2,6,3,8,7,4] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 1

[5,1,2,7,3,8,6,4] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 1

[6,1,2,7,3,5,8,4] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 1

[7,5,3,2,1,8,6,4] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4

[4,2,1,5,3,6,7,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2

[6,2,5,4,1,8,7,3] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[4,6,3,2,1,8,7,5] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 2

[6,5,3,2,1,8,7,4] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4

[8,4,3,2,7,6,1,5] => [[[[[.,.],.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3

[3,2,7,4,8,6,1,5] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[7,4,3,2,8,6,1,5] => [[[[[.,.],.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3

[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

[6,4,3,8,5,2,1,7] => [[[[[.,.],.],[[.,.],.]],.],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 3

[8,2,5,4,7,6,1,3] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[7,2,5,4,8,6,1,3] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[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

[3,2,5,4,8,6,1,7] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[3,2,8,6,5,4,1,7] => [[[.,.],[[[[.,.],.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1

[8,4,3,6,5,2,1,7] => [[[[[.,.],.],[[.,.],.]],.],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 3

[8,4,3,7,5,2,1,6] => [[[[[.,.],.],[[.,.],.]],.],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 3

[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

[6,8,7,4,3,2,1,5] => [[[[[.,[[.,.],.]],.],.],.],[.,.]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 3

[3,6,1,4,8,7,2,5] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 0

[5,8,1,3,7,2,6,4] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[6,3,2,1,8,7,4,5] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 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

[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

[7,2,1,5,8,4,6,3] => [[[.,.],.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[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

[7,3,1,5,2,8,6,4] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 2

[7,1,6,4,2,8,5,3] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 1

[6,8,1,4,3,7,5,2] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 0

[6,7,1,4,3,8,5,2] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 0

[4,7,1,5,3,8,6,2] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 0

[6,8,1,2,4,7,5,3] => [[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 0

[7,1,6,4,8,3,5,2] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 1

[8,6,4,1,3,7,5,2] => [[[[.,.],.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[8,5,3,6,1,7,4,2] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2

[7,2,1,4,5,8,6,3] => [[[.,.],.],[[.,[.,[[.,.],.]]],.]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 2

[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

[8,6,2,5,4,7,3,1] => [[[[.,.],.],[[[.,.],[.,.]],.]],.] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[8,5,2,1,4,3,6,7] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 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

[6,1,4,3,2,7,8,5] => [[.,.],[[[.,.],.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 1

[8,2,6,5,4,3,1,7] => [[[.,.],[[[[.,.],.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1

[8,2,7,6,4,5,3,1] => [[[.,.],[[[[.,.],.],[.,.]],.]],.] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 2

[8,7,3,5,4,2,6,1] => [[[[[.,.],.],[[.,.],.]],[.,.]],.] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 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] => 0

[4,2,5,6,7,8,3,1] => [[[.,.],[[.,[.,[.,[.,.]]]],.]],.] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 2

[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

[3,8,1,7,4,5,2,6] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[3,6,1,5,7,8,2,4] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 0

[3,8,2,5,4,7,1,6] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[7,8,2,3,5,4,1,6] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 0

[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

[6,3,2,5,1,7,4,8] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[6,1,2,4,8,5,3,7] => [[.,.],[.,[[.,[[.,.],.]],[.,.]]]] => [1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 1

[6,3,1,7,2,5,8,4] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[5,2,7,3,4,6,1,8] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[6,1,7,4,8,5,3,2] => [[.,.],[[[[.,.],[[.,.],.]],.],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 1

[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

[7,4,3,1,6,5,8,2] => [[[[.,.],.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 3

[8,6,1,7,5,3,2,4] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 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] => 0

[5,1,7,6,3,4,2,8] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1

[6,2,7,3,8,5,4,1] => [[[.,.],[[.,.],[[[.,.],.],.]]],.] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 2

[7,2,8,3,6,4,5,1] => [[[.,.],[[.,.],[[.,.],[.,.]]]],.] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 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

[8,2,7,4,5,1,6,3] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[3,8,1,5,7,2,6,4] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[7,5,4,8,6,1,2,3] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[7,1,8,6,4,5,2,3] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1

[8,7,5,1,4,3,6,2] => [[[[.,.],.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 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] => 2

[8,4,1,3,7,5,6,2] => [[[.,.],.],[[.,[[.,.],[.,.]]],.]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 2

[4,8,1,3,7,5,6,2] => [[.,[.,.]],[[.,[[.,.],[.,.]]],.]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 0

[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

[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

[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

[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

[5,1,4,2,6,8,7,3] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 1

[6,3,2,4,7,1,8,5] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[5,1,8,6,2,4,3,7] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[6,8,7,5,3,1,2,4] => [[[[.,[[.,.],.]],.],.],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => 2

[6,8,7,2,1,5,3,4] => [[[.,[[.,.],.]],.],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[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

[8,7,3,2,1,4,6,5] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 4

[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

[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

[4,3,6,2,8,5,7,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[6,4,8,7,2,1,5,3] => [[[[.,.],[[.,.],.]],.],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2

[7,3,2,5,6,1,8,4] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[4,1,2,8,5,3,7,6] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 1

[4,1,5,7,6,8,2,3] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 1

[7,6,8,3,2,5,1,4] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 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] => 0

[6,5,8,7,1,3,2,4] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[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

[8,2,1,4,6,7,3,5] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 2

[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

[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

[6,2,7,5,1,3,8,4] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 1

[8,6,1,3,5,7,2,4] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 2

[6,1,5,3,4,8,2,7] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[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

[5,8,1,3,6,7,2,4] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 0

[6,3,8,4,7,1,2,5] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[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

[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

[8,3,1,4,7,2,5,6] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[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

[6,2,7,3,8,5,1,4] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[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

[8,1,7,4,6,2,3,5] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[4,1,8,5,7,2,3,6] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[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

[6,5,4,1,3,8,2,7] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3

[6,3,5,4,2,8,1,7] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[8,7,4,3,1,5,2,6] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4

[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

[8,5,4,1,3,6,7,2] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 3

[8,3,1,7,5,6,4,2] => [[[.,.],.],[[[[.,.],[.,.]],.],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 2

[8,4,7,6,5,3,1,2] => [[[[.,.],[[[.,.],.],.]],.],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 2

[8,1,4,5,7,6,3,2] => [[.,.],[[[.,[.,[[.,.],.]]],.],.]] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 1

[2,4,1,8,5,7,6,3] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 0

[8,2,1,4,7,6,3,5] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 2

[8,3,1,7,4,2,6,5] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[8,2,7,3,1,6,5,4] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[3,1,2,8,7,4,6,5] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 1

[8,5,1,2,4,3,7,6] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2

[8,4,5,7,6,2,3,1] => [[[[.,.],[.,[[.,.],.]]],[.,.]],.] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 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] => 0

[4,2,8,7,3,1,5,6] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 1

[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

[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

[8,4,2,1,7,5,6,3] => [[[[.,.],.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 3

[8,2,7,5,6,4,1,3] => [[[.,.],[[[.,.],[.,.]],.]],[.,.]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1

[6,2,8,5,4,1,7,3] => [[[.,.],[[[.,.],.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 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] => 2

[2,8,1,5,7,6,3,4] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 0

[3,1,8,2,7,5,6,4] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1

[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

[8,4,7,2,1,6,5,3] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 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

[3,8,1,2,5,6,4,7] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 0

[3,7,1,2,5,6,4,8] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 0

[8,5,2,1,4,6,7,3] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 3

[4,8,1,6,5,2,7,3] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[4,2,6,3,8,5,7,1] => [[[.,.],[[.,.],[[.,.],[.,.]]]],.] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 2

[4,5,2,6,7,1,8,3] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0

[8,3,5,4,2,7,1,6] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[3,1,8,6,5,2,7,4] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 1

[8,3,1,5,2,6,7,4] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 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] => 2

[6,5,3,2,4,8,1,7] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3

[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

[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

[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

[6,8,3,4,7,5,2,1] => [[[[.,[.,.]],[.,[[.,.],.]]],.],.] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 2

[4,8,1,5,7,6,3,2] => [[.,[.,.]],[[[.,[[.,.],.]],.],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 0

[4,7,1,6,8,3,2,5] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 0

[4,5,2,8,1,7,3,6] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[5,4,8,6,1,2,7,3] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 1

[8,4,6,5,2,7,3,1] => [[[[.,.],[[.,.],.]],[[.,.],.]],.] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 2

[8,1,6,4,7,5,2,3] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1

[5,2,7,6,4,8,1,3] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[8,6,2,3,5,1,7,4] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[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

[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

[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

[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

[6,3,8,4,7,1,5,2] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[7,1,4,3,2,8,5,6] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[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

[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

[7,1,8,3,5,2,4,6] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[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

[7,1,8,4,2,5,6,3] => [[.,.],[[[.,.],.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 1

[6,4,2,5,8,1,7,3] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[2,1,7,5,8,3,6,4] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[7,3,8,5,6,2,1,4] => [[[[.,.],[[.,.],[.,.]]],.],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 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] => 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

[8,6,5,3,7,2,1,4] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 4

[7,4,8,6,5,3,2,1] => [[[[[.,.],[[[.,.],.],.]],.],.],.] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 4

[7,4,8,5,6,3,1,2] => [[[[.,.],[[.,.],[.,.]]],.],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 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

[7,8,3,4,1,5,6,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0

[7,3,1,8,2,5,6,4] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 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

[6,4,8,7,3,2,1,5] => [[[[[.,.],[[.,.],.]],.],.],[.,.]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 3

[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

[7,2,1,8,3,5,6,4] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[5,1,6,3,8,2,4,7] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[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

[7,5,4,8,1,6,2,3] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[4,3,5,8,2,1,6,7] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2

[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

[6,8,1,5,4,2,7,3] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[7,8,6,3,1,4,2,5] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 2

[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

[7,2,8,5,4,6,3,1] => [[[.,.],[[[[.,.],.],[.,.]],.]],.] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 2

[6,1,8,4,7,2,3,5] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[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

[6,5,3,7,2,4,8,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3

[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

[7,1,3,6,5,8,4,2] => [[.,.],[[.,[[[.,.],[.,.]],.]],.]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 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

[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

[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

[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

[5,2,6,4,1,7,8,3] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 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] => 2

[5,4,3,8,6,2,7,1] => [[[[[.,.],.],[[.,.],.]],[.,.]],.] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 3

[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

[6,4,7,8,2,3,5,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[6,4,7,3,2,5,8,1] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 3

[5,7,3,2,8,4,6,1] => [[[[.,[.,.]],.],[[.,.],[.,.]]],.] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => 2

[5,3,7,2,8,4,6,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[4,3,7,2,5,8,6,1] => [[[[.,.],[.,.]],[.,[[.,.],.]]],.] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 2

[4,7,3,2,5,8,6,1] => [[[[.,[.,.]],.],[.,[[.,.],.]]],.] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => 2

[4,7,3,2,6,8,5,1] => [[[[.,[.,.]],.],[[.,[.,.]],.]],.] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 2

[7,5,3,2,6,4,8,1] => [[[[[.,.],.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 4

[8,5,2,6,7,3,4,1] => [[[[.,.],.],[[.,[.,.]],[.,.]]],.] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 3

[8,4,2,6,3,7,5,1] => [[[[.,.],.],[[.,.],[[.,.],.]]],.] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3

[7,4,6,2,3,8,5,1] => [[[[.,.],[.,.]],[.,[[.,.],.]]],.] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 2

[7,5,6,2,8,3,4,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[7,6,3,2,5,8,1,4] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3

[7,6,4,2,5,8,3,1] => [[[[[.,.],.],.],[[.,[.,.]],.]],.] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 4

[6,3,8,5,4,7,2,1] => [[[[.,.],[[[.,.],.],[.,.]]],.],.] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 3

[6,1,4,7,5,8,2,3] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 1

[4,6,1,7,8,5,3,2] => [[.,[.,.]],[[[[.,[.,.]],.],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 0

[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

[6,1,3,2,7,8,5,4] => [[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 1

[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

[4,8,3,7,1,6,5,2] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 0

[8,7,2,6,5,1,4,3] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 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] => 2

[5,4,3,8,1,7,6,2] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2

[6,5,3,8,7,1,4,2] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 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] => 2

[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

[7,8,2,6,5,4,1,3] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 0

[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

[8,6,3,1,7,5,4,2] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3

[8,6,3,7,1,5,4,2] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 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

[5,8,2,7,6,4,1,3] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 0

[8,4,2,1,7,6,5,3] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3

[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

[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

[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

[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

[7,2,4,8,6,3,1,5] => [[[.,.],[[.,[[.,.],.]],.]],[.,.]] => [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 1

[7,4,5,2,1,8,6,3] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 2

[4,7,5,2,1,8,6,3] => [[[.,[[.,.],.]],.],[[[.,.],.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1

[8,5,3,6,2,1,7,4] => [[[[[.,.],.],[.,.]],.],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 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] => 0

[5,7,4,6,3,2,1,8] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 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] => 0

[7,5,2,3,1,8,6,4] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2

[6,3,1,2,4,8,7,5] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 2

[7,2,6,5,3,4,1,8] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[8,2,6,5,4,1,3,7] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 1

[6,2,8,4,5,1,3,7] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[2,3,1,7,8,5,6,4] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 0

[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

[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

[8,7,1,6,5,2,3,4] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[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

[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

[7,8,3,6,1,5,4,2] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 0

[6,2,1,7,4,5,3,8] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 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] => 3

[8,5,4,2,1,6,7,3] => [[[[[.,.],.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 4

[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

[7,4,1,6,5,3,8,2] => [[[.,.],.],[[[[.,.],.],[.,.]],.]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 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

[7,5,4,1,8,2,6,3] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3

[6,4,1,8,2,7,5,3] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 2

[7,8,5,3,2,6,1,4] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 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

[6,7,4,3,8,2,5,1] => [[[[[.,[.,.]],.],[.,.]],[.,.]],.] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[3,4,2,7,8,6,1,5] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 0

[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

[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

[4,6,2,5,3,1,7,8] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 0

[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

[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

[6,7,4,3,1,5,2,8] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 2

[7,6,5,3,1,8,4,2] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4

[7,8,6,4,3,1,5,2] => [[[[[.,[.,.]],.],.],.],[[.,.],.]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 3

[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

[6,8,5,3,7,2,1,4] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 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] => 0

[7,4,8,2,6,5,3,1] => [[[[.,.],[.,.]],[[[.,.],.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 2

[7,5,4,8,2,6,3,1] => [[[[[.,.],.],[.,.]],[[.,.],.]],.] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[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

[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

[7,3,4,8,5,2,1,6] => [[[[.,.],[.,[[.,.],.]]],.],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 2

[7,3,8,4,1,5,6,2] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 1

[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

[7,3,1,2,8,5,6,4] => [[[.,.],.],[.,[[[.,.],[.,.]],.]]] => [1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2

[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

[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

[6,7,4,8,5,3,2,1] => [[[[[.,[.,.]],[[.,.],.]],.],.],.] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 3

[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

[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

[4,1,2,8,5,7,6,3] => [[.,.],[.,[[[.,.],[[.,.],.]],.]]] => [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 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

[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

[6,4,1,3,5,8,2,7] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 2

[3,4,1,7,2,6,8,5] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 0

[3,1,6,4,8,7,5,2] => [[.,.],[[[.,.],[[[.,.],.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 1

[3,7,6,2,1,5,8,4] => [[[.,[[.,.],.]],.],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 1

[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

[8,5,4,2,7,6,3,1] => [[[[[.,.],.],.],[[[.,.],.],.]],.] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 4

[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

[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

[5,6,2,8,7,1,3,4] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 0

[7,1,3,8,4,5,6,2] => [[.,.],[[.,[[.,.],[.,[.,.]]]],.]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 1

[7,8,1,4,3,5,6,2] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 0

[3,4,1,8,7,2,6,5] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[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

[3,8,1,4,7,2,6,5] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[4,8,1,3,2,7,6,5] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 0

[4,1,8,3,2,7,6,5] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 1

[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

[3,8,2,4,7,1,6,5] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0

[3,2,4,8,7,1,6,5] => [[[.,.],[.,[[.,.],.]]],[[.,.],.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 1

[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

[4,2,8,3,1,7,6,5] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[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

[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

[5,6,4,7,1,2,8,3] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 0

[3,2,7,6,8,1,4,5] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[4,5,1,7,6,8,2,3] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[6,7,2,8,3,1,4,5] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 0

[7,6,3,1,2,8,4,5] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 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

[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

[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

[7,6,2,3,1,8,4,5] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[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

[3,4,1,7,8,5,2,6] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 0

[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

[4,3,1,8,5,2,7,6] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[7,6,3,5,8,4,2,1] => [[[[[.,.],.],[[.,[.,.]],.]],.],.] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[4,5,1,3,2,7,8,6] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 0

[5,1,3,2,4,7,8,6] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 1

[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

[5,3,6,7,8,2,1,4] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 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

[6,7,2,3,4,8,1,5] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0

[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

[4,2,6,3,5,7,8,1] => [[[.,.],[[.,.],[.,[.,[.,.]]]]],.] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 2

[7,2,8,4,5,1,6,3] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[8,6,2,4,1,5,7,3] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[8,5,3,2,1,6,7,4] => [[[[[.,.],.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 4

[7,1,5,2,3,6,8,4] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 1

[8,1,2,5,3,6,7,4] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 1

[8,4,1,6,3,7,2,5] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[6,7,5,3,8,2,1,4] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 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

[4,2,5,8,6,7,1,3] => [[[.,.],[.,[[.,.],[.,.]]]],[.,.]] => [1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1

[8,1,7,2,4,3,5,6] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[8,7,3,1,4,2,5,6] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[3,2,8,7,4,1,5,6] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 1

[3,2,1,7,4,6,5,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[3,2,6,5,1,7,8,4] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 1

[5,3,2,6,7,1,8,4] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[3,2,8,6,7,4,1,5] => [[[.,.],[[[.,.],[.,.]],.]],[.,.]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1

[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

[4,3,8,6,7,2,1,5] => [[[[.,.],[[.,.],[.,.]]],.],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 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

[7,8,4,2,6,3,5,1] => [[[[.,[.,.]],.],[[.,.],[.,.]]],.] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => 2

[3,2,7,8,6,4,5,1] => [[[.,.],[[[.,[.,.]],.],[.,.]]],.] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[3,2,7,5,6,8,4,1] => [[[.,.],[[[.,.],[.,[.,.]]],.]],.] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 2

[6,5,4,2,1,7,8,3] => [[[[[.,.],.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 4

[5,4,2,1,7,6,3,8] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[4,1,6,5,2,7,8,3] => [[.,.],[[[.,.],.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 1

[5,4,1,6,7,2,8,3] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[6,8,5,3,1,7,2,4] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 2

[5,2,6,3,8,7,1,4] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[8,6,1,7,3,4,2,5] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[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

[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

[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

[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

[8,7,2,6,3,5,1,4] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2

[8,1,7,6,5,2,3,4] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 1

[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

[6,7,1,5,2,4,8,3] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 0

[7,6,1,5,2,4,3,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[7,1,6,3,5,4,2,8] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1

[8,2,7,4,6,5,1,3] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[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

[4,1,7,5,6,8,3,2] => [[.,.],[[[[.,.],[.,[.,.]]],.],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 1

[8,1,3,4,6,5,2,7] => [[.,.],[[.,[.,[[.,.],.]]],[.,.]]] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 1

[8,3,1,4,6,5,2,7] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 2

[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

[4,8,1,7,5,2,3,6] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0

[4,8,1,7,5,2,6,3] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[8,5,1,4,2,6,3,7] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[8,4,1,3,5,6,2,7] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 2

[8,5,3,2,1,6,4,7] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4

[8,1,5,4,2,6,3,7] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[8,5,2,4,1,6,3,7] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[7,6,8,4,1,3,2,5] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2

[7,6,8,4,1,3,5,2] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 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] => 0

[7,6,8,4,1,5,2,3] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2

[8,7,6,1,5,2,3,4] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[7,1,4,8,6,3,5,2] => [[.,.],[[[.,[[.,.],.]],[.,.]],.]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 1

[8,1,6,5,3,4,7,2] => [[.,.],[[[[.,.],.],[.,[.,.]]],.]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 1

[8,6,2,5,3,4,7,1] => [[[[.,.],.],[[.,.],[.,[.,.]]]],.] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 3

[8,6,5,1,3,4,7,2] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 3

[8,7,5,1,3,6,2,4] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3

[8,7,1,5,3,6,2,4] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[8,6,1,3,5,4,7,2] => [[[.,.],.],[[.,[[.,.],[.,.]]],.]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 2

[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

[7,8,5,2,4,3,6,1] => [[[[.,[.,.]],.],[[.,.],[.,.]]],.] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => 2

[7,3,8,2,5,4,6,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[8,4,2,5,3,7,6,1] => [[[[.,.],.],[[.,.],[[.,.],.]]],.] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3

[4,8,1,5,3,7,6,2] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 0

[7,4,8,2,6,3,5,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[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

[8,7,3,1,6,4,2,5] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[8,7,3,1,6,4,5,2] => [[[[.,.],.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 3

[8,7,3,1,4,6,5,2] => [[[[.,.],.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[8,4,3,2,7,5,6,1] => [[[[[.,.],.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 4

[6,4,1,7,8,5,3,2] => [[[.,.],.],[[[[.,[.,.]],.],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 2

[7,6,3,4,1,8,5,2] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2

[8,7,3,1,6,2,5,4] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3

[7,8,6,4,2,5,1,3] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 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] => 0

[8,1,7,3,5,6,2,4] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[8,7,5,2,4,6,1,3] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3

[8,1,7,5,4,6,2,3] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1

[8,7,3,2,6,1,5,4] => [[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3

[5,3,1,7,6,4,2,8] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 2

[7,5,3,2,1,6,4,8] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4

[7,6,5,3,1,4,2,8] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4

[8,4,6,7,5,3,2,1] => [[[[[.,.],[[.,[.,.]],.]],.],.],.] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 4

[7,6,2,5,8,4,3,1] => [[[[.,.],.],[[[.,[.,.]],.],.]],.] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 3

[8,6,2,5,7,4,3,1] => [[[[.,.],.],[[[.,[.,.]],.],.]],.] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 3

[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

[8,1,7,6,4,5,3,2] => [[.,.],[[[[[.,.],.],[.,.]],.],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 1

[7,1,8,6,4,5,3,2] => [[.,.],[[[[[.,.],.],[.,.]],.],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 1

[6,5,7,2,8,3,4,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[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

[6,2,7,5,8,1,4,3] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[6,7,2,5,8,1,4,3] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0

[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

[6,3,7,4,8,2,5,1] => [[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[6,3,7,4,8,1,5,2] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[6,2,7,4,8,1,5,3] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[8,7,6,4,2,5,3,1] => [[[[[[.,.],.],.],.],[[.,.],.]],.] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 5

[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

[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

[7,2,1,5,3,8,6,4] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 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] => 0

[5,1,8,7,3,4,2,6] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1

[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

[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

[6,5,1,2,4,3,8,7] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2

[4,6,5,3,1,2,8,7] => [[[.,[[.,.],.]],.],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => 1

[6,8,7,5,3,1,4,2] => [[[[.,[[.,.],.]],.],.],[[.,.],.]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2

[8,7,5,6,3,1,4,2] => [[[[[.,.],.],[.,.]],.],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 3

[8,7,3,4,6,5,1,2] => [[[[.,.],.],[.,[[.,.],.]]],[.,.]] => [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 2

[2,1,4,8,7,3,6,5] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 1

[4,8,7,3,1,2,6,5] => [[[.,[[.,.],.]],.],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => 1

[8,7,3,4,1,2,6,5] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[8,7,3,1,6,5,2,4] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[8,7,3,2,6,5,1,4] => [[[[[.,.],.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3

[8,7,1,2,6,5,3,4] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 2

[8,7,1,2,4,3,6,5] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2

[2,1,8,7,3,4,6,5] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1

[8,7,5,1,2,4,3,6] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3

[4,3,1,2,6,8,7,5] => [[[.,.],.],[.,[[.,[[.,.],.]],.]]] => [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 2

[6,8,7,5,1,2,4,3] => [[[.,[[.,.],.]],.],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => 1

[8,7,5,6,1,2,4,3] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[8,7,1,2,4,6,5,3] => [[[.,.],.],[.,[[.,[[.,.],.]],.]]] => [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 2

[8,7,2,4,3,6,5,1] => [[[[.,.],.],[[.,.],[[.,.],.]]],.] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3

[8,7,5,3,1,2,6,4] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 4

[8,7,5,3,6,4,1,2] => [[[[[.,.],.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3

[8,7,1,4,3,6,5,2] => [[[.,.],.],[[[.,.],[[.,.],.]],.]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 2

[8,7,3,4,1,6,5,2] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2

[7,1,2,3,5,4,6,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1

[7,1,2,6,4,5,3,8] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 1

[7,1,2,4,3,5,6,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1

[4,7,3,6,5,1,2,8] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 0

[7,5,4,2,8,3,1,6] => [[[[[.,.],.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 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

[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

[7,2,8,6,4,3,1,5] => [[[.,.],[[[[.,.],.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1

[6,3,8,7,4,2,1,5] => [[[[.,.],[[[.,.],.],.]],.],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 2

[7,6,3,2,8,4,1,5] => [[[[[.,.],.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3

[8,6,1,3,2,4,5,7] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 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

[4,1,7,3,5,8,6,2] => [[.,.],[[[.,.],[.,[[.,.],.]]],.]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 1

[8,4,7,3,5,2,1,6] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 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

[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

[8,1,4,2,7,6,3,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1

[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

[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

[3,1,4,7,6,8,2,5] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 1

[4,1,3,7,6,8,2,5] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 1

[5,1,7,3,6,8,2,4] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[3,8,2,6,5,7,1,4] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[8,7,2,5,6,3,1,4] => [[[[.,.],.],[[.,[.,.]],.]],[.,.]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 2

[8,7,1,6,4,3,2,5] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 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] => 0

[6,7,1,2,8,4,3,5] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 0

[2,1,3,8,6,5,4,7] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 1

[8,2,1,7,5,4,3,6] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 2

[3,4,1,7,6,8,2,5] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[5,4,7,6,8,3,1,2] => [[[[.,.],[[.,.],[.,.]]],.],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 2

[8,4,6,7,5,2,1,3] => [[[[.,.],[[.,[.,.]],.]],.],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 2

[8,3,7,5,6,2,1,4] => [[[[.,.],[[.,.],[.,.]]],.],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 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

[8,2,7,6,4,3,1,5] => [[[.,.],[[[[.,.],.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1

[8,1,7,6,4,3,2,5] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 1

[4,1,8,6,7,3,2,5] => [[.,.],[[[[.,.],[.,.]],.],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 1

[8,1,7,2,5,6,4,3] => [[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 1

[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

[2,7,1,5,4,8,6,3] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 0

[8,6,2,4,3,7,5,1] => [[[[.,.],.],[[.,.],[[.,.],.]]],.] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3

[2,4,1,6,7,5,8,3] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 0

[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

[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

[8,1,4,7,6,2,5,3] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 1

[2,5,1,7,8,6,4,3] => [[.,[.,.]],[[[[.,[.,.]],.],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 0

[7,3,1,5,6,4,2,8] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 2

[8,3,2,5,6,7,1,4] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2

[8,4,5,3,7,6,2,1] => [[[[[.,.],[.,.]],[[.,.],.]],.],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 3

[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

[7,2,1,6,3,4,8,5] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2

[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

[2,7,1,3,6,8,5,4] => [[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 0

[2,7,1,3,8,4,6,5] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 0

[3,7,4,2,1,8,6,5] => [[[.,[[.,.],.]],.],[[[.,.],.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1

[8,4,5,7,3,2,6,1] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 3

[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

[8,6,7,2,1,4,3,5] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2

[8,3,7,5,1,2,6,4] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 1

[7,3,4,6,2,1,5,8] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2

[8,7,3,5,6,1,4,2] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[8,5,2,7,6,1,3,4] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[6,4,7,2,1,5,8,3] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[8,4,2,5,1,6,7,3] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[8,5,3,1,6,4,7,2] => [[[[.,.],.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 3

[8,7,3,1,4,5,6,2] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 3

[8,5,3,7,1,6,4,2] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2

[7,6,3,8,1,4,2,5] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 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

[8,5,3,1,6,4,2,7] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[8,7,5,1,2,6,3,4] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3

[8,6,4,1,2,7,5,3] => [[[[.,.],.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 3

[8,7,4,1,2,5,3,6] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3

[6,5,3,7,4,2,1,8] => [[[[[.,.],.],[[.,.],.]],.],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 3

[4,7,2,5,3,6,1,8] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[8,2,6,4,1,5,7,3] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 1

[7,8,3,4,6,1,5,2] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0

[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

[4,1,8,5,3,2,6,7] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 1

[8,1,6,4,2,7,3,5] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[3,1,7,4,2,5,8,6] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1

[6,1,8,5,2,4,3,7] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[6,8,2,5,1,4,7,3] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0

[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

[7,2,8,6,5,1,4,3] => [[[.,.],[[[.,.],.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 1

[7,4,8,6,1,5,3,2] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[8,7,2,6,1,4,5,3] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[7,6,3,1,2,5,4,8] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3

[8,5,3,1,2,4,7,6] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3

[8,2,1,6,5,3,4,7] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[3,8,1,5,6,2,4,7] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[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

[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

[5,2,1,3,7,6,4,8] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 2

[5,4,1,2,8,3,7,6] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2

[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

[7,1,2,5,3,4,6,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1

[2,6,1,7,8,5,3,4] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 0

[3,2,1,6,8,4,7,5] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[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

[6,5,8,4,2,1,7,3] => [[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 3

[2,1,5,8,6,4,7,3] => [[.,.],[[[.,[[.,.],.]],[.,.]],.]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 1

[4,2,8,5,6,3,7,1] => [[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2

[5,3,7,2,6,8,4,1] => [[[[.,.],[.,.]],[[.,[.,.]],.]],.] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 2

[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

[5,7,1,2,3,8,6,4] => [[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 0

[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

[7,2,8,4,6,1,5,3] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[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

[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

[7,6,4,8,2,1,5,3] => [[[[[.,.],.],[.,.]],.],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 3

[6,1,8,4,2,3,5,7] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1

[7,3,6,2,1,8,5,4] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 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

[5,1,6,4,3,8,7,2] => [[.,.],[[[[.,.],.],[[.,.],.]],.]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 1

[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

[3,7,1,6,4,5,8,2] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 0

[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

[6,7,3,4,8,5,1,2] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 0

[7,4,1,8,2,5,6,3] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[3,1,7,2,5,6,8,4] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 1

[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

[6,4,1,7,2,8,5,3] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 2

[7,3,1,6,2,8,5,4] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 2

[4,8,2,5,3,1,6,7] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 0

[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

[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

[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

[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

[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

[8,5,2,7,6,3,1,4] => [[[[.,.],.],[[[.,.],.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 2

[8,3,2,5,6,1,7,4] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 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

[5,4,2,7,8,6,1,3] => [[[[.,.],.],[[.,[.,.]],.]],[.,.]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 2

[6,8,7,2,1,3,4,5] => [[[.,[[.,.],.]],.],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1

[7,6,1,2,5,3,8,4] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2

[7,6,2,4,8,1,5,3] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[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

[7,6,1,2,4,3,8,5] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2

[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

[4,3,2,8,7,1,6,5] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[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

[5,3,8,7,1,6,4,2] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[5,8,7,3,1,6,4,2] => [[[.,[[.,.],.]],.],[[[.,.],.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1

[5,3,8,2,1,7,6,4] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 2

[7,4,1,8,6,5,3,2] => [[[.,.],.],[[[[[.,.],.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2

[5,4,2,8,1,7,6,3] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 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] => 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] => 0

[5,4,8,3,1,7,6,2] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 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

[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

[5,2,1,6,8,4,7,3] => [[[.,.],.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[6,5,8,7,4,2,3,1] => [[[[[.,.],[[.,.],.]],.],[.,.]],.] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 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] => 2

[4,7,5,3,1,6,2,8] => [[[.,[[.,.],.]],.],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[8,7,5,3,1,4,6,2] => [[[[[.,.],.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 4

[5,1,6,3,2,4,8,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1

[3,8,7,2,1,5,4,6] => [[[.,[[.,.],.]],.],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[6,1,7,2,8,4,3,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1

[6,1,7,3,8,5,2,4] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1

[7,1,8,3,2,5,4,6] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[5,8,7,3,2,4,1,6] => [[[[.,[[.,.],.]],.],[.,.]],[.,.]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[8,3,1,7,2,6,4,5] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 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] => 0

[5,6,1,2,8,3,7,4] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 0

[6,3,1,4,8,2,7,5] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[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

[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

[6,7,1,4,2,8,5,3] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 0

[2,1,6,4,8,3,7,5] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[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

[6,8,4,7,3,2,1,5] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 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] => 2

[6,4,8,5,3,2,1,7] => [[[[[.,.],[[.,.],.]],.],.],[.,.]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 3

[7,1,3,2,4,6,8,5] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 1

[4,1,8,2,6,7,5,3] => [[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 1

[4,2,8,3,6,5,1,7] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[6,3,8,7,2,4,5,1] => [[[[.,.],[[.,.],.]],[.,[.,.]]],.] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 2

[7,6,1,8,2,4,5,3] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 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

[7,2,1,3,4,8,5,6] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 2

[8,1,6,2,3,4,7,5] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 1

[6,1,4,2,5,7,8,3] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 1

[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

[4,1,5,3,6,8,7,2] => [[.,.],[[[.,.],[.,[[.,.],.]]],.]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 1

[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

[7,2,1,8,6,4,5,3] => [[[.,.],.],[[[[.,.],.],[.,.]],.]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 2

[4,3,6,5,1,8,2,7] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[4,1,7,6,8,3,2,5] => [[.,.],[[[[.,.],[.,.]],.],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 1

[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

[7,2,3,8,4,5,6,1] => [[[.,.],[.,[[.,.],[.,[.,.]]]]],.] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 2

[6,5,1,8,7,2,4,3] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[5,8,4,3,7,2,1,6] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2

[6,1,2,8,7,3,4,5] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 1

[4,5,1,7,6,2,8,3] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[6,5,1,8,7,4,3,2] => [[[.,.],.],[[[[[.,.],.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2

[7,5,1,8,6,4,3,2] => [[[.,.],.],[[[[[.,.],.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2

[8,5,1,7,6,4,3,2] => [[[.,.],.],[[[[[.,.],.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2

[8,5,3,7,6,1,4,2] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[8,3,7,5,4,1,6,2] => [[[.,.],[[[.,.],.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 1

[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

[8,6,5,7,1,3,2,4] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[3,1,8,5,7,2,6,4] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[6,8,5,3,4,2,1,7] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2

[8,5,2,6,4,3,1,7] => [[[[.,.],.],[[[.,.],.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 2

[8,5,2,6,1,4,7,3] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 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

[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

[6,2,7,4,8,5,1,3] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[6,7,1,3,8,5,4,2] => [[.,[.,.]],[[.,[[[.,.],.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 0

[6,7,1,8,5,2,4,3] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[8,7,2,1,5,4,6,3] => [[[[.,.],.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 3

[7,6,5,2,4,1,8,3] => [[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3

[7,6,4,3,1,5,8,2] => [[[[[.,.],.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 4

[6,1,8,7,2,3,5,4] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1

[8,6,1,2,7,3,4,5] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 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] => 0

[4,3,6,8,7,2,5,1] => [[[[.,.],[.,[[.,.],.]]],[.,.]],.] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 2

[4,1,8,3,5,2,7,6] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[4,2,8,3,5,1,7,6] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[3,8,1,5,2,4,7,6] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0

[7,5,6,4,1,3,2,8] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2

[7,8,6,4,1,3,2,5] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 2

[7,1,4,2,5,6,3,8] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[7,3,2,1,4,6,5,8] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3

[7,6,1,4,3,2,5,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[7,4,1,3,5,6,2,8] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 2

[2,7,1,3,5,6,8,4] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 0

[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

[4,3,2,7,1,6,8,5] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[7,3,2,8,1,6,4,5] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[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

[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

[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

[5,3,2,6,4,8,7,1] => [[[[.,.],.],[[.,.],[[.,.],.]]],.] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3

[4,3,5,2,8,6,7,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[4,8,5,3,2,6,7,1] => [[[[.,[[.,.],.]],.],[.,[.,.]]],.] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2

[4,1,2,7,5,6,8,3] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 1

[7,5,2,4,3,8,6,1] => [[[[.,.],.],[[.,.],[[.,.],.]]],.] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3

[6,8,1,2,5,4,7,3] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 0

[6,4,1,8,5,2,7,3] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[2,6,1,8,5,4,7,3] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 0

[7,1,2,8,5,6,4,3] => [[.,.],[.,[[[[.,.],[.,.]],.],.]]] => [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 1

[4,3,2,6,8,5,7,1] => [[[[.,.],.],[[.,[.,.]],[.,.]]],.] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 3

[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

[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

[5,4,2,8,3,6,7,1] => [[[[.,.],.],[[.,.],[.,[.,.]]]],.] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 3

[5,3,4,8,2,6,7,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[6,3,2,5,8,4,7,1] => [[[[.,.],.],[[.,[.,.]],[.,.]]],.] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 3

[6,1,8,3,5,4,7,2] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 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] => 3

[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

[6,2,1,7,8,5,4,3] => [[[.,.],.],[[[[.,[.,.]],.],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 2

[7,4,6,8,3,2,5,1] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 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

[8,4,6,7,3,2,5,1] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 3

[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

[7,5,2,1,4,3,8,6] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 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

[7,6,4,8,3,1,2,5] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3

[7,4,8,5,6,1,2,3] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[6,2,8,5,1,3,4,7] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1

[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

[6,8,2,5,1,3,7,4] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 0

[6,7,4,2,1,5,3,8] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 2

[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

[4,2,7,5,1,8,3,6] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[4,1,6,5,3,8,2,7] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1

[4,7,1,8,6,3,5,2] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 0

[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

[4,3,8,6,2,1,7,5] => [[[[.,.],[[.,.],.]],.],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 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

[7,8,3,2,4,6,5,1] => [[[[.,[.,.]],.],[.,[[.,.],.]]],.] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => 2

[7,2,8,5,3,1,6,4] => [[[.,.],[[[.,.],.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 1

[6,4,2,8,7,3,1,5] => [[[[.,.],.],[[[.,.],.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 2

[7,8,6,3,1,4,5,2] => [[[[.,[.,.]],.],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[6,8,7,5,2,1,3,4] => [[[[.,[[.,.],.]],.],.],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => 2

[7,6,2,8,5,1,3,4] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[8,6,4,1,2,5,7,3] => [[[[.,.],.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 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

[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

[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

[8,5,2,4,3,6,1,7] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2

[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

[7,4,8,2,1,5,6,3] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 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

[8,2,1,7,6,5,3,4] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 2

[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

[6,5,1,2,8,3,4,7] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2

[5,8,1,6,7,4,2,3] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 0

[7,2,8,4,6,1,3,5] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[6,2,7,4,3,8,1,5] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[7,1,8,4,6,2,3,5] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[8,1,6,5,4,7,2,3] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1

[4,1,6,8,7,3,2,5] => [[.,.],[[[.,[[.,.],.]],.],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 1

[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

[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

[4,7,2,8,5,3,1,6] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 0

[8,7,1,4,6,3,2,5] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 2

[6,1,8,3,4,7,2,5] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[4,7,1,6,8,3,5,2] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 0

[7,1,8,4,2,5,3,6] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[5,7,3,6,8,4,2,1] => [[[[.,[.,.]],[[.,[.,.]],.]],.],.] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 2

[5,8,7,4,2,1,3,6] => [[[[.,[[.,.],.]],.],.],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => 2

[8,6,3,5,7,4,1,2] => [[[[.,.],.],[[.,[.,.]],.]],[.,.]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 2

[8,5,3,2,1,4,7,6] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 4

[4,1,8,6,2,3,7,5] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1

[7,5,8,6,2,3,4,1] => [[[[.,.],[[.,.],.]],[.,[.,.]]],.] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 2

[6,8,5,2,1,7,4,3] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 2

[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

[7,6,2,5,3,4,1,8] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2

[7,6,2,4,5,3,1,8] => [[[[.,.],.],[[.,[.,.]],.]],[.,.]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 2

[7,6,2,4,3,5,1,8] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2

[7,6,2,3,5,4,1,8] => [[[[.,.],.],[.,[[.,.],.]]],[.,.]] => [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 2

[8,4,2,7,1,6,3,5] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 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

[8,7,6,1,5,3,2,4] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[8,7,6,1,4,3,5,2] => [[[[.,.],.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 3

[8,7,6,1,3,5,4,2] => [[[[.,.],.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[8,7,6,1,5,4,2,3] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[8,6,2,7,1,5,3,4] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 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

[8,3,5,4,2,1,6,7] => [[[[.,.],[[.,.],.]],.],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 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] => 2

[8,7,6,1,2,5,3,4] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3

[8,7,6,1,2,5,4,3] => [[[[.,.],.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 3

[8,7,6,1,4,2,5,3] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 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

[8,7,5,4,1,2,6,3] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 4

[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

[5,7,1,3,4,2,8,6] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[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

[5,3,7,6,8,1,2,4] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[3,1,2,7,5,8,4,6] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 1

[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

[3,7,1,2,8,5,6,4] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 0

[5,3,1,7,4,6,8,2] => [[[.,.],.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[5,7,6,4,2,3,1,8] => [[[[.,[[.,.],.]],.],[.,.]],[.,.]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[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

[5,8,2,4,6,1,3,7] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[6,1,4,8,5,2,7,3] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 1

[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

[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

[4,1,8,2,3,6,7,5] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 1

[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

[8,6,2,7,5,1,4,3] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[2,7,1,8,6,3,5,4] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[8,1,7,5,3,6,4,2] => [[.,.],[[[[.,.],.],[[.,.],.]],.]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 1

[8,6,5,3,7,4,2,1] => [[[[[[.,.],.],.],[[.,.],.]],.],.] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 5

[8,1,5,4,6,3,7,2] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 1

[2,7,1,5,6,4,3,8] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 0

[8,4,6,3,1,7,2,5] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2

[8,4,2,5,6,3,7,1] => [[[[.,.],.],[[.,[.,.]],[.,.]]],.] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 3

[8,6,2,7,5,4,3,1] => [[[[.,.],.],[[[[.,.],.],.],.]],.] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 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

[2,7,1,8,6,5,4,3] => [[.,[.,.]],[[[[[.,.],.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 0

[6,2,8,3,1,4,5,7] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1

[5,8,2,7,3,4,1,6] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[4,8,7,3,2,5,1,6] => [[[[.,[[.,.],.]],.],[.,.]],[.,.]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[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

[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

[5,1,8,3,6,7,4,2] => [[.,.],[[[.,.],[[.,[.,.]],.]],.]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 1

[3,1,8,4,6,2,7,5] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[6,1,8,7,5,3,4,2] => [[.,.],[[[[[.,.],.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 1

[3,2,4,7,5,8,1,6] => [[[.,.],[.,[[.,.],[.,.]]]],[.,.]] => [1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1

[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

[5,3,2,6,4,7,8,1] => [[[[.,.],.],[[.,.],[.,[.,.]]]],.] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 3

[5,3,2,6,7,4,8,1] => [[[[.,.],.],[[.,[.,.]],[.,.]]],.] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 3

[5,3,2,7,6,4,8,1] => [[[[.,.],.],[[[.,.],.],[.,.]]],.] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 3

[7,3,5,2,8,4,6,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[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

[3,2,5,7,4,6,8,1] => [[[.,.],[[.,[.,.]],[.,[.,.]]]],.] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2

[3,2,7,5,4,8,6,1] => [[[.,.],[[[.,.],.],[[.,.],.]]],.] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 2

[5,2,8,4,1,3,6,7] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1

[3,8,5,2,1,4,6,7] => [[[.,[[.,.],.]],.],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1

[7,6,4,1,8,2,5,3] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3

[7,5,4,2,1,6,3,8] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4

[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

[8,2,1,6,7,4,3,5] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 2

[5,2,8,6,3,7,1,4] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[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

[2,1,3,4,8,5,7,6] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 1

[5,7,1,2,6,8,3,4] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 0

[8,6,4,7,5,1,2,3] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[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

[3,1,2,8,5,7,4,6] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 1

[7,3,1,2,5,8,4,6] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 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] => 2

[2,1,3,8,5,7,4,6] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 1

[7,3,1,2,8,4,5,6] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2

[2,1,4,7,6,3,5,8] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 1

[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

[8,4,2,5,6,7,3,1] => [[[[.,.],.],[[.,[.,[.,.]]],.]],.] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3

[5,4,1,6,3,7,8,2] => [[[.,.],.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 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] => 0

[5,1,7,6,3,4,8,2] => [[.,.],[[[[.,.],.],[.,[.,.]]],.]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 1

[6,1,7,5,4,8,2,3] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1

[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

[5,8,1,6,4,7,3,2] => [[.,[.,.]],[[[[.,.],[.,.]],.],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 0

[6,8,1,4,7,3,5,2] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 0

[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

[5,7,1,6,8,3,2,4] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 0

[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

[6,4,1,7,3,8,2,5] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[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

[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

[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

[6,1,4,3,2,8,5,7] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[6,2,8,4,7,5,1,3] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[4,2,8,5,1,6,3,7] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[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

[5,1,8,7,4,6,3,2] => [[.,.],[[[[[.,.],.],[.,.]],.],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 1

[6,1,4,3,8,7,5,2] => [[.,.],[[[.,.],[[[.,.],.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 1

[6,3,1,8,7,4,2,5] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 2

[5,3,6,2,8,7,4,1] => [[[[.,.],[.,.]],[[[.,.],.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 2

[6,3,5,2,1,8,7,4] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 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] => 0

[6,2,3,8,7,5,4,1] => [[[.,.],[.,[[[[.,.],.],.],.]]],.] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 2

[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

[5,3,6,2,8,4,7,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[8,1,6,3,7,4,5,2] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 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] => 0

[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

[5,8,3,4,6,1,7,2] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0

[6,1,7,4,2,5,8,3] => [[.,.],[[[.,.],.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 1

[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

[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

[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

[7,1,5,2,6,3,4,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[3,7,1,5,2,6,8,4] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 0

[6,7,1,8,3,4,5,2] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 0

[3,7,1,6,8,4,5,2] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 0

[6,8,3,4,7,1,5,2] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0

[3,7,1,6,5,2,8,4] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[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

[7,1,8,4,6,3,5,2] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 1

[3,7,1,4,8,6,5,2] => [[.,[.,.]],[[.,[[[.,.],.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 0

[3,7,1,4,5,2,8,6] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[4,2,5,3,7,6,1,8] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[6,2,4,3,7,5,1,8] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[8,2,5,3,6,4,1,7] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[7,2,5,3,6,4,1,8] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[6,2,5,3,7,4,1,8] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[4,2,6,3,7,5,1,8] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[5,2,7,3,6,4,1,8] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[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

[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

[7,3,1,4,6,5,2,8] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 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

[5,2,8,3,6,4,1,7] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[3,2,8,4,6,5,1,7] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[8,2,5,4,1,6,3,7] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[8,2,6,4,1,5,3,7] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[6,2,1,4,8,5,3,7] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 2

[5,2,1,4,8,6,3,7] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 2

[3,2,1,5,8,6,4,7] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 2

[4,2,8,3,7,5,1,6] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[5,2,8,3,7,4,1,6] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[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

[7,3,1,4,8,5,2,6] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 2

[8,2,6,3,7,4,1,5] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[7,2,6,3,8,4,1,5] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[5,2,7,3,8,4,1,6] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[3,2,7,4,8,5,1,6] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[5,2,6,3,8,4,1,7] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[6,2,5,3,8,4,1,7] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[7,2,5,3,8,4,1,6] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[8,2,5,3,7,4,1,6] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[8,2,4,3,7,5,1,6] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[7,2,4,3,8,5,1,6] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[6,2,4,3,8,5,1,7] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[5,2,4,3,8,6,1,7] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[4,2,5,3,8,6,1,7] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[4,2,5,3,1,7,6,8] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[6,2,4,3,1,7,5,8] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[7,2,4,3,1,6,5,8] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[8,5,1,3,6,4,2,7] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 2

[8,4,1,3,6,5,2,7] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 2

[7,2,5,3,1,6,4,8] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[6,2,5,3,1,7,4,8] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[4,2,6,3,1,7,5,8] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[3,2,6,4,1,7,5,8] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[3,2,7,4,1,6,5,8] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[4,2,7,3,1,6,5,8] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[5,2,7,3,1,6,4,8] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[6,2,7,3,1,5,4,8] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[7,2,6,3,1,5,4,8] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[8,4,1,3,7,5,2,6] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 2

[6,2,1,5,3,7,4,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[3,2,1,6,4,7,5,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[3,2,8,5,1,6,4,7] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[6,2,8,4,1,5,3,7] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[8,3,7,4,1,5,2,6] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[7,1,3,2,5,6,4,8] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[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

[5,7,2,8,1,4,3,6] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[5,8,2,7,1,4,3,6] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[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

[7,1,5,3,2,6,8,4] => [[.,.],[[[.,.],.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 1

[8,6,2,3,1,5,7,4] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[3,2,1,7,8,5,4,6] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 2

[7,3,4,2,1,5,8,6] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2

[2,1,6,4,7,8,5,3] => [[.,.],[[[.,.],[[.,[.,.]],.]],.]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 1

[7,1,4,3,8,5,6,2] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 1

[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

[7,4,1,8,5,6,2,3] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[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

[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

[6,2,1,4,7,5,8,3] => [[[.,.],.],[[.,[[.,.],[.,.]]],.]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 2

[8,4,2,3,7,1,6,5] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[5,2,4,8,7,3,1,6] => [[[.,.],[[.,[[.,.],.]],.]],[.,.]] => [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 1

[8,3,2,6,7,4,1,5] => [[[[.,.],.],[[.,[.,.]],.]],[.,.]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 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

[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

[4,8,1,6,3,7,5,2] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 0

[7,1,5,2,6,4,3,8] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1

[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

[8,3,2,4,6,7,1,5] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2

[4,2,7,6,1,8,5,3] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[7,2,4,8,6,3,5,1] => [[[.,.],[[.,[[.,.],.]],[.,.]]],.] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2

[7,3,2,1,8,5,4,6] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[7,3,2,1,6,4,8,5] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 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

[4,3,8,2,1,5,7,6] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2

[4,3,2,8,1,6,7,5] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 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] => 2

[5,4,7,8,2,3,6,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[4,3,8,2,1,6,7,5] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[5,3,7,6,2,4,8,1] => [[[[.,.],[[.,.],.]],[.,[.,.]]],.] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 2

[6,4,7,8,3,1,5,2] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 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] => 0

[7,1,8,6,2,5,4,3] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 1

[8,5,1,7,6,4,2,3] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 2

[8,1,2,6,4,5,7,3] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 1

[4,8,1,7,2,5,6,3] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 0

[3,2,7,6,5,8,1,4] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[7,1,8,4,5,6,3,2] => [[.,.],[[[[.,.],[.,[.,.]]],.],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 1

[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

[6,1,8,4,5,3,7,2] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 1

[4,6,2,5,1,8,7,3] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 0

[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

[7,3,5,2,1,6,8,4] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[8,5,1,2,6,3,7,4] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 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

[3,7,2,6,8,1,5,4] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0

[7,4,8,6,5,1,3,2] => [[[.,.],[[[.,.],.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 1

[7,3,1,6,8,2,5,4] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 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

[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

[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

[5,8,1,7,6,4,3,2] => [[.,[.,.]],[[[[[.,.],.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 0

[8,6,3,2,1,5,4,7] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4

[8,5,3,2,4,1,7,6] => [[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3

[7,5,2,4,3,6,8,1] => [[[[.,.],.],[[.,.],[.,[.,.]]]],.] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 3

[8,5,1,4,6,3,2,7] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 2

[8,5,1,6,3,4,2,7] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[8,4,3,6,1,5,2,7] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[8,4,3,5,2,1,7,6] => [[[[[.,.],.],[.,.]],.],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 3

[6,4,3,2,8,7,1,5] => [[[[[.,.],.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3

[8,5,1,4,3,7,2,6] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[8,5,4,2,1,3,7,6] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 4

[4,7,3,6,1,8,5,2] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 0

[7,6,2,4,1,5,8,3] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[8,1,6,3,7,4,2,5] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1

[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

[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

[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

[7,2,6,4,3,5,8,1] => [[[.,.],[[[.,.],.],[.,[.,.]]]],.] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 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] => 2

[8,3,7,2,1,4,6,5] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2

[7,6,4,1,3,2,8,5] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 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] => 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] => 2

[6,2,5,4,8,7,1,3] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[7,2,4,8,5,1,6,3] => [[[.,.],[.,[[.,.],.]]],[[.,.],.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 1

[4,2,7,6,8,5,1,3] => [[[.,.],[[[.,.],[.,.]],.]],[.,.]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1

[7,1,6,2,8,5,4,3] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 1

[7,1,6,3,8,5,2,4] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 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

[7,2,8,5,1,3,6,4] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 1

[7,1,8,5,3,2,6,4] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 1

[7,1,8,2,5,6,4,3] => [[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 1

[6,1,5,8,7,2,4,3] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 1

[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

[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

[4,2,6,3,1,8,7,5] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[6,1,4,2,5,8,7,3] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 1

[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

[7,6,4,2,8,5,1,3] => [[[[[.,.],.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3

[8,7,4,2,1,5,6,3] => [[[[[.,.],.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 4

[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

[8,7,4,1,3,2,6,5] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3

[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

[4,1,8,5,7,6,2,3] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1

[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

[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

[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

[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

[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

[7,8,4,5,1,3,6,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0

[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

[4,8,1,5,6,3,7,2] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 0

[3,8,1,7,2,6,5,4] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 0

[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

[8,1,4,2,3,5,7,6] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 1

[8,1,2,4,6,5,7,3] => [[.,.],[.,[[.,[[.,.],[.,.]]],.]]] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 1

[5,1,8,3,7,4,6,2] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 1

[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

[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

[7,2,5,3,4,6,1,8] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[7,6,4,2,5,3,1,8] => [[[[[.,.],.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3

[5,8,4,3,6,2,7,1] => [[[[[.,[.,.]],.],[.,.]],[.,.]],.] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[7,5,1,6,3,2,4,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[7,1,2,6,3,4,5,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1

[7,3,1,4,6,2,5,8] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[7,1,6,5,4,2,3,8] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 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] => 2

[6,7,1,3,2,8,5,4] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 0

[5,4,3,1,7,2,8,6] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 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

[5,4,3,7,8,2,6,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3

[7,6,8,4,3,1,5,2] => [[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 3

[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

[8,7,4,6,5,1,3,2] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 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

[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

[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

[5,4,7,3,8,2,1,6] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 2

[8,7,2,4,6,3,5,1] => [[[[.,.],.],[[.,[.,.]],[.,.]]],.] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 3

[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

[5,4,8,3,6,2,1,7] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 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] => 0

[5,8,4,2,7,3,6,1] => [[[[.,[.,.]],.],[[.,.],[.,.]]],.] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => 2

[8,2,7,3,4,5,1,6] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[8,1,5,2,4,6,3,7] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[8,6,1,3,4,5,7,2] => [[[.,.],.],[[.,[.,[.,[.,.]]]],.]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[8,5,1,2,4,6,7,3] => [[[.,.],.],[.,[[.,[.,[.,.]]],.]]] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[8,3,1,2,4,6,7,5] => [[[.,.],.],[.,[.,[[.,[.,.]],.]]]] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[3,1,7,5,8,2,4,6] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[8,1,3,2,4,6,5,7] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 1

[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

[8,1,6,5,4,3,2,7] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 1

[4,2,8,5,3,7,6,1] => [[[.,.],[[[.,.],.],[[.,.],.]]],.] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 2

[4,2,7,5,3,8,6,1] => [[[.,.],[[[.,.],.],[[.,.],.]]],.] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 2

[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

[5,4,7,8,3,1,2,6] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2

[7,6,2,8,1,4,3,5] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[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

[6,3,2,8,7,4,5,1] => [[[[.,.],.],[[[.,.],.],[.,.]]],.] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 3

[7,4,3,8,5,6,2,1] => [[[[[.,.],.],[[.,.],[.,.]]],.],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 4

[3,1,5,8,7,6,2,4] => [[.,.],[[.,[[[.,.],.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 1

[8,2,1,6,5,7,3,4] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[3,1,8,6,5,7,2,4] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1

[7,2,6,5,1,8,3,4] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[4,2,8,5,6,3,1,7] => [[[.,.],[[[.,.],[.,.]],.]],[.,.]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1

[6,4,2,1,8,7,3,5] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[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

[4,2,5,3,8,7,1,6] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[7,2,5,3,8,4,6,1] => [[[.,.],[[.,.],[[.,.],[.,.]]]],.] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 2

[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

[3,5,1,4,6,8,2,7] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 0

[8,5,7,4,2,1,3,6] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 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] => 0

[7,8,1,4,2,3,5,6] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0

[6,5,2,4,8,7,1,3] => [[[[.,.],.],[.,[[.,.],.]]],[.,.]] => [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 2

[8,5,2,4,1,3,7,6] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[5,1,2,4,3,6,8,7] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 1

[8,6,2,7,5,3,1,4] => [[[[.,.],.],[[[.,.],.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 2

[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

[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

[7,8,1,6,5,2,4,3] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[8,4,5,7,2,6,3,1] => [[[[.,.],[.,[.,.]]],[[.,.],.]],.] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 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

[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

[7,8,1,3,6,4,2,5] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 0

[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

[5,7,4,2,3,6,8,1] => [[[[.,[.,.]],.],[.,[.,[.,.]]]],.] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2

[5,4,7,3,2,8,1,6] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 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

[5,8,3,4,6,1,2,7] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[6,4,3,8,5,1,2,7] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[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

[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

[6,4,8,5,1,2,3,7] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1

[7,4,8,3,1,2,5,6] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2

[5,4,7,8,2,1,3,6] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2

[5,8,6,3,1,2,4,7] => [[[.,[[.,.],.]],.],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1

[6,8,5,2,1,3,4,7] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2

[5,6,1,3,2,4,8,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0

[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

[4,6,3,2,8,5,7,1] => [[[[.,[.,.]],.],[[.,.],[.,.]]],.] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => 2

[5,3,7,2,1,8,6,4] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 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] => 2

[6,1,5,4,7,2,8,3] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[5,4,8,3,2,7,1,6] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2

[5,4,3,7,2,1,6,8] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3

[5,4,3,7,8,2,1,6] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3

[4,1,8,6,2,5,7,3] => [[.,.],[[[.,.],.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 1

[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

[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

[7,1,3,2,6,5,8,4] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1

[6,1,3,5,8,7,4,2] => [[.,.],[[.,[[.,[[.,.],.]],.]],.]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 1

[6,8,5,7,3,4,2,1] => [[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2

[5,3,6,8,4,2,1,7] => [[[[.,.],[[.,[.,.]],.]],.],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 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

[6,2,8,3,4,1,5,7] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[2,4,1,8,7,6,3,5] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 0

[8,5,4,7,6,1,3,2] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[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

[6,3,8,5,1,7,4,2] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[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

[6,4,8,7,3,5,2,1] => [[[[[.,.],[[.,.],.]],[.,.]],.],.] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 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

[4,3,5,6,8,2,7,1] => [[[[.,.],[.,[.,[.,.]]]],[.,.]],.] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2

[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

[3,8,2,7,6,4,1,5] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 0

[5,3,6,2,1,8,4,7] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2

[4,3,8,6,2,7,1,5] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[8,2,1,4,6,3,7,5] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[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

[5,3,8,6,7,2,1,4] => [[[[.,.],[[.,.],[.,.]]],.],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 2

[2,7,1,4,6,5,3,8] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 0

[4,7,1,2,6,5,8,3] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 0

[4,2,5,6,8,7,3,1] => [[[.,.],[[.,[.,[[.,.],.]]],.]],.] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 2

[6,5,8,3,7,4,2,1] => [[[[[.,.],[.,.]],[[.,.],.]],.],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 3

[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

[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

[7,8,1,3,5,4,6,2] => [[.,[.,.]],[[.,[[.,.],[.,.]]],.]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 0

[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

[2,1,7,4,3,8,5,6] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[7,2,3,8,5,4,1,6] => [[[.,.],[.,[[[.,.],.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 1

[4,2,6,5,3,1,7,8] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 1

[5,2,1,6,8,7,4,3] => [[[.,.],.],[[[.,[[.,.],.]],.],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 2

[8,3,2,7,5,6,1,4] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2

[6,1,8,2,5,3,4,7] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[3,1,2,4,8,6,7,5] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 1

[3,1,2,5,8,7,4,6] => [[.,.],[.,[[.,[[.,.],.]],[.,.]]]] => [1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 1

[6,5,2,1,8,4,7,3] => [[[[.,.],.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 3

[5,6,2,4,3,8,1,7] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[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

[8,3,2,4,1,7,6,5] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 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] => 0

[4,1,8,6,3,5,2,7] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1

[4,1,5,8,6,2,3,7] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 1

[5,3,4,6,2,8,7,1] => [[[[.,.],[.,[.,.]]],[[.,.],.]],.] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 2

[5,4,8,6,3,7,1,2] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 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

[5,6,4,2,7,8,3,1] => [[[[.,[.,.]],.],[[.,[.,.]],.]],.] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 2

[6,5,2,3,7,4,1,8] => [[[[.,.],.],[.,[[.,.],.]]],[.,.]] => [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 2

[6,5,2,3,1,8,7,4] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2

[6,5,3,7,4,1,2,8] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[6,4,7,5,3,8,1,2] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 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

[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

[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

[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

[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

[8,6,1,3,2,5,7,4] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 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

[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

[4,7,3,8,5,1,6,2] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[4,3,2,7,5,8,1,6] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2

[4,8,5,3,2,6,1,7] => [[[[.,[[.,.],.]],.],[.,.]],[.,.]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[8,1,5,3,2,4,7,6] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1

[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

[8,6,1,3,2,7,4,5] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 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

[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

[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

[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

[8,1,4,3,7,5,6,2] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 1

[8,2,7,6,4,1,5,3] => [[[.,.],[[[.,.],.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 1

[6,8,2,7,3,1,5,4] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[8,2,6,3,4,1,7,5] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[6,1,2,8,5,3,7,4] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 1

[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

[7,5,2,8,1,6,3,4] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[4,8,2,7,1,3,6,5] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 0

[8,2,1,7,4,6,3,5] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[4,2,5,8,3,6,7,1] => [[[.,.],[[.,[.,.]],[.,[.,.]]]],.] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2

[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

[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

[4,5,2,8,7,3,1,6] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 0

[4,8,5,3,1,6,7,2] => [[[.,[[.,.],.]],.],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 1

[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

[5,2,3,6,8,4,7,1] => [[[.,.],[.,[[.,[.,.]],[.,.]]]],.] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[6,2,1,7,8,4,3,5] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 2

[5,2,1,3,8,4,7,6] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2

[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

[6,2,7,8,3,5,4,1] => [[[.,.],[[.,[.,.]],[[.,.],.]]],.] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 2

[5,2,8,6,4,1,7,3] => [[[.,.],[[[.,.],.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 1

[5,1,2,8,4,3,7,6] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 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] => 0

[6,2,3,4,7,8,5,1] => [[[.,.],[.,[.,[[.,[.,.]],.]]]],.] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 2

[7,2,1,8,4,3,5,6] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[6,2,1,3,7,5,8,4] => [[[.,.],.],[.,[[[.,.],[.,.]],.]]] => [1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2

[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

[7,4,3,2,5,8,1,6] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3

[7,2,4,3,5,8,1,6] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[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

[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

[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

[4,3,1,8,5,2,6,7] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[7,3,8,2,1,4,5,6] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2

[8,2,5,3,1,7,4,6] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[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

[7,5,2,3,8,4,6,1] => [[[[.,.],.],[.,[[.,.],[.,.]]]],.] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 3

[7,4,6,5,1,8,2,3] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[7,1,3,2,6,8,4,5] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[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

[6,1,3,8,4,2,7,5] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 1

[5,4,1,8,6,2,7,3] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[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

[3,6,1,5,8,4,7,2] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 0

[6,4,8,3,5,7,2,1] => [[[[[.,.],[.,.]],[.,[.,.]]],.],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3

[7,2,8,4,1,3,6,5] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 1

[5,8,1,2,4,3,6,7] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 0

[8,4,3,5,7,2,6,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3

[4,1,5,2,3,8,7,6] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 1

[6,3,5,8,2,4,7,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[7,5,6,2,8,4,3,1] => [[[[.,.],[.,.]],[[[.,.],.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 2

[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

[7,6,4,8,5,3,2,1] => [[[[[[.,.],.],[[.,.],.]],.],.],.] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5

[6,3,7,5,4,2,8,1] => [[[[.,.],[[[.,.],.],.]],[.,.]],.] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 2

[7,5,2,6,3,4,8,1] => [[[[.,.],.],[[.,.],[.,[.,.]]]],.] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 3

[3,8,2,7,5,4,1,6] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 0

[5,4,8,6,7,1,2,3] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[3,7,2,8,1,6,4,5] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[8,5,2,4,6,7,3,1] => [[[[.,.],.],[[.,[.,[.,.]]],.]],.] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 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

[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

[5,2,8,6,4,7,1,3] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[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

[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

[8,3,4,5,2,1,7,6] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 2

[8,6,1,4,7,3,5,2] => [[[.,.],.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 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] => 2

[5,3,6,7,2,4,8,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[8,6,1,4,7,5,2,3] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 2

[7,1,3,6,5,2,8,4] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 1

[8,2,1,4,5,7,6,3] => [[[.,.],.],[[.,[.,[[.,.],.]]],.]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 2

[6,1,7,5,4,2,8,3] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 1

[8,6,5,1,3,7,4,2] => [[[[.,.],.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 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

[8,7,1,4,6,5,3,2] => [[[.,.],.],[[[.,[[.,.],.]],.],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 2

[3,1,5,8,6,2,4,7] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 1

[6,5,2,4,7,8,1,3] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2

[7,2,5,8,6,4,1,3] => [[[.,.],[[.,[[.,.],.]],.]],[.,.]] => [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 1

[5,2,8,3,4,7,6,1] => [[[.,.],[[.,.],[.,[[.,.],.]]]],.] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 2

[6,8,7,5,4,3,1,2] => [[[[[.,[[.,.],.]],.],.],.],[.,.]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 3

[5,3,4,8,6,2,7,1] => [[[[.,.],[.,[[.,.],.]]],[.,.]],.] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 2

[5,4,2,3,6,1,8,7] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[4,3,7,6,8,2,1,5] => [[[[.,.],[[.,.],[.,.]]],.],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 2

[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

[6,1,8,5,2,7,3,4] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[8,7,2,6,3,1,4,5] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[8,7,1,6,4,5,2,3] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[5,4,1,3,7,2,8,6] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[8,3,4,7,6,2,1,5] => [[[[.,.],[.,[[.,.],.]]],.],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 2

[3,1,8,7,5,2,4,6] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 1

[6,5,8,7,2,4,3,1] => [[[[.,.],[[.,.],.]],[[.,.],.]],.] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 2

[4,3,6,5,8,2,1,7] => [[[[.,.],[[.,.],[.,.]]],.],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 2

[7,6,3,2,8,5,4,1] => [[[[[.,.],.],.],[[[.,.],.],.]],.] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 4

[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

[3,2,8,5,6,7,1,4] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[8,3,2,1,4,7,5,6] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 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

[7,5,1,4,2,3,6,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 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

[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

[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

[8,5,1,6,7,2,3,4] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[7,5,1,2,4,6,8,3] => [[[.,.],.],[.,[[.,[.,[.,.]]],.]]] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[6,1,5,2,7,3,4,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[7,1,2,6,4,5,8,3] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 1

[8,1,6,2,7,3,4,5] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[7,1,6,2,5,3,4,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[8,1,6,2,5,3,4,7] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[8,1,7,2,5,3,4,6] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[8,1,2,7,4,5,6,3] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 1

[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

[7,3,1,2,6,4,5,8] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2

[3,1,2,8,5,6,7,4] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 1

[6,3,1,2,7,4,5,8] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2

[6,1,7,4,2,3,5,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1

[7,1,8,2,5,3,4,6] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[6,1,7,2,5,3,4,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[5,1,7,2,6,3,4,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[5,1,8,2,6,3,4,7] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[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

[4,6,3,7,1,5,2,8] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[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

[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

[8,6,5,1,2,4,3,7] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3

[7,6,1,4,2,3,5,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2

[6,5,1,4,8,3,2,7] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 2

[8,7,5,1,4,2,3,6] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[8,4,1,2,5,3,6,7] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2

[8,7,5,1,4,2,6,3] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3

[8,6,1,4,2,5,3,7] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[8,7,1,4,3,2,6,5] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[8,7,5,2,4,3,6,1] => [[[[[.,.],.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 4

[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

[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

[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

[4,3,7,5,2,1,6,8] => [[[[.,.],[[.,.],.]],.],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 2

[3,5,1,4,7,2,6,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[2,5,1,4,7,8,3,6] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 0

[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

[3,5,1,6,4,2,7,8] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0

[6,4,3,1,7,2,5,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[6,2,7,4,3,1,5,8] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 1

[6,3,2,7,4,5,1,8] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2

[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

[6,3,2,5,7,1,4,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[3,2,6,5,7,1,4,8] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[2,1,7,3,5,6,8,4] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 1

[2,1,6,3,5,7,8,4] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 1

[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

[2,5,1,6,4,3,7,8] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0

[4,6,1,5,2,7,3,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[5,2,7,6,1,8,4,3] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[5,8,2,6,1,7,4,3] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 0

[2,6,1,8,5,4,3,7] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 0

[5,8,6,2,1,4,3,7] => [[[.,[[.,.],.]],.],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[6,4,7,5,8,2,1,3] => [[[[.,.],[[.,.],[.,.]]],.],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 2

[6,3,7,4,2,5,8,1] => [[[[.,.],[[.,.],.]],[.,[.,.]]],.] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 2

[7,5,6,2,4,3,8,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[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

[4,2,8,5,3,6,1,7] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[8,1,7,4,5,6,2,3] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 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

[8,2,1,4,3,7,6,5] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 2

[7,6,5,3,1,2,8,4] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 4

[5,4,1,6,2,8,3,7] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 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

[3,1,8,6,7,2,4,5] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[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

[4,5,3,7,1,6,8,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0

[4,2,8,5,3,6,7,1] => [[[.,.],[[[.,.],.],[.,[.,.]]]],.] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 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

[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

[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

[2,7,1,4,8,5,6,3] => [[.,[.,.]],[[.,[[.,.],[.,.]]],.]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 0

[8,4,6,2,5,3,7,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[8,3,7,6,2,1,5,4] => [[[[.,.],[[.,.],.]],.],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2

[8,5,2,7,6,1,4,3] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[5,8,2,7,6,1,4,3] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[8,3,7,6,2,5,1,4] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[7,3,8,6,5,1,4,2] => [[[.,.],[[[.,.],.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 1

[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

[8,1,7,6,3,4,2,5] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1

[7,2,6,5,8,4,3,1] => [[[.,.],[[[[.,.],[.,.]],.],.]],.] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 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] => 0

[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

[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

[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

[6,5,1,3,4,2,7,8] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 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] => 2

[6,8,7,4,3,5,1,2] => [[[[.,[[.,.],.]],.],[.,.]],[.,.]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[7,1,8,5,3,4,6,2] => [[.,.],[[[[.,.],.],[.,[.,.]]],.]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 1

[5,7,4,2,1,6,3,8] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 2

[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

[7,4,8,6,3,5,2,1] => [[[[[.,.],[[.,.],.]],[.,.]],.],.] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3

[6,1,3,8,7,5,2,4] => [[.,.],[[.,[[[.,.],.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 1

[7,6,2,1,8,3,5,4] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 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

[7,5,4,2,1,8,6,3] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4

[4,6,3,2,7,8,5,1] => [[[[.,[.,.]],.],[[.,[.,.]],.]],.] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 2

[7,6,1,3,4,2,5,8] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[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

[7,2,5,4,6,1,3,8] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 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

[7,3,2,1,5,6,4,8] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3

[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

[2,1,6,4,7,5,3,8] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1

[7,2,8,5,6,4,3,1] => [[[.,.],[[[[.,.],[.,.]],.],.]],.] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 2

[7,6,8,5,4,1,3,2] => [[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 3

[7,1,8,4,6,5,3,2] => [[.,.],[[[[.,.],[[.,.],.]],.],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 1

[7,8,6,3,1,5,4,2] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 2

[7,6,1,4,5,3,2,8] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 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

[4,1,3,8,6,2,7,5] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 1

[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

[8,2,6,3,1,5,7,4] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 1

[8,2,5,6,7,4,3,1] => [[[.,.],[[[.,[.,[.,.]]],.],.]],.] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 2

[7,5,3,2,4,1,8,6] => [[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3

[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

[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

[3,1,8,4,6,5,7,2] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 1

[6,1,2,3,8,4,7,5] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 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

[8,1,6,4,5,2,3,7] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[8,1,6,4,5,2,7,3] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[8,6,4,1,2,3,7,5] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3

[8,6,1,4,2,5,7,3] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[8,6,4,1,5,7,2,3] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3

[8,6,1,4,7,2,5,3] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[8,6,4,1,5,2,3,7] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[8,7,1,4,6,5,2,3] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 2

[8,3,7,6,4,5,1,2] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[5,3,8,6,4,1,7,2] => [[[.,.],[[[.,.],.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 1

[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

[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

[5,7,4,2,3,8,6,1] => [[[[.,[.,.]],.],[.,[[.,.],.]]],.] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => 2

[3,8,2,5,1,7,4,6] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[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

[4,8,5,2,1,7,3,6] => [[[.,[[.,.],.]],.],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[8,5,7,6,1,2,4,3] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 1

[6,8,7,5,2,4,1,3] => [[[[.,[[.,.],.]],.],[.,.]],[.,.]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[7,3,1,6,8,5,4,2] => [[[.,.],.],[[[[.,[.,.]],.],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 2

[5,3,1,7,4,8,6,2] => [[[.,.],.],[[[.,.],[[.,.],.]],.]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 2

[7,3,1,8,6,4,5,2] => [[[.,.],.],[[[[.,.],.],[.,.]],.]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 2

[8,6,4,1,7,3,2,5] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 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] => 0

[6,4,8,3,7,2,1,5] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 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] => 0

[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

[4,7,3,2,5,6,8,1] => [[[[.,[.,.]],.],[.,[.,[.,.]]]],.] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2

[3,2,7,6,4,5,8,1] => [[[.,.],[[[.,.],.],[.,[.,.]]]],.] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 2

[8,3,1,2,6,4,7,5] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2

[5,7,4,8,1,3,2,6] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[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

[8,5,4,2,6,1,7,3] => [[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3

[3,2,6,8,7,4,1,5] => [[[.,.],[[.,[[.,.],.]],.]],[.,.]] => [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 1

[6,3,1,2,8,7,4,5] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 2

[5,2,1,3,8,7,6,4] => [[[.,.],.],[.,[[[[.,.],.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 2

[7,2,1,5,3,8,4,6] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[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

[5,4,6,8,3,1,7,2] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 2

[8,6,1,7,2,4,3,5] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[7,3,1,2,8,6,4,5] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 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

[6,2,8,3,1,4,7,5] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 1

[3,1,2,8,7,4,5,6] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 1

[2,1,3,8,7,4,6,5] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 1

[2,1,3,8,7,4,5,6] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 1

[8,5,1,7,2,4,3,6] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[8,4,1,7,3,2,5,6] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[8,3,1,6,2,7,5,4] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 2

[2,1,3,8,7,6,4,5] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 1

[5,6,2,8,4,1,3,7] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 0

[2,8,1,3,5,7,4,6] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 0

[5,4,7,8,3,2,6,1] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 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

[4,3,8,2,6,5,7,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[5,7,1,4,8,2,3,6] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[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

[3,2,1,4,8,5,7,6] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2

[7,3,1,4,2,6,5,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[7,4,1,6,2,5,3,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[5,4,1,8,2,6,3,7] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[5,3,1,8,2,6,4,7] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[4,7,1,5,2,6,3,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[6,5,1,4,2,7,3,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[8,4,2,3,1,6,5,7] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 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

[6,4,2,3,5,8,1,7] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 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

[6,5,1,8,3,2,7,4] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[6,1,7,2,8,4,5,3] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1

[8,3,2,1,5,6,7,4] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 3

[3,2,6,7,8,4,5,1] => [[[.,.],[[.,[.,[.,.]]],[.,.]]],.] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[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

[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

[6,3,4,2,7,8,5,1] => [[[[.,.],[.,.]],[[.,[.,.]],.]],.] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 2

[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

[5,1,8,4,3,7,2,6] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1

[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

[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

[7,5,2,3,6,8,4,1] => [[[[.,.],.],[.,[[.,[.,.]],.]]],.] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[8,1,4,6,5,3,2,7] => [[.,.],[[[.,[[.,.],.]],.],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 1

[8,1,4,7,6,5,2,3] => [[.,.],[[.,[[[.,.],.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 1

[8,1,2,7,6,5,4,3] => [[.,.],[.,[[[[[.,.],.],.],.],.]]] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 1

[3,2,8,6,1,5,7,4] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 1

[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

[6,2,8,3,5,1,4,7] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[6,2,7,4,5,3,1,8] => [[[.,.],[[[.,.],[.,.]],.]],[.,.]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1

[6,8,2,5,3,4,1,7] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[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

[6,1,8,7,4,5,2,3] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1

[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

[8,2,3,7,4,5,6,1] => [[[.,.],[.,[[.,.],[.,[.,.]]]]],.] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 2

[8,5,7,2,3,6,4,1] => [[[[.,.],[.,.]],[.,[[.,.],.]]],.] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 2

[7,5,2,1,6,8,3,4] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3

[7,6,1,5,4,8,2,3] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[7,6,3,2,1,8,4,5] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4

[6,5,1,3,7,2,8,4] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[8,1,7,3,4,5,2,6] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[7,1,8,3,4,5,2,6] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[7,1,6,5,4,3,8,2] => [[.,.],[[[[[.,.],.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 1

[7,1,3,6,4,5,8,2] => [[.,.],[[.,[[.,.],[.,[.,.]]]],.]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 1

[7,1,5,3,6,4,8,2] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 1

[6,1,5,3,7,8,2,4] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 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] => 0

[5,1,7,3,8,6,2,4] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1

[6,1,3,2,4,7,8,5] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 1

[6,2,1,3,4,7,8,5] => [[[.,.],.],[.,[.,[[.,[.,.]],.]]]] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[3,2,5,8,7,4,1,6] => [[[.,.],[[.,[[.,.],.]],.]],[.,.]] => [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 1

[4,2,5,8,7,3,1,6] => [[[.,.],[[.,[[.,.],.]],.]],[.,.]] => [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 1

[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

[5,8,4,7,3,6,2,1] => [[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2

[4,2,8,7,3,1,6,5] => [[[.,.],[[[.,.],.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 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] => 2

[6,1,4,3,8,7,2,5] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1

[5,1,3,2,6,8,7,4] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 1

[6,1,3,8,7,2,4,5] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 1

[4,2,1,8,7,6,3,5] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 2

[3,2,5,8,7,1,4,6] => [[[.,.],[.,[[.,.],.]]],[.,[.,.]]] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 1

[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

[3,1,6,5,8,7,2,4] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1

[2,7,1,3,6,4,5,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 0

[8,1,7,3,5,4,6,2] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 1

[3,2,4,8,5,7,1,6] => [[[.,.],[.,[[.,.],[.,.]]]],[.,.]] => [1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1

[8,1,2,4,7,5,6,3] => [[.,.],[.,[[.,[[.,.],[.,.]]],.]]] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 1

[6,4,5,8,3,1,7,2] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 2

[8,6,2,1,5,7,3,4] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3

[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

[8,7,2,4,1,5,3,6] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[7,5,3,4,8,6,2,1] => [[[[[.,.],.],[.,[[.,.],.]]],.],.] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4

[4,3,6,5,1,2,7,8] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 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] => 2

[8,7,2,1,4,3,5,6] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[4,2,8,7,6,5,1,3] => [[[.,.],[[[[.,.],.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1

[6,2,1,8,7,5,3,4] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 2

[6,3,8,7,4,5,2,1] => [[[[.,.],[[[.,.],.],[.,.]]],.],.] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 3

[4,6,5,3,2,8,1,7] => [[[[.,[[.,.],.]],.],[.,.]],[.,.]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[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

[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

[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

[6,3,8,7,2,5,4,1] => [[[[.,.],[[.,.],.]],[[.,.],.]],.] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 2

[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

[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

[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

[8,2,1,6,7,4,5,3] => [[[.,.],.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[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

[8,1,2,6,4,7,5,3] => [[.,.],[.,[[[.,.],[[.,.],.]],.]]] => [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 1

[8,4,1,6,2,7,5,3] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 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] => 0

[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

[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

[5,4,7,6,3,1,2,8] => [[[[.,.],[[.,.],.]],.],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 2

[8,7,1,4,2,3,5,6] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2

[8,2,6,5,7,1,3,4] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[4,6,1,3,2,8,7,5] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 0

[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

[4,5,3,6,7,1,8,2] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0

[6,1,2,5,4,8,7,3] => [[.,.],[.,[[[.,.],[[.,.],.]],.]]] => [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 1

[8,4,1,7,3,5,6,2] => [[[.,.],.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[8,4,1,2,5,7,3,6] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 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] => 0

[8,3,7,2,1,6,5,4] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 2

[8,4,7,6,2,5,1,3] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[8,4,7,3,6,2,1,5] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 2

[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

[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

[8,5,1,3,6,2,4,7] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[7,5,1,8,3,4,2,6] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[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

[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

[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

[7,3,6,8,5,2,1,4] => [[[[.,.],[[.,[.,.]],.]],.],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 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] => 2

[8,4,5,7,3,6,2,1] => [[[[[.,.],[.,[.,.]]],[.,.]],.],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[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

[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

[6,8,4,7,5,1,3,2] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[8,7,6,4,2,1,5,3] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5

[5,8,3,7,1,4,6,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0

[2,5,1,4,3,6,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0

[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

[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

[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

[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

[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

[2,7,1,3,8,5,4,6] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 0

[7,1,2,6,3,8,4,5] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 1

[8,1,2,6,5,3,7,4] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 1

[8,5,4,6,1,2,7,3] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[7,4,1,8,2,5,3,6] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 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] => 2

[8,4,5,3,1,6,7,2] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 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

[8,2,1,7,4,3,5,6] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[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

[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

[6,2,1,7,4,8,3,5] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[5,2,1,6,3,4,8,7] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2

[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

[4,2,8,6,3,7,5,1] => [[[.,.],[[[.,.],.],[[.,.],.]]],.] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 2

[4,1,7,6,3,8,5,2] => [[.,.],[[[[.,.],.],[[.,.],.]],.]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 1

[7,4,1,8,5,3,6,2] => [[[.,.],.],[[[[.,.],.],[.,.]],.]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 2

[5,4,1,8,6,7,2,3] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[6,2,8,4,5,3,7,1] => [[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 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

[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

[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

[6,2,1,3,7,4,8,5] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2

[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

[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

[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

[8,3,6,7,2,4,5,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2

[6,8,3,2,5,7,4,1] => [[[[.,[.,.]],.],[[.,[.,.]],.]],.] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 2

[4,1,5,6,8,7,3,2] => [[.,.],[[[.,[.,[[.,.],.]]],.],.]] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 1

[8,4,2,3,6,7,5,1] => [[[[.,.],.],[.,[[.,[.,.]],.]]],.] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[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

[4,5,1,3,7,6,8,2] => [[.,[.,.]],[[.,[[.,.],[.,.]]],.]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 0

[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

[8,1,3,7,4,5,6,2] => [[.,.],[[.,[[.,.],[.,[.,.]]]],.]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 1

[8,1,5,3,6,4,7,2] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 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] => 0

[8,1,5,4,7,3,6,2] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 1

[7,6,5,4,1,8,2,3] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4

[8,1,5,4,7,6,3,2] => [[.,.],[[[[.,.],[[.,.],.]],.],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 1

[2,5,1,4,6,7,3,8] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 0

[7,6,5,2,8,4,1,3] => [[[[[.,.],.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3

[3,1,6,5,2,8,7,4] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 1

[3,8,1,7,4,2,6,5] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[8,1,7,4,3,5,6,2] => [[.,.],[[[[.,.],.],[.,[.,.]]],.]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 1

[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

[8,6,3,2,7,4,1,5] => [[[[[.,.],.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3

[2,8,1,3,5,4,6,7] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 0

[7,4,8,6,3,1,2,5] => [[[[.,.],[[.,.],.]],.],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 2

[6,1,5,2,8,7,3,4] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1

[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

[3,1,8,5,4,7,2,6] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1

[3,1,6,4,8,5,2,7] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1

[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

[3,2,6,4,1,5,7,8] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1

[5,4,2,1,8,3,6,7] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[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

[6,8,2,7,1,4,3,5] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[8,6,3,1,5,7,2,4] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 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

[4,7,1,2,5,3,6,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 0

[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

[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

[7,6,4,1,8,3,5,2] => [[[[.,.],.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 3

[5,4,1,6,7,3,2,8] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 2

[7,4,1,6,5,8,2,3] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[8,5,4,1,6,7,3,2] => [[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[5,2,1,6,4,7,8,3] => [[[.,.],.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 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

[7,3,1,4,2,5,8,6] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2

[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

[8,6,3,5,4,1,2,7] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[8,3,2,6,1,5,4,7] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[8,5,1,7,4,6,2,3] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[4,8,1,7,6,3,5,2] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 0

[8,5,1,7,4,3,6,2] => [[[.,.],.],[[[[.,.],.],[.,.]],.]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 2

[8,5,7,6,2,1,3,4] => [[[[.,.],[[.,.],.]],.],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 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] => 2

[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

[4,8,1,7,6,5,2,3] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 0

[4,3,8,7,2,6,1,5] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[8,2,5,7,4,3,6,1] => [[[.,.],[[[.,[.,.]],.],[.,.]]],.] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[8,7,6,3,5,4,1,2] => [[[[[.,.],.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3

[5,4,8,2,1,3,7,6] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2

[7,1,5,4,6,2,3,8] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[7,4,1,3,6,2,5,8] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[7,5,2,4,8,3,6,1] => [[[[.,.],.],[[.,[.,.]],[.,.]]],.] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 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

[7,2,6,5,8,3,4,1] => [[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2

[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

[2,6,1,5,3,4,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0

[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

[5,3,6,4,8,7,2,1] => [[[[.,.],[[.,.],[[.,.],.]]],.],.] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 3

[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

[7,6,2,5,3,8,4,1] => [[[[.,.],.],[[.,.],[[.,.],.]]],.] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 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

[4,5,1,3,8,6,2,7] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 0

[7,4,2,3,6,8,5,1] => [[[[.,.],.],[.,[[.,[.,.]],.]]],.] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 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

[7,8,1,3,6,4,5,2] => [[.,[.,.]],[[.,[[.,.],[.,.]]],.]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 0

[7,2,6,8,4,5,3,1] => [[[.,.],[[[.,[.,.]],[.,.]],.]],.] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 2

[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

[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

[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

[7,5,2,4,8,3,1,6] => [[[[.,.],.],[[.,[.,.]],.]],[.,.]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 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

[7,8,3,6,4,1,5,2] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[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

[7,5,2,8,1,4,6,3] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[7,8,1,6,3,5,4,2] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 0

[7,8,1,6,2,5,4,3] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 0

[5,6,1,4,3,8,2,7] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[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

[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

[4,8,1,2,7,6,5,3] => [[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => 0

[4,6,1,2,8,5,7,3] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 0

[6,4,7,3,5,2,1,8] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 2

[3,1,6,2,5,7,8,4] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 1

[6,2,1,4,5,3,7,8] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[6,2,1,5,7,3,4,8] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[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

[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

[8,1,4,3,6,7,2,5] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[8,1,5,2,6,4,3,7] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1

[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

[3,8,1,6,4,2,7,5] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[3,1,5,7,6,2,8,4] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 1

[6,3,1,4,2,7,8,5] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[3,1,7,6,5,2,8,4] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 1

[7,2,1,5,6,3,8,4] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[4,3,1,8,6,2,7,5] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[3,1,5,2,8,7,6,4] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 1

[2,6,1,8,7,4,3,5] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 0

[7,5,1,8,3,2,6,4] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[4,7,6,3,1,8,2,5] => [[[.,[[.,.],.]],.],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[5,3,1,8,6,2,4,7] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[5,1,8,6,3,2,4,7] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 1

[8,3,1,6,4,2,5,7] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[7,3,2,4,8,5,1,6] => [[[[.,.],.],[.,[[.,.],.]]],[.,.]] => [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 2

[2,5,1,8,6,3,7,4] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[6,5,1,7,2,8,4,3] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 2

[2,8,1,7,5,3,6,4] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[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

[4,1,8,7,6,3,5,2] => [[.,.],[[[[[.,.],.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 1

[4,8,2,6,3,5,1,7] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[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

[4,1,8,5,3,6,2,7] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1

[6,4,2,5,3,1,7,8] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[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

[6,4,1,5,3,2,7,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[6,2,1,5,4,3,7,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[3,1,8,5,4,6,2,7] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1

[6,1,8,4,5,3,2,7] => [[.,.],[[[[.,.],[.,.]],.],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 1

[4,5,2,7,1,6,3,8] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[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

[4,1,8,5,3,6,7,2] => [[.,.],[[[[.,.],.],[.,[.,.]]],.]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 1

[6,3,8,4,5,1,7,2] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[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

[2,6,1,8,5,7,4,3] => [[.,[.,.]],[[[[.,.],[.,.]],.],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 0

[6,3,8,4,5,2,1,7] => [[[[.,.],[[.,.],[.,.]]],.],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 2

[6,5,8,7,2,3,4,1] => [[[[.,.],[[.,.],.]],[.,[.,.]]],.] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 2

[6,3,8,4,5,2,7,1] => [[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 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

[3,2,6,8,5,4,7,1] => [[[.,.],[[[.,[.,.]],.],[.,.]]],.] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2

[4,1,8,5,2,6,3,7] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 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

[6,5,8,7,4,1,2,3] => [[[[.,.],[[.,.],.]],.],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 2

[6,5,8,7,4,2,1,3] => [[[[[.,.],[[.,.],.]],.],.],[.,.]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 3

[6,5,8,7,2,4,1,3] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[6,2,8,4,5,7,1,3] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[6,1,8,4,5,7,3,2] => [[.,.],[[[[.,.],[.,[.,.]]],.],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 1

[4,2,7,3,5,8,6,1] => [[[.,.],[[.,.],[.,[[.,.],.]]]],.] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 2

[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

[3,5,1,8,4,7,6,2] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 0

[3,6,1,8,5,4,7,2] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 0

[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

[3,6,1,8,5,7,4,2] => [[.,[.,.]],[[[[.,.],[.,.]],.],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 0

[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

[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

[7,5,1,6,3,2,8,4] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[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

[6,3,8,5,7,2,4,1] => [[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[8,2,1,7,5,3,6,4] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[8,2,1,6,7,3,5,4] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 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

[3,5,1,8,7,6,2,4] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 0

[5,6,2,7,8,1,3,4] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[3,2,5,6,8,4,7,1] => [[[.,.],[[.,[.,[.,.]]],[.,.]]],.] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[5,3,2,4,7,8,1,6] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2

[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

[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

[4,2,7,6,8,1,3,5] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[4,7,2,5,6,3,1,8] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 0

[5,4,1,3,7,8,2,6] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 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

[7,2,1,6,8,3,5,4] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[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

[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

[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

[5,1,2,6,4,8,3,7] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 1

[8,6,2,3,7,5,1,4] => [[[[.,.],.],[.,[[.,.],.]]],[.,.]] => [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 2

[4,5,2,8,6,1,3,7] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 0

[6,8,2,7,5,3,1,4] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 0

[5,8,3,6,4,1,7,2] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[4,3,8,5,2,7,1,6] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[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

[3,5,1,8,7,4,2,6] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 0

[4,6,1,3,8,2,7,5] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[8,6,1,2,3,5,7,4] => [[[.,.],.],[.,[.,[[.,[.,.]],.]]]] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[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

[5,3,6,7,4,2,8,1] => [[[[.,.],[[.,[.,.]],.]],[.,.]],.] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[5,4,2,8,6,7,3,1] => [[[[.,.],.],[[[.,.],[.,.]],.]],.] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[6,1,4,2,8,7,3,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 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

[5,4,6,2,7,8,3,1] => [[[[.,.],[.,.]],[[.,[.,.]],.]],.] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 2

[5,1,8,6,4,2,7,3] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 1

[6,2,1,8,5,7,4,3] => [[[.,.],.],[[[[.,.],[.,.]],.],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 2

[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

[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

[2,1,7,6,8,4,5,3] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 1

[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

[6,3,2,7,8,4,5,1] => [[[[.,.],.],[[.,[.,.]],[.,.]]],.] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 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

[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

[4,7,6,3,1,5,8,2] => [[[.,[[.,.],.]],.],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 1

[6,7,5,2,1,4,8,3] => [[[[.,[.,.]],.],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[8,1,2,6,5,3,4,7] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 1

[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

[3,6,1,5,2,7,8,4] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 0

[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

[8,1,2,6,3,5,7,4] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 1

[6,2,8,4,7,1,3,5] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 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] => 0

[6,8,2,7,5,4,1,3] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 0

[4,3,8,7,1,2,6,5] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 1

[3,2,8,7,1,6,4,5] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[5,4,7,8,6,3,1,2] => [[[[.,.],[[.,[.,.]],.]],.],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 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

[6,1,5,3,8,4,7,2] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 1

[6,2,7,4,8,3,1,5] => [[[.,.],[[[.,.],[.,.]],.]],[.,.]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1

[6,8,2,7,5,1,4,3] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[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

[5,3,6,4,7,2,1,8] => [[[[.,.],[[.,.],[.,.]]],.],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 2

[4,2,6,5,7,3,1,8] => [[[.,.],[[[.,.],[.,.]],.]],[.,.]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1

[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

[3,2,6,5,8,4,1,7] => [[[.,.],[[[.,.],[.,.]],.]],[.,.]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1

[3,2,6,5,8,7,1,4] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[4,2,6,5,8,7,1,3] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[5,2,6,4,8,7,1,3] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[5,4,7,6,8,2,1,3] => [[[[.,.],[[.,.],[.,.]]],.],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 2

[6,4,7,5,8,3,1,2] => [[[[.,.],[[.,.],[.,.]]],.],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 2

[4,2,7,5,8,6,1,3] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[3,2,7,5,8,4,1,6] => [[[.,.],[[[.,.],[.,.]],.]],[.,.]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1

[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

[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

[4,3,7,6,8,5,1,2] => [[[.,.],[[[.,.],[.,.]],.]],[.,.]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1

[5,3,7,6,8,2,1,4] => [[[[.,.],[[.,.],[.,.]]],.],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 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

[3,2,6,4,8,7,1,5] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[4,2,7,3,8,6,1,5] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[5,2,7,6,8,3,1,4] => [[[.,.],[[[.,.],[.,.]],.]],[.,.]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1

[3,2,7,6,8,4,1,5] => [[[.,.],[[[.,.],[.,.]],.]],[.,.]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1

[3,2,7,6,8,5,1,4] => [[[.,.],[[[.,.],[.,.]],.]],[.,.]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1

[6,2,7,5,8,4,1,3] => [[[.,.],[[[.,.],[.,.]],.]],[.,.]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1

[4,8,1,7,3,2,5,6] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0

[6,7,1,3,2,5,8,4] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 0

[8,7,6,4,1,5,3,2] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4

[7,2,5,3,4,8,1,6] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[4,2,5,3,7,8,6,1] => [[[.,.],[[.,.],[[.,[.,.]],.]]],.] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 2

[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

[7,8,6,2,3,5,4,1] => [[[[.,[.,.]],.],[.,[[.,.],.]]],.] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => 2

[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

[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

[7,5,6,2,3,8,4,1] => [[[[.,.],[.,.]],[.,[[.,.],.]]],.] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 2

[7,8,6,3,5,4,2,1] => [[[[[.,[.,.]],.],[[.,.],.]],.],.] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 3

[7,4,2,5,6,3,8,1] => [[[[.,.],.],[[.,[.,.]],[.,.]]],.] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 3

[6,2,7,5,3,8,4,1] => [[[.,.],[[[.,.],.],[[.,.],.]]],.] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 2

[4,8,3,7,5,6,2,1] => [[[[.,[.,.]],[[.,.],[.,.]]],.],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 2

[6,2,5,8,3,7,4,1] => [[[.,.],[[.,[.,.]],[[.,.],.]]],.] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 2

[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

[8,2,5,6,3,7,4,1] => [[[.,.],[[.,[.,.]],[[.,.],.]]],.] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 2

[4,5,3,7,1,2,6,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0

[8,5,6,4,1,3,2,7] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2

[6,7,2,8,4,3,1,5] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 0

[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

[4,7,1,3,8,6,5,2] => [[.,[.,.]],[[.,[[[.,.],.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 0

[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

[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

[3,1,5,8,6,4,7,2] => [[.,.],[[[.,[[.,.],.]],[.,.]],.]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 1

[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

[8,5,6,3,1,4,2,7] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2

[3,5,1,8,6,4,2,7] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 0

[7,5,3,8,6,4,2,1] => [[[[[.,.],.],[[[.,.],.],.]],.],.] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 4

[5,1,3,8,6,4,2,7] => [[.,.],[[.,[[[.,.],.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 1

[7,5,8,3,6,4,2,1] => [[[[[.,.],[.,.]],[[.,.],.]],.],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 3

[6,1,2,5,3,4,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1

[6,7,3,5,4,1,2,8] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 0

[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

[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

[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

[8,1,7,5,4,2,6,3] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 1

[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

[8,6,4,3,7,1,5,2] => [[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3

[7,3,1,8,6,5,2,4] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 2

[3,1,6,5,7,8,4,2] => [[.,.],[[[[.,.],[.,[.,.]]],.],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 1

[4,3,1,5,8,7,6,2] => [[[.,.],.],[[.,[[[.,.],.],.]],.]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 2

[7,1,5,4,2,3,6,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1

[7,1,3,6,4,5,2,8] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 1

[6,1,3,8,4,5,2,7] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 1

[2,1,8,7,3,6,5,4] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 1

[5,8,2,7,1,3,6,4] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 0

[4,1,5,7,6,3,2,8] => [[.,.],[[[.,[[.,.],.]],.],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 1

[4,5,1,7,6,3,2,8] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 0

[5,4,2,1,8,7,3,6] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[6,2,1,5,4,3,8,7] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[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

[6,5,2,8,7,4,3,1] => [[[[.,.],.],[[[[.,.],.],.],.]],.] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 3

[7,8,5,4,2,1,6,3] => [[[[[.,[.,.]],.],.],.],[[.,.],.]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 3

[7,5,2,8,6,4,3,1] => [[[[.,.],.],[[[[.,.],.],.],.]],.] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 3

[7,8,3,2,6,5,4,1] => [[[[.,[.,.]],.],[[[.,.],.],.]],.] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 2

[8,2,6,3,7,5,1,4] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 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

[8,6,2,7,5,4,1,3] => [[[[.,.],.],[[[.,.],.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 2

[7,6,3,2,8,1,5,4] => [[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3

[8,6,3,7,2,4,1,5] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[7,2,8,6,4,1,3,5] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 1

[8,1,3,2,6,5,7,4] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1

[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

[3,2,7,5,6,1,8,4] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[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

[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

[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

[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

[4,2,7,6,8,3,5,1] => [[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2

[3,2,6,4,8,5,7,1] => [[[.,.],[[.,.],[[.,.],[.,.]]]],.] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 2

[4,2,8,3,6,5,7,1] => [[[.,.],[[.,.],[[.,.],[.,.]]]],.] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 2

[8,1,4,3,5,2,7,6] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[6,2,8,5,7,1,4,3] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[6,4,8,5,7,1,3,2] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[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

[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

[5,2,7,6,8,1,4,3] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[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

[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

[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

[8,3,6,5,4,1,2,7] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 1

[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

[7,1,4,2,3,8,6,5] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 1

[8,1,2,5,3,7,6,4] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 1

[8,6,5,2,4,1,7,3] => [[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3

[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

[3,4,2,8,6,7,1,5] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[3,7,1,6,2,5,8,4] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 0

[3,6,2,5,1,7,8,4] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0

[3,4,2,7,8,1,5,6] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[7,1,4,2,5,8,6,3] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 1

[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

[5,8,1,4,3,6,7,2] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 0

[5,2,3,8,7,4,1,6] => [[[.,.],[.,[[[.,.],.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 1

[4,6,2,7,8,1,3,5] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[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

[8,6,3,2,1,7,5,4] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4

[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

[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

[5,7,1,3,8,4,2,6] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 0

[2,6,1,4,3,7,8,5] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 0

[5,3,7,6,1,8,4,2] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[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

[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

[7,3,5,4,1,2,6,8] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 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

[7,5,1,3,8,6,2,4] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 2

[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

[3,1,5,4,7,2,6,8] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[5,1,3,7,6,2,4,8] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 1

[5,3,2,4,8,1,7,6] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[6,8,5,3,2,7,1,4] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 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

[4,6,2,7,1,3,8,5] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 0

[3,5,1,4,7,2,8,6] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[5,1,4,8,7,3,2,6] => [[.,.],[[[.,[[.,.],.]],.],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 1

[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

[6,5,2,3,7,8,1,4] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2

[5,4,2,1,8,3,7,6] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3

[3,1,7,4,2,6,8,5] => [[.,.],[[[.,.],.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 1

[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

[8,4,1,3,2,6,7,5] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[8,1,7,3,2,5,6,4] => [[.,.],[[[.,.],.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 1

[8,6,5,2,7,3,1,4] => [[[[[.,.],.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3

[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

[5,6,2,3,7,4,1,8] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 0

[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

[4,5,1,2,7,8,6,3] => [[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 0

[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

[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

[7,1,6,3,4,8,2,5] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[8,2,6,3,5,1,4,7] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[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

[8,5,1,3,6,7,2,4] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 2

[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

[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

[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

[5,6,1,3,7,2,8,4] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[5,6,1,8,2,3,7,4] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0

[5,6,1,2,8,4,7,3] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 0

[5,7,1,8,6,4,2,3] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 0

[7,8,1,5,6,4,2,3] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 0

[7,1,8,5,6,4,2,3] => [[.,.],[[[[.,.],[.,.]],.],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 1

[7,1,5,8,6,4,2,3] => [[.,.],[[[.,[[.,.],.]],.],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 1

[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

[8,6,1,5,2,3,4,7] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2

[8,5,1,6,2,3,4,7] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2

[7,6,1,2,3,8,4,5] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 2

[6,8,1,2,3,7,4,5] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 0

[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

[8,1,2,5,3,4,7,6] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 1

[5,2,7,3,4,8,1,6] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[6,8,7,5,2,1,4,3] => [[[[.,[[.,.],.]],.],.],[[.,.],.]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2

[6,5,3,7,4,1,8,2] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[3,1,5,4,6,8,7,2] => [[.,.],[[[.,.],[.,[[.,.],.]]],.]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 1

[3,1,6,4,2,5,8,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1

[3,6,1,4,5,7,8,2] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 0

[5,4,2,3,6,8,1,7] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 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] => 0

[7,3,2,1,8,6,4,5] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[8,7,2,4,1,3,6,5] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[8,2,6,3,5,7,1,4] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[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

[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

[4,8,1,2,6,5,7,3] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 0

[5,6,1,8,3,7,2,4] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[2,8,1,6,5,3,7,4] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[2,1,5,7,6,3,8,4] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 1

[4,1,2,5,7,6,8,3] => [[.,.],[.,[[.,[[.,.],[.,.]]],.]]] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 1

[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

[4,3,8,7,6,2,5,1] => [[[[.,.],[[[.,.],.],.]],[.,.]],.] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 2

[5,4,8,2,7,6,3,1] => [[[[.,.],[.,.]],[[[.,.],.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 2

[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

[3,6,4,2,1,5,7,8] => [[[.,[[.,.],.]],.],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1

[4,3,2,6,5,8,1,7] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2

[4,6,5,2,1,7,8,3] => [[[.,[[.,.],.]],.],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 1

[4,6,1,7,5,8,3,2] => [[.,[.,.]],[[[[.,.],[.,.]],.],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 0

[4,2,6,5,1,7,8,3] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 1

[4,1,5,7,6,8,3,2] => [[.,.],[[[.,[[.,.],[.,.]]],.],.]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 1

[4,2,5,7,6,8,3,1] => [[[.,.],[[.,[[.,.],[.,.]]],.]],.] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 2

[4,3,6,5,2,8,1,7] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[4,3,6,5,1,7,8,2] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 1

[4,6,5,3,1,7,8,2] => [[[.,[[.,.],.]],.],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 1

[5,8,1,4,2,3,6,7] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0

[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

[3,5,1,8,6,4,7,2] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 0

[4,7,2,8,3,1,6,5] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[5,3,8,4,6,2,7,1] => [[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[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

[8,3,2,1,6,5,7,4] => [[[[.,.],.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 3

[4,1,5,6,8,7,2,3] => [[.,.],[[.,[.,[[.,.],.]]],[.,.]]] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 1

[6,8,1,4,5,7,2,3] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 0

[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

[6,5,1,2,4,8,7,3] => [[[.,.],.],[.,[[.,[[.,.],.]],.]]] => [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 2

[5,8,7,2,1,3,6,4] => [[[.,[[.,.],.]],.],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => 1

[5,1,7,2,8,6,3,4] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1

[6,1,5,3,4,8,7,2] => [[.,.],[[[.,.],[.,[[.,.],.]]],.]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 1

[5,8,6,3,2,1,4,7] => [[[[.,[[.,.],.]],.],.],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => 2

[8,7,1,6,3,5,4,2] => [[[.,.],.],[[[.,.],[[.,.],.]],.]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 2

[3,2,1,7,8,6,4,5] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 2

[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

[7,5,1,4,8,2,3,6] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[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

[8,4,3,1,7,5,6,2] => [[[[.,.],.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 3

[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

[7,4,3,1,8,5,2,6] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[7,8,1,6,3,4,5,2] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 0

[6,8,1,7,3,4,2,5] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[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

[6,3,7,5,2,4,1,8] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[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

[7,8,1,5,6,4,3,2] => [[.,[.,.]],[[[[.,[.,.]],.],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 0

[6,3,7,5,1,4,2,8] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[6,1,7,3,4,2,5,8] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[3,1,7,2,5,8,6,4] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 1

[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

[7,2,8,4,5,6,3,1] => [[[.,.],[[[.,.],[.,[.,.]]],.]],.] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 2

[6,8,7,3,2,4,5,1] => [[[[.,[[.,.],.]],.],[.,[.,.]]],.] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2

[7,5,8,6,4,1,3,2] => [[[[.,.],[[.,.],.]],.],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2

[2,3,1,8,4,6,5,7] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[2,3,1,7,6,8,4,5] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[2,3,1,8,4,6,7,5] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 0

[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

[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

[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

[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

[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

[6,3,2,8,1,7,5,4] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2

[5,3,8,7,6,2,1,4] => [[[[.,.],[[[.,.],.],.]],.],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 2

[4,1,6,2,7,5,3,8] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1

[7,6,2,5,3,1,4,8] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[4,3,1,7,6,2,5,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 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

[4,1,3,7,5,2,6,8] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 1

[4,1,6,3,2,7,5,8] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[7,5,4,1,3,2,6,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[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

[5,2,3,7,4,1,6,8] => [[[.,.],[.,[[.,.],.]]],[.,[.,.]]] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 1

[4,5,1,6,3,2,7,8] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0

[5,1,6,3,2,4,7,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1

[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

[5,1,6,2,4,3,7,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[5,3,4,8,7,6,2,1] => [[[[.,.],[.,[[[.,.],.],.]]],.],.] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 3

[8,3,1,6,7,5,4,2] => [[[.,.],.],[[[[.,[.,.]],.],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 2

[8,4,6,5,7,2,3,1] => [[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[8,5,7,2,4,3,6,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[8,5,3,6,4,7,2,1] => [[[[[.,.],.],[[.,.],[.,.]]],.],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 4

[8,2,5,3,6,7,4,1] => [[[.,.],[[.,.],[[.,[.,.]],.]]],.] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 2

[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

[7,6,4,5,2,1,8,3] => [[[[[.,.],.],[.,.]],.],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 3

[8,2,4,7,6,3,1,5] => [[[.,.],[[.,[[.,.],.]],.]],[.,.]] => [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 1

[8,7,5,1,4,6,3,2] => [[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[7,3,8,5,4,2,1,6] => [[[[.,.],[[[.,.],.],.]],.],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 2

[6,3,4,7,2,8,5,1] => [[[[.,.],[.,[.,.]]],[[.,.],.]],.] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 2

[8,1,7,3,6,4,2,5] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1

[7,1,8,5,3,4,2,6] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 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] => 2

[5,2,7,4,3,8,6,1] => [[[.,.],[[[.,.],.],[[.,.],.]]],.] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 2

[6,2,3,7,4,5,8,1] => [[[.,.],[.,[[.,.],[.,[.,.]]]]],.] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 2

[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

[6,4,2,7,1,5,8,3] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[4,2,5,3,6,7,8,1] => [[[.,.],[[.,.],[.,[.,[.,.]]]]],.] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 2

[5,4,2,8,7,6,1,3] => [[[[.,.],.],[[[.,.],.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 2

[8,6,3,2,5,7,4,1] => [[[[[.,.],.],.],[[.,[.,.]],.]],.] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 4

[7,3,2,1,6,5,8,4] => [[[[.,.],.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 3

[7,3,2,6,1,5,8,4] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[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

[6,8,2,5,1,7,4,3] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 0

[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

[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

[6,2,1,7,5,8,4,3] => [[[.,.],.],[[[[.,.],[.,.]],.],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 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

[5,1,7,2,6,4,8,3] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1

[4,1,7,6,5,8,2,3] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1

[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

[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

[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

[6,5,1,3,7,8,2,4] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 2

[7,2,1,4,3,5,8,6] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2

[6,1,2,4,3,7,8,5] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 1

[8,1,5,4,2,3,6,7] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1

[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

[7,1,2,6,5,3,8,4] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 1

[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

[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

[6,1,4,8,7,2,3,5] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 1

[6,1,8,5,7,2,3,4] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[6,1,7,5,8,2,3,4] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[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

[8,1,2,3,7,5,4,6] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 1

[6,1,8,7,5,2,3,4] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 1

[8,3,1,2,4,6,5,7] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 2

[8,3,1,2,4,5,7,6] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2

[6,3,1,2,4,7,5,8] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 2

[6,7,1,4,2,3,5,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0

[6,1,7,4,8,2,3,5] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[4,3,8,5,6,2,7,1] => [[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[4,3,8,6,7,2,5,1] => [[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[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

[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

[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

[6,1,5,4,8,2,7,3] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[6,2,5,4,7,1,8,3] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[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

[8,2,1,6,5,7,4,3] => [[[.,.],.],[[[[.,.],[.,.]],.],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 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

[3,5,1,6,4,8,2,7] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[4,8,2,5,6,1,3,7] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[5,3,8,4,2,7,6,1] => [[[[.,.],[[.,.],.]],[[.,.],.]],.] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 2

[8,7,2,4,6,3,1,5] => [[[[.,.],.],[[.,[.,.]],.]],[.,.]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 2

[8,7,3,2,1,6,4,5] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4

[7,8,3,4,6,5,2,1] => [[[[.,[.,.]],[.,[[.,.],.]]],.],.] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 2

[8,7,3,6,5,2,4,1] => [[[[[.,.],.],[[.,.],.]],[.,.]],.] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 3

[3,1,2,8,6,5,7,4] => [[.,.],[.,[[[[.,.],.],[.,.]],.]]] => [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 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

[8,7,1,4,5,3,6,2] => [[[.,.],.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[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

[8,4,1,3,2,5,7,6] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2

[7,3,8,6,2,1,4,5] => [[[[.,.],[[.,.],.]],.],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 2

[7,2,8,4,6,5,1,3] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[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

[6,7,5,2,4,8,3,1] => [[[[.,[.,.]],.],[[.,[.,.]],.]],.] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 2

[8,1,2,7,5,6,3,4] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 1

[8,2,7,3,4,6,1,5] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 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

[8,3,5,6,4,7,2,1] => [[[[.,.],[[.,[.,.]],[.,.]]],.],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[8,5,6,2,4,3,7,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[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

[6,8,4,5,1,3,2,7] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[6,4,8,7,5,3,2,1] => [[[[[.,.],[[[.,.],.],.]],.],.],.] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 4

[6,7,1,4,3,2,8,5] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[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

[5,8,1,3,4,2,7,6] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[3,2,7,6,8,4,5,1] => [[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2

[6,4,1,5,2,8,7,3] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 2

[7,6,5,3,1,8,2,4] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4

[2,6,1,5,7,4,8,3] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 0

[3,6,5,2,1,4,7,8] => [[[.,[[.,.],.]],.],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1

[5,4,2,6,3,7,8,1] => [[[[.,.],.],[[.,.],[.,[.,.]]]],.] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 3

[5,3,8,2,1,4,6,7] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2

[5,3,1,8,2,4,6,7] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2

[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

[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

[5,8,2,4,1,6,7,3] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0

[5,8,2,4,6,3,1,7] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 0

[5,8,2,4,3,6,1,7] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[5,8,1,4,6,2,3,7] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[5,1,8,4,6,7,2,3] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[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

[8,4,3,6,7,2,5,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3

[8,4,3,6,7,2,1,5] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3

[8,6,2,4,5,3,7,1] => [[[[.,.],.],[[.,[.,.]],[.,.]]],.] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 3

[8,6,2,4,5,3,1,7] => [[[[.,.],.],[[.,[.,.]],.]],[.,.]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 2

[3,8,1,6,2,4,5,7] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0

[3,8,6,2,1,4,5,7] => [[[.,[[.,.],.]],.],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1

[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

[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

[8,3,6,7,2,1,4,5] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2

[8,2,6,4,5,1,7,3] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[8,4,6,2,3,7,5,1] => [[[[.,.],[.,.]],[.,[[.,.],.]]],.] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 2

[8,4,7,2,1,3,6,5] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2

[2,7,1,6,3,5,8,4] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 0

[8,4,2,1,5,3,7,6] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3

[8,2,1,4,7,3,6,5] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[2,1,5,8,7,3,6,4] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 1

[3,2,1,6,7,4,8,5] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[4,3,1,7,8,5,2,6] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 2

[5,3,2,7,8,6,4,1] => [[[[.,.],.],[[[.,[.,.]],.],.]],.] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 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] => 2

[7,3,5,6,4,2,8,1] => [[[[.,.],[[.,[.,.]],.]],[.,.]],.] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[3,2,4,8,7,5,6,1] => [[[.,.],[.,[[[.,.],.],[.,.]]]],.] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 2

[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

[3,8,1,6,4,5,2,7] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[8,1,3,6,5,4,2,7] => [[.,.],[[.,[[[.,.],.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 1

[7,4,3,6,2,1,8,5] => [[[[[.,.],.],[.,.]],.],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 3

[7,2,1,5,3,4,8,6] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2

[5,7,2,3,1,4,8,6] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 0

[7,1,5,2,4,6,8,3] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 1

[8,4,2,7,3,5,6,1] => [[[[.,.],.],[[.,.],[.,[.,.]]]],.] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 3

[7,4,1,5,8,6,3,2] => [[[.,.],.],[[[.,[[.,.],.]],.],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 2

[4,1,8,6,3,7,5,2] => [[.,.],[[[[.,.],.],[[.,.],.]],.]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 1

[8,4,3,1,6,2,5,7] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[7,5,4,3,8,1,6,2] => [[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3

[5,3,1,6,2,8,7,4] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 2

[3,2,5,7,8,4,6,1] => [[[.,.],[[.,[.,[.,.]]],[.,.]]],.] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[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

[6,1,3,7,4,5,2,8] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 1

[2,6,1,8,5,3,4,7] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0

[4,1,5,3,8,6,7,2] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 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

[7,1,3,2,4,5,6,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1

[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

[8,5,4,6,1,7,3,2] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2

[5,3,2,1,4,6,8,7] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3

[5,3,2,4,7,1,8,6] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[4,8,1,7,3,5,6,2] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 0

[5,3,2,4,6,8,1,7] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2

[7,6,4,2,8,3,1,5] => [[[[[.,.],.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3

[8,5,2,4,3,7,1,6] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2

[8,5,1,4,3,7,6,2] => [[[.,.],.],[[[.,.],[[.,.],.]],.]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 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] => 0

[8,1,2,4,7,6,5,3] => [[.,.],[.,[[.,[[[.,.],.],.]],.]]] => [1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 1

[3,4,1,8,6,7,5,2] => [[.,[.,.]],[[[[.,.],[.,.]],.],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 0

[4,3,8,5,1,7,6,2] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[6,1,3,2,8,5,7,4] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1

[8,5,3,2,4,7,1,6] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3

[6,7,4,2,5,8,3,1] => [[[[.,[.,.]],.],[[.,[.,.]],.]],.] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 2

[8,5,4,2,6,3,1,7] => [[[[[.,.],.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3

[8,5,2,1,6,4,3,7] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[8,4,6,5,1,3,2,7] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 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

[5,7,2,6,1,4,8,3] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0

[8,4,7,5,2,1,3,6] => [[[[.,.],[[.,.],.]],.],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 2

[5,2,7,4,6,8,3,1] => [[[.,.],[[[.,.],[.,[.,.]]],.]],.] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 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

[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

[3,5,1,4,2,8,7,6] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 0

[3,5,1,4,2,6,8,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0

[3,5,1,4,2,6,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0

[8,6,2,4,5,7,1,3] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2

[6,5,2,4,1,3,8,7] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[7,6,3,2,5,1,8,4] => [[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 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

[4,6,3,7,5,8,2,1] => [[[[.,[.,.]],[[.,.],[.,.]]],.],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 2

[4,2,5,7,8,6,3,1] => [[[.,.],[[.,[[.,[.,.]],.]],.]],.] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 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

[4,2,5,8,7,6,3,1] => [[[.,.],[[.,[[[.,.],.],.]],.]],.] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 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] => 0

[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

[7,2,8,3,1,6,4,5] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[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

[8,5,1,2,3,7,4,6] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 2

[8,7,2,5,1,4,3,6] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[8,4,1,3,2,7,6,5] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 2

[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

[8,6,5,1,7,4,2,3] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[3,8,4,2,1,7,6,5] => [[[.,[[.,.],.]],.],[[[.,.],.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1

[8,3,1,7,5,6,2,4] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[8,4,1,7,5,2,6,3] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[8,4,2,7,5,3,1,6] => [[[[.,.],.],[[[.,.],.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 2

[8,4,3,7,5,1,2,6] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[8,5,7,6,4,3,1,2] => [[[[[.,.],[[.,.],.]],.],.],[.,.]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 3

[8,4,7,6,5,2,1,3] => [[[[.,.],[[[.,.],.],.]],.],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 2

[8,3,1,4,7,6,2,5] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 2

[8,3,5,7,6,2,4,1] => [[[[.,.],[.,[[.,.],.]]],[.,.]],.] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 2

[3,6,2,4,8,1,7,5] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0

[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

[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

[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

[7,2,8,4,1,3,5,6] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1

[6,1,7,3,2,8,4,5] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[6,2,1,7,3,8,4,5] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[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

[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

[7,4,2,8,3,1,5,6] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[7,4,2,8,3,5,1,6] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 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

[5,7,1,4,6,2,8,3] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[6,3,1,4,7,8,2,5] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 2

[4,3,8,6,5,2,7,1] => [[[[.,.],[[[.,.],.],.]],[.,.]],.] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 2

[5,4,7,3,1,2,6,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2

[3,1,2,6,5,7,8,4] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 1

[7,3,2,6,1,4,8,5] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[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

[7,2,6,8,5,4,3,1] => [[[.,.],[[[[.,[.,.]],.],.],.]],.] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 2

[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

[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

[6,5,2,1,3,8,4,7] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3

[6,3,1,2,7,8,4,5] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 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

[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

[8,5,6,7,2,1,4,3] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 2

[4,1,3,8,5,2,7,6] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 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

[5,1,7,3,2,8,4,6] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[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

[8,7,3,6,2,4,1,5] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[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

[6,3,1,2,7,8,5,4] => [[[.,.],.],[.,[[[.,[.,.]],.],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 2

[8,2,7,5,3,4,1,6] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[6,3,1,2,8,7,5,4] => [[[.,.],.],[.,[[[[.,.],.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 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

[7,6,3,4,2,1,8,5] => [[[[[.,.],.],[.,.]],.],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 3

[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

[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

[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

[8,6,3,4,7,2,1,5] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3

[4,3,8,6,7,5,1,2] => [[[.,.],[[[.,.],[.,.]],.]],[.,.]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1

[4,5,1,6,7,3,2,8] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 0

[2,5,1,8,3,7,4,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[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

[7,1,5,4,2,6,3,8] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[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

[7,5,4,1,6,8,2,3] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3

[8,5,2,1,7,6,3,4] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[7,2,1,8,5,6,4,3] => [[[.,.],.],[[[[.,.],[.,.]],.],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 2

[6,3,5,4,8,1,2,7] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[2,5,1,4,6,3,8,7] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[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

[8,5,6,4,3,1,7,2] => [[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 3

[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

[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

[5,3,7,6,4,8,2,1] => [[[[.,.],[[[.,.],.],[.,.]]],.],.] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 3

[8,6,1,4,3,7,2,5] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[8,4,7,5,1,6,3,2] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[2,1,5,3,7,8,6,4] => [[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 1

[5,1,4,7,6,8,2,3] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 1

[8,4,1,3,7,6,5,2] => [[[.,.],.],[[.,[[[.,.],.],.]],.]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 2

[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

[8,1,4,2,6,5,7,3] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1

[8,6,4,3,7,2,1,5] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 4

[5,8,1,4,3,2,6,7] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0

[5,6,4,3,8,2,7,1] => [[[[[.,[.,.]],.],[.,.]],[.,.]],.] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[7,8,1,4,3,2,5,6] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0

[7,1,8,4,5,3,6,2] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 1

[4,3,1,8,6,5,7,2] => [[[.,.],.],[[[[.,.],.],[.,.]],.]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 2

[4,3,2,7,5,1,8,6] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[5,2,3,7,4,1,8,6] => [[[.,.],[.,[[.,.],.]]],[[.,.],.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 1

[2,1,7,4,3,6,8,5] => [[.,.],[[[.,.],.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 1

[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

[8,7,1,3,4,5,6,2] => [[[.,.],.],[[.,[.,[.,[.,.]]]],.]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[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

[6,5,3,4,1,7,8,2] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 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] => 0

[6,8,2,3,1,5,7,4] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0

[4,3,1,5,2,7,8,6] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 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

[7,2,1,3,5,6,8,4] => [[[.,.],.],[.,[[.,[.,[.,.]]],.]]] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[7,3,6,4,5,8,1,2] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[6,4,3,7,5,8,2,1] => [[[[[.,.],.],[[.,.],[.,.]]],.],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 4

[5,2,4,7,8,6,3,1] => [[[.,.],[[.,[[.,[.,.]],.]],.]],.] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 2

[5,4,8,7,2,3,1,6] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 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

[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

[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

[6,5,7,2,1,8,4,3] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 2

[7,4,1,3,8,5,6,2] => [[[.,.],.],[[.,[[.,.],[.,.]]],.]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 2

[2,1,8,4,7,6,3,5] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1

[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

[7,5,6,3,8,2,1,4] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 2

[7,4,2,6,1,5,8,3] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[8,4,1,6,2,5,7,3] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 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

[8,4,2,7,6,1,5,3] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 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

[8,4,7,6,1,2,5,3] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 1

[8,7,6,2,1,5,3,4] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4

[6,8,7,4,2,5,1,3] => [[[[.,[[.,.],.]],.],[.,.]],[.,.]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[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

[4,1,2,6,5,3,7,8] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 1

[4,6,1,3,5,2,7,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[4,2,6,3,5,1,7,8] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[4,6,1,2,5,3,7,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 0

[5,8,4,7,1,3,6,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0

[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

[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

[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

[4,2,8,6,7,1,3,5] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[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

[5,3,1,6,4,7,2,8] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[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

[5,6,1,4,8,3,2,7] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 0

[5,2,6,3,7,8,4,1] => [[[.,.],[[.,.],[[.,[.,.]],.]]],.] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 2

[2,4,1,3,7,8,6,5] => [[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 0

[2,6,1,5,7,8,4,3] => [[.,[.,.]],[[[.,[.,[.,.]]],.],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 0

[5,1,6,4,7,8,2,3] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[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

[5,7,4,8,1,2,6,3] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 0

[2,7,1,6,8,4,5,3] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 0

[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

[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

[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

[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

[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

[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

[5,7,1,4,3,2,6,8] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0

[7,8,5,3,2,1,6,4] => [[[[[.,[.,.]],.],.],.],[[.,.],.]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 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

[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

[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

[5,4,1,7,3,2,8,6] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[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

[6,3,2,5,7,4,8,1] => [[[[.,.],.],[[.,[.,.]],[.,.]]],.] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 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] => 0

[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

[6,3,2,5,1,7,8,4] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[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

[3,7,1,2,8,6,5,4] => [[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => 0

[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

[5,8,2,7,6,3,1,4] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 0

[2,5,1,8,4,7,6,3] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 0

[3,4,2,8,1,7,6,5] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 0

[3,1,8,2,6,7,5,4] => [[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 1

[2,6,1,5,8,7,3,4] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 0

[8,1,7,3,5,2,4,6] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[8,1,3,2,7,6,4,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1

[7,3,4,8,6,2,5,1] => [[[[.,.],[.,[[.,.],.]]],[.,.]],.] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 2

[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

[6,2,5,3,8,1,4,7] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[7,6,1,3,5,2,4,8] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[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

[6,1,5,4,7,2,3,8] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[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

[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

[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

[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

[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

[4,8,1,3,7,6,2,5] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 0

[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

[6,4,2,3,1,8,7,5] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2

[6,5,2,1,3,8,7,4] => [[[[.,.],.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 3

[7,6,1,8,2,5,3,4] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[8,4,2,3,7,6,1,5] => [[[[.,.],.],[.,[[.,.],.]]],[.,.]] => [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 2

[5,7,6,4,2,1,3,8] => [[[[.,[[.,.],.]],.],.],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => 2

[6,5,7,4,1,3,2,8] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2

[4,6,1,8,3,5,2,7] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[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

[4,7,1,8,3,2,5,6] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0

[4,8,3,6,1,5,2,7] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[3,2,8,6,4,5,1,7] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[8,4,3,6,2,5,1,7] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[3,1,2,6,8,7,5,4] => [[.,.],[.,[[[.,[[.,.],.]],.],.]]] => [1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 1

[5,7,4,2,1,8,6,3] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 2

[8,6,5,7,2,4,3,1] => [[[[[.,.],.],[.,.]],[[.,.],.]],.] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[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

[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

[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

[7,4,8,3,6,2,1,5] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 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

[6,2,4,5,8,3,7,1] => [[[.,.],[[.,[.,[.,.]]],[.,.]]],.] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[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

[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

[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

[6,8,2,4,1,7,3,5] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[7,5,1,6,2,4,8,3] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[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

[4,5,2,3,8,7,1,6] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 0

[5,2,3,7,6,1,4,8] => [[[.,.],[.,[[.,.],.]]],[.,[.,.]]] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 1

[4,2,3,7,6,1,5,8] => [[[.,.],[.,[[.,.],.]]],[.,[.,.]]] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 1

[4,2,7,3,5,1,6,8] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[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

[5,6,2,3,1,7,8,4] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0

[5,7,2,3,4,1,6,8] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[6,2,7,3,5,1,4,8] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[7,2,6,3,5,1,4,8] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[6,5,2,3,1,7,8,4] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[6,5,2,3,8,4,7,1] => [[[[.,.],.],[.,[[.,.],[.,.]]]],.] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 3

[7,5,2,1,4,6,8,3] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 3

[8,5,2,3,1,6,4,7] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[8,6,2,3,1,5,4,7] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[8,2,6,3,1,7,4,5] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[8,5,2,7,3,4,6,1] => [[[[.,.],.],[[.,.],[.,[.,.]]]],.] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 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

[6,8,2,3,1,5,4,7] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[5,8,2,3,1,6,4,7] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[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

[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

[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

[4,2,1,5,3,7,6,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[5,1,3,8,4,6,7,2] => [[.,.],[[.,[[.,.],[.,[.,.]]]],.]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 1

[5,1,3,2,6,7,8,4] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 1

[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

[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

[7,2,1,3,5,8,4,6] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 2

[6,2,7,3,4,5,1,8] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[5,2,1,3,6,7,8,4] => [[[.,.],.],[.,[[.,[.,[.,.]]],.]]] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[7,5,2,6,1,8,4,3] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2

[6,1,5,2,7,8,4,3] => [[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 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] => 2

[8,3,7,5,1,4,2,6] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[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

[8,3,2,6,4,5,1,7] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2

[8,5,3,7,4,1,2,6] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[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

[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

[8,5,7,3,2,6,1,4] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2

[8,1,2,3,6,4,7,5] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 1

[7,6,2,3,5,8,1,4] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 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] => 0

[3,4,2,8,1,6,7,5] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0

[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

[4,3,7,5,1,6,2,8] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[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

[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

[5,3,7,4,2,8,6,1] => [[[[.,.],[[.,.],.]],[[.,.],.]],.] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 2

[7,4,8,2,3,5,6,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2

[5,6,2,8,7,1,4,3] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[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

[4,1,6,3,5,7,2,8] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 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

[7,2,5,8,6,1,4,3] => [[[.,.],[.,[[.,.],.]]],[[.,.],.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 1

[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

[5,3,1,4,6,7,8,2] => [[[.,.],.],[[.,[.,[.,[.,.]]]],.]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 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] => 0

[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

[3,6,2,4,1,7,5,8] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[3,2,6,7,4,8,5,1] => [[[.,.],[[.,[.,.]],[[.,.],.]]],.] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 2

[7,1,3,8,4,5,2,6] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 1

[7,1,8,3,4,6,2,5] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[6,3,2,7,5,8,4,1] => [[[[.,.],.],[[[.,.],[.,.]],.]],.] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[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

[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

[5,4,1,2,6,7,3,8] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 2

[6,5,2,7,4,1,3,8] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[6,5,7,3,1,4,2,8] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2

[6,7,4,3,1,5,8,2] => [[[[.,[.,.]],.],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 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

[7,4,5,6,2,1,8,3] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 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

[6,4,1,2,7,8,3,5] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 2

[6,4,1,3,5,2,7,8] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[5,1,8,3,4,6,2,7] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[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

[6,8,1,5,4,2,3,7] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0

[4,7,2,5,1,6,8,3] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0

[6,5,4,7,2,8,3,1] => [[[[[.,.],.],[.,.]],[[.,.],.]],.] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3

[3,2,4,6,5,8,1,7] => [[[.,.],[.,[[.,.],[.,.]]]],[.,.]] => [1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1

[7,5,2,1,6,3,4,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[6,3,1,7,4,2,5,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[8,7,2,1,5,3,6,4] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3

[6,8,5,3,7,4,2,1] => [[[[[.,[.,.]],.],[[.,.],.]],.],.] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 3

[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

[8,3,6,4,1,5,7,2] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 1

[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

[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

[8,4,1,2,3,6,7,5] => [[[.,.],.],[.,[.,[[.,[.,.]],.]]]] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[5,6,4,2,1,8,3,7] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 2

[6,8,1,3,2,7,5,4] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 0

[5,7,3,6,4,1,2,8] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 0

[7,2,4,3,8,1,5,6] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[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

[6,1,2,4,3,5,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 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] => 2

[6,1,2,4,3,5,8,7] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 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] => 0

[8,4,1,5,2,6,7,3] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[5,3,2,6,8,7,1,4] => [[[[.,.],.],[.,[[.,.],.]]],[.,.]] => [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 2

[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

[8,5,2,6,7,1,4,3] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[5,3,8,7,1,4,2,6] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[6,4,5,3,1,8,7,2] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 2

[8,5,1,2,3,6,7,4] => [[[.,.],.],[.,[.,[[.,[.,.]],.]]]] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[8,3,2,6,1,5,7,4] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[8,6,4,7,1,3,2,5] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[3,1,4,7,6,2,5,8] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 1

[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

[2,7,1,4,6,3,5,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[7,3,1,6,5,2,4,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[7,1,5,2,4,6,3,8] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[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

[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

[7,1,2,3,6,4,5,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1

[7,4,1,3,6,5,2,8] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 2

[5,7,2,8,1,3,6,4] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 0

[5,4,1,2,6,3,8,7] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2

[6,5,1,4,7,3,2,8] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 2

[5,2,8,3,4,1,6,7] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[4,1,7,3,8,6,2,5] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1

[8,4,1,2,5,3,7,6] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 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] => 0

[7,4,2,8,6,5,1,3] => [[[[.,.],.],[[[.,.],.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 2

[8,6,5,2,7,1,4,3] => [[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3

[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

[7,5,8,2,1,6,4,3] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 2

[3,2,1,6,5,8,4,7] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[6,3,1,4,5,8,2,7] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 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] => 0

[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

[4,6,1,3,2,8,5,7] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[3,2,8,4,5,7,1,6] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[6,1,8,2,4,5,3,7] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[8,3,6,4,2,7,1,5] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[8,3,7,5,4,1,2,6] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 1

[5,4,3,7,6,1,8,2] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[8,6,3,7,1,4,2,5] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[3,1,2,8,7,6,4,5] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 1

[8,5,4,1,2,3,7,6] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3

[8,3,2,1,6,4,7,5] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3

[4,6,1,3,2,7,8,5] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 0

[6,7,2,5,8,4,1,3] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 0

[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

[6,3,1,5,8,4,2,7] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 2

[3,2,8,5,6,1,4,7] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[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

[4,3,2,5,7,8,1,6] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2

[8,5,4,7,6,3,1,2] => [[[[[.,.],.],[[.,.],.]],.],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 3

[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

[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

[7,4,1,6,2,8,5,3] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 2

[7,3,1,6,5,2,8,4] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[8,5,4,1,6,2,7,3] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 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] => 0

[7,8,6,2,1,5,4,3] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 2

[2,1,3,8,7,5,6,4] => [[.,.],[.,[[[[.,.],.],[.,.]],.]]] => [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 1

[8,1,7,3,6,5,2,4] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1

[4,8,1,6,3,7,2,5] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[3,8,1,4,6,5,2,7] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 0

[4,6,1,8,5,3,2,7] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 0

[3,8,5,2,1,6,4,7] => [[[.,[[.,.],.]],.],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[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

[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

[8,5,2,6,3,4,7,1] => [[[[.,.],.],[[.,.],[.,[.,.]]]],.] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 3

[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

[3,7,6,2,1,8,5,4] => [[[.,[[.,.],.]],.],[[[.,.],.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1

[4,3,7,6,1,8,5,2] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[8,6,3,2,7,1,5,4] => [[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3

[6,8,1,5,4,7,2,3] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[6,7,2,5,4,8,1,3] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[7,6,2,4,8,5,1,3] => [[[[.,.],.],[.,[[.,.],.]]],[.,.]] => [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 2

[6,1,8,2,4,3,5,7] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[8,5,2,7,3,6,4,1] => [[[[.,.],.],[[.,.],[[.,.],.]]],.] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3

[5,4,8,7,1,2,6,3] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 1

[8,6,3,5,2,1,4,7] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3

[8,7,3,5,2,4,6,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3

[8,4,2,7,6,5,1,3] => [[[[.,.],.],[[[.,.],.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 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

[4,1,3,8,5,6,2,7] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 1

[5,2,8,3,1,6,7,4] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 1

[5,7,6,2,1,8,3,4] => [[[.,[[.,.],.]],.],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[4,2,5,3,8,6,7,1] => [[[.,.],[[.,.],[[.,.],[.,.]]]],.] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 2

[3,2,7,4,8,5,6,1] => [[[.,.],[[.,.],[[.,.],[.,.]]]],.] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 2

[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

[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

[4,5,2,8,3,7,1,6] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[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

[8,7,5,1,6,4,3,2] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3

[7,3,1,8,4,5,6,2] => [[[.,.],.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[3,2,8,7,4,5,6,1] => [[[.,.],[[[.,.],.],[.,[.,.]]]],.] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 2

[6,2,4,3,7,5,8,1] => [[[.,.],[[.,.],[[.,.],[.,.]]]],.] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 2

[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

[7,5,2,8,3,1,6,4] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 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] => 0

[6,2,5,4,1,7,8,3] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 1

[8,5,1,6,3,2,4,7] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[8,1,5,4,6,7,3,2] => [[.,.],[[[[.,.],[.,[.,.]]],.],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 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

[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

[6,1,3,5,4,8,2,7] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 1

[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

[8,4,1,2,7,6,5,3] => [[[.,.],.],[.,[[[[.,.],.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 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] => 2

[5,3,1,2,4,6,8,7] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2

[8,5,7,3,1,2,4,6] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2

[3,1,2,8,7,5,4,6] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 1

[6,7,1,5,2,8,4,3] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 0

[4,8,1,3,6,2,7,5] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[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

[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

[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

[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

[4,8,1,6,2,5,3,7] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[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

[7,1,4,2,6,8,3,5] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[8,7,1,3,2,5,4,6] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[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

[4,1,6,8,7,2,3,5] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 1

[6,1,7,3,5,8,2,4] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[2,1,8,7,3,5,4,6] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[6,1,8,5,7,4,3,2] => [[.,.],[[[[[.,.],[.,.]],.],.],.]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 1

[8,5,1,4,7,6,3,2] => [[[.,.],.],[[[.,[[.,.],.]],.],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 2

[5,3,1,6,4,8,2,7] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[4,7,5,3,2,8,1,6] => [[[[.,[[.,.],.]],.],[.,.]],[.,.]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[5,8,1,2,7,4,3,6] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 0

[6,3,1,8,2,4,5,7] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2

[4,6,3,7,8,1,5,2] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0

[6,3,1,8,4,5,2,7] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[7,6,2,4,8,3,1,5] => [[[[.,.],.],[[.,[.,.]],.]],[.,.]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 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

[8,1,4,2,7,5,6,3] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1

[8,6,3,5,2,1,7,4] => [[[[[.,.],.],[.,.]],.],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 3

[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

[2,5,1,8,7,3,4,6] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0

[7,2,4,3,8,6,1,5] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[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

[3,7,1,4,6,8,2,5] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 0

[8,5,7,6,1,3,2,4] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[6,5,2,8,7,1,4,3] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[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

[2,6,1,3,8,5,4,7] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 0

[6,4,1,8,3,2,5,7] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[5,8,1,4,2,7,3,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[2,3,1,6,8,7,4,5] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 0

[6,4,8,2,1,7,3,5] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2

[2,3,1,8,7,5,6,4] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 0

[6,8,3,7,1,2,5,4] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 0

[6,7,4,5,1,3,8,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0

[8,7,4,5,1,3,2,6] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[8,5,1,2,7,4,3,6] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 2

[4,1,8,7,2,5,3,6] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[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

[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

[8,1,7,2,4,6,3,5] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[4,8,1,2,6,3,7,5] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 0

[5,8,1,2,6,3,7,4] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 0

[4,1,2,6,5,7,8,3] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 1

[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

[8,4,3,6,1,7,2,5] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[2,6,1,8,3,7,4,5] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[8,4,2,1,3,7,5,6] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3

[2,5,1,7,6,8,3,4] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[5,3,1,8,2,4,7,6] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2

[5,1,8,3,2,4,7,6] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1

[3,1,5,4,6,7,8,2] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 1

[7,4,2,1,3,8,5,6] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3

[7,2,1,3,8,5,4,6] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 2

[2,1,7,3,8,6,4,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1

[3,4,1,6,5,7,8,2] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 0

[3,1,8,7,5,2,6,4] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 1

[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

[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

[5,4,3,1,2,7,6,8] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3

[4,1,6,5,2,3,7,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1

[7,1,5,2,3,6,4,8] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 1

[4,1,6,3,7,2,5,8] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[4,6,1,2,8,3,7,5] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 0

[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

[6,5,3,7,2,4,1,8] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2

[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

[5,6,1,4,7,2,3,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[8,6,5,2,1,7,4,3] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4

[4,3,8,6,7,1,5,2] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[8,3,2,4,7,1,6,5] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[7,3,2,8,6,1,5,4] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[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

[7,4,1,2,6,5,8,3] => [[[.,.],.],[.,[[[.,.],[.,.]],.]]] => [1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2

[5,2,7,4,6,1,8,3] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[7,4,1,2,3,6,8,5] => [[[.,.],.],[.,[.,[[.,[.,.]],.]]]] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[5,4,8,6,3,2,1,7] => [[[[[.,.],[[.,.],.]],.],.],[.,.]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 3

[8,4,6,7,3,1,5,2] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 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

[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

[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

[8,5,6,2,1,4,7,3] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[2,1,6,4,7,8,3,5] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[7,8,4,5,6,1,3,2] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0

[2,5,1,8,4,6,7,3] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 0

[6,5,8,3,4,2,1,7] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 2

[8,2,7,6,3,4,5,1] => [[[.,.],[[[.,.],.],[.,[.,.]]]],.] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 2

[6,8,7,3,2,1,4,5] => [[[[.,[[.,.],.]],.],.],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => 2

[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

[7,8,1,2,4,6,3,5] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 0

[7,2,8,3,4,5,1,6] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[6,1,8,3,4,2,5,7] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[7,5,1,2,4,3,8,6] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2

[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

[2,1,7,6,3,4,5,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1

[6,1,5,3,8,2,4,7] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[3,2,4,8,6,1,7,5] => [[[.,.],[.,[[.,.],.]]],[[.,.],.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 1

[2,1,3,8,4,5,7,6] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 1

[3,1,2,8,5,4,7,6] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 1

[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

[2,1,3,8,4,7,6,5] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 1

[3,1,2,8,4,5,7,6] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 1

[3,2,6,5,7,8,1,4] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[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

[6,1,5,4,2,3,8,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1

[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

[8,4,1,5,7,6,3,2] => [[[.,.],.],[[[.,[[.,.],.]],.],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 2

[8,1,6,3,5,2,4,7] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[4,6,2,5,3,8,1,7] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[4,6,5,2,1,8,3,7] => [[[.,[[.,.],.]],.],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[5,8,4,3,6,7,2,1] => [[[[[.,[.,.]],.],[.,[.,.]]],.],.] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3

[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

[3,2,6,5,1,8,4,7] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[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

[5,1,8,4,6,7,3,2] => [[.,.],[[[[.,.],[.,[.,.]]],.],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 1

[6,5,3,8,1,7,2,4] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 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

[8,1,4,6,5,7,2,3] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 1

[8,1,7,5,6,4,2,3] => [[.,.],[[[[.,.],[.,.]],.],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 1

[8,6,1,5,3,7,2,4] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[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

[6,3,8,7,2,1,5,4] => [[[[.,.],[[.,.],.]],.],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2

[7,2,5,6,3,4,8,1] => [[[.,.],[[.,[.,.]],[.,[.,.]]]],.] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2

[7,2,8,6,3,1,5,4] => [[[.,.],[[[.,.],.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 1

[7,2,4,5,8,6,3,1] => [[[.,.],[[.,[.,[[.,.],.]]],.]],.] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 2

[6,3,8,4,7,2,5,1] => [[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[7,2,3,6,8,5,4,1] => [[[.,.],[.,[[[.,[.,.]],.],.]]],.] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 2

[7,2,8,5,4,1,3,6] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 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

[7,5,4,2,8,1,6,3] => [[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3

[7,6,3,2,8,4,5,1] => [[[[[.,.],.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 4

[7,2,3,6,8,4,5,1] => [[[.,.],[.,[[.,[.,.]],[.,.]]]],.] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[7,2,5,4,8,3,6,1] => [[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2

[7,2,8,3,6,1,4,5] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 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] => 2

[5,1,3,2,4,6,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 1

[6,5,3,4,1,8,2,7] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[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

[7,2,4,6,3,8,5,1] => [[[.,.],[[.,[.,.]],[[.,.],.]]],.] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 2

[5,4,2,6,8,7,3,1] => [[[[.,.],.],[[.,[[.,.],.]],.]],.] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 3

[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

[3,2,8,7,4,6,5,1] => [[[.,.],[[[.,.],.],[[.,.],.]]],.] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 2

[8,2,6,5,1,4,3,7] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 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] => 0

[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

[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

[3,2,5,7,4,8,6,1] => [[[.,.],[[.,[.,.]],[[.,.],.]]],.] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 2

[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

[4,2,5,6,7,3,8,1] => [[[.,.],[[.,[.,[.,.]]],[.,.]]],.] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[8,6,1,4,3,5,2,7] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[6,1,8,4,3,5,2,7] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1

[5,1,6,4,8,2,3,7] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[8,1,4,2,5,3,6,7] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[8,4,1,3,5,2,6,7] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[4,1,8,3,5,2,6,7] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[8,3,1,2,5,4,6,7] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2

[3,1,8,2,5,4,6,7] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 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

[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

[7,3,2,4,6,8,1,5] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2

[8,2,5,4,1,3,7,6] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 1

[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

[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

[7,5,3,8,6,2,1,4] => [[[[[.,.],.],[[.,.],.]],.],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 3

[7,3,1,8,2,6,5,4] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 2

[5,1,2,8,6,7,3,4] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 1

[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

[5,1,7,6,8,2,3,4] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[7,1,6,2,4,5,3,8] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[5,7,1,6,2,3,4,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0

[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

[2,1,3,6,5,8,4,7] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 1

[5,1,2,8,6,3,7,4] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 1

[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

[4,6,1,5,7,2,8,3] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[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

[8,1,6,5,2,7,4,3] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 1

[6,8,1,5,2,7,4,3] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 0

[4,3,1,8,2,6,7,5] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[4,8,1,3,2,5,7,6] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0

[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

[8,1,2,4,3,5,7,6] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 1

[3,1,7,4,8,6,5,2] => [[.,.],[[[.,.],[[[.,.],.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 1

[6,4,5,3,2,8,7,1] => [[[[[.,.],[.,.]],.],[[.,.],.]],.] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3

[8,7,3,2,5,6,4,1] => [[[[[.,.],.],.],[[.,[.,.]],.]],.] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 4

[3,1,8,2,6,5,4,7] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1

[7,6,2,8,1,4,5,3] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[8,4,2,3,1,5,7,6] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[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

[7,1,6,2,4,8,3,5] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[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

[2,1,8,5,3,4,6,7] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1

[8,4,1,3,2,5,6,7] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2

[8,6,1,2,3,5,4,7] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 2

[7,8,1,5,2,4,6,3] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 0

[5,7,2,8,4,1,6,3] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[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

[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

[7,5,1,8,4,6,3,2] => [[[.,.],.],[[[[.,.],[.,.]],.],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 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] => 0

[7,3,6,2,5,4,8,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[5,3,2,1,7,8,4,6] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3

[8,4,1,3,6,7,2,5] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 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

[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

[4,6,2,5,1,7,8,3] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0

[2,3,1,7,4,8,6,5] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 0

[2,1,7,4,8,5,3,6] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1

[8,1,7,3,2,5,4,6] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[7,8,5,2,6,4,3,1] => [[[[.,[.,.]],.],[[[.,.],.],.]],.] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 2

[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

[8,2,5,3,6,1,4,7] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[6,8,7,4,1,5,2,3] => [[[.,[[.,.],.]],.],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[8,6,4,7,5,1,3,2] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[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

[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

[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

[4,8,1,2,6,5,3,7] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 0

[7,1,6,3,2,4,8,5] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1

[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

[7,4,1,3,6,8,5,2] => [[[.,.],.],[[.,[[.,[.,.]],.]],.]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 2

[7,1,8,3,2,6,5,4] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 1

[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

[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

[6,3,8,5,7,1,4,2] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[3,7,1,6,5,8,2,4] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[7,4,3,6,8,2,1,5] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 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] => 2

[3,2,8,5,1,4,6,7] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1

[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

[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

[8,5,7,6,3,4,1,2] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[7,5,2,6,1,4,8,3] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[7,2,8,5,3,4,1,6] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[6,4,5,3,1,7,8,2] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 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

[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

[4,5,3,7,8,1,2,6] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[8,6,1,5,4,2,7,3] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[4,8,2,6,1,5,7,3] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0

[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

[5,6,2,7,8,3,1,4] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 0

[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

[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

[5,1,4,8,7,3,6,2] => [[.,.],[[[.,[[.,.],.]],[.,.]],.]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 1

[4,3,1,8,7,5,6,2] => [[[.,.],.],[[[[.,.],.],[.,.]],.]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 2

[4,3,2,7,6,1,5,8] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[7,2,6,5,3,1,4,8] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 1

[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

[4,3,2,8,1,7,5,6] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[7,5,4,1,6,3,8,2] => [[[[.,.],.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 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

[5,1,4,3,2,6,8,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1

[7,2,1,3,5,4,6,8] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2

[8,3,7,5,4,2,6,1] => [[[[.,.],[[[.,.],.],.]],[.,.]],.] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 2

[5,4,1,8,7,3,6,2] => [[[.,.],.],[[[[.,.],.],[.,.]],.]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 2

[6,2,4,7,5,3,1,8] => [[[.,.],[[.,[[.,.],.]],.]],[.,.]] => [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 1

[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

[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

[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

[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

[8,1,5,2,4,7,3,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[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

[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

[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

[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

[6,7,2,3,8,1,4,5] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[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

[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

[7,4,6,8,3,1,2,5] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2

[8,5,4,7,3,1,2,6] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3

[7,3,2,1,5,4,8,6] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3

[5,4,1,2,7,6,3,8] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 2

[5,8,7,3,1,2,4,6] => [[[.,[[.,.],.]],.],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1

[4,1,2,8,7,3,6,5] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 1

[6,1,2,4,3,8,7,5] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 1

[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

[8,4,3,1,2,6,5,7] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 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] => 0

[8,6,2,3,5,4,1,7] => [[[[.,.],.],[.,[[.,.],.]]],[.,.]] => [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 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

[8,4,3,7,2,5,6,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3

[8,3,1,7,4,5,2,6] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[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

[6,8,2,4,5,1,7,3] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0

[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

[8,4,3,7,1,5,6,2] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 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] => 2

[8,1,3,7,6,4,5,2] => [[.,.],[[.,[[[.,.],.],[.,.]]],.]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 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

[8,7,3,6,1,2,5,4] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[8,3,7,6,2,4,5,1] => [[[[.,.],[[.,.],.]],[.,[.,.]]],.] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 2

[8,7,2,3,6,1,5,4] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 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

[5,1,8,4,2,3,7,6] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1

[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

[8,2,7,6,3,1,4,5] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 1

[6,8,1,4,7,3,2,5] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 0

[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

[5,8,2,7,3,1,6,4] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[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

[8,4,1,7,5,6,2,3] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[8,2,4,7,6,5,1,3] => [[[.,.],[.,[[[.,.],.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 1

[8,2,7,6,4,5,1,3] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[8,4,7,2,3,6,5,1] => [[[[.,.],[.,.]],[.,[[.,.],.]]],.] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 2

[8,2,4,7,3,6,5,1] => [[[.,.],[[.,[.,.]],[[.,.],.]]],.] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 2

[8,1,7,6,4,5,2,3] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1

[8,1,2,7,6,4,5,3] => [[.,.],[.,[[[[.,.],.],[.,.]],.]]] => [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 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

[2,8,1,5,3,7,6,4] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 0

[5,8,2,3,7,4,1,6] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 0

[4,2,8,3,7,6,1,5] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[4,6,1,8,2,7,5,3] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 0

[5,6,1,7,4,3,8,2] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 0

[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

[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

[8,1,6,4,3,5,2,7] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1

[2,1,6,5,3,8,7,4] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 1

[6,1,4,3,7,5,8,2] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 1

[4,5,1,6,8,3,7,2] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 0

[8,3,5,4,6,1,2,7] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[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

[8,2,6,3,4,1,5,7] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[4,3,1,8,5,7,2,6] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[7,3,2,4,8,1,6,5] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[3,7,2,4,5,8,1,6] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0

[3,2,7,4,6,1,8,5] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[8,3,2,4,6,1,7,5] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[8,3,2,4,5,7,1,6] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 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] => 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] => 2

[4,3,2,8,6,1,5,7] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[4,1,6,3,2,5,7,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 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] => 0

[5,4,8,7,6,2,3,1] => [[[[.,.],[[[.,.],.],.]],[.,.]],.] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 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] => 2

[3,6,1,5,2,4,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0

[2,7,1,5,3,4,6,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0

[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

[5,2,3,8,7,1,6,4] => [[[.,.],[.,[[.,.],.]]],[[.,.],.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 1

[7,5,2,4,1,3,8,6] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[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

[8,6,5,4,1,3,7,2] => [[[[[.,.],.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 4

[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

[7,4,3,8,1,6,5,2] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2

[6,5,1,4,3,8,7,2] => [[[.,.],.],[[[.,.],[[.,.],.]],.]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 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

[6,4,1,5,7,2,3,8] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[6,4,1,5,7,3,8,2] => [[[.,.],.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[7,4,1,6,3,8,2,5] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 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] => 2

[8,4,3,1,7,6,5,2] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3

[7,2,1,4,5,6,3,8] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 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] => 0

[6,4,1,8,5,7,3,2] => [[[.,.],.],[[[[.,.],[.,.]],.],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 2

[4,1,3,8,7,5,2,6] => [[.,.],[[.,[[[.,.],.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 1

[8,5,1,6,7,2,4,3] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[6,7,1,4,5,2,8,3] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[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

[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

[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

[8,1,6,2,3,7,5,4] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 1

[5,1,8,7,3,2,6,4] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 1

[6,5,3,4,8,2,1,7] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3

[5,2,7,6,8,3,4,1] => [[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 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] => 2

[6,3,7,4,5,2,8,1] => [[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[7,3,4,2,8,5,6,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[4,3,6,5,8,2,7,1] => [[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[8,2,7,4,5,3,6,1] => [[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2

[7,2,8,4,5,3,6,1] => [[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2

[6,3,8,2,7,4,5,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[3,2,8,4,7,5,6,1] => [[[.,.],[[.,.],[[.,.],[.,.]]]],.] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 2

[8,3,6,2,7,4,5,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 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] => 0

[8,3,5,2,1,6,7,4] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[6,5,1,3,8,4,2,7] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 2

[6,1,4,2,7,8,3,5] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[6,5,1,3,7,8,4,2] => [[[.,.],.],[[.,[[.,[.,.]],.]],.]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 2

[5,8,7,3,2,4,6,1] => [[[[.,[[.,.],.]],.],[.,[.,.]]],.] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2

[5,1,3,2,6,8,4,7] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[2,4,1,7,5,6,3,8] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[3,7,2,8,4,1,5,6] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 0

[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

[7,2,6,3,1,8,4,5] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[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

[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

[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

[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

[5,8,6,4,7,3,2,1] => [[[[[.,[[.,.],.]],[.,.]],.],.],.] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 3

[8,5,2,3,1,6,7,4] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[8,3,2,6,4,1,7,5] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[8,4,1,5,3,6,7,2] => [[[.,.],.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[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

[8,5,1,3,4,6,7,2] => [[[.,.],.],[[.,[.,[.,[.,.]]]],.]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2

[8,1,7,4,2,5,3,6] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[8,3,2,5,1,4,7,6] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 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

[8,1,5,3,2,6,7,4] => [[.,.],[[[.,.],.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 1

[8,1,5,2,4,6,7,3] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 1

[5,2,6,4,1,3,8,7] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 1

[8,6,4,7,1,3,5,2] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[2,1,8,5,4,3,7,6] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 1

[6,4,8,5,3,2,7,1] => [[[[[.,.],[[.,.],.]],.],[.,.]],.] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 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] => 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

[5,6,2,8,1,7,3,4] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[6,8,4,5,1,3,7,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0

[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

[7,3,5,4,8,2,6,1] => [[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2

[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

[3,2,7,5,8,4,6,1] => [[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2

[6,4,2,5,7,1,8,3] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 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

[8,3,7,2,4,5,6,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2

[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

[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

[4,6,1,3,5,7,2,8] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 0

[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

[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

[4,5,1,3,2,8,6,7] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[6,4,1,3,7,8,2,5] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 2

[6,3,1,2,5,4,8,7] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2

[8,2,6,4,1,3,7,5] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 1

[4,3,7,8,2,6,5,1] => [[[[.,.],[.,[.,.]]],[[.,.],.]],.] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 2

[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

[6,8,1,3,2,5,7,4] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 0

[8,6,2,7,3,4,1,5] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2

[8,6,2,7,3,4,5,1] => [[[[.,.],.],[[.,.],[.,[.,.]]]],.] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 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

[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

[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

[8,6,1,7,3,4,5,2] => [[[.,.],.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[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

[8,4,2,3,5,7,6,1] => [[[[.,.],.],[.,[.,[[.,.],.]]]],.] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 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] => 2

[8,4,7,3,2,5,6,1] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 3

[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

[6,2,7,3,8,1,4,5] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[8,4,2,6,7,1,5,3] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[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

[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

[6,4,2,3,7,5,8,1] => [[[[.,.],.],[.,[[.,.],[.,.]]]],.] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 3

[6,3,7,5,1,2,8,4] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 1

[7,2,5,4,8,6,3,1] => [[[.,.],[[[.,.],[[.,.],.]],.]],.] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 2

[6,2,3,8,7,4,5,1] => [[[.,.],[.,[[[.,.],.],[.,.]]]],.] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 2

[7,1,2,8,4,6,5,3] => [[.,.],[.,[[[.,.],[[.,.],.]],.]]] => [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 1

[7,6,2,8,5,3,4,1] => [[[[.,.],.],[[[.,.],.],[.,.]]],.] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 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] => 2

[8,2,7,6,4,1,3,5] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 1

[8,3,7,5,1,6,2,4] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 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

[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

[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

[4,7,1,5,6,3,2,8] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 0

[2,7,1,4,8,3,6,5] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[2,7,1,5,6,8,4,3] => [[.,[.,.]],[[[.,[.,[.,.]]],.],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 0

[2,3,1,8,7,4,6,5] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[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

[4,2,7,8,3,6,5,1] => [[[.,.],[[.,[.,.]],[[.,.],.]]],.] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 2

[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

[5,4,3,7,8,1,6,2] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 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

[5,6,3,2,8,4,7,1] => [[[[.,[.,.]],.],[[.,.],[.,.]]],.] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => 2

[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

[5,2,4,8,6,7,3,1] => [[[.,.],[[.,[[.,.],[.,.]]],.]],.] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 2

[5,2,6,4,8,7,3,1] => [[[.,.],[[[.,.],[[.,.],.]],.]],.] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 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

[4,8,2,7,5,3,1,6] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 0

[5,4,2,3,1,7,8,6] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[5,1,4,3,8,2,6,7] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[8,4,7,5,6,2,1,3] => [[[[.,.],[[.,.],[.,.]]],.],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 2

[8,2,5,4,7,3,6,1] => [[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2

[4,2,8,7,3,6,5,1] => [[[.,.],[[[.,.],.],[[.,.],.]]],.] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 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] => 0

[8,7,5,1,6,3,2,4] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[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

[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

[8,6,3,4,1,2,7,5] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 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] => 2

[7,4,5,8,3,6,2,1] => [[[[[.,.],[.,[.,.]]],[.,.]],.],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3

[3,8,6,2,1,7,4,5] => [[[.,[[.,.],.]],.],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1

[3,1,8,2,4,6,5,7] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 1

[8,1,7,6,2,5,4,3] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 1

[8,5,4,3,7,6,1,2] => [[[[[.,.],.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3

[4,8,1,3,6,7,5,2] => [[.,[.,.]],[[.,[[.,[.,.]],.]],.]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 0

[8,1,4,7,5,2,6,3] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 1

[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

[4,6,1,5,7,2,3,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[4,8,5,3,2,7,1,6] => [[[[.,[[.,.],.]],.],[.,.]],[.,.]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1

[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

[8,4,5,3,1,7,2,6] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2

[7,4,5,3,1,8,6,2] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 2

[6,8,7,5,1,3,2,4] => [[[.,[[.,.],.]],.],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 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] => 0

[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

[7,6,4,2,8,1,5,3] => [[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3

[6,3,4,8,7,1,2,5] => [[[.,.],[.,[[.,.],.]]],[.,[.,.]]] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 1

[5,3,1,6,7,8,2,4] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 2

[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

[6,4,8,5,7,3,1,2] => [[[[.,.],[[.,.],[.,.]]],.],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 2

[4,7,1,6,5,3,8,2] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 0

[7,2,6,4,5,8,1,3] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[2,7,1,5,3,8,6,4] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 0

[7,3,2,1,4,8,6,5] => [[[[.,.],.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 3

[8,7,1,6,3,5,2,4] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[8,7,2,6,1,5,3,4] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 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

[6,2,5,3,4,7,1,8] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[6,2,8,3,4,5,1,7] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[3,5,1,7,6,2,8,4] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[8,5,1,2,4,3,6,7] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2

[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

[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

[7,6,1,4,2,3,8,5] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2

[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

[7,8,1,2,5,3,4,6] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 0

[8,4,7,2,1,6,3,5] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2

[7,4,2,5,3,6,1,8] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 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

[8,4,2,5,3,6,7,1] => [[[[.,.],.],[[.,.],[.,[.,.]]]],.] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 3

[4,8,1,5,3,6,7,2] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 0

[4,1,7,5,2,6,3,8] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[7,1,5,3,6,8,2,4] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[4,5,2,6,1,8,3,7] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[5,1,8,6,7,3,4,2] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 1

[6,5,2,4,1,7,8,3] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[5,4,8,2,1,3,6,7] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2

[7,2,8,3,1,4,5,6] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1

[8,1,3,2,7,5,4,6] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1

[7,6,1,8,2,5,4,3] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 2

[8,4,1,6,7,3,5,2] => [[[.,.],.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[5,4,2,8,1,6,3,7] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[8,7,2,6,4,5,3,1] => [[[[.,.],.],[[[.,.],[.,.]],.]],.] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[7,2,8,4,3,6,1,5] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[5,7,3,2,8,6,4,1] => [[[[.,[.,.]],.],[[[.,.],.],.]],.] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 2

[4,5,1,6,8,2,7,3] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[4,3,1,6,7,2,5,8] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[5,2,1,4,8,6,7,3] => [[[.,.],.],[[.,[[.,.],[.,.]]],.]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 2

[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

[8,2,7,4,1,6,5,3] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[3,2,8,4,1,6,5,7] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[7,1,6,5,4,2,8,3] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 1

[7,1,8,4,2,3,6,5] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1

[4,5,1,3,2,6,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0

[4,7,3,2,1,6,5,8] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 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] => 0

[4,8,3,2,1,6,7,5] => [[[[.,[.,.]],.],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 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

[5,6,3,7,8,1,4,2] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0

[5,7,1,4,3,6,2,8] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[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

[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

[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

[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

[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

[6,5,2,7,8,4,3,1] => [[[[.,.],.],[[[.,[.,.]],.],.]],.] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 3

[7,5,3,6,4,2,1,8] => [[[[[.,.],.],[[.,.],.]],.],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 3

[4,2,3,7,6,1,8,5] => [[[.,.],[.,[[.,.],.]]],[[.,.],.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 1

[4,2,6,3,1,5,7,8] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1

[4,6,3,2,5,8,7,1] => [[[[.,[.,.]],.],[.,[[.,.],.]]],.] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => 2

[5,8,4,3,2,6,1,7] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2

[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

[3,5,1,7,8,6,2,4] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 0

[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

[5,4,3,8,1,7,2,6] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[7,3,1,5,6,8,4,2] => [[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 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

[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

[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

[4,8,2,5,1,6,3,7] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[5,8,1,2,4,6,3,7] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 0

[5,1,7,3,6,4,2,8] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1

[3,2,7,5,6,1,4,8] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[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

[6,3,1,7,5,4,2,8] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 2

[6,2,8,7,3,4,5,1] => [[[.,.],[[[.,.],.],[.,[.,.]]]],.] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 2

[7,3,4,8,5,6,2,1] => [[[[.,.],[.,[[.,.],[.,.]]]],.],.] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 3

[7,3,6,8,4,5,2,1] => [[[[.,.],[[.,[.,.]],[.,.]]],.],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3

[5,6,2,8,3,1,7,4] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[5,3,1,4,8,6,2,7] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 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

[8,7,3,5,4,1,6,2] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[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

[8,1,5,7,6,3,2,4] => [[.,.],[[[.,[[.,.],.]],.],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 1

[7,4,8,3,1,6,5,2] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 2

[6,4,8,7,3,5,1,2] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[6,1,4,2,3,5,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1

[6,5,1,8,3,7,4,2] => [[[.,.],.],[[[.,.],[[.,.],.]],.]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 2

[7,1,4,3,8,6,5,2] => [[.,.],[[[.,.],[[[.,.],.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 1

[8,5,4,1,7,3,2,6] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[4,5,3,8,1,7,6,2] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 0

[4,7,6,3,2,8,5,1] => [[[[.,[[.,.],.]],.],[[.,.],.]],.] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 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] => 0

[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

[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

[7,3,2,1,4,6,8,5] => [[[[.,.],.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 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] => 0

[7,5,3,2,1,6,8,4] => [[[[[.,.],.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 4

[6,8,1,3,4,2,5,7] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[3,6,1,4,7,8,2,5] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 0

[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

[4,5,1,3,8,2,6,7] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[4,1,5,3,2,7,6,8] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[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

[6,2,1,7,4,3,8,5] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[7,3,5,2,1,6,4,8] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2

[4,6,5,2,1,3,7,8] => [[[.,[[.,.],.]],.],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1

[6,1,5,3,7,2,4,8] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[6,8,7,5,4,2,1,3] => [[[[[.,[[.,.],.]],.],.],.],[.,.]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 3

[8,7,5,4,6,1,3,2] => [[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3

[5,6,1,8,4,3,7,2] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 0

[8,5,4,2,7,3,6,1] => [[[[[.,.],.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 4

[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

[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

[6,5,1,7,2,3,4,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2

[7,4,1,5,6,8,3,2] => [[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 2

[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

[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

[5,2,4,7,8,3,6,1] => [[[.,.],[[.,[.,[.,.]]],[.,.]]],.] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[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

[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

[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

[7,2,4,5,6,8,3,1] => [[[.,.],[[.,[.,[.,[.,.]]]],.]],.] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 2

[5,4,3,6,8,1,7,2] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[4,6,1,7,3,2,8,5] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[4,7,3,5,1,2,8,6] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 0

[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

[4,7,1,6,8,2,3,5] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[7,1,8,2,4,5,3,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[5,2,3,8,7,1,4,6] => [[[.,.],[.,[[.,.],.]]],[.,[.,.]]] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 1

[8,7,1,3,2,6,4,5] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[7,5,1,2,3,8,4,6] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 2

[8,6,2,1,3,7,4,5] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3

[4,2,3,6,8,5,7,1] => [[[.,.],[.,[[.,[.,.]],[.,.]]]],.] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[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

[4,3,7,8,2,1,6,5] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 2

[4,8,7,2,1,5,6,3] => [[[.,[[.,.],.]],.],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 1

[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

[4,5,3,8,6,1,2,7] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 0

[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

[7,3,8,4,5,1,2,6] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[7,8,4,6,1,3,5,2] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0

[4,5,3,6,8,1,2,7] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[7,8,6,2,1,4,3,5] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 2

[7,8,6,3,1,2,5,4] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => 2

[5,2,8,4,7,1,3,6] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[7,3,1,2,8,6,5,4] => [[[.,.],.],[.,[[[[.,.],.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 2

[8,7,1,3,2,4,5,6] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2

[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

[4,3,1,2,6,5,7,8] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2

[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

[6,1,5,2,8,7,4,3] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 1

[4,6,3,5,7,1,2,8] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[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

[3,4,1,7,8,6,5,2] => [[.,[.,.]],[[[[.,[.,.]],.],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 0

[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

[8,7,3,6,1,4,2,5] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[6,5,1,8,3,4,7,2] => [[[.,.],.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[8,2,1,5,6,4,7,3] => [[[.,.],.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[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

[5,7,2,4,6,1,8,3] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0

[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

[3,2,7,5,8,6,4,1] => [[[.,.],[[[.,.],[[.,.],.]],.]],.] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 2

[7,2,5,4,3,8,6,1] => [[[.,.],[[[.,.],.],[[.,.],.]]],.] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 2

[8,5,3,1,2,6,7,4] => [[[[.,.],.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 3

[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

[3,1,8,2,6,5,7,4] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1

[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

[5,6,2,8,4,1,7,3] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[5,7,2,4,8,6,1,3] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 0

[6,7,2,4,8,5,1,3] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 0

[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

[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

[7,2,8,3,5,6,1,4] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[7,2,3,8,4,6,1,5] => [[[.,.],[.,[[.,.],[.,.]]]],[.,.]] => [1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1

[7,2,8,4,5,3,1,6] => [[[.,.],[[[.,.],[.,.]],.]],[.,.]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1

[5,7,1,6,4,8,3,2] => [[.,[.,.]],[[[[.,.],[.,.]],.],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 0

[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

[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

[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

[8,5,6,4,1,7,3,2] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 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

[5,8,2,6,3,1,7,4] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[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

[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

[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

[2,1,4,8,5,3,7,6] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 1

[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

[7,4,6,5,2,8,3,1] => [[[[.,.],[[.,.],.]],[[.,.],.]],.] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 2

[4,1,3,8,5,7,6,2] => [[.,.],[[.,[[.,.],[[.,.],.]]],.]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 1

[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

[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

[7,2,6,3,1,8,5,4] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[2,8,1,7,5,4,6,3] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 0

[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

[8,7,3,1,2,5,6,4] => [[[[.,.],.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 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

[5,4,3,6,1,7,8,2] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[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

[4,8,3,2,1,7,5,6] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 2

[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

[4,8,3,7,6,1,2,5] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 0

[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

[3,7,1,4,5,6,2,8] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 0

[3,6,1,4,5,2,7,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[3,8,2,4,5,1,7,6] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0

[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

[6,8,5,3,2,4,1,7] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2

[4,6,1,8,7,5,3,2] => [[.,[.,.]],[[[[[.,.],.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 0

[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

[4,5,2,6,7,8,1,3] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0

[4,5,1,3,7,6,2,8] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 0

[7,2,3,8,6,4,5,1] => [[[.,.],[.,[[[.,.],.],[.,.]]]],.] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 2

[5,8,1,2,7,6,4,3] => [[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => 0

[7,2,1,6,4,3,8,5] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[4,1,3,6,5,8,2,7] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 1

[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

[6,4,1,8,3,7,5,2] => [[[.,.],.],[[[.,.],[[.,.],.]],.]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 2

[6,8,7,2,1,5,4,3] => [[[.,[[.,.],.]],.],[[[.,.],.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1

[8,1,6,3,7,5,4,2] => [[.,.],[[[.,.],[[[.,.],.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 1

[8,5,1,3,7,6,4,2] => [[[.,.],.],[[.,[[[.,.],.],.]],.]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 2

[8,3,6,5,4,2,1,7] => [[[[.,.],[[[.,.],.],.]],.],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 2

[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

[2,8,1,5,6,4,3,7] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 0

[7,4,1,6,5,2,8,3] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[7,4,2,8,6,5,3,1] => [[[[.,.],.],[[[[.,.],.],.],.]],.] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 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] => 2

[5,8,7,3,2,1,6,4] => [[[[.,[[.,.],.]],.],.],[[.,.],.]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2

[7,2,5,6,8,3,4,1] => [[[.,.],[[.,[.,[.,.]]],[.,.]]],.] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2

[8,6,7,2,3,5,4,1] => [[[[.,.],[.,.]],[.,[[.,.],.]]],.] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 2

[5,4,8,6,7,3,1,2] => [[[[.,.],[[.,.],[.,.]]],.],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 2

[4,2,7,3,1,6,8,5] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 1

[7,3,6,4,2,1,8,5] => [[[[.,.],[[.,.],.]],.],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2

[6,4,3,1,8,5,2,7] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[7,4,3,1,5,8,6,2] => [[[[.,.],.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3

[7,4,8,6,5,3,1,2] => [[[[.,.],[[[.,.],.],.]],.],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 2

[7,3,2,1,8,5,6,4] => [[[[.,.],.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 3

[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

[5,7,1,3,2,8,4,6] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[7,1,6,3,2,8,4,5] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[8,1,7,2,3,6,5,4] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 1

[7,1,2,6,4,3,8,5] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 1

[8,7,1,3,2,4,6,5] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2

[8,1,6,3,2,4,7,5] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1

[8,1,6,3,2,7,4,5] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[8,2,1,7,6,3,4,5] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[8,7,2,4,3,1,5,6] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[2,8,1,3,5,6,4,7] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 0

[7,6,3,1,8,5,2,4] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[7,2,1,3,6,8,5,4] => [[[.,.],.],[.,[[[.,[.,.]],.],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 2

[7,6,3,8,1,5,2,4] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[7,2,5,8,6,1,3,4] => [[[.,.],[.,[[.,.],.]]],[.,[.,.]]] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 1

[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

[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

[7,4,5,8,6,2,3,1] => [[[[.,.],[.,[[.,.],.]]],[.,.]],.] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 2

[6,7,2,3,8,4,1,5] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 0

[8,1,3,6,5,2,7,4] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 1

[7,1,3,8,5,2,6,4] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 1

[4,7,1,5,2,6,8,3] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 0

[7,4,1,5,2,6,8,3] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[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

[8,6,2,4,5,1,7,3] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[8,6,7,5,2,1,4,3] => [[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 3

[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

[4,1,6,2,3,8,7,5] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 1

[4,1,7,6,5,2,8,3] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 1

[8,4,1,5,6,2,7,3] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[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

[8,7,1,3,5,2,6,4] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2

[4,8,6,3,2,1,7,5] => [[[[.,[[.,.],.]],.],.],[[.,.],.]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2

[5,1,4,7,6,8,3,2] => [[.,.],[[[.,[[.,.],[.,.]]],.],.]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 1

[5,6,4,7,1,8,3,2] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 0

[5,3,7,4,6,1,8,2] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[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

[8,1,7,3,2,4,5,6] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1

[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

[3,2,5,8,6,1,7,4] => [[[.,.],[.,[[.,.],.]]],[[.,.],.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 1

[4,5,1,7,2,8,6,3] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 0

[4,7,1,8,5,3,6,2] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 0

[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

[7,1,4,3,6,8,2,5] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[5,3,8,7,1,6,2,4] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[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

[8,5,1,6,4,3,2,7] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 2

[8,6,3,5,2,7,1,4] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 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] => 2

[8,5,2,1,6,4,7,3] => [[[[.,.],.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 3

[6,7,1,4,8,5,3,2] => [[.,[.,.]],[[[.,[[.,.],.]],.],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 0

[7,3,2,8,5,1,4,6] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[4,1,7,3,2,8,5,6] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[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

[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

[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

[4,5,1,8,6,2,7,3] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[5,6,1,8,7,2,3,4] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0

[4,5,1,6,8,7,3,2] => [[.,[.,.]],[[[.,[[.,.],.]],.],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 0

[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

[5,8,7,3,2,1,4,6] => [[[[.,[[.,.],.]],.],.],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => 2

[2,8,1,3,7,5,6,4] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 0

[7,6,1,2,5,8,4,3] => [[[.,.],.],[.,[[[.,[.,.]],.],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 2

[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

[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

[6,5,1,3,8,4,7,2] => [[[.,.],.],[[.,[[.,.],[.,.]]],.]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 2

[7,3,1,6,8,4,5,2] => [[[.,.],.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2

[8,5,1,4,6,7,3,2] => [[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 2

[4,8,1,7,5,6,3,2] => [[.,[.,.]],[[[[.,.],[.,.]],.],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 0

[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

[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

[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

[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

[6,4,7,5,2,3,1,8] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[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

[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

[5,3,2,1,7,8,6,4] => [[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3

[7,4,3,8,6,1,5,2] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[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

[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

[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

[6,3,1,8,2,7,5,4] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 2

[7,6,2,8,4,5,3,1] => [[[[.,.],.],[[[.,.],[.,.]],.]],.] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 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

[8,5,1,7,3,4,6,2] => [[[.,.],.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2

[7,1,2,6,4,3,5,8] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 1

[7,1,2,6,5,3,4,8] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 1

[7,1,2,4,8,6,5,3] => [[.,.],[.,[[.,[[[.,.],.],.]],.]]] => [1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 1

[7,4,3,1,6,5,2,8] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[3,5,1,2,6,8,7,4] => [[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 0

[3,1,2,4,8,7,5,6] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 1

[5,4,1,2,3,7,8,6] => [[[.,.],.],[.,[.,[[.,[.,.]],.]]]] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2

[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

[5,3,8,6,2,4,1,7] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 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] => 2

[8,2,1,3,7,4,6,5] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 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] => 2

[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

[8,1,2,7,5,3,4,6] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 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

[7,5,1,8,2,3,4,6] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2

[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

[8,1,6,2,3,7,4,5] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 1

[7,1,8,2,3,6,4,5] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 1

[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

[4,7,2,5,3,8,1,6] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[8,5,2,1,6,3,4,7] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[7,1,8,5,3,2,4,6] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 1

[8,2,7,5,4,1,6,3] => [[[.,.],[[[.,.],.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 1

[6,8,7,4,5,3,2,1] => [[[[[.,[[.,.],.]],[.,.]],.],.],.] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 3

[5,2,6,7,4,8,3,1] => [[[.,.],[[[.,[.,.]],[.,.]],.]],.] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 2

[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

[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

[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

[2,6,1,5,3,4,8,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0

[5,6,1,2,4,7,8,3] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 0

[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

[8,2,7,5,4,6,1,3] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[8,4,7,6,3,1,2,5] => [[[[.,.],[[.,.],.]],.],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 2

[6,4,7,5,3,2,8,1] => [[[[[.,.],[[.,.],.]],.],[.,.]],.] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 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] => 2

[7,3,1,4,5,6,8,2] => [[[.,.],.],[[.,[.,[.,[.,.]]]],.]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 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] => 0

[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

[5,3,4,7,6,1,8,2] => [[[.,.],[.,[[.,.],.]]],[[.,.],.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 1

[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

[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

[5,3,8,6,2,4,7,1] => [[[[.,.],[[.,.],.]],[.,[.,.]]],.] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 2

[2,5,1,6,4,3,8,7] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[3,6,2,8,5,7,1,4] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[4,1,2,5,7,6,3,8] => [[.,.],[.,[[.,[[.,.],.]],[.,.]]]] => [1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 1

[2,1,3,6,4,8,7,5] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 1

[4,8,1,2,7,5,6,3] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 0

[2,5,1,8,6,4,7,3] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 0

[2,5,1,8,3,6,4,7] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[5,8,4,7,3,2,1,6] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2

[4,3,8,6,1,2,5,7] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1

[7,2,3,5,6,8,4,1] => [[[.,.],[.,[[.,[.,[.,.]]],.]]],.] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 2

[5,8,1,3,4,7,2,6] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 0

[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

[8,7,5,6,4,1,3,2] => [[[[[.,.],.],[.,.]],.],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 3

[8,7,4,2,3,6,5,1] => [[[[[.,.],.],.],[.,[[.,.],.]]],.] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 4

[8,4,2,3,7,6,5,1] => [[[[.,.],.],[.,[[[.,.],.],.]]],.] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 3

[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

[7,6,3,1,4,5,8,2] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 3

[5,4,1,7,8,6,2,3] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 2

[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

[4,3,7,6,5,1,8,2] => [[[.,.],[[[.,.],.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 1

[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

[3,2,8,5,4,1,6,7] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 1

[8,1,2,7,3,5,4,6] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 1

[5,7,1,2,6,3,4,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 0

[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

[4,8,1,2,3,6,5,7] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 0

[4,5,1,3,2,6,8,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0

[6,4,7,5,1,3,2,8] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[5,3,1,6,2,7,8,4] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[6,7,2,4,1,8,3,5] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[5,1,6,3,2,7,8,4] => [[.,.],[[[.,.],.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 1

[5,2,1,6,4,7,3,8] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[5,4,1,6,2,7,8,3] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[6,7,2,5,4,1,3,8] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 0

[7,1,3,5,4,2,8,6] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 1

[7,6,8,2,4,5,3,1] => [[[[.,.],[.,.]],[[.,[.,.]],.]],.] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 2

[4,2,8,6,5,1,3,7] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 1

[6,3,2,4,8,7,1,5] => [[[[.,.],.],[.,[[.,.],.]]],[.,.]] => [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 2

[8,3,2,7,4,1,5,6] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2

[7,3,2,6,5,8,1,4] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2

[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

[2,7,1,5,8,6,4,3] => [[.,[.,.]],[[[.,[[.,.],.]],.],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 0

[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

[6,4,7,2,3,8,5,1] => [[[[.,.],[.,.]],[.,[[.,.],.]]],.] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 2

[6,1,8,5,7,4,2,3] => [[.,.],[[[[.,.],[.,.]],.],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 1

[7,1,4,3,6,5,8,2] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 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

[6,1,8,5,4,7,3,2] => [[.,.],[[[[[.,.],.],[.,.]],.],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 1

[7,6,1,5,4,2,8,3] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2

[5,1,6,8,7,2,4,3] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 1

[5,3,2,6,8,7,4,1] => [[[[.,.],.],[[.,[[.,.],.]],.]],.] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 3

[5,4,6,2,8,7,3,1] => [[[[.,.],[.,.]],[[[.,.],.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 2

[7,4,8,6,3,5,1,2] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[7,2,4,3,6,1,8,5] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1

[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

[8,5,7,6,2,3,4,1] => [[[[.,.],[[.,.],.]],[.,[.,.]]],.] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 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

[4,1,7,6,2,8,3,5] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[4,1,8,2,7,5,3,6] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1

[4,1,7,2,8,5,3,6] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1

[7,1,6,3,5,4,8,2] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 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

[8,1,5,2,7,4,3,6] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1

[7,1,4,2,8,5,3,6] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1

[3,1,6,8,7,5,4,2] => [[.,.],[[[[.,[[.,.],.]],.],.],.]] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 1

[3,1,8,7,5,6,4,2] => [[.,.],[[[[[.,.],.],[.,.]],.],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 1

[5,1,8,7,6,3,4,2] => [[.,.],[[[[[.,.],.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 1

[8,2,7,5,3,6,4,1] => [[[.,.],[[[.,.],.],[[.,.],.]]],.] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 2

[8,7,2,3,1,5,6,4] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[8,7,2,1,6,4,5,3] => [[[[.,.],.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 3

[8,7,1,6,4,3,5,2] => [[[.,.],.],[[[[.,.],.],[.,.]],.]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 2

[8,4,1,7,3,6,5,2] => [[[.,.],.],[[[.,.],[[.,.],.]],.]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 2

[4,5,1,8,7,3,6,2] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 0

[4,3,8,5,2,6,1,7] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[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

[8,4,7,3,1,2,5,6] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2

[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

[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

[8,5,3,4,1,7,2,6] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[8,6,5,3,1,2,7,4] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 4

[7,4,6,5,3,2,8,1] => [[[[[.,.],[[.,.],.]],.],[.,.]],.] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 3

[8,4,2,6,5,7,3,1] => [[[[.,.],.],[[[.,.],[.,.]],.]],.] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[3,2,1,7,4,6,8,5] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[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

[4,8,5,3,1,2,6,7] => [[[.,[[.,.],.]],.],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1

[8,5,2,4,6,1,3,7] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2

[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

[6,4,7,2,1,3,8,5] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2

[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

[3,1,8,7,6,2,5,4] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 1

[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

[3,2,6,4,7,1,5,8] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1

[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

[7,1,3,8,6,2,4,5] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 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] => 0

[8,1,5,2,6,4,7,3] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1

[5,3,4,7,6,2,1,8] => [[[[.,.],[.,[[.,.],.]]],.],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 2

[4,1,8,5,7,2,6,3] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[4,1,8,2,7,5,6,3] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1

[7,6,8,2,4,3,5,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[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

[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

[8,7,2,6,4,5,1,3] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2

[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

[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

[2,7,1,5,6,4,8,3] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 0

[2,8,1,5,6,4,7,3] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 0

[3,7,2,8,1,5,6,4] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0

[7,3,2,5,1,6,8,4] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[8,7,2,1,3,6,5,4] => [[[[.,.],.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 3

[7,3,2,8,1,4,6,5] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 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

[3,5,1,7,6,4,8,2] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 0

[8,7,4,2,1,6,5,3] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4

[5,4,7,6,2,1,8,3] => [[[[.,.],[[.,.],.]],.],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 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] => 0

[4,6,5,3,1,8,7,2] => [[[.,[[.,.],.]],.],[[[.,.],.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1

[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

[8,6,7,4,3,1,5,2] => [[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 3

[4,7,1,8,5,3,2,6] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 0

[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

[8,6,7,2,1,3,5,4] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2

[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

[6,4,1,2,5,7,8,3] => [[[.,.],.],[.,[[.,[.,[.,.]]],.]]] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2

[6,1,5,4,2,7,3,8] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[6,4,2,3,1,7,5,8] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[5,3,1,4,7,6,2,8] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 2

[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

[7,4,3,5,1,6,2,8] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[7,5,3,6,2,1,4,8] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3

[6,4,3,7,1,8,2,5] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[3,1,2,7,6,4,5,8] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 1

[5,1,2,7,6,3,4,8] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 1

[5,6,1,7,2,4,3,8] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0

[2,6,1,3,5,4,7,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 0

[4,6,1,5,2,8,7,3] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 0

[6,1,5,4,2,7,8,3] => [[.,.],[[[.,.],.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 1

[4,6,1,5,2,7,8,3] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 0

[5,1,8,6,2,7,4,3] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 1

[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

[8,1,6,3,4,2,5,7] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[7,4,2,3,1,6,8,5] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[6,4,2,3,7,8,1,5] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2

[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

[8,2,4,3,1,7,5,6] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[8,2,1,4,3,7,5,6] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[7,6,8,2,1,5,3,4] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2

[8,6,2,5,1,3,7,4] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[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

[5,7,2,6,4,1,8,3] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[6,3,5,7,4,2,8,1] => [[[[.,.],[[.,[.,.]],.]],[.,.]],.] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2

[7,6,4,8,5,3,1,2] => [[[[[.,.],.],[[.,.],.]],.],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 3

[8,2,1,6,4,7,3,5] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[5,7,1,8,3,2,6,4] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[8,2,5,4,3,7,1,6] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1

[5,8,4,3,7,6,2,1] => [[[[[.,[.,.]],.],[[.,.],.]],.],.] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 3

[8,1,5,3,4,7,2,6] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[6,1,8,7,4,5,3,2] => [[.,.],[[[[[.,.],.],[.,.]],.],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 1

[5,8,6,4,2,1,7,3] => [[[[.,[[.,.],.]],.],.],[[.,.],.]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2

[2,6,1,8,4,7,5,3] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 0

[5,3,8,6,1,2,7,4] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 1

[5,8,1,4,6,2,7,3] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0

[3,7,6,2,1,4,8,5] => [[[.,[[.,.],.]],.],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => 1

[4,6,2,3,7,1,8,5] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0

[6,8,7,5,1,3,4,2] => [[[.,[[.,.],.]],.],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 1

[6,4,3,2,7,8,5,1] => [[[[[.,.],.],.],[[.,[.,.]],.]],.] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 4

[7,8,6,4,2,5,3,1] => [[[[[.,[.,.]],.],.],[[.,.],.]],.] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 3

[6,4,5,8,7,1,3,2] => [[[.,.],[.,[[.,.],.]]],[[.,.],.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 1

[6,4,1,7,8,3,2,5] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 2

[6,4,3,8,7,2,5,1] => [[[[[.,.],.],[[.,.],.]],[.,.]],.] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 3

[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

[4,8,3,5,1,2,7,6] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 0

[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

[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

[6,5,2,3,7,1,8,4] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2

[7,2,1,6,4,8,3,5] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[2,1,3,7,5,8,4,6] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 1

[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

[4,2,7,5,6,8,1,3] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[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

[5,3,2,7,6,1,8,4] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[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

[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

[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

[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

[6,1,7,3,8,4,5,2] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 1

[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

[8,2,3,6,7,4,5,1] => [[[.,.],[.,[[.,[.,.]],[.,.]]]],.] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2

[6,2,1,5,3,7,8,4] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2

[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

[6,2,8,5,1,3,7,4] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 1

[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

[5,8,1,6,4,7,2,3] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0

[6,5,1,2,7,4,8,3] => [[[.,.],.],[.,[[[.,.],[.,.]],.]]] => [1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2

[7,8,1,2,5,4,3,6] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 0

[5,2,4,7,6,8,1,3] => [[[.,.],[.,[[.,.],[.,.]]]],[.,.]] => [1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1

[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

[4,1,7,6,8,2,5,3] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1

[7,2,6,4,1,5,3,8] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[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

[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

[4,7,1,6,8,5,2,3] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 0

[5,3,1,8,6,7,4,2] => [[[.,.],.],[[[[.,.],[.,.]],.],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 2

[5,7,1,6,4,2,8,3] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0

[2,7,1,6,5,8,4,3] => [[.,[.,.]],[[[[.,.],[.,.]],.],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 0

[2,7,1,4,8,6,5,3] => [[.,[.,.]],[[.,[[[.,.],.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 0

[6,7,5,4,1,3,2,8] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 2

[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

[8,3,2,6,5,1,7,4] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[7,8,6,3,2,5,4,1] => [[[[[.,[.,.]],.],.],[[.,.],.]],.] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 3

[8,6,1,4,3,2,7,5] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 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

[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

[7,6,1,5,2,3,8,4] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2

[5,1,8,6,7,2,3,4] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[5,7,1,6,8,2,3,4] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[6,8,4,2,1,7,3,5] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 2

[6,3,2,8,1,7,4,5] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[6,4,1,3,7,8,5,2] => [[[.,.],.],[[.,[[.,[.,.]],.]],.]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 2

[6,8,5,4,3,7,1,2] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 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

[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

[8,5,6,2,4,7,3,1] => [[[[.,.],[.,.]],[[.,[.,.]],.]],.] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 2

[8,1,3,6,4,5,2,7] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 1

[4,3,1,6,2,5,8,7] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2

[7,5,2,1,8,4,3,6] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3

[5,3,1,4,7,8,2,6] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 2

[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

[8,6,1,3,5,7,4,2] => [[[.,.],.],[[.,[[.,[.,.]],.]],.]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 2

[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

[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

[4,3,1,2,5,7,6,8] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 2

[8,3,6,5,7,4,2,1] => [[[[.,.],[[[.,.],[.,.]],.]],.],.] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 3

[8,2,6,5,7,4,3,1] => [[[.,.],[[[[.,.],[.,.]],.],.]],.] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 2

[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

[8,2,6,3,7,5,4,1] => [[[.,.],[[.,.],[[[.,.],.],.]]],.] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 2

[8,2,5,3,7,6,4,1] => [[[.,.],[[.,.],[[[.,.],.],.]]],.] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 2

[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

[5,3,1,8,4,2,6,7] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[2,1,6,5,8,7,3,4] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1

[6,1,5,4,7,3,8,2] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 1

[3,1,8,4,2,7,6,5] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 1

[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

[8,7,2,3,1,6,4,5] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[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

[6,8,2,3,1,7,4,5] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0

[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

[8,2,7,3,1,4,5,6] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1

[5,3,2,8,7,1,6,4] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2

[8,6,7,4,1,3,5,2] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2

[4,1,3,6,5,2,8,7] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 1

[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

[4,8,3,2,6,5,7,1] => [[[[.,[.,.]],.],[[.,.],[.,.]]],.] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => 2

[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

[8,1,6,2,5,4,7,3] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1

[6,1,3,2,5,8,7,4] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 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] => 2

[6,8,4,3,5,2,7,1] => [[[[[.,[.,.]],.],[.,.]],[.,.]],.] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2

[8,1,4,6,5,3,7,2] => [[.,.],[[[.,[[.,.],.]],[.,.]],.]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 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

[6,5,4,8,7,2,3,1] => [[[[[.,.],.],[[.,.],.]],[.,.]],.] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 3

[5,7,4,3,6,2,1,8] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 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

[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

[8,2,6,4,3,7,5,1] => [[[.,.],[[[.,.],.],[[.,.],.]]],.] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 2

[6,3,1,8,7,4,5,2] => [[[.,.],.],[[[[.,.],.],[.,.]],.]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 2

[8,6,3,2,7,4,5,1] => [[[[[.,.],.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 4

[5,7,1,3,6,2,4,8] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0

[4,7,1,3,2,5,8,6] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0

[8,5,2,3,7,4,6,1] => [[[[.,.],.],[.,[[.,.],[.,.]]]],.] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 3

[5,3,1,6,4,8,7,2] => [[[.,.],.],[[[.,.],[[.,.],.]],.]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 2

[8,5,1,2,7,6,4,3] => [[[.,.],.],[.,[[[[.,.],.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 2

[7,4,3,6,2,5,8,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3

[4,3,8,7,1,6,2,5] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 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

[8,4,2,7,1,3,6,5] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2

[8,4,2,3,1,6,7,5] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 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

[3,8,2,6,4,7,1,5] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0

[6,5,1,7,4,8,3,2] => [[[.,.],.],[[[[.,.],[.,.]],.],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 2

[7,6,3,5,1,4,8,2] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2

[6,5,4,1,7,2,3,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3

[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

[7,1,2,6,4,8,3,5] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 1

[3,5,1,8,6,2,4,7] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0

[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

[8,1,6,4,7,5,3,2] => [[.,.],[[[[.,.],[[.,.],.]],.],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 1

[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

[5,1,4,3,7,8,6,2] => [[.,.],[[[.,.],[[.,[.,.]],.]],.]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 1

[5,7,1,8,6,3,2,4] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 0

[4,1,3,7,6,5,2,8] => [[.,.],[[.,[[[.,.],.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 1

[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

[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

[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

[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

[8,1,6,2,5,7,4,3] => [[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 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] => 0

[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

[5,7,3,6,4,1,8,2] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[6,7,2,3,5,8,1,4] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0

[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

[2,1,3,8,5,4,6,7] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 1

[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

[7,1,2,5,3,8,4,6] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 1

[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

[5,3,7,8,4,2,1,6] => [[[[.,.],[[.,[.,.]],.]],.],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 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

[7,5,8,2,4,3,6,1] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2

[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

[8,1,5,3,4,6,2,7] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[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

[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

[8,4,1,3,2,6,5,7] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2

[8,7,2,3,5,4,6,1] => [[[[.,.],.],[.,[[.,.],[.,.]]]],.] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 3

[3,8,5,2,1,6,7,4] => [[[.,[[.,.],.]],.],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 1

[8,7,2,6,1,4,3,5] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2

[6,1,7,3,8,2,4,5] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[7,1,8,6,4,2,3,5] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 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

[5,7,1,6,4,2,3,8] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0

[4,8,2,7,5,1,6,3] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0

[3,1,2,5,7,6,8,4] => [[.,.],[.,[[.,[[.,.],[.,.]]],.]]] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 1

[5,1,7,3,2,6,8,4] => [[.,.],[[[.,.],.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 1

[4,7,2,3,5,1,6,8] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0

[4,8,2,3,7,5,1,6] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 0

[8,7,2,4,3,5,6,1] => [[[[.,.],.],[[.,.],[.,[.,.]]]],.] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 3

[8,6,2,4,3,5,1,7] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 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

[7,6,2,8,4,5,1,3] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2

[6,8,1,5,7,3,2,4] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 0

[4,1,7,5,6,8,2,3] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[3,7,6,2,1,4,5,8] => [[[.,[[.,.],.]],.],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1

[6,2,5,3,1,8,7,4] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[6,2,5,3,8,7,1,4] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1

[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

[8,4,7,5,2,3,1,6] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[8,2,7,4,5,3,1,6] => [[[.,.],[[[.,.],[.,.]],.]],[.,.]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1

[8,2,4,7,5,3,1,6] => [[[.,.],[[.,[[.,.],.]],.]],[.,.]] => [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 1

[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

[8,4,6,7,5,3,1,2] => [[[[.,.],[[.,[.,.]],.]],.],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 2

[6,4,5,8,7,3,1,2] => [[[[.,.],[.,[[.,.],.]]],.],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 2

[6,2,8,7,5,3,1,4] => [[[.,.],[[[[.,.],.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1

[6,7,2,4,5,3,1,8] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 0

[6,5,8,4,7,2,1,3] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 2

[8,1,6,2,5,7,3,4] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1

[6,8,1,2,4,7,3,5] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 0

[8,1,5,3,2,7,4,6] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1

[8,3,7,6,2,5,4,1] => [[[[.,.],[[.,.],.]],[[.,.],.]],.] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 2

[4,6,1,3,5,8,2,7] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 0

[4,5,1,3,8,7,2,6] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 0

[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

[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

[6,2,8,5,1,4,7,3] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 1

[7,4,5,8,6,3,2,1] => [[[[[.,.],[.,[[.,.],.]]],.],.],.] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 4

[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

[7,4,1,3,6,8,2,5] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 2

[6,8,1,2,7,3,4,5] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 0

[3,8,1,2,4,7,6,5] => [[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 0

[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

[3,1,8,4,6,2,5,7] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[4,2,7,3,5,8,1,6] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[3,1,8,4,5,6,2,7] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 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

[7,1,4,2,8,6,3,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1

[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

[7,3,2,6,8,4,5,1] => [[[[.,.],.],[[.,[.,.]],[.,.]]],.] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 3

[8,4,2,6,7,3,5,1] => [[[[.,.],.],[[.,[.,.]],[.,.]]],.] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 3

[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

[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

[7,6,2,3,5,8,4,1] => [[[[.,.],.],[.,[[.,[.,.]],.]]],.] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[7,4,1,6,2,5,8,3] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 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

[8,5,6,2,3,7,4,1] => [[[[.,.],[.,.]],[.,[[.,.],.]]],.] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 2

[7,8,1,4,5,6,2,3] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 0

[8,3,1,2,5,4,7,6] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2

[8,1,5,3,7,4,2,6] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1

[8,1,2,6,5,7,3,4] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 1

[7,1,2,6,5,8,3,4] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 1

[2,6,1,4,7,5,8,3] => [[.,[.,.]],[[.,[[.,.],[.,.]]],.]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 0

[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

[3,1,7,5,2,6,8,4] => [[.,.],[[[.,.],.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 1

[3,2,7,5,1,6,8,4] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 1

[5,2,7,3,1,6,8,4] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 1

[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

[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

[8,7,4,6,5,3,1,2] => [[[[[.,.],.],[[.,.],.]],.],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 3

[8,1,4,3,6,2,5,7] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1

[7,4,2,8,5,6,3,1] => [[[[.,.],.],[[[.,.],[.,.]],.]],.] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3

[5,2,1,3,8,4,6,7] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2

[2,1,3,8,6,4,5,7] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 1

[6,1,4,3,5,8,2,7] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1

[6,5,1,3,8,2,4,7] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2

[4,1,3,8,6,2,5,7] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 1

[7,1,5,4,6,3,8,2] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 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

[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

[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

[4,2,6,3,5,8,1,7] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1

[7,4,2,6,8,5,3,1] => [[[[.,.],.],[[[.,[.,.]],.],.]],.] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 3

[8,5,2,4,6,3,1,7] => [[[[.,.],.],[[.,[.,.]],.]],[.,.]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 2

[7,4,1,2,8,5,6,3] => [[[.,.],.],[.,[[[.,.],[.,.]],.]]] => [1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2

[6,4,1,8,5,2,3,7] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2

[8,4,1,6,3,5,2,7] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[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

[8,6,2,3,5,7,4,1] => [[[[.,.],.],[.,[[.,[.,.]],.]]],.] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3

[8,6,2,5,7,3,4,1] => [[[[.,.],.],[[.,[.,.]],[.,.]]],.] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 3

[6,3,4,8,5,1,2,7] => [[[.,.],[.,[[.,.],.]]],[.,[.,.]]] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 1

[8,5,1,2,7,4,6,3] => [[[.,.],.],[.,[[[.,.],[.,.]],.]]] => [1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 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] => 2

[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

[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

[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

[3,6,1,8,7,4,5,2] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 0

[4,7,1,3,5,6,8,2] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 0

[4,3,5,7,8,2,6,1] => [[[[.,.],[.,[.,[.,.]]]],[.,.]],.] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2

[5,3,2,7,6,4,1,8] => [[[[.,.],.],[[[.,.],.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 2

[5,3,7,4,6,2,1,8] => [[[[.,.],[[.,.],[.,.]]],.],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 2

[5,7,3,2,1,8,6,4] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 2

[5,7,6,3,2,1,8,4] => [[[[.,[[.,.],.]],.],.],[[.,.],.]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2

[3,2,7,5,4,1,8,6] => [[[.,.],[[[.,.],.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 1

[5,3,7,4,1,8,6,2] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[7,3,5,4,1,6,8,2] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 1

[7,5,1,6,8,3,2,4] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 2

[5,3,1,7,6,8,2,4] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2

[7,1,5,3,2,4,8,6] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1

[7,1,5,2,4,3,6,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1

[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

[6,3,2,1,5,8,4,7] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 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

[6,3,5,2,7,8,4,1] => [[[[.,.],[.,.]],[[.,[.,.]],.]],.] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 2

[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

[7,4,1,2,5,6,8,3] => [[[.,.],.],[.,[[.,[.,[.,.]]],.]]] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 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] => 0

[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

[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

[5,7,1,3,6,4,8,2] => [[.,[.,.]],[[.,[[.,.],[.,.]]],.]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 0

[8,2,5,4,1,7,3,6] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1

[8,1,7,6,4,2,3,5] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 1

[6,4,8,7,3,2,5,1] => [[[[[.,.],[[.,.],.]],.],[.,.]],.] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 3

[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

[6,2,8,3,7,4,5,1] => [[[.,.],[[.,.],[[.,.],[.,.]]]],.] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 2

[5,2,3,8,6,1,4,7] => [[[.,.],[.,[[.,.],.]]],[.,[.,.]]] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 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

[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

[8,3,6,5,2,7,1,4] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1

[5,1,3,6,4,2,7,8] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 1

[6,1,2,4,7,5,3,8] => [[.,.],[.,[[.,[[.,.],.]],[.,.]]]] => [1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 1

[8,3,1,4,6,7,2,5] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 2

[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

[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

[8,6,2,1,7,3,5,4] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3

[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

[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

[8,2,6,5,1,7,4,3] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1

[7,6,4,1,2,5,8,3] => [[[[.,.],.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 3

[7,1,8,4,3,2,6,5] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 1

[7,5,3,6,8,4,2,1] => [[[[[.,.],.],[[.,[.,.]],.]],.],.] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4

[7,2,5,6,4,8,3,1] => [[[.,.],[[[.,[.,.]],[.,.]],.]],.] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 2

[7,4,6,2,8,5,3,1] => [[[[.,.],[.,.]],[[[.,.],.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 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

[5,6,1,4,3,8,7,2] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 0

[5,8,6,4,3,1,7,2] => [[[[.,[[.,.],.]],.],.],[[.,.],.]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 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

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$F_{2} = 1 + q^{2}$

$F_{3} = 2 + 3\ q + q^{3}$

$F_{4} = 9 + 8\ q + 6\ q^{2} + q^{4}$

$F_{5} = 44 + 45\ q + 20\ q^{2} + 10\ q^{3} + q^{5}$

$F_{6} = 265 + 264\ q + 135\ q^{2} + 40\ q^{3} + 15\ q^{4} + q^{6}$

$F_{7} = 1854 + 1855\ q + 924\ q^{2} + 315\ q^{3} + 70\ q^{4} + 21\ q^{5} + q^{7}$

Description

The number of hills of a Dyck path.
A hill is a peak with up step starting and down step ending at height zero.

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.