- FindStat

Identifier

Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Mp00020: Binary trees —to Tamari-corresponding Dyck path⟶ Dyck paths
Mp00027: Dyck paths —to partition⟶ Integer partitions
St001484: Integer partitions ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

[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] => [1] => 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[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] => [1] => 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 13368 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[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] => [1] => 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[6,3,1,5,4,2] => [[[.,[.,.]],[[.,.],.]],.] => [1,1,0,0,1,1,0,1,0,0,1,0] => [5,3,2,2] => 2

[6,3,2,1,4,5] => [[[[.,.],.],[.,[.,.]]],.] => [1,0,1,0,1,1,1,0,0,0,1,0] => [5,2,2,2,1] => 2

[6,3,2,1,5,4] => [[[[.,.],.],[[.,.],.]],.] => [1,0,1,0,1,1,0,1,0,0,1,0] => [5,3,2,2,1] => 3

[6,3,2,4,1,5] => [[[[.,.],.],[.,[.,.]]],.] => [1,0,1,0,1,1,1,0,0,0,1,0] => [5,2,2,2,1] => 2

[6,3,2,4,5,1] => [[[[.,.],.],[.,[.,.]]],.] => [1,0,1,0,1,1,1,0,0,0,1,0] => [5,2,2,2,1] => 2

[6,3,2,5,1,4] => [[[[.,.],.],[[.,.],.]],.] => [1,0,1,0,1,1,0,1,0,0,1,0] => [5,3,2,2,1] => 3

[6,3,2,5,4,1] => [[[[.,.],.],[[.,.],.]],.] => [1,0,1,0,1,1,0,1,0,0,1,0] => [5,3,2,2,1] => 3

[6,3,4,1,2,5] => [[[.,[.,.]],[.,[.,.]]],.] => [1,1,0,0,1,1,1,0,0,0,1,0] => [5,2,2,2] => 1

[6,3,4,1,5,2] => [[[.,[.,.]],[.,[.,.]]],.] => [1,1,0,0,1,1,1,0,0,0,1,0] => [5,2,2,2] => 1

[6,3,4,2,1,5] => [[[[.,.],.],[.,[.,.]]],.] => [1,0,1,0,1,1,1,0,0,0,1,0] => [5,2,2,2,1] => 2

[6,3,4,2,5,1] => [[[[.,.],.],[.,[.,.]]],.] => [1,0,1,0,1,1,1,0,0,0,1,0] => [5,2,2,2,1] => 2

[6,3,4,5,1,2] => [[[.,[.,.]],[.,[.,.]]],.] => [1,1,0,0,1,1,1,0,0,0,1,0] => [5,2,2,2] => 1

[6,3,4,5,2,1] => [[[[.,.],.],[.,[.,.]]],.] => [1,0,1,0,1,1,1,0,0,0,1,0] => [5,2,2,2,1] => 2

[6,3,5,1,2,4] => [[[.,[.,.]],[[.,.],.]],.] => [1,1,0,0,1,1,0,1,0,0,1,0] => [5,3,2,2] => 2

[6,3,5,1,4,2] => [[[.,[.,.]],[[.,.],.]],.] => [1,1,0,0,1,1,0,1,0,0,1,0] => [5,3,2,2] => 2

[6,3,5,2,1,4] => [[[[.,.],.],[[.,.],.]],.] => [1,0,1,0,1,1,0,1,0,0,1,0] => [5,3,2,2,1] => 3

[6,3,5,2,4,1] => [[[[.,.],.],[[.,.],.]],.] => [1,0,1,0,1,1,0,1,0,0,1,0] => [5,3,2,2,1] => 3

[6,3,5,4,1,2] => [[[.,[.,.]],[[.,.],.]],.] => [1,1,0,0,1,1,0,1,0,0,1,0] => [5,3,2,2] => 2

[6,3,5,4,2,1] => [[[[.,.],.],[[.,.],.]],.] => [1,0,1,0,1,1,0,1,0,0,1,0] => [5,3,2,2,1] => 3

[6,4,1,2,3,5] => [[[.,[.,[.,.]]],[.,.]],.] => [1,1,1,0,0,0,1,1,0,0,1,0] => [5,3,3] => 1

[6,4,1,2,5,3] => [[[.,[.,[.,.]]],[.,.]],.] => [1,1,1,0,0,0,1,1,0,0,1,0] => [5,3,3] => 1

[6,4,1,3,2,5] => [[[.,[[.,.],.]],[.,.]],.] => [1,1,0,1,0,0,1,1,0,0,1,0] => [5,3,3,1] => 2

[6,4,1,3,5,2] => [[[.,[[.,.],.]],[.,.]],.] => [1,1,0,1,0,0,1,1,0,0,1,0] => [5,3,3,1] => 2

[6,4,1,5,2,3] => [[[.,[.,[.,.]]],[.,.]],.] => [1,1,1,0,0,0,1,1,0,0,1,0] => [5,3,3] => 1

[6,4,1,5,3,2] => [[[.,[[.,.],.]],[.,.]],.] => [1,1,0,1,0,0,1,1,0,0,1,0] => [5,3,3,1] => 2

[6,4,2,1,3,5] => [[[[.,.],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,0] => [5,3,3,1,1] => 1

[6,4,2,1,5,3] => [[[[.,.],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,0] => [5,3,3,1,1] => 1

[6,4,2,3,1,5] => [[[[.,.],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,0] => [5,3,3,1,1] => 1

[6,4,2,3,5,1] => [[[[.,.],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,0] => [5,3,3,1,1] => 1

[6,4,2,5,1,3] => [[[[.,.],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,0] => [5,3,3,1,1] => 1

[6,4,2,5,3,1] => [[[[.,.],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,0] => [5,3,3,1,1] => 1

[6,4,3,1,2,5] => [[[[.,[.,.]],.],[.,.]],.] => [1,1,0,0,1,0,1,1,0,0,1,0] => [5,3,3,2] => 2

[6,4,3,1,5,2] => [[[[.,[.,.]],.],[.,.]],.] => [1,1,0,0,1,0,1,1,0,0,1,0] => [5,3,3,2] => 2

[6,4,3,2,1,5] => [[[[[.,.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,0] => [5,3,3,2,1] => 3

[6,4,3,2,5,1] => [[[[[.,.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,0] => [5,3,3,2,1] => 3

[6,4,3,5,1,2] => [[[[.,[.,.]],.],[.,.]],.] => [1,1,0,0,1,0,1,1,0,0,1,0] => [5,3,3,2] => 2

[6,4,3,5,2,1] => [[[[[.,.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,0] => [5,3,3,2,1] => 3

[6,4,5,1,2,3] => [[[.,[.,[.,.]]],[.,.]],.] => [1,1,1,0,0,0,1,1,0,0,1,0] => [5,3,3] => 1

[6,4,5,1,3,2] => [[[.,[[.,.],.]],[.,.]],.] => [1,1,0,1,0,0,1,1,0,0,1,0] => [5,3,3,1] => 2

[6,4,5,2,1,3] => [[[[.,.],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,0] => [5,3,3,1,1] => 1

[6,4,5,2,3,1] => [[[[.,.],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,0] => [5,3,3,1,1] => 1

[6,4,5,3,1,2] => [[[[.,[.,.]],.],[.,.]],.] => [1,1,0,0,1,0,1,1,0,0,1,0] => [5,3,3,2] => 2

[6,4,5,3,2,1] => [[[[[.,.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,0] => [5,3,3,2,1] => 3

[6,5,1,2,3,4] => [[[.,[.,[.,[.,.]]]],.],.] => [1,1,1,1,0,0,0,0,1,0,1,0] => [5,4] => 2

[6,5,1,2,4,3] => [[[.,[.,[[.,.],.]]],.],.] => [1,1,1,0,1,0,0,0,1,0,1,0] => [5,4,1] => 3

[6,5,1,3,2,4] => [[[.,[[.,.],[.,.]]],.],.] => [1,1,0,1,1,0,0,0,1,0,1,0] => [5,4,1,1] => 2

[6,5,1,3,4,2] => [[[.,[[.,.],[.,.]]],.],.] => [1,1,0,1,1,0,0,0,1,0,1,0] => [5,4,1,1] => 2

[6,5,1,4,2,3] => [[[.,[[.,[.,.]],.]],.],.] => [1,1,1,0,0,1,0,0,1,0,1,0] => [5,4,2] => 3

[6,5,1,4,3,2] => [[[.,[[[.,.],.],.]],.],.] => [1,1,0,1,0,1,0,0,1,0,1,0] => [5,4,2,1] => 4

[6,5,2,1,3,4] => [[[[.,.],[.,[.,.]]],.],.] => [1,0,1,1,1,0,0,0,1,0,1,0] => [5,4,1,1,1] => 2

[6,5,2,1,4,3] => [[[[.,.],[[.,.],.]],.],.] => [1,0,1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,1] => 3

[6,5,2,3,1,4] => [[[[.,.],[.,[.,.]]],.],.] => [1,0,1,1,1,0,0,0,1,0,1,0] => [5,4,1,1,1] => 2

[6,5,2,3,4,1] => [[[[.,.],[.,[.,.]]],.],.] => [1,0,1,1,1,0,0,0,1,0,1,0] => [5,4,1,1,1] => 2

[6,5,2,4,1,3] => [[[[.,.],[[.,.],.]],.],.] => [1,0,1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,1] => 3

[6,5,2,4,3,1] => [[[[.,.],[[.,.],.]],.],.] => [1,0,1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,1] => 3

[6,5,3,1,2,4] => [[[[.,[.,.]],[.,.]],.],.] => [1,1,0,0,1,1,0,0,1,0,1,0] => [5,4,2,2] => 2

[6,5,3,1,4,2] => [[[[.,[.,.]],[.,.]],.],.] => [1,1,0,0,1,1,0,0,1,0,1,0] => [5,4,2,2] => 2

[6,5,3,2,1,4] => [[[[[.,.],.],[.,.]],.],.] => [1,0,1,0,1,1,0,0,1,0,1,0] => [5,4,2,2,1] => 3

[6,5,3,2,4,1] => [[[[[.,.],.],[.,.]],.],.] => [1,0,1,0,1,1,0,0,1,0,1,0] => [5,4,2,2,1] => 3

[6,5,3,4,1,2] => [[[[.,[.,.]],[.,.]],.],.] => [1,1,0,0,1,1,0,0,1,0,1,0] => [5,4,2,2] => 2

[6,5,3,4,2,1] => [[[[[.,.],.],[.,.]],.],.] => [1,0,1,0,1,1,0,0,1,0,1,0] => [5,4,2,2,1] => 3

[6,5,4,1,2,3] => [[[[.,[.,[.,.]]],.],.],.] => [1,1,1,0,0,0,1,0,1,0,1,0] => [5,4,3] => 3

[6,5,4,1,3,2] => [[[[.,[[.,.],.]],.],.],.] => [1,1,0,1,0,0,1,0,1,0,1,0] => [5,4,3,1] => 4

[6,5,4,2,1,3] => [[[[[.,.],[.,.]],.],.],.] => [1,0,1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,1] => 3

[6,5,4,2,3,1] => [[[[[.,.],[.,.]],.],.],.] => [1,0,1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,1] => 3

[6,5,4,3,1,2] => [[[[[.,[.,.]],.],.],.],.] => [1,1,0,0,1,0,1,0,1,0,1,0] => [5,4,3,2] => 4

[6,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],.] => [1,0,1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => 5

[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] => [1] => 1

[1,2,3,4,6,5,7] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1] => 0

[1,2,3,4,6,7,5] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1] => 0

[1,2,3,4,7,5,6] => [.,[.,[.,[.,[[.,[.,.]],.]]]]] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2] => 1

[1,2,3,4,7,6,5] => [.,[.,[.,[.,[[[.,.],.],.]]]]] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,1] => 2

[1,2,3,5,4,6,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1] => 0

[1,2,3,5,4,7,6] => [.,[.,[.,[[.,.],[[.,.],.]]]]] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,1,1] => 1

[1,2,3,5,6,4,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1] => 0

[1,2,3,5,6,7,4] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1] => 0

[1,2,3,5,7,4,6] => [.,[.,[.,[[.,.],[[.,.],.]]]]] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,1,1] => 1

[1,2,3,5,7,6,4] => [.,[.,[.,[[.,.],[[.,.],.]]]]] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,1,1] => 1

[1,2,3,6,4,5,7] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,2] => 0

[1,2,3,6,4,7,5] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,2] => 0

[1,2,3,6,5,4,7] => [.,[.,[.,[[[.,.],.],[.,.]]]]] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,2,1] => 1

[1,2,3,6,5,7,4] => [.,[.,[.,[[[.,.],.],[.,.]]]]] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,2,1] => 1

[1,2,3,6,7,4,5] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,2] => 0

[1,2,3,6,7,5,4] => [.,[.,[.,[[[.,.],.],[.,.]]]]] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,2,1] => 1

[1,2,3,7,4,5,6] => [.,[.,[.,[[.,[.,[.,.]]],.]]]] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3] => 1

[1,2,3,7,4,6,5] => [.,[.,[.,[[.,[[.,.],.]],.]]]] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [3,1] => 2

[1,2,3,7,5,4,6] => [.,[.,[.,[[[.,.],[.,.]],.]]]] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [3,1,1] => 1

[1,2,3,7,5,6,4] => [.,[.,[.,[[[.,.],[.,.]],.]]]] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [3,1,1] => 1

[1,2,3,7,6,4,5] => [.,[.,[.,[[[.,[.,.]],.],.]]]] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [3,2] => 2

[1,2,3,7,6,5,4] => [.,[.,[.,[[[[.,.],.],.],.]]]] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1] => 3

[1,2,4,3,5,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1] => 0

[1,2,4,3,5,7,6] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1] => 1

[1,2,4,3,6,5,7] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1] => 0

[1,2,4,3,6,7,5] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1] => 0

[1,2,4,3,7,5,6] => [.,[.,[[.,.],[[.,[.,.]],.]]]] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1] => 1

[1,2,4,3,7,6,5] => [.,[.,[[.,.],[[[.,.],.],.]]]] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1] => 2

[1,2,4,5,3,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1] => 0

[1,2,4,5,3,7,6] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1] => 1

[1,2,4,5,6,3,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1] => 0

[1,2,4,5,6,7,3] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1] => 0

[1,2,4,5,7,3,6] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1] => 1

[1,2,4,5,7,6,3] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1] => 1

[1,2,4,6,3,5,7] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1] => 0

[1,2,4,6,3,7,5] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1] => 0

[1,2,4,6,5,3,7] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1] => 0

[1,2,4,6,5,7,3] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1] => 0

[1,2,4,6,7,3,5] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1] => 0

[1,2,4,6,7,5,3] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1] => 0

[1,2,4,7,3,5,6] => [.,[.,[[.,.],[[.,[.,.]],.]]]] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1] => 1

[1,2,4,7,3,6,5] => [.,[.,[[.,.],[[[.,.],.],.]]]] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1] => 2

[1,2,4,7,5,3,6] => [.,[.,[[.,.],[[.,[.,.]],.]]]] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1] => 1

[1,2,4,7,5,6,3] => [.,[.,[[.,.],[[.,[.,.]],.]]]] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1] => 1

[1,2,4,7,6,3,5] => [.,[.,[[.,.],[[[.,.],.],.]]]] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1] => 2

[1,2,4,7,6,5,3] => [.,[.,[[.,.],[[[.,.],.],.]]]] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1] => 2

[1,2,5,3,4,6,7] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,2,2] => 0

[1,2,5,3,4,7,6] => [.,[.,[[.,[.,.]],[[.,.],.]]]] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [3,2,2] => 1

[1,2,5,3,6,4,7] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,2,2] => 0

[1,2,5,3,6,7,4] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,2,2] => 0

[1,2,5,3,7,4,6] => [.,[.,[[.,[.,.]],[[.,.],.]]]] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [3,2,2] => 1

[1,2,5,3,7,6,4] => [.,[.,[[.,[.,.]],[[.,.],.]]]] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [3,2,2] => 1

[1,2,5,4,3,6,7] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1] => 1

[1,2,5,4,3,7,6] => [.,[.,[[[.,.],.],[[.,.],.]]]] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => 2

[1,2,5,4,6,3,7] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1] => 1

[1,2,5,4,6,7,3] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1] => 1

[1,2,5,4,7,3,6] => [.,[.,[[[.,.],.],[[.,.],.]]]] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => 2

[1,2,5,4,7,6,3] => [.,[.,[[[.,.],.],[[.,.],.]]]] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => 2

[1,2,5,6,3,4,7] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,2,2] => 0

[1,2,5,6,3,7,4] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,2,2] => 0

[1,2,5,6,4,3,7] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1] => 1

[1,2,5,6,4,7,3] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1] => 1

[1,2,5,6,7,3,4] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,2,2] => 0

[1,2,5,6,7,4,3] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1] => 1

[1,2,5,7,3,4,6] => [.,[.,[[.,[.,.]],[[.,.],.]]]] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [3,2,2] => 1

[1,2,5,7,3,6,4] => [.,[.,[[.,[.,.]],[[.,.],.]]]] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [3,2,2] => 1

[1,2,5,7,4,3,6] => [.,[.,[[[.,.],.],[[.,.],.]]]] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => 2

[1,2,5,7,4,6,3] => [.,[.,[[[.,.],.],[[.,.],.]]]] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => 2

[1,2,5,7,6,3,4] => [.,[.,[[.,[.,.]],[[.,.],.]]]] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [3,2,2] => 1

[1,2,5,7,6,4,3] => [.,[.,[[[.,.],.],[[.,.],.]]]] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => 2

[1,2,6,3,4,5,7] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [3,3] => 0

[1,2,6,3,4,7,5] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [3,3] => 0

[1,2,6,3,5,4,7] => [.,[.,[[.,[[.,.],.]],[.,.]]]] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [3,3,1] => 1

[1,2,6,3,5,7,4] => [.,[.,[[.,[[.,.],.]],[.,.]]]] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [3,3,1] => 1

[1,2,6,3,7,4,5] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [3,3] => 0

[1,2,6,3,7,5,4] => [.,[.,[[.,[[.,.],.]],[.,.]]]] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [3,3,1] => 1

[1,2,6,4,3,5,7] => [.,[.,[[[.,.],[.,.]],[.,.]]]] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1] => 0

[1,2,6,4,3,7,5] => [.,[.,[[[.,.],[.,.]],[.,.]]]] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1] => 0

[1,2,6,4,5,3,7] => [.,[.,[[[.,.],[.,.]],[.,.]]]] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1] => 0

[1,2,6,4,5,7,3] => [.,[.,[[[.,.],[.,.]],[.,.]]]] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1] => 0

[1,2,6,4,7,3,5] => [.,[.,[[[.,.],[.,.]],[.,.]]]] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1] => 0

[1,2,6,4,7,5,3] => [.,[.,[[[.,.],[.,.]],[.,.]]]] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1] => 0

[1,2,6,5,3,4,7] => [.,[.,[[[.,[.,.]],.],[.,.]]]] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [3,3,2] => 1

[1,2,6,5,3,7,4] => [.,[.,[[[.,[.,.]],.],[.,.]]]] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [3,3,2] => 1

[1,2,6,5,4,3,7] => [.,[.,[[[[.,.],.],.],[.,.]]]] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1] => 2

[1,2,6,5,4,7,3] => [.,[.,[[[[.,.],.],.],[.,.]]]] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1] => 2

[1,2,6,5,7,3,4] => [.,[.,[[[.,[.,.]],.],[.,.]]]] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [3,3,2] => 1

[1,2,6,5,7,4,3] => [.,[.,[[[[.,.],.],.],[.,.]]]] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1] => 2

[1,2,6,7,3,4,5] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [3,3] => 0

[1,2,6,7,3,5,4] => [.,[.,[[.,[[.,.],.]],[.,.]]]] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [3,3,1] => 1

[1,2,6,7,4,3,5] => [.,[.,[[[.,.],[.,.]],[.,.]]]] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1] => 0

[1,2,6,7,4,5,3] => [.,[.,[[[.,.],[.,.]],[.,.]]]] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1] => 0

[1,2,6,7,5,3,4] => [.,[.,[[[.,[.,.]],.],[.,.]]]] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [3,3,2] => 1

[1,2,6,7,5,4,3] => [.,[.,[[[[.,.],.],.],[.,.]]]] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1] => 2

[1,2,7,3,4,5,6] => [.,[.,[[.,[.,[.,[.,.]]]],.]]] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [4] => 1

[1,2,7,3,4,6,5] => [.,[.,[[.,[.,[[.,.],.]]],.]]] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [4,1] => 2

[1,2,7,3,5,4,6] => [.,[.,[[.,[[.,.],[.,.]]],.]]] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,1,1] => 1

[1,2,7,3,5,6,4] => [.,[.,[[.,[[.,.],[.,.]]],.]]] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,1,1] => 1

[1,2,7,3,6,4,5] => [.,[.,[[.,[[.,[.,.]],.]],.]]] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [4,2] => 2

[1,2,7,3,6,5,4] => [.,[.,[[.,[[[.,.],.],.]],.]]] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,2,1] => 3

[1,2,7,4,3,5,6] => [.,[.,[[[.,.],[.,[.,.]]],.]]] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1] => 1

[1,2,7,4,3,6,5] => [.,[.,[[[.,.],[[.,.],.]],.]]] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1] => 2

[1,2,7,4,5,3,6] => [.,[.,[[[.,.],[.,[.,.]]],.]]] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1] => 1

[1,2,7,4,5,6,3] => [.,[.,[[[.,.],[.,[.,.]]],.]]] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1] => 1

[1,2,7,4,6,3,5] => [.,[.,[[[.,.],[[.,.],.]],.]]] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1] => 2

[1,2,7,4,6,5,3] => [.,[.,[[[.,.],[[.,.],.]],.]]] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1] => 2

[1,2,7,5,3,4,6] => [.,[.,[[[.,[.,.]],[.,.]],.]]] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,2,2] => 1

[1,2,7,5,3,6,4] => [.,[.,[[[.,[.,.]],[.,.]],.]]] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,2,2] => 1

[1,2,7,5,4,3,6] => [.,[.,[[[[.,.],.],[.,.]],.]]] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1] => 2

[1,2,7,5,4,6,3] => [.,[.,[[[[.,.],.],[.,.]],.]]] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1] => 2

[1,2,7,5,6,3,4] => [.,[.,[[[.,[.,.]],[.,.]],.]]] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,2,2] => 1

[1,2,7,5,6,4,3] => [.,[.,[[[[.,.],.],[.,.]],.]]] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1] => 2

[1,2,7,6,3,4,5] => [.,[.,[[[.,[.,[.,.]]],.],.]]] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [4,3] => 2

[1,2,7,6,3,5,4] => [.,[.,[[[.,[[.,.],.]],.],.]]] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,3,1] => 3

[1,2,7,6,4,3,5] => [.,[.,[[[[.,.],[.,.]],.],.]]] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1] => 2

[1,2,7,6,4,5,3] => [.,[.,[[[[.,.],[.,.]],.],.]]] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1] => 2

[1,2,7,6,5,3,4] => [.,[.,[[[[.,[.,.]],.],.],.]]] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,3,2] => 3

[1,2,7,6,5,4,3] => [.,[.,[[[[[.,.],.],.],.],.]]] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1] => 4

[1,3,2,4,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1] => 0

[1,3,2,4,5,7,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1] => 1

[1,3,2,4,6,5,7] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1] => 0

[1,3,2,4,6,7,5] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1] => 0

[1,3,2,4,7,5,6] => [.,[[.,.],[.,[[.,[.,.]],.]]]] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1] => 1

[1,3,2,4,7,6,5] => [.,[[.,.],[.,[[[.,.],.],.]]]] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1] => 2

[1,3,2,5,4,6,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1] => 0

[1,3,2,5,4,7,6] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1] => 1

[1,3,2,5,6,4,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1] => 0

[1,3,2,5,6,7,4] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1] => 0

[1,3,2,5,7,4,6] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1] => 1

[1,3,2,5,7,6,4] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1] => 1

[1,3,2,6,4,5,7] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1] => 0

[1,3,2,6,4,7,5] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1] => 0

[1,3,2,6,5,4,7] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1] => 1

[1,3,2,6,5,7,4] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1] => 1

[1,3,2,6,7,4,5] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1] => 0

[1,3,2,6,7,5,4] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1] => 1

[1,3,2,7,4,5,6] => [.,[[.,.],[[.,[.,[.,.]]],.]]] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1] => 1

[1,3,2,7,4,6,5] => [.,[[.,.],[[.,[[.,.],.]],.]]] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1] => 2

[1,3,2,7,5,4,6] => [.,[[.,.],[[[.,.],[.,.]],.]]] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1] => 1

[1,3,2,7,5,6,4] => [.,[[.,.],[[[.,.],[.,.]],.]]] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1] => 1

[1,3,2,7,6,4,5] => [.,[[.,.],[[[.,[.,.]],.],.]]] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1,1] => 2

[1,3,2,7,6,5,4] => [.,[[.,.],[[[[.,.],.],.],.]]] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,1] => 3

[1,3,4,2,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1] => 0

[1,3,4,2,5,7,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1] => 1

[1,3,4,2,6,5,7] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1] => 0

[1,3,4,2,6,7,5] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1] => 0

[1,3,4,2,7,5,6] => [.,[[.,.],[.,[[.,[.,.]],.]]]] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1] => 1

[1,3,4,2,7,6,5] => [.,[[.,.],[.,[[[.,.],.],.]]]] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1] => 2

[1,3,4,5,2,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1] => 0

[1,3,4,5,2,7,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1] => 1

[1,3,4,5,6,2,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1] => 0

[1,3,4,5,6,7,2] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1] => 0

[1,3,4,5,7,2,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1] => 1

[1,3,4,5,7,6,2] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1] => 1

[1,3,4,6,2,5,7] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1] => 0

[1,3,4,6,2,7,5] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1] => 0

[1,3,4,6,5,2,7] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1] => 0

[1,3,4,6,5,7,2] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1] => 0

[1,3,4,6,7,2,5] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1] => 0

[1,3,4,6,7,5,2] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1] => 0

[1,3,4,7,2,5,6] => [.,[[.,.],[.,[[.,[.,.]],.]]]] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1] => 1

[1,3,4,7,2,6,5] => [.,[[.,.],[.,[[[.,.],.],.]]]] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1] => 2

[1,3,4,7,5,2,6] => [.,[[.,.],[.,[[.,[.,.]],.]]]] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1] => 1

[1,3,4,7,5,6,2] => [.,[[.,.],[.,[[.,[.,.]],.]]]] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1] => 1

[1,3,4,7,6,2,5] => [.,[[.,.],[.,[[[.,.],.],.]]]] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1] => 2

[1,3,4,7,6,5,2] => [.,[[.,.],[.,[[[.,.],.],.]]]] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1] => 2

[1,3,5,2,4,6,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1] => 0

[1,3,5,2,4,7,6] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1] => 1

[1,3,5,2,6,4,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1] => 0

[1,3,5,2,6,7,4] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1] => 0

[1,3,5,2,7,4,6] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1] => 1

[1,3,5,2,7,6,4] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1] => 1

[1,3,5,4,2,6,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1] => 0

[1,3,5,4,2,7,6] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1] => 1

[1,3,5,4,6,2,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1] => 0

[1,3,5,4,6,7,2] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1] => 0

[1,3,5,4,7,2,6] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1] => 1

[1,3,5,4,7,6,2] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1] => 1

[1,3,5,6,2,4,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1] => 0

[1,3,5,6,2,7,4] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1] => 0

[1,3,5,6,4,2,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1] => 0

[1,3,5,6,4,7,2] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1] => 0

[1,3,5,6,7,2,4] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1] => 0

[1,3,5,6,7,4,2] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1] => 0

[1,3,5,7,2,4,6] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1] => 1

[1,3,5,7,2,6,4] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1] => 1

[1,3,5,7,4,2,6] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1] => 1

[1,3,5,7,4,6,2] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1] => 1

[1,3,5,7,6,2,4] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1] => 1

[1,3,5,7,6,4,2] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1] => 1

[1,3,6,2,4,5,7] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1] => 0

[1,3,6,2,4,7,5] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1] => 0

[1,3,6,2,5,4,7] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1] => 1

[1,3,6,2,5,7,4] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1] => 1

[1,3,6,2,7,4,5] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1] => 0

[1,3,6,2,7,5,4] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1] => 1

[1,3,6,4,2,5,7] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1] => 0

[1,3,6,4,2,7,5] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1] => 0

[1,3,6,4,5,2,7] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1] => 0

[1,3,6,4,5,7,2] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1] => 0

[1,3,6,4,7,2,5] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1] => 0

[1,3,6,4,7,5,2] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1] => 0

[1,3,6,5,2,4,7] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1] => 1

[1,3,6,5,2,7,4] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1] => 1

[1,3,6,5,4,2,7] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1] => 1

[1,3,6,5,4,7,2] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1] => 1

[1,3,6,5,7,2,4] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1] => 1

[1,3,6,5,7,4,2] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1] => 1

[1,3,6,7,2,4,5] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1] => 0

[1,3,6,7,2,5,4] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1] => 1

[1,3,6,7,4,2,5] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1] => 0

[1,3,6,7,4,5,2] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1] => 0

[1,3,6,7,5,2,4] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1] => 1

[1,3,6,7,5,4,2] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1] => 1

[1,3,7,2,4,5,6] => [.,[[.,.],[[.,[.,[.,.]]],.]]] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1] => 1

[1,3,7,2,4,6,5] => [.,[[.,.],[[.,[[.,.],.]],.]]] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1] => 2

[1,3,7,2,5,4,6] => [.,[[.,.],[[[.,.],[.,.]],.]]] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1] => 1

[1,3,7,2,5,6,4] => [.,[[.,.],[[[.,.],[.,.]],.]]] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1] => 1

[1,3,7,2,6,4,5] => [.,[[.,.],[[[.,[.,.]],.],.]]] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1,1] => 2

[1,3,7,2,6,5,4] => [.,[[.,.],[[[[.,.],.],.],.]]] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,1] => 3

[1,3,7,4,2,5,6] => [.,[[.,.],[[.,[.,[.,.]]],.]]] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1] => 1

[1,3,7,4,2,6,5] => [.,[[.,.],[[.,[[.,.],.]],.]]] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1] => 2

[1,3,7,4,5,2,6] => [.,[[.,.],[[.,[.,[.,.]]],.]]] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1] => 1

[1,3,7,4,5,6,2] => [.,[[.,.],[[.,[.,[.,.]]],.]]] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1] => 1

[1,3,7,4,6,2,5] => [.,[[.,.],[[.,[[.,.],.]],.]]] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1] => 2

[1,3,7,4,6,5,2] => [.,[[.,.],[[.,[[.,.],.]],.]]] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1] => 2

[1,3,7,5,2,4,6] => [.,[[.,.],[[[.,.],[.,.]],.]]] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1] => 1

[1,3,7,5,2,6,4] => [.,[[.,.],[[[.,.],[.,.]],.]]] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1] => 1

[1,3,7,5,4,2,6] => [.,[[.,.],[[[.,.],[.,.]],.]]] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1] => 1

[1,3,7,5,4,6,2] => [.,[[.,.],[[[.,.],[.,.]],.]]] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1] => 1

[1,3,7,5,6,2,4] => [.,[[.,.],[[[.,.],[.,.]],.]]] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1] => 1

[1,3,7,5,6,4,2] => [.,[[.,.],[[[.,.],[.,.]],.]]] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1] => 1

[1,3,7,6,2,4,5] => [.,[[.,.],[[[.,[.,.]],.],.]]] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1,1] => 2

[1,3,7,6,2,5,4] => [.,[[.,.],[[[[.,.],.],.],.]]] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,1] => 3

[1,3,7,6,4,2,5] => [.,[[.,.],[[[.,[.,.]],.],.]]] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1,1] => 2

[1,3,7,6,4,5,2] => [.,[[.,.],[[[.,[.,.]],.],.]]] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1,1] => 2

[1,3,7,6,5,2,4] => [.,[[.,.],[[[[.,.],.],.],.]]] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,1] => 3

[1,3,7,6,5,4,2] => [.,[[.,.],[[[[.,.],.],.],.]]] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,1] => 3

[1,4,2,3,5,6,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2] => 0

[1,4,2,3,5,7,6] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2] => 1

[1,4,2,3,6,5,7] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2] => 0

[1,4,2,3,6,7,5] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2] => 0

[1,4,2,3,7,5,6] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2] => 1

[1,4,2,3,7,6,5] => [.,[[.,[.,.]],[[[.,.],.],.]]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2] => 2

[1,4,2,5,3,6,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2] => 0

[1,4,2,5,3,7,6] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2] => 1

[1,4,2,5,6,3,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2] => 0

[1,4,2,5,6,7,3] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2] => 0

[1,4,2,5,7,3,6] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2] => 1

[1,4,2,5,7,6,3] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2] => 1

[1,4,2,6,3,5,7] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2] => 0

[1,4,2,6,3,7,5] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2] => 0

[1,4,2,6,5,3,7] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2] => 0

[1,4,2,6,5,7,3] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2] => 0

[1,4,2,6,7,3,5] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2] => 0

[1,4,2,6,7,5,3] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2] => 0

[1,4,2,7,3,5,6] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2] => 1

[1,4,2,7,3,6,5] => [.,[[.,[.,.]],[[[.,.],.],.]]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2] => 2

[1,4,2,7,5,3,6] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2] => 1

[1,4,2,7,5,6,3] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2] => 1

[1,4,2,7,6,3,5] => [.,[[.,[.,.]],[[[.,.],.],.]]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2] => 2

[1,4,2,7,6,5,3] => [.,[[.,[.,.]],[[[.,.],.],.]]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2] => 2

[1,4,3,2,5,6,7] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1] => 1

[1,4,3,2,5,7,6] => [.,[[[.,.],.],[.,[[.,.],.]]]] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1] => 2

[1,4,3,2,6,5,7] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1] => 1

[1,4,3,2,6,7,5] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1] => 1

[1,4,3,2,7,5,6] => [.,[[[.,.],.],[[.,[.,.]],.]]] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1] => 2

[1,4,3,2,7,6,5] => [.,[[[.,.],.],[[[.,.],.],.]]] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1] => 3

[1,4,3,5,2,6,7] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1] => 1

[1,4,3,5,2,7,6] => [.,[[[.,.],.],[.,[[.,.],.]]]] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1] => 2

[1,4,3,5,6,2,7] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1] => 1

[1,4,3,5,6,7,2] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1] => 1

[1,4,3,5,7,2,6] => [.,[[[.,.],.],[.,[[.,.],.]]]] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1] => 2

[1,4,3,5,7,6,2] => [.,[[[.,.],.],[.,[[.,.],.]]]] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1] => 2

[1,4,3,6,2,5,7] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1] => 1

[1,4,3,6,2,7,5] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1] => 1

[1,4,3,6,5,2,7] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1] => 1

[1,4,3,6,5,7,2] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1] => 1

[1,4,3,6,7,2,5] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1] => 1

[1,4,3,6,7,5,2] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1] => 1

[1,4,3,7,2,5,6] => [.,[[[.,.],.],[[.,[.,.]],.]]] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1] => 2

[1,4,3,7,2,6,5] => [.,[[[.,.],.],[[[.,.],.],.]]] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1] => 3

[1,4,3,7,5,2,6] => [.,[[[.,.],.],[[.,[.,.]],.]]] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1] => 2

[1,4,3,7,5,6,2] => [.,[[[.,.],.],[[.,[.,.]],.]]] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1] => 2

[1,4,3,7,6,2,5] => [.,[[[.,.],.],[[[.,.],.],.]]] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1] => 3

[1,4,3,7,6,5,2] => [.,[[[.,.],.],[[[.,.],.],.]]] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1] => 3

[1,4,5,2,3,6,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2] => 0

[1,4,5,2,3,7,6] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2] => 1

[1,4,5,2,6,3,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2] => 0

[1,4,5,2,6,7,3] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2] => 0

[1,4,5,2,7,3,6] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2] => 1

[1,4,5,2,7,6,3] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2] => 1

[1,4,5,3,2,6,7] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1] => 1

[1,4,5,3,2,7,6] => [.,[[[.,.],.],[.,[[.,.],.]]]] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1] => 2

[1,4,5,3,6,2,7] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1] => 1

[1,4,5,3,6,7,2] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1] => 1

[1,4,5,3,7,2,6] => [.,[[[.,.],.],[.,[[.,.],.]]]] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1] => 2

[1,4,5,3,7,6,2] => [.,[[[.,.],.],[.,[[.,.],.]]]] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1] => 2

[1,4,5,6,2,3,7] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2] => 0

[1,4,5,6,2,7,3] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2] => 0

[1,4,5,6,3,2,7] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1] => 1

[1,4,5,6,3,7,2] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1] => 1

[1,4,5,6,7,2,3] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2] => 0

[1,4,5,6,7,3,2] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1] => 1

[1,4,5,7,2,3,6] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2] => 1

[1,4,5,7,2,6,3] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2] => 1

[1,4,5,7,3,2,6] => [.,[[[.,.],.],[.,[[.,.],.]]]] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1] => 2

[1,4,5,7,3,6,2] => [.,[[[.,.],.],[.,[[.,.],.]]]] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1] => 2

[1,4,5,7,6,2,3] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2] => 1

[1,4,5,7,6,3,2] => [.,[[[.,.],.],[.,[[.,.],.]]]] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1] => 2

[1,4,6,2,3,5,7] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2] => 0

[1,4,6,2,3,7,5] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2] => 0

[1,4,6,2,5,3,7] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2] => 0

[1,4,6,2,5,7,3] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2] => 0

[1,4,6,2,7,3,5] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2] => 0

[1,4,6,2,7,5,3] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2] => 0

[1,4,6,3,2,5,7] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1] => 1

[1,4,6,3,2,7,5] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1] => 1

[1,4,6,3,5,2,7] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1] => 1

[1,4,6,3,5,7,2] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1] => 1

[1,4,6,3,7,2,5] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1] => 1

[1,4,6,3,7,5,2] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1] => 1

[1,4,6,5,2,3,7] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2] => 0

[1,4,6,5,2,7,3] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2] => 0

[1,4,6,5,3,2,7] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1] => 1

[1,4,6,5,3,7,2] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1] => 1

[1,4,6,5,7,2,3] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2] => 0

[1,4,6,5,7,3,2] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1] => 1

[1,4,6,7,2,3,5] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2] => 0

[1,4,6,7,2,5,3] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2] => 0

[1,4,6,7,3,2,5] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1] => 1

[1,4,6,7,3,5,2] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1] => 1

[1,4,6,7,5,2,3] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2] => 0

[1,4,6,7,5,3,2] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1] => 1

[1,4,7,2,3,5,6] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2] => 1

[1,4,7,2,3,6,5] => [.,[[.,[.,.]],[[[.,.],.],.]]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2] => 2

[1,4,7,2,5,3,6] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2] => 1

[1,4,7,2,5,6,3] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2] => 1

[1,4,7,2,6,3,5] => [.,[[.,[.,.]],[[[.,.],.],.]]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2] => 2

[1,4,7,2,6,5,3] => [.,[[.,[.,.]],[[[.,.],.],.]]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2] => 2

[1,4,7,3,2,5,6] => [.,[[[.,.],.],[[.,[.,.]],.]]] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1] => 2

[1,4,7,3,2,6,5] => [.,[[[.,.],.],[[[.,.],.],.]]] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1] => 3

[1,4,7,3,5,2,6] => [.,[[[.,.],.],[[.,[.,.]],.]]] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1] => 2

[1,4,7,3,5,6,2] => [.,[[[.,.],.],[[.,[.,.]],.]]] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1] => 2

[1,4,7,3,6,2,5] => [.,[[[.,.],.],[[[.,.],.],.]]] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1] => 3

[1,4,7,3,6,5,2] => [.,[[[.,.],.],[[[.,.],.],.]]] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1] => 3

[1,4,7,5,2,3,6] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2] => 1

[1,4,7,5,2,6,3] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2] => 1

[1,4,7,5,3,2,6] => [.,[[[.,.],.],[[.,[.,.]],.]]] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1] => 2

[1,4,7,5,3,6,2] => [.,[[[.,.],.],[[.,[.,.]],.]]] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1] => 2

[1,4,7,5,6,2,3] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2] => 1

[1,4,7,5,6,3,2] => [.,[[[.,.],.],[[.,[.,.]],.]]] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1] => 2

[1,4,7,6,2,3,5] => [.,[[.,[.,.]],[[[.,.],.],.]]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2] => 2

[1,4,7,6,2,5,3] => [.,[[.,[.,.]],[[[.,.],.],.]]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2] => 2

[1,4,7,6,3,2,5] => [.,[[[.,.],.],[[[.,.],.],.]]] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1] => 3

[1,4,7,6,3,5,2] => [.,[[[.,.],.],[[[.,.],.],.]]] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1] => 3

[1,4,7,6,5,2,3] => [.,[[.,[.,.]],[[[.,.],.],.]]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2] => 2

[1,4,7,6,5,3,2] => [.,[[[.,.],.],[[[.,.],.],.]]] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1] => 3

[1,5,2,3,4,6,7] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [3,3,3] => 0

[1,5,2,3,4,7,6] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,3] => 1

[1,5,2,3,6,4,7] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [3,3,3] => 0

[1,5,2,3,6,7,4] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [3,3,3] => 0

[1,5,2,3,7,4,6] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,3] => 1

[1,5,2,3,7,6,4] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,3] => 1

[1,5,2,4,3,6,7] => [.,[[.,[[.,.],.]],[.,[.,.]]]] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1] => 1

[1,5,2,4,3,7,6] => [.,[[.,[[.,.],.]],[[.,.],.]]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1] => 2

[1,5,2,4,6,3,7] => [.,[[.,[[.,.],.]],[.,[.,.]]]] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1] => 1

[1,5,2,4,6,7,3] => [.,[[.,[[.,.],.]],[.,[.,.]]]] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1] => 1

[1,5,2,4,7,3,6] => [.,[[.,[[.,.],.]],[[.,.],.]]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1] => 2

[1,5,2,4,7,6,3] => [.,[[.,[[.,.],.]],[[.,.],.]]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1] => 2

[1,5,2,6,3,4,7] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [3,3,3] => 0

[1,5,2,6,3,7,4] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [3,3,3] => 0

[1,5,2,6,4,3,7] => [.,[[.,[[.,.],.]],[.,[.,.]]]] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1] => 1

[1,5,2,6,4,7,3] => [.,[[.,[[.,.],.]],[.,[.,.]]]] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1] => 1

[1,5,2,6,7,3,4] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [3,3,3] => 0

[1,5,2,6,7,4,3] => [.,[[.,[[.,.],.]],[.,[.,.]]]] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1] => 1

[1,5,2,7,3,4,6] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,3] => 1

[1,5,2,7,3,6,4] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,3] => 1

[1,5,2,7,4,3,6] => [.,[[.,[[.,.],.]],[[.,.],.]]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1] => 2

[1,5,2,7,4,6,3] => [.,[[.,[[.,.],.]],[[.,.],.]]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1] => 2

[1,5,2,7,6,3,4] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,3] => 1

[1,5,2,7,6,4,3] => [.,[[.,[[.,.],.]],[[.,.],.]]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1] => 2

[1,5,3,2,4,6,7] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1] => 0

[1,5,3,2,4,7,6] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1] => 1

[1,5,3,2,6,4,7] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1] => 0

[1,5,3,2,6,7,4] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1] => 0

[1,5,3,2,7,4,6] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1] => 1

[1,5,3,2,7,6,4] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1] => 1

[1,5,3,4,2,6,7] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1] => 0

[1,5,3,4,2,7,6] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1] => 1

[1,5,3,4,6,2,7] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1] => 0

[1,5,3,4,6,7,2] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1] => 0

[1,5,3,4,7,2,6] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1] => 1

[1,5,3,4,7,6,2] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1] => 1

[1,5,3,6,2,4,7] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1] => 0

[1,5,3,6,2,7,4] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1] => 0

[1,5,3,6,4,2,7] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1] => 0

[1,5,3,6,4,7,2] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1] => 0

[1,5,3,6,7,2,4] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1] => 0

[1,5,3,6,7,4,2] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1] => 0

[1,5,3,7,2,4,6] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1] => 1

[1,5,3,7,2,6,4] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1] => 1

[1,5,3,7,4,2,6] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1] => 1

[1,5,3,7,4,6,2] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1] => 1

[1,5,3,7,6,2,4] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1] => 1

[1,5,3,7,6,4,2] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1] => 1

[1,5,4,2,3,6,7] => [.,[[[.,[.,.]],.],[.,[.,.]]]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2] => 1

[1,5,4,2,3,7,6] => [.,[[[.,[.,.]],.],[[.,.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2] => 2

[1,5,4,2,6,3,7] => [.,[[[.,[.,.]],.],[.,[.,.]]]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2] => 1

[1,5,4,2,6,7,3] => [.,[[[.,[.,.]],.],[.,[.,.]]]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2] => 1

[1,5,4,2,7,3,6] => [.,[[[.,[.,.]],.],[[.,.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2] => 2

[1,5,4,2,7,6,3] => [.,[[[.,[.,.]],.],[[.,.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2] => 2

[1,5,4,3,2,6,7] => [.,[[[[.,.],.],.],[.,[.,.]]]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1] => 2

[1,5,4,3,2,7,6] => [.,[[[[.,.],.],.],[[.,.],.]]] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1] => 3

[1,5,4,3,6,2,7] => [.,[[[[.,.],.],.],[.,[.,.]]]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1] => 2

[1,5,4,3,6,7,2] => [.,[[[[.,.],.],.],[.,[.,.]]]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1] => 2

[1,5,4,3,7,2,6] => [.,[[[[.,.],.],.],[[.,.],.]]] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1] => 3

[1,5,4,3,7,6,2] => [.,[[[[.,.],.],.],[[.,.],.]]] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1] => 3

[1,5,4,6,2,3,7] => [.,[[[.,[.,.]],.],[.,[.,.]]]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2] => 1

[1,5,4,6,2,7,3] => [.,[[[.,[.,.]],.],[.,[.,.]]]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2] => 1

[1,5,4,6,3,2,7] => [.,[[[[.,.],.],.],[.,[.,.]]]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1] => 2

[1,5,4,6,3,7,2] => [.,[[[[.,.],.],.],[.,[.,.]]]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1] => 2

[1,5,4,6,7,2,3] => [.,[[[.,[.,.]],.],[.,[.,.]]]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2] => 1

[1,5,4,6,7,3,2] => [.,[[[[.,.],.],.],[.,[.,.]]]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1] => 2

[1,5,4,7,2,3,6] => [.,[[[.,[.,.]],.],[[.,.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2] => 2

[1,5,4,7,2,6,3] => [.,[[[.,[.,.]],.],[[.,.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2] => 2

[1,5,4,7,3,2,6] => [.,[[[[.,.],.],.],[[.,.],.]]] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1] => 3

[1,5,4,7,3,6,2] => [.,[[[[.,.],.],.],[[.,.],.]]] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1] => 3

[1,5,4,7,6,2,3] => [.,[[[.,[.,.]],.],[[.,.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2] => 2

[1,5,4,7,6,3,2] => [.,[[[[.,.],.],.],[[.,.],.]]] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1] => 3

[1,5,6,2,3,4,7] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [3,3,3] => 0

[1,5,6,2,3,7,4] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [3,3,3] => 0

[1,5,6,2,4,3,7] => [.,[[.,[[.,.],.]],[.,[.,.]]]] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1] => 1

[1,5,6,2,4,7,3] => [.,[[.,[[.,.],.]],[.,[.,.]]]] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1] => 1

[1,5,6,2,7,3,4] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [3,3,3] => 0

[1,5,6,2,7,4,3] => [.,[[.,[[.,.],.]],[.,[.,.]]]] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1] => 1

[1,5,6,3,2,4,7] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1] => 0

[1,5,6,3,2,7,4] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1] => 0

[1,5,6,3,4,2,7] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1] => 0

[1,5,6,3,4,7,2] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1] => 0

[1,5,6,3,7,2,4] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1] => 0

[1,5,6,3,7,4,2] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1] => 0

[1,5,6,4,2,3,7] => [.,[[[.,[.,.]],.],[.,[.,.]]]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2] => 1

[1,5,6,4,2,7,3] => [.,[[[.,[.,.]],.],[.,[.,.]]]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2] => 1

[1,5,6,4,3,2,7] => [.,[[[[.,.],.],.],[.,[.,.]]]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1] => 2

[1,5,6,4,3,7,2] => [.,[[[[.,.],.],.],[.,[.,.]]]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1] => 2

[1,5,6,4,7,2,3] => [.,[[[.,[.,.]],.],[.,[.,.]]]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2] => 1

[1,5,6,4,7,3,2] => [.,[[[[.,.],.],.],[.,[.,.]]]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1] => 2

[1,5,6,7,2,3,4] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [3,3,3] => 0

[1,5,6,7,2,4,3] => [.,[[.,[[.,.],.]],[.,[.,.]]]] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1] => 1

[1,5,6,7,3,2,4] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1] => 0

[1,5,6,7,3,4,2] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1] => 0

[1,5,6,7,4,2,3] => [.,[[[.,[.,.]],.],[.,[.,.]]]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2] => 1

[1,5,6,7,4,3,2] => [.,[[[[.,.],.],.],[.,[.,.]]]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1] => 2

[1,5,7,2,3,4,6] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,3] => 1

[1,5,7,2,3,6,4] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,3] => 1

[1,5,7,2,4,3,6] => [.,[[.,[[.,.],.]],[[.,.],.]]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1] => 2

[1,5,7,2,4,6,3] => [.,[[.,[[.,.],.]],[[.,.],.]]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1] => 2

[1,5,7,2,6,3,4] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,3] => 1

[1,5,7,2,6,4,3] => [.,[[.,[[.,.],.]],[[.,.],.]]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1] => 2

[1,5,7,3,2,4,6] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1] => 1

[1,5,7,3,2,6,4] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1] => 1

[1,5,7,3,4,2,6] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1] => 1

[1,5,7,3,4,6,2] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1] => 1

[1,5,7,3,6,2,4] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1] => 1

[1,5,7,3,6,4,2] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1] => 1

[1,5,7,4,2,3,6] => [.,[[[.,[.,.]],.],[[.,.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2] => 2

[1,5,7,4,2,6,3] => [.,[[[.,[.,.]],.],[[.,.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2] => 2

[1,5,7,4,3,2,6] => [.,[[[[.,.],.],.],[[.,.],.]]] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1] => 3

[1,5,7,4,3,6,2] => [.,[[[[.,.],.],.],[[.,.],.]]] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1] => 3

[1,5,7,4,6,2,3] => [.,[[[.,[.,.]],.],[[.,.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2] => 2

[1,5,7,4,6,3,2] => [.,[[[[.,.],.],.],[[.,.],.]]] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1] => 3

[1,5,7,6,2,3,4] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,3] => 1

[1,5,7,6,2,4,3] => [.,[[.,[[.,.],.]],[[.,.],.]]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1] => 2

[1,5,7,6,3,2,4] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1] => 1

[1,5,7,6,3,4,2] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1] => 1

[1,5,7,6,4,2,3] => [.,[[[.,[.,.]],.],[[.,.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2] => 2

[1,5,7,6,4,3,2] => [.,[[[[.,.],.],.],[[.,.],.]]] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1] => 3

[1,6,2,3,4,5,7] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [4,4] => 0

[1,6,2,3,4,7,5] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [4,4] => 0

[1,6,2,3,5,4,7] => [.,[[.,[.,[[.,.],.]]],[.,.]]] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,4,1] => 1

[1,6,2,3,5,7,4] => [.,[[.,[.,[[.,.],.]]],[.,.]]] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,4,1] => 1

[1,6,2,3,7,4,5] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [4,4] => 0

[1,6,2,3,7,5,4] => [.,[[.,[.,[[.,.],.]]],[.,.]]] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,4,1] => 1

[1,6,2,4,3,5,7] => [.,[[.,[[.,.],[.,.]]],[.,.]]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1] => 0

[1,6,2,4,3,7,5] => [.,[[.,[[.,.],[.,.]]],[.,.]]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1] => 0

[1,6,2,4,5,3,7] => [.,[[.,[[.,.],[.,.]]],[.,.]]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1] => 0

[1,6,2,4,5,7,3] => [.,[[.,[[.,.],[.,.]]],[.,.]]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1] => 0

[1,6,2,4,7,3,5] => [.,[[.,[[.,.],[.,.]]],[.,.]]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1] => 0

[1,6,2,4,7,5,3] => [.,[[.,[[.,.],[.,.]]],[.,.]]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1] => 0

[1,6,2,5,3,4,7] => [.,[[.,[[.,[.,.]],.]],[.,.]]] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,4,2] => 1

[1,6,2,5,3,7,4] => [.,[[.,[[.,[.,.]],.]],[.,.]]] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,4,2] => 1

[1,6,2,5,4,3,7] => [.,[[.,[[[.,.],.],.]],[.,.]]] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1] => 2

[1,6,2,5,4,7,3] => [.,[[.,[[[.,.],.],.]],[.,.]]] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1] => 2

[1,6,2,5,7,3,4] => [.,[[.,[[.,[.,.]],.]],[.,.]]] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,4,2] => 1

[1,6,2,5,7,4,3] => [.,[[.,[[[.,.],.],.]],[.,.]]] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1] => 2

[1,6,2,7,3,4,5] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [4,4] => 0

[1,6,2,7,3,5,4] => [.,[[.,[.,[[.,.],.]]],[.,.]]] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,4,1] => 1

[1,6,2,7,4,3,5] => [.,[[.,[[.,.],[.,.]]],[.,.]]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1] => 0

[1,6,2,7,4,5,3] => [.,[[.,[[.,.],[.,.]]],[.,.]]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1] => 0

[1,6,2,7,5,3,4] => [.,[[.,[[.,[.,.]],.]],[.,.]]] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,4,2] => 1

[1,6,2,7,5,4,3] => [.,[[.,[[[.,.],.],.]],[.,.]]] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1] => 2

[1,6,3,2,4,5,7] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1] => 0

[1,6,3,2,4,7,5] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1] => 0

[1,6,3,2,5,4,7] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1] => 1

[1,6,3,2,5,7,4] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1] => 1

[1,6,3,2,7,4,5] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1] => 0

[1,6,3,2,7,5,4] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1] => 1

[1,6,3,4,2,5,7] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1] => 0

[1,6,3,4,2,7,5] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1] => 0

[1,6,3,4,5,2,7] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1] => 0

[1,6,3,4,5,7,2] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1] => 0

[1,6,3,4,7,2,5] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1] => 0

[1,6,3,4,7,5,2] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1] => 0

[1,6,3,5,2,4,7] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1] => 1

[1,6,3,5,2,7,4] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1] => 1

[1,6,3,5,4,2,7] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1] => 1

[1,6,3,5,4,7,2] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1] => 1

[1,6,3,5,7,2,4] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1] => 1

[1,6,3,5,7,4,2] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1] => 1

[1,6,3,7,2,4,5] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1] => 0

[1,6,3,7,2,5,4] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1] => 1

[1,6,3,7,4,2,5] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1] => 0

[1,6,3,7,4,5,2] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1] => 0

[1,6,3,7,5,2,4] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1] => 1

[1,6,3,7,5,4,2] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1] => 1

[1,6,4,2,3,5,7] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2] => 0

[1,6,4,2,3,7,5] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2] => 0

[1,6,4,2,5,3,7] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2] => 0

[1,6,4,2,5,7,3] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2] => 0

[1,6,4,2,7,3,5] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2] => 0

[1,6,4,2,7,5,3] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2] => 0

[1,6,4,3,2,5,7] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1] => 1

[1,6,4,3,2,7,5] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1] => 1

[1,6,4,3,5,2,7] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1] => 1

[1,6,4,3,5,7,2] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1] => 1

[1,6,4,3,7,2,5] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1] => 1

[1,6,4,3,7,5,2] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1] => 1

[1,6,4,5,2,3,7] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2] => 0

[1,6,4,5,2,7,3] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2] => 0

[1,6,4,5,3,2,7] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1] => 1

[1,6,4,5,3,7,2] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1] => 1

[1,6,4,5,7,2,3] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2] => 0

[1,6,4,5,7,3,2] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1] => 1

[1,6,4,7,2,3,5] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2] => 0

[1,6,4,7,2,5,3] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2] => 0

[1,6,4,7,3,2,5] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1] => 1

[1,6,4,7,3,5,2] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1] => 1

[1,6,4,7,5,2,3] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2] => 0

[1,6,4,7,5,3,2] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1] => 1

[1,6,5,2,3,4,7] => [.,[[[.,[.,[.,.]]],.],[.,.]]] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,4,3] => 1

[1,6,5,2,3,7,4] => [.,[[[.,[.,[.,.]]],.],[.,.]]] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,4,3] => 1

[1,6,5,2,4,3,7] => [.,[[[.,[[.,.],.]],.],[.,.]]] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1] => 2

[1,6,5,2,4,7,3] => [.,[[[.,[[.,.],.]],.],[.,.]]] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1] => 2

[1,6,5,2,7,3,4] => [.,[[[.,[.,[.,.]]],.],[.,.]]] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,4,3] => 1

[1,6,5,2,7,4,3] => [.,[[[.,[[.,.],.]],.],[.,.]]] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1] => 2

[1,6,5,3,2,4,7] => [.,[[[[.,.],[.,.]],.],[.,.]]] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1,1] => 1

[1,6,5,3,2,7,4] => [.,[[[[.,.],[.,.]],.],[.,.]]] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1,1] => 1

[1,6,5,3,4,2,7] => [.,[[[[.,.],[.,.]],.],[.,.]]] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1,1] => 1

[1,6,5,3,4,7,2] => [.,[[[[.,.],[.,.]],.],[.,.]]] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1,1] => 1

[1,6,5,3,7,2,4] => [.,[[[[.,.],[.,.]],.],[.,.]]] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1,1] => 1

[1,6,5,3,7,4,2] => [.,[[[[.,.],[.,.]],.],[.,.]]] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1,1] => 1

[1,6,5,4,2,3,7] => [.,[[[[.,[.,.]],.],.],[.,.]]] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2] => 2

[1,6,5,4,2,7,3] => [.,[[[[.,[.,.]],.],.],[.,.]]] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2] => 2

[1,6,5,4,3,2,7] => [.,[[[[[.,.],.],.],.],[.,.]]] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2,1] => 3

[1,6,5,4,3,7,2] => [.,[[[[[.,.],.],.],.],[.,.]]] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2,1] => 3

[1,6,5,4,7,2,3] => [.,[[[[.,[.,.]],.],.],[.,.]]] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2] => 2

[1,6,5,4,7,3,2] => [.,[[[[[.,.],.],.],.],[.,.]]] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2,1] => 3

[1,6,5,7,2,3,4] => [.,[[[.,[.,[.,.]]],.],[.,.]]] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,4,3] => 1

[1,6,5,7,2,4,3] => [.,[[[.,[[.,.],.]],.],[.,.]]] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1] => 2

[1,6,5,7,3,2,4] => [.,[[[[.,.],[.,.]],.],[.,.]]] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1,1] => 1

[1,6,5,7,3,4,2] => [.,[[[[.,.],[.,.]],.],[.,.]]] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1,1] => 1

[1,6,5,7,4,2,3] => [.,[[[[.,[.,.]],.],.],[.,.]]] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2] => 2

[1,6,5,7,4,3,2] => [.,[[[[[.,.],.],.],.],[.,.]]] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2,1] => 3

[1,6,7,2,3,4,5] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [4,4] => 0

[1,6,7,2,3,5,4] => [.,[[.,[.,[[.,.],.]]],[.,.]]] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,4,1] => 1

[1,6,7,2,4,3,5] => [.,[[.,[[.,.],[.,.]]],[.,.]]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1] => 0

[1,6,7,2,4,5,3] => [.,[[.,[[.,.],[.,.]]],[.,.]]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1] => 0

[1,6,7,2,5,3,4] => [.,[[.,[[.,[.,.]],.]],[.,.]]] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,4,2] => 1

[1,6,7,2,5,4,3] => [.,[[.,[[[.,.],.],.]],[.,.]]] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1] => 2

[1,6,7,3,2,4,5] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1] => 0

[1,6,7,3,2,5,4] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1] => 1

[1,6,7,3,4,2,5] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1] => 0

[1,6,7,3,4,5,2] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1] => 0

[1,6,7,3,5,2,4] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1] => 1

[1,6,7,3,5,4,2] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1] => 1

[1,6,7,4,2,3,5] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2] => 0

[1,6,7,4,2,5,3] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2] => 0

[1,6,7,4,3,2,5] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1] => 1

[1,6,7,4,3,5,2] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1] => 1

[1,6,7,4,5,2,3] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2] => 0

[1,6,7,4,5,3,2] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1] => 1

[1,6,7,5,2,3,4] => [.,[[[.,[.,[.,.]]],.],[.,.]]] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,4,3] => 1

[1,6,7,5,2,4,3] => [.,[[[.,[[.,.],.]],.],[.,.]]] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1] => 2

[1,6,7,5,3,2,4] => [.,[[[[.,.],[.,.]],.],[.,.]]] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1,1] => 1

[1,6,7,5,3,4,2] => [.,[[[[.,.],[.,.]],.],[.,.]]] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1,1] => 1

[1,6,7,5,4,2,3] => [.,[[[[.,[.,.]],.],.],[.,.]]] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2] => 2

[1,6,7,5,4,3,2] => [.,[[[[[.,.],.],.],.],[.,.]]] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2,1] => 3

[1,7,2,3,4,5,6] => [.,[[.,[.,[.,[.,[.,.]]]]],.]] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => 1

[1,7,2,3,4,6,5] => [.,[[.,[.,[.,[[.,.],.]]]],.]] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,1] => 2

[1,7,2,3,5,4,6] => [.,[[.,[.,[[.,.],[.,.]]]],.]] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [5,1,1] => 1

[1,7,2,3,5,6,4] => [.,[[.,[.,[[.,.],[.,.]]]],.]] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [5,1,1] => 1

[1,7,2,3,6,4,5] => [.,[[.,[.,[[.,[.,.]],.]]],.]] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,2] => 2

[1,7,2,3,6,5,4] => [.,[[.,[.,[[[.,.],.],.]]],.]] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [5,2,1] => 3

[1,7,2,4,3,5,6] => [.,[[.,[[.,.],[.,[.,.]]]],.]] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1] => 1

[1,7,2,4,3,6,5] => [.,[[.,[[.,.],[[.,.],.]]],.]] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1] => 2

[1,7,2,4,5,3,6] => [.,[[.,[[.,.],[.,[.,.]]]],.]] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1] => 1

[1,7,2,4,5,6,3] => [.,[[.,[[.,.],[.,[.,.]]]],.]] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1] => 1

[1,7,2,4,6,3,5] => [.,[[.,[[.,.],[[.,.],.]]],.]] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1] => 2

[1,7,2,4,6,5,3] => [.,[[.,[[.,.],[[.,.],.]]],.]] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1] => 2

[1,7,2,5,3,4,6] => [.,[[.,[[.,[.,.]],[.,.]]],.]] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [5,2,2] => 1

[1,7,2,5,3,6,4] => [.,[[.,[[.,[.,.]],[.,.]]],.]] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [5,2,2] => 1

[1,7,2,5,4,3,6] => [.,[[.,[[[.,.],.],[.,.]]],.]] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1] => 2

[1,7,2,5,4,6,3] => [.,[[.,[[[.,.],.],[.,.]]],.]] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1] => 2

[1,7,2,5,6,3,4] => [.,[[.,[[.,[.,.]],[.,.]]],.]] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [5,2,2] => 1

[1,7,2,5,6,4,3] => [.,[[.,[[[.,.],.],[.,.]]],.]] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1] => 2

[1,7,2,6,3,4,5] => [.,[[.,[[.,[.,[.,.]]],.]],.]] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,3] => 2

[1,7,2,6,3,5,4] => [.,[[.,[[.,[[.,.],.]],.]],.]] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [5,3,1] => 3

[1,7,2,6,4,3,5] => [.,[[.,[[[.,.],[.,.]],.]],.]] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1] => 2

[1,7,2,6,4,5,3] => [.,[[.,[[[.,.],[.,.]],.]],.]] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1] => 2

[1,7,2,6,5,3,4] => [.,[[.,[[[.,[.,.]],.],.]],.]] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [5,3,2] => 3

[1,7,2,6,5,4,3] => [.,[[.,[[[[.,.],.],.],.]],.]] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1] => 4

[1,7,3,2,4,5,6] => [.,[[[.,.],[.,[.,[.,.]]]],.]] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1] => 1

[1,7,3,2,4,6,5] => [.,[[[.,.],[.,[[.,.],.]]],.]] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1,1] => 2

[1,7,3,2,5,4,6] => [.,[[[.,.],[[.,.],[.,.]]],.]] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1] => 1

[1,7,3,2,5,6,4] => [.,[[[.,.],[[.,.],[.,.]]],.]] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1] => 1

[1,7,3,2,6,4,5] => [.,[[[.,.],[[.,[.,.]],.]],.]] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1,1] => 2

[1,7,3,2,6,5,4] => [.,[[[.,.],[[[.,.],.],.]],.]] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,1] => 3

[1,7,3,4,2,5,6] => [.,[[[.,.],[.,[.,[.,.]]]],.]] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1] => 1

[1,7,3,4,2,6,5] => [.,[[[.,.],[.,[[.,.],.]]],.]] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1,1] => 2

[1,7,3,4,5,2,6] => [.,[[[.,.],[.,[.,[.,.]]]],.]] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1] => 1

[1,7,3,4,5,6,2] => [.,[[[.,.],[.,[.,[.,.]]]],.]] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1] => 1

[1,7,3,4,6,2,5] => [.,[[[.,.],[.,[[.,.],.]]],.]] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1,1] => 2

[1,7,3,4,6,5,2] => [.,[[[.,.],[.,[[.,.],.]]],.]] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1,1] => 2

[1,7,3,5,2,4,6] => [.,[[[.,.],[[.,.],[.,.]]],.]] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1] => 1

[1,7,3,5,2,6,4] => [.,[[[.,.],[[.,.],[.,.]]],.]] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1] => 1

[1,7,3,5,4,2,6] => [.,[[[.,.],[[.,.],[.,.]]],.]] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1] => 1

[1,7,3,5,4,6,2] => [.,[[[.,.],[[.,.],[.,.]]],.]] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1] => 1

[1,7,3,5,6,2,4] => [.,[[[.,.],[[.,.],[.,.]]],.]] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1] => 1

[1,7,3,5,6,4,2] => [.,[[[.,.],[[.,.],[.,.]]],.]] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1] => 1

[1,7,3,6,2,4,5] => [.,[[[.,.],[[.,[.,.]],.]],.]] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1,1] => 2

[1,7,3,6,2,5,4] => [.,[[[.,.],[[[.,.],.],.]],.]] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,1] => 3

[1,7,3,6,4,2,5] => [.,[[[.,.],[[.,[.,.]],.]],.]] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1,1] => 2

[1,7,3,6,4,5,2] => [.,[[[.,.],[[.,[.,.]],.]],.]] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1,1] => 2

[1,7,3,6,5,2,4] => [.,[[[.,.],[[[.,.],.],.]],.]] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,1] => 3

[1,7,3,6,5,4,2] => [.,[[[.,.],[[[.,.],.],.]],.]] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,1] => 3

[1,7,4,2,3,5,6] => [.,[[[.,[.,.]],[.,[.,.]]],.]] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2] => 1

[1,7,4,2,3,6,5] => [.,[[[.,[.,.]],[[.,.],.]],.]] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2] => 2

[1,7,4,2,5,3,6] => [.,[[[.,[.,.]],[.,[.,.]]],.]] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2] => 1

[1,7,4,2,5,6,3] => [.,[[[.,[.,.]],[.,[.,.]]],.]] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2] => 1

[1,7,4,2,6,3,5] => [.,[[[.,[.,.]],[[.,.],.]],.]] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2] => 2

[1,7,4,2,6,5,3] => [.,[[[.,[.,.]],[[.,.],.]],.]] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2] => 2

[1,7,4,3,2,5,6] => [.,[[[[.,.],.],[.,[.,.]]],.]] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2,1] => 2

[1,7,4,3,2,6,5] => [.,[[[[.,.],.],[[.,.],.]],.]] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2,1] => 3

[1,7,4,3,5,2,6] => [.,[[[[.,.],.],[.,[.,.]]],.]] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2,1] => 2

[1,7,4,3,5,6,2] => [.,[[[[.,.],.],[.,[.,.]]],.]] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2,1] => 2

[1,7,4,3,6,2,5] => [.,[[[[.,.],.],[[.,.],.]],.]] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2,1] => 3

[1,7,4,3,6,5,2] => [.,[[[[.,.],.],[[.,.],.]],.]] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2,1] => 3

[1,7,4,5,2,3,6] => [.,[[[.,[.,.]],[.,[.,.]]],.]] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2] => 1

[1,7,4,5,2,6,3] => [.,[[[.,[.,.]],[.,[.,.]]],.]] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2] => 1

[1,7,4,5,3,2,6] => [.,[[[[.,.],.],[.,[.,.]]],.]] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2,1] => 2

[1,7,4,5,3,6,2] => [.,[[[[.,.],.],[.,[.,.]]],.]] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2,1] => 2

[1,7,4,5,6,2,3] => [.,[[[.,[.,.]],[.,[.,.]]],.]] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2] => 1

[1,7,4,5,6,3,2] => [.,[[[[.,.],.],[.,[.,.]]],.]] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2,1] => 2

[1,7,4,6,2,3,5] => [.,[[[.,[.,.]],[[.,.],.]],.]] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2] => 2

[1,7,4,6,2,5,3] => [.,[[[.,[.,.]],[[.,.],.]],.]] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2] => 2

[1,7,4,6,3,2,5] => [.,[[[[.,.],.],[[.,.],.]],.]] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2,1] => 3

[1,7,4,6,3,5,2] => [.,[[[[.,.],.],[[.,.],.]],.]] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2,1] => 3

[1,7,4,6,5,2,3] => [.,[[[.,[.,.]],[[.,.],.]],.]] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2] => 2

[1,7,4,6,5,3,2] => [.,[[[[.,.],.],[[.,.],.]],.]] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2,1] => 3

[1,7,5,2,3,4,6] => [.,[[[.,[.,[.,.]]],[.,.]],.]] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [5,3,3] => 1

[1,7,5,2,3,6,4] => [.,[[[.,[.,[.,.]]],[.,.]],.]] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [5,3,3] => 1

[1,7,5,2,4,3,6] => [.,[[[.,[[.,.],.]],[.,.]],.]] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1] => 2

[1,7,5,2,4,6,3] => [.,[[[.,[[.,.],.]],[.,.]],.]] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1] => 2

[1,7,5,2,6,3,4] => [.,[[[.,[.,[.,.]]],[.,.]],.]] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [5,3,3] => 1

[1,7,5,2,6,4,3] => [.,[[[.,[[.,.],.]],[.,.]],.]] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1] => 2

[1,7,5,3,2,4,6] => [.,[[[[.,.],[.,.]],[.,.]],.]] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1,1] => 1

[1,7,5,3,2,6,4] => [.,[[[[.,.],[.,.]],[.,.]],.]] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1,1] => 1

[1,7,5,3,4,2,6] => [.,[[[[.,.],[.,.]],[.,.]],.]] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1,1] => 1

[1,7,5,3,4,6,2] => [.,[[[[.,.],[.,.]],[.,.]],.]] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1,1] => 1

[1,7,5,3,6,2,4] => [.,[[[[.,.],[.,.]],[.,.]],.]] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1,1] => 1

[1,7,5,3,6,4,2] => [.,[[[[.,.],[.,.]],[.,.]],.]] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1,1] => 1

[1,7,5,4,2,3,6] => [.,[[[[.,[.,.]],.],[.,.]],.]] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2] => 2

[1,7,5,4,2,6,3] => [.,[[[[.,[.,.]],.],[.,.]],.]] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2] => 2

[1,7,5,4,3,2,6] => [.,[[[[[.,.],.],.],[.,.]],.]] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2,1] => 3

[1,7,5,4,3,6,2] => [.,[[[[[.,.],.],.],[.,.]],.]] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2,1] => 3

[1,7,5,4,6,2,3] => [.,[[[[.,[.,.]],.],[.,.]],.]] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2] => 2

[1,7,5,4,6,3,2] => [.,[[[[[.,.],.],.],[.,.]],.]] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2,1] => 3

[1,7,5,6,2,3,4] => [.,[[[.,[.,[.,.]]],[.,.]],.]] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [5,3,3] => 1

[1,7,5,6,2,4,3] => [.,[[[.,[[.,.],.]],[.,.]],.]] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1] => 2

[1,7,5,6,3,2,4] => [.,[[[[.,.],[.,.]],[.,.]],.]] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1,1] => 1

[1,7,5,6,3,4,2] => [.,[[[[.,.],[.,.]],[.,.]],.]] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1,1] => 1

[1,7,5,6,4,2,3] => [.,[[[[.,[.,.]],.],[.,.]],.]] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2] => 2

[1,7,5,6,4,3,2] => [.,[[[[[.,.],.],.],[.,.]],.]] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2,1] => 3

[1,7,6,2,3,4,5] => [.,[[[.,[.,[.,[.,.]]]],.],.]] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4] => 2

[1,7,6,2,3,5,4] => [.,[[[.,[.,[[.,.],.]]],.],.]] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,4,1] => 3

[1,7,6,2,4,3,5] => [.,[[[.,[[.,.],[.,.]]],.],.]] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1] => 2

[1,7,6,2,4,5,3] => [.,[[[.,[[.,.],[.,.]]],.],.]] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1] => 2

[1,7,6,2,5,3,4] => [.,[[[.,[[.,[.,.]],.]],.],.]] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [5,4,2] => 3

[1,7,6,2,5,4,3] => [.,[[[.,[[[.,.],.],.]],.],.]] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1] => 4

[1,7,6,3,2,4,5] => [.,[[[[.,.],[.,[.,.]]],.],.]] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1,1] => 2

[1,7,6,3,2,5,4] => [.,[[[[.,.],[[.,.],.]],.],.]] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,1] => 3

[1,7,6,3,4,2,5] => [.,[[[[.,.],[.,[.,.]]],.],.]] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1,1] => 2

[1,7,6,3,4,5,2] => [.,[[[[.,.],[.,[.,.]]],.],.]] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1,1] => 2

[1,7,6,3,5,2,4] => [.,[[[[.,.],[[.,.],.]],.],.]] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,1] => 3

[1,7,6,3,5,4,2] => [.,[[[[.,.],[[.,.],.]],.],.]] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,1] => 3

[1,7,6,4,2,3,5] => [.,[[[[.,[.,.]],[.,.]],.],.]] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2] => 2

[1,7,6,4,2,5,3] => [.,[[[[.,[.,.]],[.,.]],.],.]] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2] => 2

[1,7,6,4,3,2,5] => [.,[[[[[.,.],.],[.,.]],.],.]] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2,1] => 3

[1,7,6,4,3,5,2] => [.,[[[[[.,.],.],[.,.]],.],.]] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2,1] => 3

[1,7,6,4,5,2,3] => [.,[[[[.,[.,.]],[.,.]],.],.]] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2] => 2

[1,7,6,4,5,3,2] => [.,[[[[[.,.],.],[.,.]],.],.]] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2,1] => 3

[1,7,6,5,2,3,4] => [.,[[[[.,[.,[.,.]]],.],.],.]] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [5,4,3] => 3

[1,7,6,5,2,4,3] => [.,[[[[.,[[.,.],.]],.],.],.]] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1] => 4

[1,7,6,5,3,2,4] => [.,[[[[[.,.],[.,.]],.],.],.]] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,1] => 3

[1,7,6,5,3,4,2] => [.,[[[[[.,.],[.,.]],.],.],.]] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,1] => 3

[1,7,6,5,4,2,3] => [.,[[[[[.,[.,.]],.],.],.],.]] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2] => 4

[1,7,6,5,4,3,2] => [.,[[[[[[.,.],.],.],.],.],.]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1] => 5

[2,1,3,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 0

[2,1,3,4,5,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1

[2,1,3,4,6,5,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1,1] => 0

[2,1,3,4,6,7,5] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1,1] => 0

[2,1,3,4,7,5,6] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1,1] => 1

[2,1,3,4,7,6,5] => [[.,.],[.,[.,[[[.,.],.],.]]]] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1,1] => 2

[2,1,3,5,4,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1,1] => 0

[2,1,3,5,4,7,6] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1,1] => 1

[2,1,3,5,6,4,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1,1] => 0

[2,1,3,5,6,7,4] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1,1] => 0

[2,1,3,5,7,4,6] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1,1] => 1

[2,1,3,5,7,6,4] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1,1] => 1

[2,1,3,6,4,5,7] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1,1] => 0

[2,1,3,6,4,7,5] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1,1] => 0

[2,1,3,6,5,4,7] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1,1] => 1

[2,1,3,6,5,7,4] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1,1] => 1

[2,1,3,6,7,4,5] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1,1] => 0

[2,1,3,6,7,5,4] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1,1] => 1

[2,1,3,7,4,5,6] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1,1] => 1

[2,1,3,7,4,6,5] => [[.,.],[.,[[.,[[.,.],.]],.]]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1,1] => 2

[2,1,3,7,5,4,6] => [[.,.],[.,[[[.,.],[.,.]],.]]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1,1] => 1

[2,1,3,7,5,6,4] => [[.,.],[.,[[[.,.],[.,.]],.]]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1,1] => 1

[2,1,3,7,6,4,5] => [[.,.],[.,[[[.,[.,.]],.],.]]] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1,1,1] => 2

[2,1,3,7,6,5,4] => [[.,.],[.,[[[[.,.],.],.],.]]] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,1,1] => 3

[2,1,4,3,5,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1,1] => 0

[2,1,4,3,5,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1,1] => 1

[2,1,4,3,6,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => 0

[2,1,4,3,6,7,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => 0

[2,1,4,3,7,5,6] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1,1] => 1

[2,1,4,3,7,6,5] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1,1] => 2

[2,1,4,5,3,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1,1] => 0

[2,1,4,5,3,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1,1] => 1

[2,1,4,5,6,3,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1,1] => 0

[2,1,4,5,6,7,3] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1,1] => 0

[2,1,4,5,7,3,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1,1] => 1

[2,1,4,5,7,6,3] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1,1] => 1

[2,1,4,6,3,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => 0

[2,1,4,6,3,7,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => 0

[2,1,4,6,5,3,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => 0

[2,1,4,6,5,7,3] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => 0

[2,1,4,6,7,3,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => 0

[2,1,4,6,7,5,3] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => 0

[2,1,4,7,3,5,6] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1,1] => 1

[2,1,4,7,3,6,5] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1,1] => 2

[2,1,4,7,5,3,6] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1,1] => 1

[2,1,4,7,5,6,3] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1,1] => 1

[2,1,4,7,6,3,5] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1,1] => 2

[2,1,4,7,6,5,3] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1,1] => 2

[2,1,5,3,4,6,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1,1] => 0

[2,1,5,3,4,7,6] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1,1] => 1

[2,1,5,3,6,4,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1,1] => 0

[2,1,5,3,6,7,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1,1] => 0

[2,1,5,3,7,4,6] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1,1] => 1

[2,1,5,3,7,6,4] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1,1] => 1

[2,1,5,4,3,6,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1,1] => 1

[2,1,5,4,3,7,6] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1,1] => 2

[2,1,5,4,6,3,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1,1] => 1

[2,1,5,4,6,7,3] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1,1] => 1

[2,1,5,4,7,3,6] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1,1] => 2

[2,1,5,4,7,6,3] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1,1] => 2

[2,1,5,6,3,4,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1,1] => 0

[2,1,5,6,3,7,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1,1] => 0

[2,1,5,6,4,3,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1,1] => 1

[2,1,5,6,4,7,3] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1,1] => 1

[2,1,5,6,7,3,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1,1] => 0

[2,1,5,6,7,4,3] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1,1] => 1

[2,1,5,7,3,4,6] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1,1] => 1

[2,1,5,7,3,6,4] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1,1] => 1

[2,1,5,7,4,3,6] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1,1] => 2

[2,1,5,7,4,6,3] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1,1] => 2

[2,1,5,7,6,3,4] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1,1] => 1

[2,1,5,7,6,4,3] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1,1] => 2

[2,1,6,3,4,5,7] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1,1] => 0

[2,1,6,3,4,7,5] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1,1] => 0

[2,1,6,3,5,4,7] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1,1] => 1

[2,1,6,3,5,7,4] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1,1] => 1

[2,1,6,3,7,4,5] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1,1] => 0

[2,1,6,3,7,5,4] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1,1] => 1

[2,1,6,4,3,5,7] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1,1] => 0

[2,1,6,4,3,7,5] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1,1] => 0

[2,1,6,4,5,3,7] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1,1] => 0

[2,1,6,4,5,7,3] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1,1] => 0

[2,1,6,4,7,3,5] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1,1] => 0

[2,1,6,4,7,5,3] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1,1] => 0

[2,1,6,5,3,4,7] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1,1,1] => 1

[2,1,6,5,3,7,4] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1,1,1] => 1

[2,1,6,5,4,3,7] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2,1,1] => 2

[2,1,6,5,4,7,3] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2,1,1] => 2

[2,1,6,5,7,3,4] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1,1,1] => 1

[2,1,6,5,7,4,3] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2,1,1] => 2

[2,1,6,7,3,4,5] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1,1] => 0

[2,1,6,7,3,5,4] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1,1] => 1

[2,1,6,7,4,3,5] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1,1] => 0

[2,1,6,7,4,5,3] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1,1] => 0

[2,1,6,7,5,3,4] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1,1,1] => 1

[2,1,6,7,5,4,3] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2,1,1] => 2

[2,1,7,3,4,5,6] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1,1] => 1

[2,1,7,3,4,6,5] => [[.,.],[[.,[.,[[.,.],.]]],.]] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1,1,1] => 2

[2,1,7,3,5,4,6] => [[.,.],[[.,[[.,.],[.,.]]],.]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1,1] => 1

[2,1,7,3,5,6,4] => [[.,.],[[.,[[.,.],[.,.]]],.]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1,1] => 1

[2,1,7,3,6,4,5] => [[.,.],[[.,[[.,[.,.]],.]],.]] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1,1,1] => 2

[2,1,7,3,6,5,4] => [[.,.],[[.,[[[.,.],.],.]],.]] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,1,1] => 3

[2,1,7,4,3,5,6] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2,1,1] => 1

[2,1,7,4,3,6,5] => [[.,.],[[[.,.],[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2,1,1] => 2

[2,1,7,4,5,3,6] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2,1,1] => 1

[2,1,7,4,5,6,3] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2,1,1] => 1

[2,1,7,4,6,3,5] => [[.,.],[[[.,.],[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2,1,1] => 2

[2,1,7,4,6,5,3] => [[.,.],[[[.,.],[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2,1,1] => 2

[2,1,7,5,3,4,6] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1,1,1] => 1

[2,1,7,5,3,6,4] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1,1,1] => 1

[2,1,7,5,4,3,6] => [[.,.],[[[[.,.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2,1,1] => 2

[2,1,7,5,4,6,3] => [[.,.],[[[[.,.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2,1,1] => 2

[2,1,7,5,6,3,4] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1,1,1] => 1

[2,1,7,5,6,4,3] => [[.,.],[[[[.,.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2,1,1] => 2

[2,1,7,6,3,4,5] => [[.,.],[[[.,[.,[.,.]]],.],.]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1,1,1] => 2

[2,1,7,6,3,5,4] => [[.,.],[[[.,[[.,.],.]],.],.]] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,1,1] => 3

[2,1,7,6,4,3,5] => [[.,.],[[[[.,.],[.,.]],.],.]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2,1,1] => 2

[2,1,7,6,4,5,3] => [[.,.],[[[[.,.],[.,.]],.],.]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2,1,1] => 2

[2,1,7,6,5,3,4] => [[.,.],[[[[.,[.,.]],.],.],.]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,1,1] => 3

[2,1,7,6,5,4,3] => [[.,.],[[[[[.,.],.],.],.],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1,1] => 4

[2,3,1,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 0

[2,3,1,4,5,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1

[2,3,1,4,6,5,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1,1] => 0

[2,3,1,4,6,7,5] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1,1] => 0

[2,3,1,4,7,5,6] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1,1] => 1

[2,3,1,4,7,6,5] => [[.,.],[.,[.,[[[.,.],.],.]]]] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1,1] => 2

[2,3,1,5,4,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1,1] => 0

[2,3,1,5,4,7,6] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1,1] => 1

[2,3,1,5,6,4,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1,1] => 0

[2,3,1,5,6,7,4] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1,1] => 0

[2,3,1,5,7,4,6] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1,1] => 1

[2,3,1,5,7,6,4] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1,1] => 1

[2,3,1,6,4,5,7] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1,1] => 0

[2,3,1,6,4,7,5] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1,1] => 0

[2,3,1,6,5,4,7] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1,1] => 1

[2,3,1,6,5,7,4] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1,1] => 1

[2,3,1,6,7,4,5] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1,1] => 0

[2,3,1,6,7,5,4] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1,1] => 1

[2,3,1,7,4,5,6] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1,1] => 1

[2,3,1,7,4,6,5] => [[.,.],[.,[[.,[[.,.],.]],.]]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1,1] => 2

[2,3,1,7,5,4,6] => [[.,.],[.,[[[.,.],[.,.]],.]]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1,1] => 1

[2,3,1,7,5,6,4] => [[.,.],[.,[[[.,.],[.,.]],.]]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1,1] => 1

[2,3,1,7,6,4,5] => [[.,.],[.,[[[.,[.,.]],.],.]]] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1,1,1] => 2

[2,3,1,7,6,5,4] => [[.,.],[.,[[[[.,.],.],.],.]]] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,1,1] => 3

[2,3,4,1,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 0

[2,3,4,1,5,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1

[2,3,4,1,6,5,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1,1] => 0

[2,3,4,1,6,7,5] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1,1] => 0

[2,3,4,1,7,5,6] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1,1] => 1

[2,3,4,1,7,6,5] => [[.,.],[.,[.,[[[.,.],.],.]]]] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1,1] => 2

[2,3,4,5,1,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 0

[2,3,4,5,1,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1

[2,3,4,5,6,1,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 0

[2,3,4,5,6,7,1] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 0

[2,3,4,5,7,1,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1

[2,3,4,5,7,6,1] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1

[2,3,4,6,1,5,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1,1] => 0

[2,3,4,6,1,7,5] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1,1] => 0

[2,3,4,6,5,1,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1,1] => 0

[2,3,4,6,5,7,1] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1,1] => 0

[2,3,4,6,7,1,5] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1,1] => 0

[2,3,4,6,7,5,1] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1,1] => 0

[2,3,4,7,1,5,6] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1,1] => 1

[2,3,4,7,1,6,5] => [[.,.],[.,[.,[[[.,.],.],.]]]] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1,1] => 2

[2,3,4,7,5,1,6] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1,1] => 1

[2,3,4,7,5,6,1] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1,1] => 1

[2,3,4,7,6,1,5] => [[.,.],[.,[.,[[[.,.],.],.]]]] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1,1] => 2

[2,3,4,7,6,5,1] => [[.,.],[.,[.,[[[.,.],.],.]]]] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1,1] => 2

[2,3,5,1,4,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1,1] => 0

[2,3,5,1,4,7,6] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1,1] => 1

[2,3,5,1,6,4,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1,1] => 0

[2,3,5,1,6,7,4] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1,1] => 0

[2,3,5,1,7,4,6] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1,1] => 1

[2,3,5,1,7,6,4] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1,1] => 1

[2,3,5,4,1,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1,1] => 0

[2,3,5,4,1,7,6] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1,1] => 1

[2,3,5,4,6,1,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1,1] => 0

[2,3,5,4,6,7,1] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1,1] => 0

[2,3,5,4,7,1,6] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1,1] => 1

[2,3,5,4,7,6,1] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1,1] => 1

[2,3,5,6,1,4,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1,1] => 0

[2,3,5,6,1,7,4] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1,1] => 0

[2,3,5,6,4,1,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1,1] => 0

[2,3,5,6,4,7,1] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1,1] => 0

[2,3,5,6,7,1,4] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1,1] => 0

[2,3,5,6,7,4,1] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1,1] => 0

[2,3,5,7,1,4,6] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1,1] => 1

[2,3,5,7,1,6,4] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1,1] => 1

[2,3,5,7,4,1,6] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1,1] => 1

[2,3,5,7,4,6,1] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1,1] => 1

[2,3,5,7,6,1,4] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1,1] => 1

[2,3,5,7,6,4,1] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1,1] => 1

[2,3,6,1,4,5,7] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1,1] => 0

[2,3,6,1,4,7,5] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1,1] => 0

[2,3,6,1,5,4,7] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1,1] => 1

[2,3,6,1,5,7,4] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1,1] => 1

[2,3,6,1,7,4,5] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1,1] => 0

[2,3,6,1,7,5,4] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1,1] => 1

[2,3,6,4,1,5,7] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1,1] => 0

[2,3,6,4,1,7,5] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1,1] => 0

[2,3,6,4,5,1,7] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1,1] => 0

[2,3,6,4,5,7,1] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1,1] => 0

[2,3,6,4,7,1,5] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1,1] => 0

[2,3,6,4,7,5,1] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1,1] => 0

[2,3,6,5,1,4,7] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1,1] => 1

[2,3,6,5,1,7,4] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1,1] => 1

[2,3,6,5,4,1,7] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1,1] => 1

[2,3,6,5,4,7,1] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1,1] => 1

[2,3,6,5,7,1,4] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1,1] => 1

[2,3,6,5,7,4,1] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1,1] => 1

[2,3,6,7,1,4,5] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1,1] => 0

[2,3,6,7,1,5,4] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1,1] => 1

[2,3,6,7,4,1,5] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1,1] => 0

[2,3,6,7,4,5,1] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1,1] => 0

[2,3,6,7,5,1,4] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1,1] => 1

[2,3,6,7,5,4,1] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1,1] => 1

[2,3,7,1,4,5,6] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1,1] => 1

[2,3,7,1,4,6,5] => [[.,.],[.,[[.,[[.,.],.]],.]]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1,1] => 2

[2,3,7,1,5,4,6] => [[.,.],[.,[[[.,.],[.,.]],.]]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1,1] => 1

[2,3,7,1,5,6,4] => [[.,.],[.,[[[.,.],[.,.]],.]]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1,1] => 1

[2,3,7,1,6,4,5] => [[.,.],[.,[[[.,[.,.]],.],.]]] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1,1,1] => 2

[2,3,7,1,6,5,4] => [[.,.],[.,[[[[.,.],.],.],.]]] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,1,1] => 3

[2,3,7,4,1,5,6] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1,1] => 1

[2,3,7,4,1,6,5] => [[.,.],[.,[[.,[[.,.],.]],.]]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1,1] => 2

[2,3,7,4,5,1,6] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1,1] => 1

[2,3,7,4,5,6,1] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1,1] => 1

[2,3,7,4,6,1,5] => [[.,.],[.,[[.,[[.,.],.]],.]]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1,1] => 2

[2,3,7,4,6,5,1] => [[.,.],[.,[[.,[[.,.],.]],.]]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1,1] => 2

[2,3,7,5,1,4,6] => [[.,.],[.,[[[.,.],[.,.]],.]]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1,1] => 1

[2,3,7,5,1,6,4] => [[.,.],[.,[[[.,.],[.,.]],.]]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1,1] => 1

[2,3,7,5,4,1,6] => [[.,.],[.,[[[.,.],[.,.]],.]]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1,1] => 1

[2,3,7,5,4,6,1] => [[.,.],[.,[[[.,.],[.,.]],.]]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1,1] => 1

[2,3,7,5,6,1,4] => [[.,.],[.,[[[.,.],[.,.]],.]]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1,1] => 1

[2,3,7,5,6,4,1] => [[.,.],[.,[[[.,.],[.,.]],.]]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1,1] => 1

[2,3,7,6,1,4,5] => [[.,.],[.,[[[.,[.,.]],.],.]]] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1,1,1] => 2

[2,3,7,6,1,5,4] => [[.,.],[.,[[[[.,.],.],.],.]]] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,1,1] => 3

[2,3,7,6,4,1,5] => [[.,.],[.,[[[.,[.,.]],.],.]]] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1,1,1] => 2

[2,3,7,6,4,5,1] => [[.,.],[.,[[[.,[.,.]],.],.]]] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1,1,1] => 2

[2,3,7,6,5,1,4] => [[.,.],[.,[[[[.,.],.],.],.]]] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,1,1] => 3

[2,3,7,6,5,4,1] => [[.,.],[.,[[[[.,.],.],.],.]]] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,1,1] => 3

[2,4,1,3,5,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1,1] => 0

[2,4,1,3,5,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1,1] => 1

[2,4,1,3,6,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => 0

[2,4,1,3,6,7,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => 0

[2,4,1,3,7,5,6] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1,1] => 1

[2,4,1,3,7,6,5] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1,1] => 2

[2,4,1,5,3,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1,1] => 0

[2,4,1,5,3,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1,1] => 1

[2,4,1,5,6,3,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1,1] => 0

[2,4,1,5,6,7,3] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1,1] => 0

[2,4,1,5,7,3,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1,1] => 1

[2,4,1,5,7,6,3] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1,1] => 1

[2,4,1,6,3,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => 0

[2,4,1,6,3,7,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => 0

[2,4,1,6,5,3,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => 0

[2,4,1,6,5,7,3] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => 0

[2,4,1,6,7,3,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => 0

[2,4,1,6,7,5,3] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => 0

[2,4,1,7,3,5,6] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1,1] => 1

[2,4,1,7,3,6,5] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1,1] => 2

[2,4,1,7,5,3,6] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1,1] => 1

[2,4,1,7,5,6,3] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1,1] => 1

[2,4,1,7,6,3,5] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1,1] => 2

[2,4,1,7,6,5,3] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1,1] => 2

[2,4,3,1,5,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1,1] => 0

[2,4,3,1,5,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1,1] => 1

[2,4,3,1,6,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => 0

[2,4,3,1,6,7,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => 0

[2,4,3,1,7,5,6] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1,1] => 1

[2,4,3,1,7,6,5] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1,1] => 2

[2,4,3,5,1,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1,1] => 0

[2,4,3,5,1,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1,1] => 1

[2,4,3,5,6,1,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1,1] => 0

[2,4,3,5,6,7,1] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1,1] => 0

[2,4,3,5,7,1,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1,1] => 1

[2,4,3,5,7,6,1] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1,1] => 1

[2,4,3,6,1,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => 0

[2,4,3,6,1,7,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => 0

[2,4,3,6,5,1,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => 0

[2,4,3,6,5,7,1] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => 0

[2,4,3,6,7,1,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => 0

[2,4,3,6,7,5,1] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => 0

[2,4,3,7,1,5,6] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1,1] => 1

[2,4,3,7,1,6,5] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1,1] => 2

[2,4,3,7,5,1,6] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1,1] => 1

[2,4,3,7,5,6,1] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1,1] => 1

[2,4,3,7,6,1,5] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1,1] => 2

[2,4,3,7,6,5,1] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1,1] => 2

[2,4,5,1,3,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1,1] => 0

[2,4,5,1,3,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1,1] => 1

[2,4,5,1,6,3,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1,1] => 0

[2,4,5,1,6,7,3] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1,1] => 0

[2,4,5,1,7,3,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1,1] => 1

[2,4,5,1,7,6,3] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1,1] => 1

[2,4,5,3,1,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1,1] => 0

[2,4,5,3,1,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1,1] => 1

[2,4,5,3,6,1,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1,1] => 0

[2,4,5,3,6,7,1] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1,1] => 0

[2,4,5,3,7,1,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1,1] => 1

[2,4,5,3,7,6,1] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1,1] => 1

[2,4,5,6,1,3,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1,1] => 0

[2,4,5,6,1,7,3] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1,1] => 0

[2,4,5,6,3,1,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1,1] => 0

[2,4,5,6,3,7,1] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1,1] => 0

[2,4,5,6,7,1,3] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1,1] => 0

[2,4,5,6,7,3,1] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1,1] => 0

[2,4,5,7,1,3,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1,1] => 1

[2,4,5,7,1,6,3] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1,1] => 1

[2,4,5,7,3,1,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1,1] => 1

[2,4,5,7,3,6,1] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1,1] => 1

[2,4,5,7,6,1,3] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1,1] => 1

[2,4,5,7,6,3,1] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1,1] => 1

[2,4,6,1,3,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => 0

[2,4,6,1,3,7,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => 0

[2,4,6,1,5,3,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => 0

[2,4,6,1,5,7,3] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => 0

[2,4,6,1,7,3,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => 0

[2,4,6,1,7,5,3] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => 0

[2,4,6,3,1,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => 0

[2,4,6,3,1,7,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => 0

[2,4,6,3,5,1,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => 0

[2,4,6,3,5,7,1] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => 0

[2,4,6,3,7,1,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => 0

[2,4,6,3,7,5,1] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => 0

[2,4,6,5,1,3,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => 0

[2,4,6,5,1,7,3] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => 0

[2,4,6,5,3,1,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => 0

[2,4,6,5,3,7,1] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => 0

[2,4,6,5,7,1,3] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => 0

[2,4,6,5,7,3,1] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => 0

[2,4,6,7,1,3,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => 0

[2,4,6,7,1,5,3] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => 0

[2,4,6,7,3,1,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => 0

[2,4,6,7,3,5,1] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => 0

[2,4,6,7,5,1,3] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => 0

[2,4,6,7,5,3,1] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => 0

[2,4,7,1,3,5,6] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1,1] => 1

[2,4,7,1,3,6,5] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1,1] => 2

[2,4,7,1,5,3,6] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1,1] => 1

[2,4,7,1,5,6,3] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1,1] => 1

[2,4,7,1,6,3,5] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1,1] => 2

[2,4,7,1,6,5,3] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1,1] => 2

[2,4,7,3,1,5,6] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1,1] => 1

[2,4,7,3,1,6,5] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1,1] => 2

[2,4,7,3,5,1,6] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1,1] => 1

[2,4,7,3,5,6,1] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1,1] => 1

[2,4,7,3,6,1,5] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1,1] => 2

[2,4,7,3,6,5,1] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1,1] => 2

[2,4,7,5,1,3,6] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1,1] => 1

[2,4,7,5,1,6,3] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1,1] => 1

[2,4,7,5,3,1,6] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1,1] => 1

[2,4,7,5,3,6,1] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1,1] => 1

[2,4,7,5,6,1,3] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1,1] => 1

[2,4,7,5,6,3,1] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1,1] => 1

[2,4,7,6,1,3,5] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1,1] => 2

[2,4,7,6,1,5,3] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1,1] => 2

[2,4,7,6,3,1,5] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1,1] => 2

[2,4,7,6,3,5,1] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1,1] => 2

[2,4,7,6,5,1,3] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1,1] => 2

[2,4,7,6,5,3,1] => [[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1,1] => 2

[2,5,1,3,4,6,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1,1] => 0

[2,5,1,3,4,7,6] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1,1] => 1

[2,5,1,3,6,4,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1,1] => 0

[2,5,1,3,6,7,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1,1] => 0

[2,5,1,3,7,4,6] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1,1] => 1

[2,5,1,3,7,6,4] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1,1] => 1

[2,5,1,4,3,6,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1,1] => 1

[2,5,1,4,3,7,6] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1,1] => 2

[2,5,1,4,6,3,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1,1] => 1

[2,5,1,4,6,7,3] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1,1] => 1

[2,5,1,4,7,3,6] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1,1] => 2

[2,5,1,4,7,6,3] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1,1] => 2

[2,5,1,6,3,4,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1,1] => 0

[2,5,1,6,3,7,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1,1] => 0

[2,5,1,6,4,3,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1,1] => 1

[2,5,1,6,4,7,3] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1,1] => 1

[2,5,1,6,7,3,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1,1] => 0

[2,5,1,6,7,4,3] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1,1] => 1

[2,5,1,7,3,4,6] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1,1] => 1

[2,5,1,7,3,6,4] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1,1] => 1

[2,5,1,7,4,3,6] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1,1] => 2

[2,5,1,7,4,6,3] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1,1] => 2

[2,5,1,7,6,3,4] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1,1] => 1

[2,5,1,7,6,4,3] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1,1] => 2

[2,5,3,1,4,6,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1,1] => 0

[2,5,3,1,4,7,6] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1,1] => 1

[2,5,3,1,6,4,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1,1] => 0

[2,5,3,1,6,7,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1,1] => 0

[2,5,3,1,7,4,6] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1,1] => 1

[2,5,3,1,7,6,4] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1,1] => 1

[2,5,3,4,1,6,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1,1] => 0

[2,5,3,4,1,7,6] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1,1] => 1

[2,5,3,4,6,1,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1,1] => 0

[2,5,3,4,6,7,1] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1,1] => 0

[2,5,3,4,7,1,6] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1,1] => 1

[2,5,3,4,7,6,1] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1,1] => 1

[2,5,3,6,1,4,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1,1] => 0

[2,5,3,6,1,7,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1,1] => 0

[2,5,3,6,4,1,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1,1] => 0

[2,5,3,6,4,7,1] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1,1] => 0

[2,5,3,6,7,1,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1,1] => 0

[2,5,3,6,7,4,1] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1,1] => 0

[2,5,3,7,1,4,6] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1,1] => 1

[2,5,3,7,1,6,4] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1,1] => 1

[2,5,3,7,4,1,6] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1,1] => 1

[2,5,3,7,4,6,1] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1,1] => 1

[2,5,3,7,6,1,4] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1,1] => 1

[2,5,3,7,6,4,1] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1,1] => 1

[2,5,4,1,3,6,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1,1] => 1

[2,5,4,1,3,7,6] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1,1] => 2

[2,5,4,1,6,3,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1,1] => 1

[2,5,4,1,6,7,3] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1,1] => 1

[2,5,4,1,7,3,6] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1,1] => 2

[2,5,4,1,7,6,3] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1,1] => 2

[2,5,4,3,1,6,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1,1] => 1

[2,5,4,3,1,7,6] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1,1] => 2

[2,5,4,3,6,1,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1,1] => 1

[2,5,4,3,6,7,1] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1,1] => 1

[2,5,4,3,7,1,6] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1,1] => 2

[2,5,4,3,7,6,1] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1,1] => 2

[2,5,4,6,1,3,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1,1] => 1

[2,5,4,6,1,7,3] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1,1] => 1

[2,5,4,6,3,1,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1,1] => 1

[2,5,4,6,3,7,1] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1,1] => 1

[2,5,4,6,7,1,3] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1,1] => 1

[2,5,4,6,7,3,1] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1,1] => 1

[2,5,4,7,1,3,6] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1,1] => 2

[2,5,4,7,1,6,3] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1,1] => 2

[2,5,4,7,3,1,6] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1,1] => 2

[2,5,4,7,3,6,1] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1,1] => 2

[2,5,4,7,6,1,3] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1,1] => 2

[2,5,4,7,6,3,1] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1,1] => 2

[2,5,6,1,3,4,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1,1] => 0

[2,5,6,1,3,7,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1,1] => 0

[2,5,6,1,4,3,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1,1] => 1

[2,5,6,1,4,7,3] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1,1] => 1

[2,5,6,1,7,3,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1,1] => 0

[2,5,6,1,7,4,3] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1,1] => 1

[2,5,6,3,1,4,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1,1] => 0

[2,5,6,3,1,7,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1,1] => 0

[2,5,6,3,4,1,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1,1] => 0

[2,5,6,3,4,7,1] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1,1] => 0

[2,5,6,3,7,1,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1,1] => 0

[2,5,6,3,7,4,1] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1,1] => 0

[2,5,6,4,1,3,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1,1] => 1

[2,5,6,4,1,7,3] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1,1] => 1

[2,5,6,4,3,1,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1,1] => 1

[2,5,6,4,3,7,1] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1,1] => 1

[2,5,6,4,7,1,3] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1,1] => 1

[2,5,6,4,7,3,1] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1,1] => 1

[2,5,6,7,1,3,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1,1] => 0

[2,5,6,7,1,4,3] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1,1] => 1

[2,5,6,7,3,1,4] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1,1] => 0

[2,5,6,7,3,4,1] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1,1] => 0

[2,5,6,7,4,1,3] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1,1] => 1

[2,5,6,7,4,3,1] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1,1] => 1

[2,5,7,1,3,4,6] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1,1] => 1

[2,5,7,1,3,6,4] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1,1] => 1

[2,5,7,1,4,3,6] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1,1] => 2

[2,5,7,1,4,6,3] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1,1] => 2

[2,5,7,1,6,3,4] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1,1] => 1

[2,5,7,1,6,4,3] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1,1] => 2

[2,5,7,3,1,4,6] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1,1] => 1

[2,5,7,3,1,6,4] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1,1] => 1

[2,5,7,3,4,1,6] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1,1] => 1

[2,5,7,3,4,6,1] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1,1] => 1

[2,5,7,3,6,1,4] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1,1] => 1

[2,5,7,3,6,4,1] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1,1] => 1

[2,5,7,4,1,3,6] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1,1] => 2

[2,5,7,4,1,6,3] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1,1] => 2

[2,5,7,4,3,1,6] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1,1] => 2

[2,5,7,4,3,6,1] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1,1] => 2

[2,5,7,4,6,1,3] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1,1] => 2

[2,5,7,4,6,3,1] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1,1] => 2

[2,5,7,6,1,3,4] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1,1] => 1

[2,5,7,6,1,4,3] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1,1] => 2

[2,5,7,6,3,1,4] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1,1] => 1

[2,5,7,6,3,4,1] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1,1] => 1

[2,5,7,6,4,1,3] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1,1] => 2

[2,5,7,6,4,3,1] => [[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1,1] => 2

[2,6,1,3,4,5,7] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1,1] => 0

[2,6,1,3,4,7,5] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1,1] => 0

[2,6,1,3,5,4,7] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1,1] => 1

[2,6,1,3,5,7,4] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1,1] => 1

[2,6,1,3,7,4,5] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1,1] => 0

[2,6,1,3,7,5,4] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1,1] => 1

[2,6,1,4,3,5,7] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1,1] => 0

[2,6,1,4,3,7,5] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1,1] => 0

[2,6,1,4,5,3,7] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1,1] => 0

[2,6,1,4,5,7,3] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1,1] => 0

[2,6,1,4,7,3,5] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1,1] => 0

[2,6,1,4,7,5,3] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1,1] => 0

[2,6,1,5,3,4,7] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1,1,1] => 1

[2,6,1,5,3,7,4] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1,1,1] => 1

[2,6,1,5,4,3,7] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2,1,1] => 2

[2,6,1,5,4,7,3] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2,1,1] => 2

[2,6,1,5,7,3,4] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1,1,1] => 1

[2,6,1,5,7,4,3] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2,1,1] => 2

[2,6,1,7,3,4,5] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1,1] => 0

[2,6,1,7,3,5,4] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1,1] => 1

[2,6,1,7,4,3,5] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1,1] => 0

[2,6,1,7,4,5,3] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1,1] => 0

[2,6,1,7,5,3,4] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1,1,1] => 1

[2,6,1,7,5,4,3] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2,1,1] => 2

[2,6,3,1,4,5,7] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1,1] => 0

[2,6,3,1,4,7,5] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1,1] => 0

[2,6,3,1,5,4,7] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1,1] => 1

[2,6,3,1,5,7,4] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1,1] => 1

[2,6,3,1,7,4,5] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1,1] => 0

[2,6,3,1,7,5,4] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1,1] => 1

[2,6,3,4,1,5,7] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1,1] => 0

[2,6,3,4,1,7,5] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1,1] => 0

[2,6,3,4,5,1,7] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1,1] => 0

[2,6,3,4,5,7,1] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1,1] => 0

[2,6,3,4,7,1,5] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1,1] => 0

[2,6,3,4,7,5,1] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1,1] => 0

[2,6,3,5,1,4,7] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1,1] => 1

[2,6,3,5,1,7,4] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1,1] => 1

[2,6,3,5,4,1,7] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1,1] => 1

[2,6,3,5,4,7,1] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1,1] => 1

[2,6,3,5,7,1,4] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1,1] => 1

[2,6,3,5,7,4,1] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1,1] => 1

[2,6,3,7,1,4,5] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1,1] => 0

[2,6,3,7,1,5,4] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1,1] => 1

[2,6,3,7,4,1,5] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1,1] => 0

[2,6,3,7,4,5,1] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1,1] => 0

[2,6,3,7,5,1,4] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1,1] => 1

[2,6,3,7,5,4,1] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1,1] => 1

[2,6,4,1,3,5,7] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1,1] => 0

[2,6,4,1,3,7,5] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1,1] => 0

[2,6,4,1,5,3,7] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1,1] => 0

[2,6,4,1,5,7,3] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1,1] => 0

[2,6,4,1,7,3,5] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1,1] => 0

[2,6,4,1,7,5,3] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1,1] => 0

[2,6,4,3,1,5,7] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1,1] => 0

[2,6,4,3,1,7,5] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1,1] => 0

[2,6,4,3,5,1,7] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1,1] => 0

[2,6,4,3,5,7,1] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1,1] => 0

[2,6,4,3,7,1,5] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1,1] => 0

[2,6,4,3,7,5,1] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1,1] => 0

[2,6,4,5,1,3,7] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1,1] => 0

[2,6,4,5,1,7,3] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1,1] => 0

[2,6,4,5,3,1,7] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1,1] => 0

[2,6,4,5,3,7,1] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1,1] => 0

[2,6,4,5,7,1,3] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1,1] => 0

[2,6,4,5,7,3,1] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1,1] => 0

[2,6,4,7,1,3,5] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1,1] => 0

[2,6,4,7,1,5,3] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1,1] => 0

[2,6,4,7,3,1,5] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1,1] => 0

[2,6,4,7,3,5,1] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1,1] => 0

[2,6,4,7,5,1,3] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1,1] => 0

[2,6,4,7,5,3,1] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1,1] => 0

[2,6,5,1,3,4,7] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1,1,1] => 1

[2,6,5,1,3,7,4] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1,1,1] => 1

[2,6,5,1,4,3,7] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2,1,1] => 2

[2,6,5,1,4,7,3] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2,1,1] => 2

[2,6,5,1,7,3,4] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1,1,1] => 1

[2,6,5,1,7,4,3] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2,1,1] => 2

[2,6,5,3,1,4,7] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1,1,1] => 1

[2,6,5,3,1,7,4] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1,1,1] => 1

[2,6,5,3,4,1,7] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1,1,1] => 1

[2,6,5,3,4,7,1] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1,1,1] => 1

[2,6,5,3,7,1,4] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1,1,1] => 1

[2,6,5,3,7,4,1] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1,1,1] => 1

[2,6,5,4,1,3,7] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2,1,1] => 2

[2,6,5,4,1,7,3] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2,1,1] => 2

[2,6,5,4,3,1,7] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2,1,1] => 2

[2,6,5,4,3,7,1] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2,1,1] => 2

[2,6,5,4,7,1,3] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2,1,1] => 2

[2,6,5,4,7,3,1] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2,1,1] => 2

[2,6,5,7,1,3,4] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1,1,1] => 1

[2,6,5,7,1,4,3] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2,1,1] => 2

[2,6,5,7,3,1,4] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1,1,1] => 1

[2,6,5,7,3,4,1] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1,1,1] => 1

[2,6,5,7,4,1,3] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2,1,1] => 2

[2,6,5,7,4,3,1] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2,1,1] => 2

[2,6,7,1,3,4,5] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1,1] => 0

[2,6,7,1,3,5,4] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1,1] => 1

[2,6,7,1,4,3,5] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1,1] => 0

[2,6,7,1,4,5,3] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1,1] => 0

[2,6,7,1,5,3,4] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1,1,1] => 1

[2,6,7,1,5,4,3] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2,1,1] => 2

[2,6,7,3,1,4,5] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1,1] => 0

[2,6,7,3,1,5,4] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1,1] => 1

[2,6,7,3,4,1,5] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1,1] => 0

[2,6,7,3,4,5,1] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1,1] => 0

[2,6,7,3,5,1,4] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1,1] => 1

[2,6,7,3,5,4,1] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1,1] => 1

[2,6,7,4,1,3,5] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1,1] => 0

[2,6,7,4,1,5,3] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1,1] => 0

[2,6,7,4,3,1,5] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1,1] => 0

[2,6,7,4,3,5,1] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1,1] => 0

[2,6,7,4,5,1,3] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1,1] => 0

[2,6,7,4,5,3,1] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1,1] => 0

[2,6,7,5,1,3,4] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1,1,1] => 1

[2,6,7,5,1,4,3] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2,1,1] => 2

[2,6,7,5,3,1,4] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1,1,1] => 1

[2,6,7,5,3,4,1] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1,1,1] => 1

[2,6,7,5,4,1,3] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2,1,1] => 2

[2,6,7,5,4,3,1] => [[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2,1,1] => 2

[2,7,1,3,4,5,6] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1,1] => 1

[2,7,1,3,4,6,5] => [[.,.],[[.,[.,[[.,.],.]]],.]] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1,1,1] => 2

[2,7,1,3,5,4,6] => [[.,.],[[.,[[.,.],[.,.]]],.]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1,1] => 1

[2,7,1,3,5,6,4] => [[.,.],[[.,[[.,.],[.,.]]],.]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1,1] => 1

[2,7,1,3,6,4,5] => [[.,.],[[.,[[.,[.,.]],.]],.]] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1,1,1] => 2

[2,7,1,3,6,5,4] => [[.,.],[[.,[[[.,.],.],.]],.]] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,1,1] => 3

[2,7,1,4,3,5,6] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2,1,1] => 1

[2,7,1,4,3,6,5] => [[.,.],[[[.,.],[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2,1,1] => 2

[2,7,1,4,5,3,6] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2,1,1] => 1

[2,7,1,4,5,6,3] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2,1,1] => 1

[2,7,1,4,6,3,5] => [[.,.],[[[.,.],[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2,1,1] => 2

[2,7,1,4,6,5,3] => [[.,.],[[[.,.],[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2,1,1] => 2

[2,7,1,5,3,4,6] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1,1,1] => 1

[2,7,1,5,3,6,4] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1,1,1] => 1

[2,7,1,5,4,3,6] => [[.,.],[[[[.,.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2,1,1] => 2

[2,7,1,5,4,6,3] => [[.,.],[[[[.,.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2,1,1] => 2

[2,7,1,5,6,3,4] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1,1,1] => 1

[2,7,1,5,6,4,3] => [[.,.],[[[[.,.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2,1,1] => 2

[2,7,1,6,3,4,5] => [[.,.],[[[.,[.,[.,.]]],.],.]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1,1,1] => 2

[2,7,1,6,3,5,4] => [[.,.],[[[.,[[.,.],.]],.],.]] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,1,1] => 3

[2,7,1,6,4,3,5] => [[.,.],[[[[.,.],[.,.]],.],.]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2,1,1] => 2

[2,7,1,6,4,5,3] => [[.,.],[[[[.,.],[.,.]],.],.]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2,1,1] => 2

[2,7,1,6,5,3,4] => [[.,.],[[[[.,[.,.]],.],.],.]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,1,1] => 3

[2,7,1,6,5,4,3] => [[.,.],[[[[[.,.],.],.],.],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1,1] => 4

[2,7,3,1,4,5,6] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1,1] => 1

[2,7,3,1,4,6,5] => [[.,.],[[.,[.,[[.,.],.]]],.]] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1,1,1] => 2

[2,7,3,1,5,4,6] => [[.,.],[[.,[[.,.],[.,.]]],.]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1,1] => 1

[2,7,3,1,5,6,4] => [[.,.],[[.,[[.,.],[.,.]]],.]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1,1] => 1

[2,7,3,1,6,4,5] => [[.,.],[[.,[[.,[.,.]],.]],.]] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1,1,1] => 2

[2,7,3,1,6,5,4] => [[.,.],[[.,[[[.,.],.],.]],.]] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,1,1] => 3

[2,7,3,4,1,5,6] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1,1] => 1

[2,7,3,4,1,6,5] => [[.,.],[[.,[.,[[.,.],.]]],.]] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1,1,1] => 2

[2,7,3,4,5,1,6] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1,1] => 1

[2,7,3,4,5,6,1] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1,1] => 1

[2,7,3,4,6,1,5] => [[.,.],[[.,[.,[[.,.],.]]],.]] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1,1,1] => 2

[2,7,3,4,6,5,1] => [[.,.],[[.,[.,[[.,.],.]]],.]] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1,1,1] => 2

[2,7,3,5,1,4,6] => [[.,.],[[.,[[.,.],[.,.]]],.]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1,1] => 1

[2,7,3,5,1,6,4] => [[.,.],[[.,[[.,.],[.,.]]],.]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1,1] => 1

[2,7,3,5,4,1,6] => [[.,.],[[.,[[.,.],[.,.]]],.]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1,1] => 1

[2,7,3,5,4,6,1] => [[.,.],[[.,[[.,.],[.,.]]],.]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1,1] => 1

[2,7,3,5,6,1,4] => [[.,.],[[.,[[.,.],[.,.]]],.]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1,1] => 1

[2,7,3,5,6,4,1] => [[.,.],[[.,[[.,.],[.,.]]],.]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1,1] => 1

[2,7,3,6,1,4,5] => [[.,.],[[.,[[.,[.,.]],.]],.]] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1,1,1] => 2

[2,7,3,6,1,5,4] => [[.,.],[[.,[[[.,.],.],.]],.]] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,1,1] => 3

[2,7,3,6,4,1,5] => [[.,.],[[.,[[.,[.,.]],.]],.]] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1,1,1] => 2

[2,7,3,6,4,5,1] => [[.,.],[[.,[[.,[.,.]],.]],.]] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1,1,1] => 2

[2,7,3,6,5,1,4] => [[.,.],[[.,[[[.,.],.],.]],.]] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,1,1] => 3

[2,7,3,6,5,4,1] => [[.,.],[[.,[[[.,.],.],.]],.]] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,1,1] => 3

[2,7,4,1,3,5,6] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2,1,1] => 1

[2,7,4,1,3,6,5] => [[.,.],[[[.,.],[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2,1,1] => 2

[2,7,4,1,5,3,6] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2,1,1] => 1

[2,7,4,1,5,6,3] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2,1,1] => 1

[2,7,4,1,6,3,5] => [[.,.],[[[.,.],[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2,1,1] => 2

[2,7,4,1,6,5,3] => [[.,.],[[[.,.],[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2,1,1] => 2

[2,7,4,3,1,5,6] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2,1,1] => 1

[2,7,4,3,1,6,5] => [[.,.],[[[.,.],[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2,1,1] => 2

[2,7,4,3,5,1,6] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2,1,1] => 1

[2,7,4,3,5,6,1] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2,1,1] => 1

[2,7,4,3,6,1,5] => [[.,.],[[[.,.],[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2,1,1] => 2

[2,7,4,3,6,5,1] => [[.,.],[[[.,.],[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2,1,1] => 2

[2,7,4,5,1,3,6] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2,1,1] => 1

[2,7,4,5,1,6,3] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2,1,1] => 1

[2,7,4,5,3,1,6] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2,1,1] => 1

[2,7,4,5,3,6,1] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2,1,1] => 1

[2,7,4,5,6,1,3] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2,1,1] => 1

[2,7,4,5,6,3,1] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2,1,1] => 1

[2,7,4,6,1,3,5] => [[.,.],[[[.,.],[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2,1,1] => 2

[2,7,4,6,1,5,3] => [[.,.],[[[.,.],[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2,1,1] => 2

[2,7,4,6,3,1,5] => [[.,.],[[[.,.],[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2,1,1] => 2

[2,7,4,6,3,5,1] => [[.,.],[[[.,.],[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2,1,1] => 2

[2,7,4,6,5,1,3] => [[.,.],[[[.,.],[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2,1,1] => 2

[2,7,4,6,5,3,1] => [[.,.],[[[.,.],[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2,1,1] => 2

[2,7,5,1,3,4,6] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1,1,1] => 1

[2,7,5,1,3,6,4] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1,1,1] => 1

[2,7,5,1,4,3,6] => [[.,.],[[[[.,.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2,1,1] => 2

[2,7,5,1,4,6,3] => [[.,.],[[[[.,.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2,1,1] => 2

[2,7,5,1,6,3,4] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1,1,1] => 1

[2,7,5,1,6,4,3] => [[.,.],[[[[.,.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2,1,1] => 2

[2,7,5,3,1,4,6] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1,1,1] => 1

[2,7,5,3,1,6,4] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1,1,1] => 1

[2,7,5,3,4,1,6] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1,1,1] => 1

[2,7,5,3,4,6,1] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1,1,1] => 1

[2,7,5,3,6,1,4] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1,1,1] => 1

[2,7,5,3,6,4,1] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1,1,1] => 1

[2,7,5,4,1,3,6] => [[.,.],[[[[.,.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2,1,1] => 2

[2,7,5,4,1,6,3] => [[.,.],[[[[.,.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2,1,1] => 2

[2,7,5,4,3,1,6] => [[.,.],[[[[.,.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2,1,1] => 2

[2,7,5,4,3,6,1] => [[.,.],[[[[.,.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2,1,1] => 2

[2,7,5,4,6,1,3] => [[.,.],[[[[.,.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2,1,1] => 2

[2,7,5,4,6,3,1] => [[.,.],[[[[.,.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2,1,1] => 2

[2,7,5,6,1,3,4] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1,1,1] => 1

[2,7,5,6,1,4,3] => [[.,.],[[[[.,.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2,1,1] => 2

[2,7,5,6,3,1,4] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1,1,1] => 1

[2,7,5,6,3,4,1] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1,1,1] => 1

[2,7,5,6,4,1,3] => [[.,.],[[[[.,.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2,1,1] => 2

[2,7,5,6,4,3,1] => [[.,.],[[[[.,.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2,1,1] => 2

[2,7,6,1,3,4,5] => [[.,.],[[[.,[.,[.,.]]],.],.]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1,1,1] => 2

[2,7,6,1,3,5,4] => [[.,.],[[[.,[[.,.],.]],.],.]] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,1,1] => 3

[2,7,6,1,4,3,5] => [[.,.],[[[[.,.],[.,.]],.],.]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2,1,1] => 2

[2,7,6,1,4,5,3] => [[.,.],[[[[.,.],[.,.]],.],.]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2,1,1] => 2

[2,7,6,1,5,3,4] => [[.,.],[[[[.,[.,.]],.],.],.]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,1,1] => 3

[2,7,6,1,5,4,3] => [[.,.],[[[[[.,.],.],.],.],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1,1] => 4

[2,7,6,3,1,4,5] => [[.,.],[[[.,[.,[.,.]]],.],.]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1,1,1] => 2

[2,7,6,3,1,5,4] => [[.,.],[[[.,[[.,.],.]],.],.]] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,1,1] => 3

[2,7,6,3,4,1,5] => [[.,.],[[[.,[.,[.,.]]],.],.]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1,1,1] => 2

[2,7,6,3,4,5,1] => [[.,.],[[[.,[.,[.,.]]],.],.]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1,1,1] => 2

[2,7,6,3,5,1,4] => [[.,.],[[[.,[[.,.],.]],.],.]] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,1,1] => 3

[2,7,6,3,5,4,1] => [[.,.],[[[.,[[.,.],.]],.],.]] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,1,1] => 3

[2,7,6,4,1,3,5] => [[.,.],[[[[.,.],[.,.]],.],.]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2,1,1] => 2

[2,7,6,4,1,5,3] => [[.,.],[[[[.,.],[.,.]],.],.]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2,1,1] => 2

[2,7,6,4,3,1,5] => [[.,.],[[[[.,.],[.,.]],.],.]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2,1,1] => 2

[2,7,6,4,3,5,1] => [[.,.],[[[[.,.],[.,.]],.],.]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2,1,1] => 2

[2,7,6,4,5,1,3] => [[.,.],[[[[.,.],[.,.]],.],.]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2,1,1] => 2

[2,7,6,4,5,3,1] => [[.,.],[[[[.,.],[.,.]],.],.]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2,1,1] => 2

[2,7,6,5,1,3,4] => [[.,.],[[[[.,[.,.]],.],.],.]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,1,1] => 3

[2,7,6,5,1,4,3] => [[.,.],[[[[[.,.],.],.],.],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1,1] => 4

[2,7,6,5,3,1,4] => [[.,.],[[[[.,[.,.]],.],.],.]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,1,1] => 3

[2,7,6,5,3,4,1] => [[.,.],[[[[.,[.,.]],.],.],.]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,1,1] => 3

[2,7,6,5,4,1,3] => [[.,.],[[[[[.,.],.],.],.],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1,1] => 4

[2,7,6,5,4,3,1] => [[.,.],[[[[[.,.],.],.],.],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1,1] => 4

[3,1,2,4,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2] => 0

[3,1,2,4,5,7,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2] => 1

[3,1,2,4,6,5,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2] => 0

[3,1,2,4,6,7,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2] => 0

[3,1,2,4,7,5,6] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [4,2,2,2,2] => 1

[3,1,2,4,7,6,5] => [[.,[.,.]],[.,[[[.,.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,2,2] => 2

[3,1,2,5,4,6,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2] => 0

[3,1,2,5,4,7,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2] => 1

[3,1,2,5,6,4,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2] => 0

[3,1,2,5,6,7,4] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2] => 0

[3,1,2,5,7,4,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2] => 1

[3,1,2,5,7,6,4] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2] => 1

[3,1,2,6,4,5,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2] => 0

[3,1,2,6,4,7,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2] => 0

[3,1,2,6,5,4,7] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2] => 1

[3,1,2,6,5,7,4] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2] => 1

[3,1,2,6,7,4,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2] => 0

[3,1,2,6,7,5,4] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2] => 1

[3,1,2,7,4,5,6] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [5,2,2,2,2] => 1

[3,1,2,7,4,6,5] => [[.,[.,.]],[[.,[[.,.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,2,2] => 2

[3,1,2,7,5,4,6] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2] => 1

[3,1,2,7,5,6,4] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2] => 1

[3,1,2,7,6,4,5] => [[.,[.,.]],[[[.,[.,.]],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,2,2] => 2

[3,1,2,7,6,5,4] => [[.,[.,.]],[[[[.,.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,2] => 3

[3,1,4,2,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2] => 0

[3,1,4,2,5,7,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2] => 1

[3,1,4,2,6,5,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2] => 0

[3,1,4,2,6,7,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2] => 0

[3,1,4,2,7,5,6] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [4,2,2,2,2] => 1

[3,1,4,2,7,6,5] => [[.,[.,.]],[.,[[[.,.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,2,2] => 2

[3,1,4,5,2,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2] => 0

[3,1,4,5,2,7,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2] => 1

[3,1,4,5,6,2,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2] => 0

[3,1,4,5,6,7,2] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2] => 0

[3,1,4,5,7,2,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2] => 1

[3,1,4,5,7,6,2] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2] => 1

[3,1,4,6,2,5,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2] => 0

[3,1,4,6,2,7,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2] => 0

[3,1,4,6,5,2,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2] => 0

[3,1,4,6,5,7,2] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2] => 0

[3,1,4,6,7,2,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2] => 0

[3,1,4,6,7,5,2] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2] => 0

[3,1,4,7,2,5,6] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [4,2,2,2,2] => 1

[3,1,4,7,2,6,5] => [[.,[.,.]],[.,[[[.,.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,2,2] => 2

[3,1,4,7,5,2,6] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [4,2,2,2,2] => 1

[3,1,4,7,5,6,2] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [4,2,2,2,2] => 1

[3,1,4,7,6,2,5] => [[.,[.,.]],[.,[[[.,.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,2,2] => 2

[3,1,4,7,6,5,2] => [[.,[.,.]],[.,[[[.,.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,2,2] => 2

[3,1,5,2,4,6,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2] => 0

[3,1,5,2,4,7,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2] => 1

[3,1,5,2,6,4,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2] => 0

[3,1,5,2,6,7,4] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2] => 0

[3,1,5,2,7,4,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2] => 1

[3,1,5,2,7,6,4] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2] => 1

[3,1,5,4,2,6,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2] => 0

[3,1,5,4,2,7,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2] => 1

[3,1,5,4,6,2,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2] => 0

[3,1,5,4,6,7,2] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2] => 0

[3,1,5,4,7,2,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2] => 1

[3,1,5,4,7,6,2] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2] => 1

[3,1,5,6,2,4,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2] => 0

[3,1,5,6,2,7,4] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2] => 0

[3,1,5,6,4,2,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2] => 0

[3,1,5,6,4,7,2] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2] => 0

[3,1,5,6,7,2,4] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2] => 0

[3,1,5,6,7,4,2] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2] => 0

[3,1,5,7,2,4,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2] => 1

[3,1,5,7,2,6,4] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2] => 1

[3,1,5,7,4,2,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2] => 1

[3,1,5,7,4,6,2] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2] => 1

[3,1,5,7,6,2,4] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2] => 1

[3,1,5,7,6,4,2] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2] => 1

[3,1,6,2,4,5,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2] => 0

[3,1,6,2,4,7,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2] => 0

[3,1,6,2,5,4,7] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2] => 1

[3,1,6,2,5,7,4] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2] => 1

[3,1,6,2,7,4,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2] => 0

[3,1,6,2,7,5,4] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2] => 1

[3,1,6,4,2,5,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2] => 0

[3,1,6,4,2,7,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2] => 0

[3,1,6,4,5,2,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2] => 0

[3,1,6,4,5,7,2] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2] => 0

[3,1,6,4,7,2,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2] => 0

[3,1,6,4,7,5,2] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2] => 0

[3,1,6,5,2,4,7] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2] => 1

[3,1,6,5,2,7,4] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2] => 1

[3,1,6,5,4,2,7] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2] => 1

[3,1,6,5,4,7,2] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2] => 1

[3,1,6,5,7,2,4] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2] => 1

[3,1,6,5,7,4,2] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2] => 1

[3,1,6,7,2,4,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2] => 0

[3,1,6,7,2,5,4] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2] => 1

[3,1,6,7,4,2,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2] => 0

[3,1,6,7,4,5,2] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2] => 0

[3,1,6,7,5,2,4] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2] => 1

[3,1,6,7,5,4,2] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2] => 1

[3,1,7,2,4,5,6] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [5,2,2,2,2] => 1

[3,1,7,2,4,6,5] => [[.,[.,.]],[[.,[[.,.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,2,2] => 2

[3,1,7,2,5,4,6] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2] => 1

[3,1,7,2,5,6,4] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2] => 1

[3,1,7,2,6,4,5] => [[.,[.,.]],[[[.,[.,.]],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,2,2] => 2

[3,1,7,2,6,5,4] => [[.,[.,.]],[[[[.,.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,2] => 3

[3,1,7,4,2,5,6] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [5,2,2,2,2] => 1

[3,1,7,4,2,6,5] => [[.,[.,.]],[[.,[[.,.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,2,2] => 2

[3,1,7,4,5,2,6] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [5,2,2,2,2] => 1

[3,1,7,4,5,6,2] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [5,2,2,2,2] => 1

[3,1,7,4,6,2,5] => [[.,[.,.]],[[.,[[.,.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,2,2] => 2

[3,1,7,4,6,5,2] => [[.,[.,.]],[[.,[[.,.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,2,2] => 2

[3,1,7,5,2,4,6] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2] => 1

[3,1,7,5,2,6,4] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2] => 1

[3,1,7,5,4,2,6] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2] => 1

[3,1,7,5,4,6,2] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2] => 1

[3,1,7,5,6,2,4] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2] => 1

[3,1,7,5,6,4,2] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2] => 1

[3,1,7,6,2,4,5] => [[.,[.,.]],[[[.,[.,.]],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,2,2] => 2

[3,1,7,6,2,5,4] => [[.,[.,.]],[[[[.,.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,2] => 3

[3,1,7,6,4,2,5] => [[.,[.,.]],[[[.,[.,.]],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,2,2] => 2

[3,1,7,6,4,5,2] => [[.,[.,.]],[[[.,[.,.]],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,2,2] => 2

[3,1,7,6,5,2,4] => [[.,[.,.]],[[[[.,.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,2] => 3

[3,1,7,6,5,4,2] => [[.,[.,.]],[[[[.,.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,2] => 3

[3,2,1,4,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2,1] => 1

[3,2,1,4,5,7,6] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2,1] => 2

[3,2,1,4,6,5,7] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2,1] => 1

[3,2,1,4,6,7,5] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2,1] => 1

[3,2,1,4,7,5,6] => [[[.,.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,2,2,2,1] => 2

[3,2,1,4,7,6,5] => [[[.,.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,2,2,1] => 3

[3,2,1,5,4,6,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2,1] => 1

[3,2,1,5,4,7,6] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2,1] => 2

[3,2,1,5,6,4,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2,1] => 1

[3,2,1,5,6,7,4] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2,1] => 1

[3,2,1,5,7,4,6] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2,1] => 2

[3,2,1,5,7,6,4] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2,1] => 2

[3,2,1,6,4,5,7] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2,1] => 1

[3,2,1,6,4,7,5] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2,1] => 1

[3,2,1,6,5,4,7] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2,1] => 2

[3,2,1,6,5,7,4] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2,1] => 2

[3,2,1,6,7,4,5] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2,1] => 1

[3,2,1,6,7,5,4] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2,1] => 2

[3,2,1,7,4,5,6] => [[[.,.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,2,2,2,1] => 2

[3,2,1,7,4,6,5] => [[[.,.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,2,2,1] => 3

[3,2,1,7,5,4,6] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2,1] => 2

[3,2,1,7,5,6,4] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2,1] => 2

[3,2,1,7,6,4,5] => [[[.,.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,2,2,1] => 3

[3,2,1,7,6,5,4] => [[[.,.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,2,1] => 4

[3,2,4,1,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2,1] => 1

[3,2,4,1,5,7,6] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2,1] => 2

[3,2,4,1,6,5,7] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2,1] => 1

[3,2,4,1,6,7,5] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2,1] => 1

[3,2,4,1,7,5,6] => [[[.,.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,2,2,2,1] => 2

[3,2,4,1,7,6,5] => [[[.,.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,2,2,1] => 3

[3,2,4,5,1,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2,1] => 1

[3,2,4,5,1,7,6] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2,1] => 2

[3,2,4,5,6,1,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2,1] => 1

[3,2,4,5,6,7,1] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2,1] => 1

[3,2,4,5,7,1,6] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2,1] => 2

[3,2,4,5,7,6,1] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2,1] => 2

[3,2,4,6,1,5,7] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2,1] => 1

[3,2,4,6,1,7,5] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2,1] => 1

[3,2,4,6,5,1,7] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2,1] => 1

[3,2,4,6,5,7,1] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2,1] => 1

[3,2,4,6,7,1,5] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2,1] => 1

[3,2,4,6,7,5,1] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2,1] => 1

[3,2,4,7,1,5,6] => [[[.,.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,2,2,2,1] => 2

[3,2,4,7,1,6,5] => [[[.,.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,2,2,1] => 3

[3,2,4,7,5,1,6] => [[[.,.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,2,2,2,1] => 2

[3,2,4,7,5,6,1] => [[[.,.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,2,2,2,1] => 2

[3,2,4,7,6,1,5] => [[[.,.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,2,2,1] => 3

[3,2,4,7,6,5,1] => [[[.,.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,2,2,1] => 3

[3,2,5,1,4,6,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2,1] => 1

[3,2,5,1,4,7,6] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2,1] => 2

[3,2,5,1,6,4,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2,1] => 1

[3,2,5,1,6,7,4] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2,1] => 1

[3,2,5,1,7,4,6] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2,1] => 2

[3,2,5,1,7,6,4] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2,1] => 2

[3,2,5,4,1,6,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2,1] => 1

[3,2,5,4,1,7,6] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2,1] => 2

[3,2,5,4,6,1,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2,1] => 1

[3,2,5,4,6,7,1] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2,1] => 1

[3,2,5,4,7,1,6] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2,1] => 2

[3,2,5,4,7,6,1] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2,1] => 2

[3,2,5,6,1,4,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2,1] => 1

[3,2,5,6,1,7,4] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2,1] => 1

[3,2,5,6,4,1,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2,1] => 1

[3,2,5,6,4,7,1] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2,1] => 1

[3,2,5,6,7,1,4] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2,1] => 1

[3,2,5,6,7,4,1] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2,1] => 1

[3,2,5,7,1,4,6] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2,1] => 2

[3,2,5,7,1,6,4] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2,1] => 2

[3,2,5,7,4,1,6] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2,1] => 2

[3,2,5,7,4,6,1] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2,1] => 2

[3,2,5,7,6,1,4] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2,1] => 2

[3,2,5,7,6,4,1] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2,1] => 2

[3,2,6,1,4,5,7] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2,1] => 1

[3,2,6,1,4,7,5] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2,1] => 1

[3,2,6,1,5,4,7] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2,1] => 2

[3,2,6,1,5,7,4] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2,1] => 2

[3,2,6,1,7,4,5] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2,1] => 1

[3,2,6,1,7,5,4] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2,1] => 2

[3,2,6,4,1,5,7] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2,1] => 1

[3,2,6,4,1,7,5] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2,1] => 1

[3,2,6,4,5,1,7] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2,1] => 1

[3,2,6,4,5,7,1] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2,1] => 1

[3,2,6,4,7,1,5] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2,1] => 1

[3,2,6,4,7,5,1] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2,1] => 1

[3,2,6,5,1,4,7] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2,1] => 2

[3,2,6,5,1,7,4] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2,1] => 2

[3,2,6,5,4,1,7] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2,1] => 2

[3,2,6,5,4,7,1] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2,1] => 2

[3,2,6,5,7,1,4] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2,1] => 2

[3,2,6,5,7,4,1] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2,1] => 2

[3,2,6,7,1,4,5] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2,1] => 1

[3,2,6,7,1,5,4] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2,1] => 2

[3,2,6,7,4,1,5] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2,1] => 1

[3,2,6,7,4,5,1] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2,1] => 1

[3,2,6,7,5,1,4] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2,1] => 2

[3,2,6,7,5,4,1] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2,1] => 2

[3,2,7,1,4,5,6] => [[[.,.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,2,2,2,1] => 2

[3,2,7,1,4,6,5] => [[[.,.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,2,2,1] => 3

[3,2,7,1,5,4,6] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2,1] => 2

[3,2,7,1,5,6,4] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2,1] => 2

[3,2,7,1,6,4,5] => [[[.,.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,2,2,1] => 3

[3,2,7,1,6,5,4] => [[[.,.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,2,1] => 4

[3,2,7,4,1,5,6] => [[[.,.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,2,2,2,1] => 2

[3,2,7,4,1,6,5] => [[[.,.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,2,2,1] => 3

[3,2,7,4,5,1,6] => [[[.,.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,2,2,2,1] => 2

[3,2,7,4,5,6,1] => [[[.,.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,2,2,2,1] => 2

[3,2,7,4,6,1,5] => [[[.,.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,2,2,1] => 3

[3,2,7,4,6,5,1] => [[[.,.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,2,2,1] => 3

[3,2,7,5,1,4,6] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2,1] => 2

[3,2,7,5,1,6,4] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2,1] => 2

[3,2,7,5,4,1,6] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2,1] => 2

[3,2,7,5,4,6,1] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2,1] => 2

[3,2,7,5,6,1,4] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2,1] => 2

[3,2,7,5,6,4,1] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2,1] => 2

[3,2,7,6,1,4,5] => [[[.,.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,2,2,1] => 3

[3,2,7,6,1,5,4] => [[[.,.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,2,1] => 4

[3,2,7,6,4,1,5] => [[[.,.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,2,2,1] => 3

[3,2,7,6,4,5,1] => [[[.,.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,2,2,1] => 3

[3,2,7,6,5,1,4] => [[[.,.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,2,1] => 4

[3,2,7,6,5,4,1] => [[[.,.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,2,1] => 4

[3,4,1,2,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2] => 0

[3,4,1,2,5,7,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2] => 1

[3,4,1,2,6,5,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2] => 0

[3,4,1,2,6,7,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2] => 0

[3,4,1,2,7,5,6] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [4,2,2,2,2] => 1

[3,4,1,2,7,6,5] => [[.,[.,.]],[.,[[[.,.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,2,2] => 2

[3,4,1,5,2,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2] => 0

[3,4,1,5,2,7,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2] => 1

[3,4,1,5,6,2,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2] => 0

[3,4,1,5,6,7,2] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2] => 0

[3,4,1,5,7,2,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2] => 1

[3,4,1,5,7,6,2] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2] => 1

[3,4,1,6,2,5,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2] => 0

[3,4,1,6,2,7,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2] => 0

[3,4,1,6,5,2,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2] => 0

[3,4,1,6,5,7,2] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2] => 0

[3,4,1,6,7,2,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2] => 0

[3,4,1,6,7,5,2] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2] => 0

[3,4,1,7,2,5,6] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [4,2,2,2,2] => 1

[3,4,1,7,2,6,5] => [[.,[.,.]],[.,[[[.,.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,2,2] => 2

[3,4,1,7,5,2,6] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [4,2,2,2,2] => 1

[3,4,1,7,5,6,2] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [4,2,2,2,2] => 1

[3,4,1,7,6,2,5] => [[.,[.,.]],[.,[[[.,.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,2,2] => 2

[3,4,1,7,6,5,2] => [[.,[.,.]],[.,[[[.,.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,2,2] => 2

[3,4,2,1,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2,1] => 1

[3,4,2,1,5,7,6] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2,1] => 2

[3,4,2,1,6,5,7] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2,1] => 1

[3,4,2,1,6,7,5] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2,1] => 1

[3,4,2,1,7,5,6] => [[[.,.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,2,2,2,1] => 2

[3,4,2,1,7,6,5] => [[[.,.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,2,2,1] => 3

[3,4,2,5,1,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2,1] => 1

[3,4,2,5,1,7,6] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2,1] => 2

[3,4,2,5,6,1,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2,1] => 1

[3,4,2,5,6,7,1] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2,1] => 1

[3,4,2,5,7,1,6] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2,1] => 2

[3,4,2,5,7,6,1] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2,1] => 2

[3,4,2,6,1,5,7] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2,1] => 1

[3,4,2,6,1,7,5] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2,1] => 1

[3,4,2,6,5,1,7] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2,1] => 1

[3,4,2,6,5,7,1] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2,1] => 1

[3,4,2,6,7,1,5] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2,1] => 1

[3,4,2,6,7,5,1] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2,1] => 1

[3,4,2,7,1,5,6] => [[[.,.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,2,2,2,1] => 2

[3,4,2,7,1,6,5] => [[[.,.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,2,2,1] => 3

[3,4,2,7,5,1,6] => [[[.,.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,2,2,2,1] => 2

[3,4,2,7,5,6,1] => [[[.,.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,2,2,2,1] => 2

[3,4,2,7,6,1,5] => [[[.,.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,2,2,1] => 3

[3,4,2,7,6,5,1] => [[[.,.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,2,2,1] => 3

[3,4,5,1,2,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2] => 0

[3,4,5,1,2,7,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2] => 1

[3,4,5,1,6,2,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2] => 0

[3,4,5,1,6,7,2] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2] => 0

[3,4,5,1,7,2,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2] => 1

[3,4,5,1,7,6,2] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2] => 1

[3,4,5,2,1,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2,1] => 1

[3,4,5,2,1,7,6] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2,1] => 2

[3,4,5,2,6,1,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2,1] => 1

[3,4,5,2,6,7,1] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2,1] => 1

[3,4,5,2,7,1,6] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2,1] => 2

[3,4,5,2,7,6,1] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2,1] => 2

[3,4,5,6,1,2,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2] => 0

[3,4,5,6,1,7,2] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2] => 0

[3,4,5,6,2,1,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2,1] => 1

[3,4,5,6,2,7,1] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2,1] => 1

[3,4,5,6,7,1,2] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2] => 0

[3,4,5,6,7,2,1] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2,1] => 1

[3,4,5,7,1,2,6] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2] => 1

[3,4,5,7,1,6,2] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2] => 1

[3,4,5,7,2,1,6] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2,1] => 2

[3,4,5,7,2,6,1] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2,1] => 2

[3,4,5,7,6,1,2] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2] => 1

[3,4,5,7,6,2,1] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2,1] => 2

[3,4,6,1,2,5,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2] => 0

[3,4,6,1,2,7,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2] => 0

[3,4,6,1,5,2,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2] => 0

[3,4,6,1,5,7,2] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2] => 0

[3,4,6,1,7,2,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2] => 0

[3,4,6,1,7,5,2] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2] => 0

[3,4,6,2,1,5,7] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2,1] => 1

[3,4,6,2,1,7,5] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2,1] => 1

[3,4,6,2,5,1,7] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2,1] => 1

[3,4,6,2,5,7,1] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2,1] => 1

[3,4,6,2,7,1,5] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2,1] => 1

[3,4,6,2,7,5,1] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2,1] => 1

[3,4,6,5,1,2,7] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2] => 0

[3,4,6,5,1,7,2] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2] => 0

[3,4,6,5,2,1,7] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2,1] => 1

[3,4,6,5,2,7,1] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2,1] => 1

[3,4,6,5,7,1,2] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2] => 0

[3,4,6,5,7,2,1] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2,1] => 1

[3,4,6,7,1,2,5] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2] => 0

[3,4,6,7,1,5,2] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2] => 0

[3,4,6,7,2,1,5] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2,1] => 1

[3,4,6,7,2,5,1] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2,1] => 1

[3,4,6,7,5,1,2] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2] => 0

[3,4,6,7,5,2,1] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2,1] => 1

[3,4,7,1,2,5,6] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [4,2,2,2,2] => 1

[3,4,7,1,2,6,5] => [[.,[.,.]],[.,[[[.,.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,2,2] => 2

[3,4,7,1,5,2,6] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [4,2,2,2,2] => 1

[3,4,7,1,5,6,2] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [4,2,2,2,2] => 1

[3,4,7,1,6,2,5] => [[.,[.,.]],[.,[[[.,.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,2,2] => 2

[3,4,7,1,6,5,2] => [[.,[.,.]],[.,[[[.,.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,2,2] => 2

[3,4,7,2,1,5,6] => [[[.,.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,2,2,2,1] => 2

[3,4,7,2,1,6,5] => [[[.,.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,2,2,1] => 3

[3,4,7,2,5,1,6] => [[[.,.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,2,2,2,1] => 2

[3,4,7,2,5,6,1] => [[[.,.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,2,2,2,1] => 2

[3,4,7,2,6,1,5] => [[[.,.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,2,2,1] => 3

[3,4,7,2,6,5,1] => [[[.,.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,2,2,1] => 3

[3,4,7,5,1,2,6] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [4,2,2,2,2] => 1

[3,4,7,5,1,6,2] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [4,2,2,2,2] => 1

[3,4,7,5,2,1,6] => [[[.,.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,2,2,2,1] => 2

[3,4,7,5,2,6,1] => [[[.,.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,2,2,2,1] => 2

[3,4,7,5,6,1,2] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [4,2,2,2,2] => 1

[3,4,7,5,6,2,1] => [[[.,.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,2,2,2,1] => 2

[3,4,7,6,1,2,5] => [[.,[.,.]],[.,[[[.,.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,2,2] => 2

[3,4,7,6,1,5,2] => [[.,[.,.]],[.,[[[.,.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,2,2] => 2

[3,4,7,6,2,1,5] => [[[.,.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,2,2,1] => 3

[3,4,7,6,2,5,1] => [[[.,.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,2,2,1] => 3

[3,4,7,6,5,1,2] => [[.,[.,.]],[.,[[[.,.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,2,2] => 2

[3,4,7,6,5,2,1] => [[[.,.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,2,2,1] => 3

[3,5,1,2,4,6,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2] => 0

[3,5,1,2,4,7,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2] => 1

[3,5,1,2,6,4,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2] => 0

[3,5,1,2,6,7,4] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2] => 0

[3,5,1,2,7,4,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2] => 1

[3,5,1,2,7,6,4] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2] => 1

[3,5,1,4,2,6,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2] => 0

[3,5,1,4,2,7,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2] => 1

[3,5,1,4,6,2,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2] => 0

[3,5,1,4,6,7,2] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2] => 0

[3,5,1,4,7,2,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2] => 1

[3,5,1,4,7,6,2] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2] => 1

[3,5,1,6,2,4,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2] => 0

[3,5,1,6,2,7,4] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2] => 0

[3,5,1,6,4,2,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2] => 0

[3,5,1,6,4,7,2] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2] => 0

[3,5,1,6,7,2,4] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2] => 0

[3,5,1,6,7,4,2] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2] => 0

[3,5,1,7,2,4,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2] => 1

[3,5,1,7,2,6,4] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2] => 1

[3,5,1,7,4,2,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2] => 1

[3,5,1,7,4,6,2] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2] => 1

[3,5,1,7,6,2,4] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2] => 1

[3,5,1,7,6,4,2] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2] => 1

[3,5,2,1,4,6,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2,1] => 1

[3,5,2,1,4,7,6] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2,1] => 2

[3,5,2,1,6,4,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2,1] => 1

[3,5,2,1,6,7,4] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2,1] => 1

[3,5,2,1,7,4,6] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2,1] => 2

[3,5,2,1,7,6,4] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2,1] => 2

[3,5,2,4,1,6,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2,1] => 1

[3,5,2,4,1,7,6] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2,1] => 2

[3,5,2,4,6,1,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2,1] => 1

[3,5,2,4,6,7,1] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2,1] => 1

[3,5,2,4,7,1,6] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2,1] => 2

[3,5,2,4,7,6,1] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2,1] => 2

[3,5,2,6,1,4,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2,1] => 1

[3,5,2,6,1,7,4] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2,1] => 1

[3,5,2,6,4,1,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2,1] => 1

[3,5,2,6,4,7,1] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2,1] => 1

[3,5,2,6,7,1,4] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2,1] => 1

[3,5,2,6,7,4,1] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2,1] => 1

[3,5,2,7,1,4,6] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2,1] => 2

[3,5,2,7,1,6,4] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2,1] => 2

[3,5,2,7,4,1,6] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2,1] => 2

[3,5,2,7,4,6,1] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2,1] => 2

[3,5,2,7,6,1,4] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2,1] => 2

[3,5,2,7,6,4,1] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2,1] => 2

[3,5,4,1,2,6,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2] => 0

[3,5,4,1,2,7,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2] => 1

[3,5,4,1,6,2,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2] => 0

[3,5,4,1,6,7,2] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2] => 0

[3,5,4,1,7,2,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2] => 1

[3,5,4,1,7,6,2] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2] => 1

[3,5,4,2,1,6,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2,1] => 1

[3,5,4,2,1,7,6] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2,1] => 2

[3,5,4,2,6,1,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2,1] => 1

[3,5,4,2,6,7,1] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2,1] => 1

[3,5,4,2,7,1,6] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2,1] => 2

[3,5,4,2,7,6,1] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2,1] => 2

[3,5,4,6,1,2,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2] => 0

[3,5,4,6,1,7,2] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2] => 0

[3,5,4,6,2,1,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2,1] => 1

[3,5,4,6,2,7,1] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2,1] => 1

[3,5,4,6,7,1,2] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2] => 0

[3,5,4,6,7,2,1] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2,1] => 1

[3,5,4,7,1,2,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2] => 1

[3,5,4,7,1,6,2] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2] => 1

[3,5,4,7,2,1,6] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2,1] => 2

[3,5,4,7,2,6,1] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2,1] => 2

[3,5,4,7,6,1,2] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2] => 1

[3,5,4,7,6,2,1] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2,1] => 2

[3,5,6,1,2,4,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2] => 0

[3,5,6,1,2,7,4] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2] => 0

[3,5,6,1,4,2,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2] => 0

[3,5,6,1,4,7,2] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2] => 0

[3,5,6,1,7,2,4] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2] => 0

[3,5,6,1,7,4,2] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2] => 0

[3,5,6,2,1,4,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2,1] => 1

[3,5,6,2,1,7,4] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2,1] => 1

[3,5,6,2,4,1,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2,1] => 1

[3,5,6,2,4,7,1] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2,1] => 1

[3,5,6,2,7,1,4] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2,1] => 1

[3,5,6,2,7,4,1] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2,1] => 1

[3,5,6,4,1,2,7] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2] => 0

[3,5,6,4,1,7,2] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2] => 0

[3,5,6,4,2,1,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2,1] => 1

[3,5,6,4,2,7,1] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2,1] => 1

[3,5,6,4,7,1,2] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2] => 0

[3,5,6,4,7,2,1] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2,1] => 1

[3,5,6,7,1,2,4] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2] => 0

[3,5,6,7,1,4,2] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2] => 0

[3,5,6,7,2,1,4] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2,1] => 1

[3,5,6,7,2,4,1] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2,1] => 1

[3,5,6,7,4,1,2] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2] => 0

[3,5,6,7,4,2,1] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2,1] => 1

[3,5,7,1,2,4,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2] => 1

[3,5,7,1,2,6,4] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2] => 1

[3,5,7,1,4,2,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2] => 1

[3,5,7,1,4,6,2] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2] => 1

[3,5,7,1,6,2,4] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2] => 1

[3,5,7,1,6,4,2] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2] => 1

[3,5,7,2,1,4,6] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2,1] => 2

[3,5,7,2,1,6,4] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2,1] => 2

[3,5,7,2,4,1,6] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2,1] => 2

[3,5,7,2,4,6,1] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2,1] => 2

[3,5,7,2,6,1,4] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2,1] => 2

[3,5,7,2,6,4,1] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2,1] => 2

[3,5,7,4,1,2,6] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2] => 1

[3,5,7,4,1,6,2] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2] => 1

[3,5,7,4,2,1,6] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2,1] => 2

[3,5,7,4,2,6,1] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2,1] => 2

[3,5,7,4,6,1,2] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2] => 1

[3,5,7,4,6,2,1] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2,1] => 2

[3,5,7,6,1,2,4] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2] => 1

[3,5,7,6,1,4,2] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2] => 1

[3,5,7,6,2,1,4] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2,1] => 2

[3,5,7,6,2,4,1] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2,1] => 2

[3,5,7,6,4,1,2] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2] => 1

[3,5,7,6,4,2,1] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2,1] => 2

[3,6,1,2,4,5,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2] => 0

[3,6,1,2,4,7,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2] => 0

[3,6,1,2,5,4,7] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2] => 1

[3,6,1,2,5,7,4] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2] => 1

[3,6,1,2,7,4,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2] => 0

[3,6,1,2,7,5,4] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2] => 1

[3,6,1,4,2,5,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2] => 0

[3,6,1,4,2,7,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2] => 0

[3,6,1,4,5,2,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2] => 0

[3,6,1,4,5,7,2] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2] => 0

[3,6,1,4,7,2,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2] => 0

[3,6,1,4,7,5,2] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2] => 0

[3,6,1,5,2,4,7] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2] => 1

[3,6,1,5,2,7,4] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2] => 1

[3,6,1,5,4,2,7] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2] => 1

[3,6,1,5,4,7,2] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2] => 1

[3,6,1,5,7,2,4] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2] => 1

[3,6,1,5,7,4,2] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2] => 1

[3,6,1,7,2,4,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2] => 0

[3,6,1,7,2,5,4] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2] => 1

[3,6,1,7,4,2,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2] => 0

[3,6,1,7,4,5,2] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2] => 0

[3,6,1,7,5,2,4] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2] => 1

[3,6,1,7,5,4,2] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2] => 1

[3,6,2,1,4,5,7] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2,1] => 1

[3,6,2,1,4,7,5] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2,1] => 1

[3,6,2,1,5,4,7] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2,1] => 2

[3,6,2,1,5,7,4] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2,1] => 2

[3,6,2,1,7,4,5] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2,1] => 1

[3,6,2,1,7,5,4] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2,1] => 2

[3,6,2,4,1,5,7] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2,1] => 1

[3,6,2,4,1,7,5] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2,1] => 1

[3,6,2,4,5,1,7] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2,1] => 1

[3,6,2,4,5,7,1] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2,1] => 1

[3,6,2,4,7,1,5] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2,1] => 1

[3,6,2,4,7,5,1] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2,1] => 1

[3,6,2,5,1,4,7] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2,1] => 2

[3,6,2,5,1,7,4] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2,1] => 2

[3,6,2,5,4,1,7] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2,1] => 2

[3,6,2,5,4,7,1] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2,1] => 2

[3,6,2,5,7,1,4] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2,1] => 2

[3,6,2,5,7,4,1] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2,1] => 2

[3,6,2,7,1,4,5] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2,1] => 1

[3,6,2,7,1,5,4] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2,1] => 2

[3,6,2,7,4,1,5] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2,1] => 1

[3,6,2,7,4,5,1] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2,1] => 1

[3,6,2,7,5,1,4] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2,1] => 2

[3,6,2,7,5,4,1] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2,1] => 2

[3,6,4,1,2,5,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2] => 0

[3,6,4,1,2,7,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2] => 0

[3,6,4,1,5,2,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2] => 0

[3,6,4,1,5,7,2] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2] => 0

[3,6,4,1,7,2,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2] => 0

[3,6,4,1,7,5,2] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2] => 0

[3,6,4,2,1,5,7] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2,1] => 1

[3,6,4,2,1,7,5] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2,1] => 1

[3,6,4,2,5,1,7] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2,1] => 1

[3,6,4,2,5,7,1] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2,1] => 1

[3,6,4,2,7,1,5] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2,1] => 1

[3,6,4,2,7,5,1] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2,1] => 1

[3,6,4,5,1,2,7] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2] => 0

[3,6,4,5,1,7,2] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2] => 0

[3,6,4,5,2,1,7] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2,1] => 1

[3,6,4,5,2,7,1] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2,1] => 1

[3,6,4,5,7,1,2] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2] => 0

[3,6,4,5,7,2,1] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2,1] => 1

[3,6,4,7,1,2,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2] => 0

[3,6,4,7,1,5,2] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2] => 0

[3,6,4,7,2,1,5] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2,1] => 1

[3,6,4,7,2,5,1] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2,1] => 1

[3,6,4,7,5,1,2] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2] => 0

[3,6,4,7,5,2,1] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2,1] => 1

[3,6,5,1,2,4,7] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2] => 1

[3,6,5,1,2,7,4] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2] => 1

[3,6,5,1,4,2,7] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2] => 1

[3,6,5,1,4,7,2] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2] => 1

[3,6,5,1,7,2,4] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2] => 1

[3,6,5,1,7,4,2] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2] => 1

[3,6,5,2,1,4,7] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2,1] => 2

[3,6,5,2,1,7,4] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2,1] => 2

[3,6,5,2,4,1,7] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2,1] => 2

[3,6,5,2,4,7,1] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2,1] => 2

[3,6,5,2,7,1,4] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2,1] => 2

[3,6,5,2,7,4,1] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2,1] => 2

[3,6,5,4,1,2,7] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2] => 1

[3,6,5,4,1,7,2] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2] => 1

[3,6,5,4,2,1,7] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2,1] => 2

[3,6,5,4,2,7,1] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2,1] => 2

[3,6,5,4,7,1,2] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2] => 1

[3,6,5,4,7,2,1] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2,1] => 2

[3,6,5,7,1,2,4] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2] => 1

[3,6,5,7,1,4,2] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2] => 1

[3,6,5,7,2,1,4] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2,1] => 2

[3,6,5,7,2,4,1] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2,1] => 2

[3,6,5,7,4,1,2] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2] => 1

[3,6,5,7,4,2,1] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2,1] => 2

[3,6,7,1,2,4,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2] => 0

[3,6,7,1,2,5,4] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2] => 1

[3,6,7,1,4,2,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2] => 0

[3,6,7,1,4,5,2] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2] => 0

[3,6,7,1,5,2,4] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2] => 1

[3,6,7,1,5,4,2] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2] => 1

[3,6,7,2,1,4,5] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2,1] => 1

[3,6,7,2,1,5,4] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2,1] => 2

[3,6,7,2,4,1,5] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2,1] => 1

[3,6,7,2,4,5,1] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2,1] => 1

[3,6,7,2,5,1,4] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2,1] => 2

[3,6,7,2,5,4,1] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2,1] => 2

[3,6,7,4,1,2,5] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2] => 0

[3,6,7,4,1,5,2] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2] => 0

[3,6,7,4,2,1,5] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2,1] => 1

[3,6,7,4,2,5,1] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2,1] => 1

[3,6,7,4,5,1,2] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2] => 0

[3,6,7,4,5,2,1] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2,1] => 1

[3,6,7,5,1,2,4] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2] => 1

[3,6,7,5,1,4,2] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2] => 1

[3,6,7,5,2,1,4] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2,1] => 2

[3,6,7,5,2,4,1] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2,1] => 2

[3,6,7,5,4,1,2] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2] => 1

[3,6,7,5,4,2,1] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2,1] => 2

[3,7,1,2,4,5,6] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [5,2,2,2,2] => 1

[3,7,1,2,4,6,5] => [[.,[.,.]],[[.,[[.,.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,2,2] => 2

[3,7,1,2,5,4,6] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2] => 1

[3,7,1,2,5,6,4] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2] => 1

[3,7,1,2,6,4,5] => [[.,[.,.]],[[[.,[.,.]],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,2,2] => 2

[3,7,1,2,6,5,4] => [[.,[.,.]],[[[[.,.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,2] => 3

[3,7,1,4,2,5,6] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [5,2,2,2,2] => 1

[3,7,1,4,2,6,5] => [[.,[.,.]],[[.,[[.,.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,2,2] => 2

[3,7,1,4,5,2,6] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [5,2,2,2,2] => 1

[3,7,1,4,5,6,2] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [5,2,2,2,2] => 1

[3,7,1,4,6,2,5] => [[.,[.,.]],[[.,[[.,.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,2,2] => 2

[3,7,1,4,6,5,2] => [[.,[.,.]],[[.,[[.,.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,2,2] => 2

[3,7,1,5,2,4,6] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2] => 1

[3,7,1,5,2,6,4] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2] => 1

[3,7,1,5,4,2,6] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2] => 1

[3,7,1,5,4,6,2] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2] => 1

[3,7,1,5,6,2,4] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2] => 1

[3,7,1,5,6,4,2] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2] => 1

[3,7,1,6,2,4,5] => [[.,[.,.]],[[[.,[.,.]],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,2,2] => 2

[3,7,1,6,2,5,4] => [[.,[.,.]],[[[[.,.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,2] => 3

[3,7,1,6,4,2,5] => [[.,[.,.]],[[[.,[.,.]],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,2,2] => 2

[3,7,1,6,4,5,2] => [[.,[.,.]],[[[.,[.,.]],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,2,2] => 2

[3,7,1,6,5,2,4] => [[.,[.,.]],[[[[.,.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,2] => 3

[3,7,1,6,5,4,2] => [[.,[.,.]],[[[[.,.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,2] => 3

[3,7,2,1,4,5,6] => [[[.,.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,2,2,2,1] => 2

[3,7,2,1,4,6,5] => [[[.,.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,2,2,1] => 3

[3,7,2,1,5,4,6] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2,1] => 2

[3,7,2,1,5,6,4] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2,1] => 2

[3,7,2,1,6,4,5] => [[[.,.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,2,2,1] => 3

[3,7,2,1,6,5,4] => [[[.,.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,2,1] => 4

[3,7,2,4,1,5,6] => [[[.,.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,2,2,2,1] => 2

[3,7,2,4,1,6,5] => [[[.,.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,2,2,1] => 3

[3,7,2,4,5,1,6] => [[[.,.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,2,2,2,1] => 2

[3,7,2,4,5,6,1] => [[[.,.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,2,2,2,1] => 2

[3,7,2,4,6,1,5] => [[[.,.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,2,2,1] => 3

[3,7,2,4,6,5,1] => [[[.,.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,2,2,1] => 3

[3,7,2,5,1,4,6] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2,1] => 2

[3,7,2,5,1,6,4] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2,1] => 2

[3,7,2,5,4,1,6] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2,1] => 2

[3,7,2,5,4,6,1] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2,1] => 2

[3,7,2,5,6,1,4] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2,1] => 2

[3,7,2,5,6,4,1] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2,1] => 2

[3,7,2,6,1,4,5] => [[[.,.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,2,2,1] => 3

[3,7,2,6,1,5,4] => [[[.,.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,2,1] => 4

[3,7,2,6,4,1,5] => [[[.,.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,2,2,1] => 3

[3,7,2,6,4,5,1] => [[[.,.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,2,2,1] => 3

[3,7,2,6,5,1,4] => [[[.,.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,2,1] => 4

[3,7,2,6,5,4,1] => [[[.,.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,2,1] => 4

[3,7,4,1,2,5,6] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [5,2,2,2,2] => 1

[3,7,4,1,2,6,5] => [[.,[.,.]],[[.,[[.,.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,2,2] => 2

[3,7,4,1,5,2,6] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [5,2,2,2,2] => 1

[3,7,4,1,5,6,2] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [5,2,2,2,2] => 1

[3,7,4,1,6,2,5] => [[.,[.,.]],[[.,[[.,.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,2,2] => 2

[3,7,4,1,6,5,2] => [[.,[.,.]],[[.,[[.,.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,2,2] => 2

[3,7,4,2,1,5,6] => [[[.,.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,2,2,2,1] => 2

[3,7,4,2,1,6,5] => [[[.,.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,2,2,1] => 3

[3,7,4,2,5,1,6] => [[[.,.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,2,2,2,1] => 2

[3,7,4,2,5,6,1] => [[[.,.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,2,2,2,1] => 2

[3,7,4,2,6,1,5] => [[[.,.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,2,2,1] => 3

[3,7,4,2,6,5,1] => [[[.,.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,2,2,1] => 3

[3,7,4,5,1,2,6] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [5,2,2,2,2] => 1

[3,7,4,5,1,6,2] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [5,2,2,2,2] => 1

[3,7,4,5,2,1,6] => [[[.,.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,2,2,2,1] => 2

[3,7,4,5,2,6,1] => [[[.,.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,2,2,2,1] => 2

[3,7,4,5,6,1,2] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [5,2,2,2,2] => 1

[3,7,4,5,6,2,1] => [[[.,.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,2,2,2,1] => 2

[3,7,4,6,1,2,5] => [[.,[.,.]],[[.,[[.,.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,2,2] => 2

[3,7,4,6,1,5,2] => [[.,[.,.]],[[.,[[.,.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,2,2] => 2

[3,7,4,6,2,1,5] => [[[.,.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,2,2,1] => 3

[3,7,4,6,2,5,1] => [[[.,.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,2,2,1] => 3

[3,7,4,6,5,1,2] => [[.,[.,.]],[[.,[[.,.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,2,2] => 2

[3,7,4,6,5,2,1] => [[[.,.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,2,2,1] => 3

[3,7,5,1,2,4,6] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2] => 1

[3,7,5,1,2,6,4] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2] => 1

[3,7,5,1,4,2,6] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2] => 1

[3,7,5,1,4,6,2] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2] => 1

[3,7,5,1,6,2,4] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2] => 1

[3,7,5,1,6,4,2] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2] => 1

[3,7,5,2,1,4,6] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2,1] => 2

[3,7,5,2,1,6,4] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2,1] => 2

[3,7,5,2,4,1,6] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2,1] => 2

[3,7,5,2,4,6,1] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2,1] => 2

[3,7,5,2,6,1,4] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2,1] => 2

[3,7,5,2,6,4,1] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2,1] => 2

[3,7,5,4,1,2,6] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2] => 1

[3,7,5,4,1,6,2] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2] => 1

[3,7,5,4,2,1,6] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2,1] => 2

[3,7,5,4,2,6,1] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2,1] => 2

[3,7,5,4,6,1,2] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2] => 1

[3,7,5,4,6,2,1] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2,1] => 2

[3,7,5,6,1,2,4] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2] => 1

[3,7,5,6,1,4,2] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2] => 1

[3,7,5,6,2,1,4] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2,1] => 2

[3,7,5,6,2,4,1] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2,1] => 2

[3,7,5,6,4,1,2] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2] => 1

[3,7,5,6,4,2,1] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2,1] => 2

[3,7,6,1,2,4,5] => [[.,[.,.]],[[[.,[.,.]],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,2,2] => 2

[3,7,6,1,2,5,4] => [[.,[.,.]],[[[[.,.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,2] => 3

[3,7,6,1,4,2,5] => [[.,[.,.]],[[[.,[.,.]],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,2,2] => 2

[3,7,6,1,4,5,2] => [[.,[.,.]],[[[.,[.,.]],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,2,2] => 2

[3,7,6,1,5,2,4] => [[.,[.,.]],[[[[.,.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,2] => 3

[3,7,6,1,5,4,2] => [[.,[.,.]],[[[[.,.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,2] => 3

[3,7,6,2,1,4,5] => [[[.,.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,2,2,1] => 3

[3,7,6,2,1,5,4] => [[[.,.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,2,1] => 4

[3,7,6,2,4,1,5] => [[[.,.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,2,2,1] => 3

[3,7,6,2,4,5,1] => [[[.,.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,2,2,1] => 3

[3,7,6,2,5,1,4] => [[[.,.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,2,1] => 4

[3,7,6,2,5,4,1] => [[[.,.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,2,1] => 4

[3,7,6,4,1,2,5] => [[.,[.,.]],[[[.,[.,.]],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,2,2] => 2

[3,7,6,4,1,5,2] => [[.,[.,.]],[[[.,[.,.]],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,2,2] => 2

[3,7,6,4,2,1,5] => [[[.,.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,2,2,1] => 3

[3,7,6,4,2,5,1] => [[[.,.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,2,2,1] => 3

[3,7,6,4,5,1,2] => [[.,[.,.]],[[[.,[.,.]],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,2,2] => 2

[3,7,6,4,5,2,1] => [[[.,.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,2,2,1] => 3

[3,7,6,5,1,2,4] => [[.,[.,.]],[[[[.,.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,2] => 3

[3,7,6,5,1,4,2] => [[.,[.,.]],[[[[.,.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,2] => 3

[3,7,6,5,2,1,4] => [[[.,.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,2,1] => 4

[3,7,6,5,2,4,1] => [[[.,.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,2,1] => 4

[3,7,6,5,4,1,2] => [[.,[.,.]],[[[[.,.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,2] => 3

[3,7,6,5,4,2,1] => [[[.,.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,2,1] => 4

[4,1,2,3,5,6,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3] => 0

[4,1,2,3,5,7,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3] => 1

[4,1,2,3,6,5,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3] => 0

[4,1,2,3,6,7,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3] => 0

[4,1,2,3,7,5,6] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3] => 1

[4,1,2,3,7,6,5] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3] => 2

[4,1,2,5,3,6,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3] => 0

[4,1,2,5,3,7,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3] => 1

[4,1,2,5,6,3,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3] => 0

[4,1,2,5,6,7,3] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3] => 0

[4,1,2,5,7,3,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3] => 1

[4,1,2,5,7,6,3] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3] => 1

[4,1,2,6,3,5,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3] => 0

[4,1,2,6,3,7,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3] => 0

[4,1,2,6,5,3,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3] => 0

[4,1,2,6,5,7,3] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3] => 0

[4,1,2,6,7,3,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3] => 0

[4,1,2,6,7,5,3] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3] => 0

[4,1,2,7,3,5,6] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3] => 1

[4,1,2,7,3,6,5] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3] => 2

[4,1,2,7,5,3,6] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3] => 1

[4,1,2,7,5,6,3] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3] => 1

[4,1,2,7,6,3,5] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3] => 2

[4,1,2,7,6,5,3] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3] => 2

[4,1,3,2,5,6,7] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1] => 1

[4,1,3,2,5,7,6] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1] => 2

[4,1,3,2,6,5,7] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1] => 1

[4,1,3,2,6,7,5] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1] => 1

[4,1,3,2,7,5,6] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1] => 2

[4,1,3,2,7,6,5] => [[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1] => 3

[4,1,3,5,2,6,7] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1] => 1

[4,1,3,5,2,7,6] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1] => 2

[4,1,3,5,6,2,7] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1] => 1

[4,1,3,5,6,7,2] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1] => 1

[4,1,3,5,7,2,6] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1] => 2

[4,1,3,5,7,6,2] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1] => 2

[4,1,3,6,2,5,7] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1] => 1

[4,1,3,6,2,7,5] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1] => 1

[4,1,3,6,5,2,7] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1] => 1

[4,1,3,6,5,7,2] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1] => 1

[4,1,3,6,7,2,5] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1] => 1

[4,1,3,6,7,5,2] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1] => 1

[4,1,3,7,2,5,6] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1] => 2

[4,1,3,7,2,6,5] => [[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1] => 3

[4,1,3,7,5,2,6] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1] => 2

[4,1,3,7,5,6,2] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1] => 2

[4,1,3,7,6,2,5] => [[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1] => 3

[4,1,3,7,6,5,2] => [[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1] => 3

[4,1,5,2,3,6,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3] => 0

[4,1,5,2,3,7,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3] => 1

[4,1,5,2,6,3,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3] => 0

[4,1,5,2,6,7,3] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3] => 0

[4,1,5,2,7,3,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3] => 1

[4,1,5,2,7,6,3] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3] => 1

[4,1,5,3,2,6,7] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1] => 1

[4,1,5,3,2,7,6] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1] => 2

[4,1,5,3,6,2,7] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1] => 1

[4,1,5,3,6,7,2] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1] => 1

[4,1,5,3,7,2,6] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1] => 2

[4,1,5,3,7,6,2] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1] => 2

[4,1,5,6,2,3,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3] => 0

[4,1,5,6,2,7,3] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3] => 0

[4,1,5,6,3,2,7] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1] => 1

[4,1,5,6,3,7,2] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1] => 1

[4,1,5,6,7,2,3] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3] => 0

[4,1,5,6,7,3,2] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1] => 1

[4,1,5,7,2,3,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3] => 1

[4,1,5,7,2,6,3] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3] => 1

[4,1,5,7,3,2,6] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1] => 2

[4,1,5,7,3,6,2] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1] => 2

[4,1,5,7,6,2,3] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3] => 1

[4,1,5,7,6,3,2] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1] => 2

[4,1,6,2,3,5,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3] => 0

[4,1,6,2,3,7,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3] => 0

[4,1,6,2,5,3,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3] => 0

[4,1,6,2,5,7,3] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3] => 0

[4,1,6,2,7,3,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3] => 0

[4,1,6,2,7,5,3] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3] => 0

[4,1,6,3,2,5,7] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1] => 1

[4,1,6,3,2,7,5] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1] => 1

[4,1,6,3,5,2,7] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1] => 1

[4,1,6,3,5,7,2] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1] => 1

[4,1,6,3,7,2,5] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1] => 1

[4,1,6,3,7,5,2] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1] => 1

[4,1,6,5,2,3,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3] => 0

[4,1,6,5,2,7,3] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3] => 0

[4,1,6,5,3,2,7] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1] => 1

[4,1,6,5,3,7,2] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1] => 1

[4,1,6,5,7,2,3] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3] => 0

[4,1,6,5,7,3,2] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1] => 1

[4,1,6,7,2,3,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3] => 0

[4,1,6,7,2,5,3] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3] => 0

[4,1,6,7,3,2,5] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1] => 1

[4,1,6,7,3,5,2] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1] => 1

[4,1,6,7,5,2,3] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3] => 0

[4,1,6,7,5,3,2] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1] => 1

[4,1,7,2,3,5,6] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3] => 1

[4,1,7,2,3,6,5] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3] => 2

[4,1,7,2,5,3,6] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3] => 1

[4,1,7,2,5,6,3] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3] => 1

[4,1,7,2,6,3,5] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3] => 2

[4,1,7,2,6,5,3] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3] => 2

[4,1,7,3,2,5,6] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1] => 2

[4,1,7,3,2,6,5] => [[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1] => 3

[4,1,7,3,5,2,6] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1] => 2

[4,1,7,3,5,6,2] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1] => 2

[4,1,7,3,6,2,5] => [[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1] => 3

[4,1,7,3,6,5,2] => [[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1] => 3

[4,1,7,5,2,3,6] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3] => 1

[4,1,7,5,2,6,3] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3] => 1

[4,1,7,5,3,2,6] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1] => 2

[4,1,7,5,3,6,2] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1] => 2

[4,1,7,5,6,2,3] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3] => 1

[4,1,7,5,6,3,2] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1] => 2

[4,1,7,6,2,3,5] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3] => 2

[4,1,7,6,2,5,3] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3] => 2

[4,1,7,6,3,2,5] => [[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1] => 3

[4,1,7,6,3,5,2] => [[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1] => 3

[4,1,7,6,5,2,3] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3] => 2

[4,1,7,6,5,3,2] => [[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1] => 3

[4,2,1,3,5,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1,1] => 0

[4,2,1,3,5,7,6] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1,1] => 1

[4,2,1,3,6,5,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,2,1,3,6,7,5] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,2,1,3,7,5,6] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1,1] => 1

[4,2,1,3,7,6,5] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1,1] => 2

[4,2,1,5,3,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1,1] => 0

[4,2,1,5,3,7,6] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1,1] => 1

[4,2,1,5,6,3,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1,1] => 0

[4,2,1,5,6,7,3] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1,1] => 0

[4,2,1,5,7,3,6] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1,1] => 1

[4,2,1,5,7,6,3] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1,1] => 1

[4,2,1,6,3,5,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,2,1,6,3,7,5] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,2,1,6,5,3,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,2,1,6,5,7,3] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,2,1,6,7,3,5] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,2,1,6,7,5,3] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,2,1,7,3,5,6] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1,1] => 1

[4,2,1,7,3,6,5] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1,1] => 2

[4,2,1,7,5,3,6] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1,1] => 1

[4,2,1,7,5,6,3] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1,1] => 1

[4,2,1,7,6,3,5] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1,1] => 2

[4,2,1,7,6,5,3] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1,1] => 2

[4,2,3,1,5,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1,1] => 0

[4,2,3,1,5,7,6] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1,1] => 1

[4,2,3,1,6,5,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,2,3,1,6,7,5] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,2,3,1,7,5,6] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1,1] => 1

[4,2,3,1,7,6,5] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1,1] => 2

[4,2,3,5,1,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1,1] => 0

[4,2,3,5,1,7,6] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1,1] => 1

[4,2,3,5,6,1,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1,1] => 0

[4,2,3,5,6,7,1] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1,1] => 0

[4,2,3,5,7,1,6] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1,1] => 1

[4,2,3,5,7,6,1] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1,1] => 1

[4,2,3,6,1,5,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,2,3,6,1,7,5] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,2,3,6,5,1,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,2,3,6,5,7,1] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,2,3,6,7,1,5] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,2,3,6,7,5,1] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,2,3,7,1,5,6] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1,1] => 1

[4,2,3,7,1,6,5] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1,1] => 2

[4,2,3,7,5,1,6] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1,1] => 1

[4,2,3,7,5,6,1] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1,1] => 1

[4,2,3,7,6,1,5] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1,1] => 2

[4,2,3,7,6,5,1] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1,1] => 2

[4,2,5,1,3,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1,1] => 0

[4,2,5,1,3,7,6] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1,1] => 1

[4,2,5,1,6,3,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1,1] => 0

[4,2,5,1,6,7,3] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1,1] => 0

[4,2,5,1,7,3,6] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1,1] => 1

[4,2,5,1,7,6,3] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1,1] => 1

[4,2,5,3,1,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1,1] => 0

[4,2,5,3,1,7,6] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1,1] => 1

[4,2,5,3,6,1,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1,1] => 0

[4,2,5,3,6,7,1] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1,1] => 0

[4,2,5,3,7,1,6] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1,1] => 1

[4,2,5,3,7,6,1] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1,1] => 1

[4,2,5,6,1,3,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1,1] => 0

[4,2,5,6,1,7,3] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1,1] => 0

[4,2,5,6,3,1,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1,1] => 0

[4,2,5,6,3,7,1] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1,1] => 0

[4,2,5,6,7,1,3] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1,1] => 0

[4,2,5,6,7,3,1] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1,1] => 0

[4,2,5,7,1,3,6] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1,1] => 1

[4,2,5,7,1,6,3] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1,1] => 1

[4,2,5,7,3,1,6] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1,1] => 1

[4,2,5,7,3,6,1] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1,1] => 1

[4,2,5,7,6,1,3] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1,1] => 1

[4,2,5,7,6,3,1] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1,1] => 1

[4,2,6,1,3,5,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,2,6,1,3,7,5] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,2,6,1,5,3,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,2,6,1,5,7,3] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,2,6,1,7,3,5] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,2,6,1,7,5,3] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,2,6,3,1,5,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,2,6,3,1,7,5] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,2,6,3,5,1,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,2,6,3,5,7,1] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,2,6,3,7,1,5] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,2,6,3,7,5,1] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,2,6,5,1,3,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,2,6,5,1,7,3] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,2,6,5,3,1,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,2,6,5,3,7,1] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,2,6,5,7,1,3] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,2,6,5,7,3,1] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,2,6,7,1,3,5] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,2,6,7,1,5,3] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,2,6,7,3,1,5] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,2,6,7,3,5,1] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,2,6,7,5,1,3] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,2,6,7,5,3,1] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,2,7,1,3,5,6] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1,1] => 1

[4,2,7,1,3,6,5] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1,1] => 2

[4,2,7,1,5,3,6] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1,1] => 1

[4,2,7,1,5,6,3] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1,1] => 1

[4,2,7,1,6,3,5] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1,1] => 2

[4,2,7,1,6,5,3] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1,1] => 2

[4,2,7,3,1,5,6] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1,1] => 1

[4,2,7,3,1,6,5] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1,1] => 2

[4,2,7,3,5,1,6] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1,1] => 1

[4,2,7,3,5,6,1] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1,1] => 1

[4,2,7,3,6,1,5] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1,1] => 2

[4,2,7,3,6,5,1] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1,1] => 2

[4,2,7,5,1,3,6] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1,1] => 1

[4,2,7,5,1,6,3] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1,1] => 1

[4,2,7,5,3,1,6] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1,1] => 1

[4,2,7,5,3,6,1] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1,1] => 1

[4,2,7,5,6,1,3] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1,1] => 1

[4,2,7,5,6,3,1] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1,1] => 1

[4,2,7,6,1,3,5] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1,1] => 2

[4,2,7,6,1,5,3] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1,1] => 2

[4,2,7,6,3,1,5] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1,1] => 2

[4,2,7,6,3,5,1] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1,1] => 2

[4,2,7,6,5,1,3] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1,1] => 2

[4,2,7,6,5,3,1] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1,1] => 2

[4,3,1,2,5,6,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2] => 1

[4,3,1,2,5,7,6] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2] => 2

[4,3,1,2,6,5,7] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2] => 1

[4,3,1,2,6,7,5] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2] => 1

[4,3,1,2,7,5,6] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [5,3,3,3,2] => 2

[4,3,1,2,7,6,5] => [[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,3,2] => 3

[4,3,1,5,2,6,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2] => 1

[4,3,1,5,2,7,6] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2] => 2

[4,3,1,5,6,2,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2] => 1

[4,3,1,5,6,7,2] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2] => 1

[4,3,1,5,7,2,6] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2] => 2

[4,3,1,5,7,6,2] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2] => 2

[4,3,1,6,2,5,7] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2] => 1

[4,3,1,6,2,7,5] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2] => 1

[4,3,1,6,5,2,7] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2] => 1

[4,3,1,6,5,7,2] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2] => 1

[4,3,1,6,7,2,5] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2] => 1

[4,3,1,6,7,5,2] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2] => 1

[4,3,1,7,2,5,6] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [5,3,3,3,2] => 2

[4,3,1,7,2,6,5] => [[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,3,2] => 3

[4,3,1,7,5,2,6] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [5,3,3,3,2] => 2

[4,3,1,7,5,6,2] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [5,3,3,3,2] => 2

[4,3,1,7,6,2,5] => [[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,3,2] => 3

[4,3,1,7,6,5,2] => [[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,3,2] => 3

[4,3,2,1,5,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2,1] => 2

[4,3,2,1,5,7,6] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2,1] => 3

[4,3,2,1,6,5,7] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2,1] => 2

[4,3,2,1,6,7,5] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2,1] => 2

[4,3,2,1,7,5,6] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,3,3,2,1] => 3

[4,3,2,1,7,6,5] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,3,2,1] => 4

[4,3,2,5,1,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2,1] => 2

[4,3,2,5,1,7,6] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2,1] => 3

[4,3,2,5,6,1,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2,1] => 2

[4,3,2,5,6,7,1] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2,1] => 2

[4,3,2,5,7,1,6] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2,1] => 3

[4,3,2,5,7,6,1] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2,1] => 3

[4,3,2,6,1,5,7] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2,1] => 2

[4,3,2,6,1,7,5] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2,1] => 2

[4,3,2,6,5,1,7] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2,1] => 2

[4,3,2,6,5,7,1] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2,1] => 2

[4,3,2,6,7,1,5] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2,1] => 2

[4,3,2,6,7,5,1] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2,1] => 2

[4,3,2,7,1,5,6] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,3,3,2,1] => 3

[4,3,2,7,1,6,5] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,3,2,1] => 4

[4,3,2,7,5,1,6] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,3,3,2,1] => 3

[4,3,2,7,5,6,1] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,3,3,2,1] => 3

[4,3,2,7,6,1,5] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,3,2,1] => 4

[4,3,2,7,6,5,1] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,3,2,1] => 4

[4,3,5,1,2,6,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2] => 1

[4,3,5,1,2,7,6] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2] => 2

[4,3,5,1,6,2,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2] => 1

[4,3,5,1,6,7,2] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2] => 1

[4,3,5,1,7,2,6] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2] => 2

[4,3,5,1,7,6,2] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2] => 2

[4,3,5,2,1,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2,1] => 2

[4,3,5,2,1,7,6] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2,1] => 3

[4,3,5,2,6,1,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2,1] => 2

[4,3,5,2,6,7,1] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2,1] => 2

[4,3,5,2,7,1,6] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2,1] => 3

[4,3,5,2,7,6,1] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2,1] => 3

[4,3,5,6,1,2,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2] => 1

[4,3,5,6,1,7,2] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2] => 1

[4,3,5,6,2,1,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2,1] => 2

[4,3,5,6,2,7,1] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2,1] => 2

[4,3,5,6,7,1,2] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2] => 1

[4,3,5,6,7,2,1] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2,1] => 2

[4,3,5,7,1,2,6] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2] => 2

[4,3,5,7,1,6,2] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2] => 2

[4,3,5,7,2,1,6] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2,1] => 3

[4,3,5,7,2,6,1] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2,1] => 3

[4,3,5,7,6,1,2] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2] => 2

[4,3,5,7,6,2,1] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2,1] => 3

[4,3,6,1,2,5,7] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2] => 1

[4,3,6,1,2,7,5] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2] => 1

[4,3,6,1,5,2,7] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2] => 1

[4,3,6,1,5,7,2] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2] => 1

[4,3,6,1,7,2,5] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2] => 1

[4,3,6,1,7,5,2] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2] => 1

[4,3,6,2,1,5,7] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2,1] => 2

[4,3,6,2,1,7,5] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2,1] => 2

[4,3,6,2,5,1,7] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2,1] => 2

[4,3,6,2,5,7,1] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2,1] => 2

[4,3,6,2,7,1,5] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2,1] => 2

[4,3,6,2,7,5,1] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2,1] => 2

[4,3,6,5,1,2,7] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2] => 1

[4,3,6,5,1,7,2] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2] => 1

[4,3,6,5,2,1,7] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2,1] => 2

[4,3,6,5,2,7,1] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2,1] => 2

[4,3,6,5,7,1,2] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2] => 1

[4,3,6,5,7,2,1] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2,1] => 2

[4,3,6,7,1,2,5] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2] => 1

[4,3,6,7,1,5,2] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2] => 1

[4,3,6,7,2,1,5] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2,1] => 2

[4,3,6,7,2,5,1] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2,1] => 2

[4,3,6,7,5,1,2] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2] => 1

[4,3,6,7,5,2,1] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2,1] => 2

[4,3,7,1,2,5,6] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [5,3,3,3,2] => 2

[4,3,7,1,2,6,5] => [[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,3,2] => 3

[4,3,7,1,5,2,6] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [5,3,3,3,2] => 2

[4,3,7,1,5,6,2] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [5,3,3,3,2] => 2

[4,3,7,1,6,2,5] => [[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,3,2] => 3

[4,3,7,1,6,5,2] => [[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,3,2] => 3

[4,3,7,2,1,5,6] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,3,3,2,1] => 3

[4,3,7,2,1,6,5] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,3,2,1] => 4

[4,3,7,2,5,1,6] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,3,3,2,1] => 3

[4,3,7,2,5,6,1] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,3,3,2,1] => 3

[4,3,7,2,6,1,5] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,3,2,1] => 4

[4,3,7,2,6,5,1] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,3,2,1] => 4

[4,3,7,5,1,2,6] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [5,3,3,3,2] => 2

[4,3,7,5,1,6,2] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [5,3,3,3,2] => 2

[4,3,7,5,2,1,6] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,3,3,2,1] => 3

[4,3,7,5,2,6,1] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,3,3,2,1] => 3

[4,3,7,5,6,1,2] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [5,3,3,3,2] => 2

[4,3,7,5,6,2,1] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,3,3,2,1] => 3

[4,3,7,6,1,2,5] => [[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,3,2] => 3

[4,3,7,6,1,5,2] => [[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,3,2] => 3

[4,3,7,6,2,1,5] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,3,2,1] => 4

[4,3,7,6,2,5,1] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,3,2,1] => 4

[4,3,7,6,5,1,2] => [[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,3,2] => 3

[4,3,7,6,5,2,1] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,3,2,1] => 4

[4,5,1,2,3,6,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3] => 0

[4,5,1,2,3,7,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3] => 1

[4,5,1,2,6,3,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3] => 0

[4,5,1,2,6,7,3] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3] => 0

[4,5,1,2,7,3,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3] => 1

[4,5,1,2,7,6,3] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3] => 1

[4,5,1,3,2,6,7] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1] => 1

[4,5,1,3,2,7,6] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1] => 2

[4,5,1,3,6,2,7] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1] => 1

[4,5,1,3,6,7,2] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1] => 1

[4,5,1,3,7,2,6] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1] => 2

[4,5,1,3,7,6,2] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1] => 2

[4,5,1,6,2,3,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3] => 0

[4,5,1,6,2,7,3] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3] => 0

[4,5,1,6,3,2,7] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1] => 1

[4,5,1,6,3,7,2] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1] => 1

[4,5,1,6,7,2,3] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3] => 0

[4,5,1,6,7,3,2] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1] => 1

[4,5,1,7,2,3,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3] => 1

[4,5,1,7,2,6,3] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3] => 1

[4,5,1,7,3,2,6] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1] => 2

[4,5,1,7,3,6,2] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1] => 2

[4,5,1,7,6,2,3] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3] => 1

[4,5,1,7,6,3,2] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1] => 2

[4,5,2,1,3,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1,1] => 0

[4,5,2,1,3,7,6] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1,1] => 1

[4,5,2,1,6,3,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1,1] => 0

[4,5,2,1,6,7,3] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1,1] => 0

[4,5,2,1,7,3,6] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1,1] => 1

[4,5,2,1,7,6,3] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1,1] => 1

[4,5,2,3,1,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1,1] => 0

[4,5,2,3,1,7,6] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1,1] => 1

[4,5,2,3,6,1,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1,1] => 0

[4,5,2,3,6,7,1] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1,1] => 0

[4,5,2,3,7,1,6] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1,1] => 1

[4,5,2,3,7,6,1] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1,1] => 1

[4,5,2,6,1,3,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1,1] => 0

[4,5,2,6,1,7,3] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1,1] => 0

[4,5,2,6,3,1,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1,1] => 0

[4,5,2,6,3,7,1] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1,1] => 0

[4,5,2,6,7,1,3] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1,1] => 0

[4,5,2,6,7,3,1] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1,1] => 0

[4,5,2,7,1,3,6] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1,1] => 1

[4,5,2,7,1,6,3] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1,1] => 1

[4,5,2,7,3,1,6] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1,1] => 1

[4,5,2,7,3,6,1] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1,1] => 1

[4,5,2,7,6,1,3] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1,1] => 1

[4,5,2,7,6,3,1] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1,1] => 1

[4,5,3,1,2,6,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2] => 1

[4,5,3,1,2,7,6] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2] => 2

[4,5,3,1,6,2,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2] => 1

[4,5,3,1,6,7,2] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2] => 1

[4,5,3,1,7,2,6] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2] => 2

[4,5,3,1,7,6,2] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2] => 2

[4,5,3,2,1,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2,1] => 2

[4,5,3,2,1,7,6] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2,1] => 3

[4,5,3,2,6,1,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2,1] => 2

[4,5,3,2,6,7,1] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2,1] => 2

[4,5,3,2,7,1,6] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2,1] => 3

[4,5,3,2,7,6,1] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2,1] => 3

[4,5,3,6,1,2,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2] => 1

[4,5,3,6,1,7,2] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2] => 1

[4,5,3,6,2,1,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2,1] => 2

[4,5,3,6,2,7,1] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2,1] => 2

[4,5,3,6,7,1,2] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2] => 1

[4,5,3,6,7,2,1] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2,1] => 2

[4,5,3,7,1,2,6] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2] => 2

[4,5,3,7,1,6,2] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2] => 2

[4,5,3,7,2,1,6] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2,1] => 3

[4,5,3,7,2,6,1] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2,1] => 3

[4,5,3,7,6,1,2] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2] => 2

[4,5,3,7,6,2,1] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2,1] => 3

[4,5,6,1,2,3,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3] => 0

[4,5,6,1,2,7,3] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3] => 0

[4,5,6,1,3,2,7] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1] => 1

[4,5,6,1,3,7,2] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1] => 1

[4,5,6,1,7,2,3] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3] => 0

[4,5,6,1,7,3,2] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1] => 1

[4,5,6,2,1,3,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1,1] => 0

[4,5,6,2,1,7,3] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1,1] => 0

[4,5,6,2,3,1,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1,1] => 0

[4,5,6,2,3,7,1] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1,1] => 0

[4,5,6,2,7,1,3] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1,1] => 0

[4,5,6,2,7,3,1] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1,1] => 0

[4,5,6,3,1,2,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2] => 1

[4,5,6,3,1,7,2] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2] => 1

[4,5,6,3,2,1,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2,1] => 2

[4,5,6,3,2,7,1] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2,1] => 2

[4,5,6,3,7,1,2] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2] => 1

[4,5,6,3,7,2,1] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2,1] => 2

[4,5,6,7,1,2,3] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3] => 0

[4,5,6,7,1,3,2] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1] => 1

[4,5,6,7,2,1,3] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1,1] => 0

[4,5,6,7,2,3,1] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1,1] => 0

[4,5,6,7,3,1,2] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2] => 1

[4,5,6,7,3,2,1] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2,1] => 2

[4,5,7,1,2,3,6] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3] => 1

[4,5,7,1,2,6,3] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3] => 1

[4,5,7,1,3,2,6] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1] => 2

[4,5,7,1,3,6,2] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1] => 2

[4,5,7,1,6,2,3] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3] => 1

[4,5,7,1,6,3,2] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1] => 2

[4,5,7,2,1,3,6] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1,1] => 1

[4,5,7,2,1,6,3] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1,1] => 1

[4,5,7,2,3,1,6] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1,1] => 1

[4,5,7,2,3,6,1] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1,1] => 1

[4,5,7,2,6,1,3] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1,1] => 1

[4,5,7,2,6,3,1] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1,1] => 1

[4,5,7,3,1,2,6] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2] => 2

[4,5,7,3,1,6,2] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2] => 2

[4,5,7,3,2,1,6] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2,1] => 3

[4,5,7,3,2,6,1] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2,1] => 3

[4,5,7,3,6,1,2] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2] => 2

[4,5,7,3,6,2,1] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2,1] => 3

[4,5,7,6,1,2,3] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3] => 1

[4,5,7,6,1,3,2] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1] => 2

[4,5,7,6,2,1,3] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1,1] => 1

[4,5,7,6,2,3,1] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1,1] => 1

[4,5,7,6,3,1,2] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2] => 2

[4,5,7,6,3,2,1] => [[[[.,.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2,1] => 3

[4,6,1,2,3,5,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3] => 0

[4,6,1,2,3,7,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3] => 0

[4,6,1,2,5,3,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3] => 0

[4,6,1,2,5,7,3] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3] => 0

[4,6,1,2,7,3,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3] => 0

[4,6,1,2,7,5,3] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3] => 0

[4,6,1,3,2,5,7] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1] => 1

[4,6,1,3,2,7,5] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1] => 1

[4,6,1,3,5,2,7] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1] => 1

[4,6,1,3,5,7,2] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1] => 1

[4,6,1,3,7,2,5] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1] => 1

[4,6,1,3,7,5,2] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1] => 1

[4,6,1,5,2,3,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3] => 0

[4,6,1,5,2,7,3] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3] => 0

[4,6,1,5,3,2,7] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1] => 1

[4,6,1,5,3,7,2] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1] => 1

[4,6,1,5,7,2,3] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3] => 0

[4,6,1,5,7,3,2] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1] => 1

[4,6,1,7,2,3,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3] => 0

[4,6,1,7,2,5,3] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3] => 0

[4,6,1,7,3,2,5] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1] => 1

[4,6,1,7,3,5,2] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1] => 1

[4,6,1,7,5,2,3] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3] => 0

[4,6,1,7,5,3,2] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1] => 1

[4,6,2,1,3,5,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,6,2,1,3,7,5] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,6,2,1,5,3,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,6,2,1,5,7,3] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,6,2,1,7,3,5] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,6,2,1,7,5,3] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,6,2,3,1,5,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,6,2,3,1,7,5] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,6,2,3,5,1,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,6,2,3,5,7,1] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,6,2,3,7,1,5] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,6,2,3,7,5,1] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,6,2,5,1,3,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,6,2,5,1,7,3] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,6,2,5,3,1,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,6,2,5,3,7,1] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,6,2,5,7,1,3] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,6,2,5,7,3,1] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,6,2,7,1,3,5] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,6,2,7,1,5,3] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,6,2,7,3,1,5] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,6,2,7,3,5,1] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,6,2,7,5,1,3] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,6,2,7,5,3,1] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,6,3,1,2,5,7] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2] => 1

[4,6,3,1,2,7,5] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2] => 1

[4,6,3,1,5,2,7] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2] => 1

[4,6,3,1,5,7,2] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2] => 1

[4,6,3,1,7,2,5] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2] => 1

[4,6,3,1,7,5,2] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2] => 1

[4,6,3,2,1,5,7] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2,1] => 2

[4,6,3,2,1,7,5] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2,1] => 2

[4,6,3,2,5,1,7] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2,1] => 2

[4,6,3,2,5,7,1] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2,1] => 2

[4,6,3,2,7,1,5] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2,1] => 2

[4,6,3,2,7,5,1] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2,1] => 2

[4,6,3,5,1,2,7] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2] => 1

[4,6,3,5,1,7,2] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2] => 1

[4,6,3,5,2,1,7] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2,1] => 2

[4,6,3,5,2,7,1] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2,1] => 2

[4,6,3,5,7,1,2] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2] => 1

[4,6,3,5,7,2,1] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2,1] => 2

[4,6,3,7,1,2,5] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2] => 1

[4,6,3,7,1,5,2] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2] => 1

[4,6,3,7,2,1,5] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2,1] => 2

[4,6,3,7,2,5,1] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2,1] => 2

[4,6,3,7,5,1,2] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2] => 1

[4,6,3,7,5,2,1] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2,1] => 2

[4,6,5,1,2,3,7] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3] => 0

[4,6,5,1,2,7,3] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3] => 0

[4,6,5,1,3,2,7] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1] => 1

[4,6,5,1,3,7,2] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1] => 1

[4,6,5,1,7,2,3] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3] => 0

[4,6,5,1,7,3,2] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1] => 1

[4,6,5,2,1,3,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,6,5,2,1,7,3] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,6,5,2,3,1,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,6,5,2,3,7,1] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,6,5,2,7,1,3] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,6,5,2,7,3,1] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,6,5,3,1,2,7] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2] => 1

[4,6,5,3,1,7,2] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2] => 1

[4,6,5,3,2,1,7] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2,1] => 2

[4,6,5,3,2,7,1] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2,1] => 2

[4,6,5,3,7,1,2] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2] => 1

[4,6,5,3,7,2,1] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2,1] => 2

[4,6,5,7,1,2,3] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3] => 0

[4,6,5,7,1,3,2] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1] => 1

[4,6,5,7,2,1,3] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,6,5,7,2,3,1] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,6,5,7,3,1,2] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2] => 1

[4,6,5,7,3,2,1] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2,1] => 2

[4,6,7,1,2,3,5] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3] => 0

[4,6,7,1,2,5,3] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3] => 0

[4,6,7,1,3,2,5] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1] => 1

[4,6,7,1,3,5,2] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1] => 1

[4,6,7,1,5,2,3] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3] => 0

[4,6,7,1,5,3,2] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1] => 1

[4,6,7,2,1,3,5] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,6,7,2,1,5,3] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,6,7,2,3,1,5] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,6,7,2,3,5,1] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,6,7,2,5,1,3] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,6,7,2,5,3,1] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,6,7,3,1,2,5] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2] => 1

[4,6,7,3,1,5,2] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2] => 1

[4,6,7,3,2,1,5] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2,1] => 2

[4,6,7,3,2,5,1] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2,1] => 2

[4,6,7,3,5,1,2] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2] => 1

[4,6,7,3,5,2,1] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2,1] => 2

[4,6,7,5,1,2,3] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3] => 0

[4,6,7,5,1,3,2] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1] => 1

[4,6,7,5,2,1,3] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,6,7,5,2,3,1] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 0

[4,6,7,5,3,1,2] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2] => 1

[4,6,7,5,3,2,1] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2,1] => 2

[4,7,1,2,3,5,6] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3] => 1

[4,7,1,2,3,6,5] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3] => 2

[4,7,1,2,5,3,6] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3] => 1

[4,7,1,2,5,6,3] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3] => 1

[4,7,1,2,6,3,5] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3] => 2

[4,7,1,2,6,5,3] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3] => 2

[4,7,1,3,2,5,6] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1] => 2

[4,7,1,3,2,6,5] => [[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1] => 3

[4,7,1,3,5,2,6] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1] => 2

[4,7,1,3,5,6,2] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1] => 2

[4,7,1,3,6,2,5] => [[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1] => 3

[4,7,1,3,6,5,2] => [[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1] => 3

[4,7,1,5,2,3,6] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3] => 1

[4,7,1,5,2,6,3] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3] => 1

[4,7,1,5,3,2,6] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1] => 2

[4,7,1,5,3,6,2] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1] => 2

[4,7,1,5,6,2,3] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3] => 1

[4,7,1,5,6,3,2] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1] => 2

[4,7,1,6,2,3,5] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3] => 2

[4,7,1,6,2,5,3] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3] => 2

[4,7,1,6,3,2,5] => [[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1] => 3

[4,7,1,6,3,5,2] => [[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1] => 3

[4,7,1,6,5,2,3] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3] => 2

[4,7,1,6,5,3,2] => [[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1] => 3

[4,7,2,1,3,5,6] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1,1] => 1

[4,7,2,1,3,6,5] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1,1] => 2

[4,7,2,1,5,3,6] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1,1] => 1

[4,7,2,1,5,6,3] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1,1] => 1

[4,7,2,1,6,3,5] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1,1] => 2

[4,7,2,1,6,5,3] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1,1] => 2

[4,7,2,3,1,5,6] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1,1] => 1

[4,7,2,3,1,6,5] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1,1] => 2

[4,7,2,3,5,1,6] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1,1] => 1

[4,7,2,3,5,6,1] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1,1] => 1

[4,7,2,3,6,1,5] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1,1] => 2

[4,7,2,3,6,5,1] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1,1] => 2

[4,7,2,5,1,3,6] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1,1] => 1

[4,7,2,5,1,6,3] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1,1] => 1

[4,7,2,5,3,1,6] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1,1] => 1

[4,7,2,5,3,6,1] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1,1] => 1

[4,7,2,5,6,1,3] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1,1] => 1

[4,7,2,5,6,3,1] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1,1] => 1

[4,7,2,6,1,3,5] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1,1] => 2

[4,7,2,6,1,5,3] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1,1] => 2

[4,7,2,6,3,1,5] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1,1] => 2

[4,7,2,6,3,5,1] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1,1] => 2

[4,7,2,6,5,1,3] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1,1] => 2

[4,7,2,6,5,3,1] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1,1] => 2

[4,7,3,1,2,5,6] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [5,3,3,3,2] => 2

[4,7,3,1,2,6,5] => [[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,3,2] => 3

[4,7,3,1,5,2,6] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [5,3,3,3,2] => 2

[4,7,3,1,5,6,2] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [5,3,3,3,2] => 2

[4,7,3,1,6,2,5] => [[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,3,2] => 3

[4,7,3,1,6,5,2] => [[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,3,2] => 3

[4,7,3,2,1,5,6] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,3,3,2,1] => 3

[4,7,3,2,1,6,5] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,3,2,1] => 4

[4,7,3,2,5,1,6] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,3,3,2,1] => 3

[4,7,3,2,5,6,1] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,3,3,2,1] => 3

[4,7,3,2,6,1,5] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,3,2,1] => 4

[4,7,3,2,6,5,1] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,3,2,1] => 4

[4,7,3,5,1,2,6] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [5,3,3,3,2] => 2

[4,7,3,5,1,6,2] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [5,3,3,3,2] => 2

[4,7,3,5,2,1,6] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,3,3,2,1] => 3

[4,7,3,5,2,6,1] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,3,3,2,1] => 3

[4,7,3,5,6,1,2] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [5,3,3,3,2] => 2

[4,7,3,5,6,2,1] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,3,3,2,1] => 3

[4,7,3,6,1,2,5] => [[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,3,2] => 3

[4,7,3,6,1,5,2] => [[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,3,2] => 3

[4,7,3,6,2,1,5] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,3,2,1] => 4

[4,7,3,6,2,5,1] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,3,2,1] => 4

[4,7,3,6,5,1,2] => [[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,3,2] => 3

[4,7,3,6,5,2,1] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,3,2,1] => 4

[4,7,5,1,2,3,6] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3] => 1

[4,7,5,1,2,6,3] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3] => 1

[4,7,5,1,3,2,6] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1] => 2

[4,7,5,1,3,6,2] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1] => 2

[4,7,5,1,6,2,3] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3] => 1

[4,7,5,1,6,3,2] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1] => 2

[4,7,5,2,1,3,6] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1,1] => 1

[4,7,5,2,1,6,3] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1,1] => 1

[4,7,5,2,3,1,6] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1,1] => 1

[4,7,5,2,3,6,1] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1,1] => 1

[4,7,5,2,6,1,3] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1,1] => 1

[4,7,5,2,6,3,1] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1,1] => 1

[4,7,5,3,1,2,6] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [5,3,3,3,2] => 2

[4,7,5,3,1,6,2] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [5,3,3,3,2] => 2

[4,7,5,3,2,1,6] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,3,3,2,1] => 3

[4,7,5,3,2,6,1] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,3,3,2,1] => 3

[4,7,5,3,6,1,2] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [5,3,3,3,2] => 2

[4,7,5,3,6,2,1] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,3,3,2,1] => 3

[4,7,5,6,1,2,3] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3] => 1

[4,7,5,6,1,3,2] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1] => 2

[4,7,5,6,2,1,3] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1,1] => 1

[4,7,5,6,2,3,1] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1,1] => 1

[4,7,5,6,3,1,2] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [5,3,3,3,2] => 2

[4,7,5,6,3,2,1] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,3,3,2,1] => 3

[4,7,6,1,2,3,5] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3] => 2

[4,7,6,1,2,5,3] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3] => 2

[4,7,6,1,3,2,5] => [[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1] => 3

[4,7,6,1,3,5,2] => [[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1] => 3

[4,7,6,1,5,2,3] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3] => 2

[4,7,6,1,5,3,2] => [[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1] => 3

[4,7,6,2,1,3,5] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1,1] => 2

[4,7,6,2,1,5,3] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1,1] => 2

[4,7,6,2,3,1,5] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1,1] => 2

[4,7,6,2,3,5,1] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1,1] => 2

[4,7,6,2,5,1,3] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1,1] => 2

[4,7,6,2,5,3,1] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1,1] => 2

[4,7,6,3,1,2,5] => [[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,3,2] => 3

[4,7,6,3,1,5,2] => [[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,3,2] => 3

[4,7,6,3,2,1,5] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,3,2,1] => 4

[4,7,6,3,2,5,1] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,3,2,1] => 4

[4,7,6,3,5,1,2] => [[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,3,2] => 3

[4,7,6,3,5,2,1] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,3,2,1] => 4

[4,7,6,5,1,2,3] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3] => 2

[4,7,6,5,1,3,2] => [[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1] => 3

[4,7,6,5,2,1,3] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1,1] => 2

[4,7,6,5,2,3,1] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1,1] => 2

[4,7,6,5,3,1,2] => [[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,3,2] => 3

[4,7,6,5,3,2,1] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,3,2,1] => 4

[5,1,2,3,4,6,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,4,4] => 0

[5,1,2,3,4,7,6] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [5,4,4] => 1

[5,1,2,3,6,4,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,4,4] => 0

[5,1,2,3,6,7,4] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,4,4] => 0

[5,1,2,3,7,4,6] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [5,4,4] => 1

[5,1,2,3,7,6,4] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [5,4,4] => 1

[5,1,2,4,3,6,7] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1] => 1

[5,1,2,4,3,7,6] => [[.,[.,[[.,.],.]]],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1] => 2

[5,1,2,4,6,3,7] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1] => 1

[5,1,2,4,6,7,3] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1] => 1

[5,1,2,4,7,3,6] => [[.,[.,[[.,.],.]]],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1] => 2

[5,1,2,4,7,6,3] => [[.,[.,[[.,.],.]]],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1] => 2

[5,1,2,6,3,4,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,4,4] => 0

[5,1,2,6,3,7,4] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,4,4] => 0

[5,1,2,6,4,3,7] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1] => 1

[5,1,2,6,4,7,3] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1] => 1

[5,1,2,6,7,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,4,4] => 0

[5,1,2,6,7,4,3] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1] => 1

[5,1,2,7,3,4,6] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [5,4,4] => 1

[5,1,2,7,3,6,4] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [5,4,4] => 1

[5,1,2,7,4,3,6] => [[.,[.,[[.,.],.]]],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1] => 2

[5,1,2,7,4,6,3] => [[.,[.,[[.,.],.]]],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1] => 2

[5,1,2,7,6,3,4] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [5,4,4] => 1

[5,1,2,7,6,4,3] => [[.,[.,[[.,.],.]]],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1] => 2

[5,1,3,2,4,6,7] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1] => 0

[5,1,3,2,4,7,6] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1] => 1

[5,1,3,2,6,4,7] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1] => 0

[5,1,3,2,6,7,4] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1] => 0

[5,1,3,2,7,4,6] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1] => 1

[5,1,3,2,7,6,4] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1] => 1

[5,1,3,4,2,6,7] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1] => 0

[5,1,3,4,2,7,6] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1] => 1

[5,1,3,4,6,2,7] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1] => 0

[5,1,3,4,6,7,2] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1] => 0

[5,1,3,4,7,2,6] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1] => 1

[5,1,3,4,7,6,2] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1] => 1

[5,1,3,6,2,4,7] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1] => 0

[5,1,3,6,2,7,4] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1] => 0

[5,1,3,6,4,2,7] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1] => 0

[5,1,3,6,4,7,2] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1] => 0

[5,1,3,6,7,2,4] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1] => 0

[5,1,3,6,7,4,2] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1] => 0

[5,1,3,7,2,4,6] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1] => 1

[5,1,3,7,2,6,4] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1] => 1

[5,1,3,7,4,2,6] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1] => 1

[5,1,3,7,4,6,2] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1] => 1

[5,1,3,7,6,2,4] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1] => 1

[5,1,3,7,6,4,2] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1] => 1

[5,1,4,2,3,6,7] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2] => 1

[5,1,4,2,3,7,6] => [[.,[[.,[.,.]],.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2] => 2

[5,1,4,2,6,3,7] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2] => 1

[5,1,4,2,6,7,3] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2] => 1

[5,1,4,2,7,3,6] => [[.,[[.,[.,.]],.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2] => 2

[5,1,4,2,7,6,3] => [[.,[[.,[.,.]],.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2] => 2

[5,1,4,3,2,6,7] => [[.,[[[.,.],.],.]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1] => 2

[5,1,4,3,2,7,6] => [[.,[[[.,.],.],.]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1] => 3

[5,1,4,3,6,2,7] => [[.,[[[.,.],.],.]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1] => 2

[5,1,4,3,6,7,2] => [[.,[[[.,.],.],.]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1] => 2

[5,1,4,3,7,2,6] => [[.,[[[.,.],.],.]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1] => 3

[5,1,4,3,7,6,2] => [[.,[[[.,.],.],.]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1] => 3

[5,1,4,6,2,3,7] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2] => 1

[5,1,4,6,2,7,3] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2] => 1

[5,1,4,6,3,2,7] => [[.,[[[.,.],.],.]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1] => 2

[5,1,4,6,3,7,2] => [[.,[[[.,.],.],.]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1] => 2

[5,1,4,6,7,2,3] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2] => 1

[5,1,4,6,7,3,2] => [[.,[[[.,.],.],.]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1] => 2

[5,1,4,7,2,3,6] => [[.,[[.,[.,.]],.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2] => 2

[5,1,4,7,2,6,3] => [[.,[[.,[.,.]],.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2] => 2

[5,1,4,7,3,2,6] => [[.,[[[.,.],.],.]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1] => 3

[5,1,4,7,3,6,2] => [[.,[[[.,.],.],.]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1] => 3

[5,1,4,7,6,2,3] => [[.,[[.,[.,.]],.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2] => 2

[5,1,4,7,6,3,2] => [[.,[[[.,.],.],.]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1] => 3

[5,1,6,2,3,4,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,4,4] => 0

[5,1,6,2,3,7,4] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,4,4] => 0

[5,1,6,2,4,3,7] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1] => 1

[5,1,6,2,4,7,3] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1] => 1

[5,1,6,2,7,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,4,4] => 0

[5,1,6,2,7,4,3] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1] => 1

[5,1,6,3,2,4,7] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1] => 0

[5,1,6,3,2,7,4] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1] => 0

[5,1,6,3,4,2,7] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1] => 0

[5,1,6,3,4,7,2] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1] => 0

[5,1,6,3,7,2,4] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1] => 0

[5,1,6,3,7,4,2] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1] => 0

[5,1,6,4,2,3,7] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2] => 1

[5,1,6,4,2,7,3] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2] => 1

[5,1,6,4,3,2,7] => [[.,[[[.,.],.],.]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1] => 2

[5,1,6,4,3,7,2] => [[.,[[[.,.],.],.]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1] => 2

[5,1,6,4,7,2,3] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2] => 1

[5,1,6,4,7,3,2] => [[.,[[[.,.],.],.]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1] => 2

[5,1,6,7,2,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,4,4] => 0

[5,1,6,7,2,4,3] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1] => 1

[5,1,6,7,3,2,4] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1] => 0

[5,1,6,7,3,4,2] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1] => 0

[5,1,6,7,4,2,3] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2] => 1

[5,1,6,7,4,3,2] => [[.,[[[.,.],.],.]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1] => 2

[5,1,7,2,3,4,6] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [5,4,4] => 1

[5,1,7,2,3,6,4] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [5,4,4] => 1

[5,1,7,2,4,3,6] => [[.,[.,[[.,.],.]]],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1] => 2

[5,1,7,2,4,6,3] => [[.,[.,[[.,.],.]]],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1] => 2

[5,1,7,2,6,3,4] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [5,4,4] => 1

[5,1,7,2,6,4,3] => [[.,[.,[[.,.],.]]],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1] => 2

[5,1,7,3,2,4,6] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1] => 1

[5,1,7,3,2,6,4] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1] => 1

[5,1,7,3,4,2,6] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1] => 1

[5,1,7,3,4,6,2] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1] => 1

[5,1,7,3,6,2,4] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1] => 1

[5,1,7,3,6,4,2] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1] => 1

[5,1,7,4,2,3,6] => [[.,[[.,[.,.]],.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2] => 2

[5,1,7,4,2,6,3] => [[.,[[.,[.,.]],.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2] => 2

[5,1,7,4,3,2,6] => [[.,[[[.,.],.],.]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1] => 3

[5,1,7,4,3,6,2] => [[.,[[[.,.],.],.]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1] => 3

[5,1,7,4,6,2,3] => [[.,[[.,[.,.]],.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2] => 2

[5,1,7,4,6,3,2] => [[.,[[[.,.],.],.]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1] => 3

[5,1,7,6,2,3,4] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [5,4,4] => 1

[5,1,7,6,2,4,3] => [[.,[.,[[.,.],.]]],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1] => 2

[5,1,7,6,3,2,4] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1] => 1

[5,1,7,6,3,4,2] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1] => 1

[5,1,7,6,4,2,3] => [[.,[[.,[.,.]],.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2] => 2

[5,1,7,6,4,3,2] => [[.,[[[.,.],.],.]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1] => 3

[5,2,1,3,4,6,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => 0

[5,2,1,3,4,7,6] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1,1] => 1

[5,2,1,3,6,4,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => 0

[5,2,1,3,6,7,4] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => 0

[5,2,1,3,7,4,6] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1,1] => 1

[5,2,1,3,7,6,4] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1,1] => 1

[5,2,1,4,3,6,7] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1,1] => 1

[5,2,1,4,3,7,6] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1,1] => 2

[5,2,1,4,6,3,7] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1,1] => 1

[5,2,1,4,6,7,3] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1,1] => 1

[5,2,1,4,7,3,6] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1,1] => 2

[5,2,1,4,7,6,3] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1,1] => 2

[5,2,1,6,3,4,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => 0

[5,2,1,6,3,7,4] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => 0

[5,2,1,6,4,3,7] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1,1] => 1

[5,2,1,6,4,7,3] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1,1] => 1

[5,2,1,6,7,3,4] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => 0

[5,2,1,6,7,4,3] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1,1] => 1

[5,2,1,7,3,4,6] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1,1] => 1

[5,2,1,7,3,6,4] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1,1] => 1

[5,2,1,7,4,3,6] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1,1] => 2

[5,2,1,7,4,6,3] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1,1] => 2

[5,2,1,7,6,3,4] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1,1] => 1

[5,2,1,7,6,4,3] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1,1] => 2

[5,2,3,1,4,6,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => 0

[5,2,3,1,4,7,6] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1,1] => 1

[5,2,3,1,6,4,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => 0

[5,2,3,1,6,7,4] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => 0

[5,2,3,1,7,4,6] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1,1] => 1

[5,2,3,1,7,6,4] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1,1] => 1

[5,2,3,4,1,6,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => 0

[5,2,3,4,1,7,6] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1,1] => 1

[5,2,3,4,6,1,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => 0

[5,2,3,4,6,7,1] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => 0

[5,2,3,4,7,1,6] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1,1] => 1

[5,2,3,4,7,6,1] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1,1] => 1

[5,2,3,6,1,4,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => 0

[5,2,3,6,1,7,4] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => 0

[5,2,3,6,4,1,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => 0

[5,2,3,6,4,7,1] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => 0

[5,2,3,6,7,1,4] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => 0

[5,2,3,6,7,4,1] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => 0

[5,2,3,7,1,4,6] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1,1] => 1

[5,2,3,7,1,6,4] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1,1] => 1

[5,2,3,7,4,1,6] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1,1] => 1

[5,2,3,7,4,6,1] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1,1] => 1

[5,2,3,7,6,1,4] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1,1] => 1

[5,2,3,7,6,4,1] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1,1] => 1

[5,2,4,1,3,6,7] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1,1] => 1

[5,2,4,1,3,7,6] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1,1] => 2

[5,2,4,1,6,3,7] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1,1] => 1

[5,2,4,1,6,7,3] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1,1] => 1

[5,2,4,1,7,3,6] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1,1] => 2

[5,2,4,1,7,6,3] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1,1] => 2

[5,2,4,3,1,6,7] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1,1] => 1

[5,2,4,3,1,7,6] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1,1] => 2

[5,2,4,3,6,1,7] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1,1] => 1

[5,2,4,3,6,7,1] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1,1] => 1

[5,2,4,3,7,1,6] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1,1] => 2

[5,2,4,3,7,6,1] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1,1] => 2

[5,2,4,6,1,3,7] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1,1] => 1

[5,2,4,6,1,7,3] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1,1] => 1

[5,2,4,6,3,1,7] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1,1] => 1

[5,2,4,6,3,7,1] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1,1] => 1

[5,2,4,6,7,1,3] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1,1] => 1

[5,2,4,6,7,3,1] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1,1] => 1

[5,2,4,7,1,3,6] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1,1] => 2

[5,2,4,7,1,6,3] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1,1] => 2

[5,2,4,7,3,1,6] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1,1] => 2

[5,2,4,7,3,6,1] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1,1] => 2

[5,2,4,7,6,1,3] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1,1] => 2

[5,2,4,7,6,3,1] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1,1] => 2

[5,2,6,1,3,4,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => 0

[5,2,6,1,3,7,4] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => 0

[5,2,6,1,4,3,7] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1,1] => 1

[5,2,6,1,4,7,3] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1,1] => 1

[5,2,6,1,7,3,4] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => 0

[5,2,6,1,7,4,3] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1,1] => 1

[5,2,6,3,1,4,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => 0

[5,2,6,3,1,7,4] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => 0

[5,2,6,3,4,1,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => 0

[5,2,6,3,4,7,1] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => 0

[5,2,6,3,7,1,4] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => 0

[5,2,6,3,7,4,1] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => 0

[5,2,6,4,1,3,7] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1,1] => 1

[5,2,6,4,1,7,3] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1,1] => 1

[5,2,6,4,3,1,7] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1,1] => 1

[5,2,6,4,3,7,1] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1,1] => 1

[5,2,6,4,7,1,3] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1,1] => 1

[5,2,6,4,7,3,1] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1,1] => 1

[5,2,6,7,1,3,4] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => 0

[5,2,6,7,1,4,3] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1,1] => 1

[5,2,6,7,3,1,4] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => 0

[5,2,6,7,3,4,1] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => 0

[5,2,6,7,4,1,3] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1,1] => 1

[5,2,6,7,4,3,1] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1,1] => 1

[5,2,7,1,3,4,6] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1,1] => 1

[5,2,7,1,3,6,4] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1,1] => 1

[5,2,7,1,4,3,6] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1,1] => 2

[5,2,7,1,4,6,3] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1,1] => 2

[5,2,7,1,6,3,4] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1,1] => 1

[5,2,7,1,6,4,3] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1,1] => 2

[5,2,7,3,1,4,6] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1,1] => 1

[5,2,7,3,1,6,4] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1,1] => 1

[5,2,7,3,4,1,6] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1,1] => 1

[5,2,7,3,4,6,1] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1,1] => 1

[5,2,7,3,6,1,4] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1,1] => 1

[5,2,7,3,6,4,1] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1,1] => 1

[5,2,7,4,1,3,6] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1,1] => 2

[5,2,7,4,1,6,3] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1,1] => 2

[5,2,7,4,3,1,6] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1,1] => 2

[5,2,7,4,3,6,1] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1,1] => 2

[5,2,7,4,6,1,3] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1,1] => 2

[5,2,7,4,6,3,1] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1,1] => 2

[5,2,7,6,1,3,4] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1,1] => 1

[5,2,7,6,1,4,3] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1,1] => 2

[5,2,7,6,3,1,4] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1,1] => 1

[5,2,7,6,3,4,1] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1,1] => 1

[5,2,7,6,4,1,3] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1,1] => 2

[5,2,7,6,4,3,1] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1,1] => 2

[5,3,1,2,4,6,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 0

[5,3,1,2,4,7,6] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [5,4,4,2,2] => 1

[5,3,1,2,6,4,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 0

[5,3,1,2,6,7,4] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 0

[5,3,1,2,7,4,6] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [5,4,4,2,2] => 1

[5,3,1,2,7,6,4] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [5,4,4,2,2] => 1

[5,3,1,4,2,6,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 0

[5,3,1,4,2,7,6] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [5,4,4,2,2] => 1

[5,3,1,4,6,2,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 0

[5,3,1,4,6,7,2] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 0

[5,3,1,4,7,2,6] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [5,4,4,2,2] => 1

[5,3,1,4,7,6,2] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [5,4,4,2,2] => 1

[5,3,1,6,2,4,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 0

[5,3,1,6,2,7,4] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 0

[5,3,1,6,4,2,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 0

[5,3,1,6,4,7,2] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 0

[5,3,1,6,7,2,4] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 0

[5,3,1,6,7,4,2] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 0

[5,3,1,7,2,4,6] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [5,4,4,2,2] => 1

[5,3,1,7,2,6,4] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [5,4,4,2,2] => 1

[5,3,1,7,4,2,6] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [5,4,4,2,2] => 1

[5,3,1,7,4,6,2] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [5,4,4,2,2] => 1

[5,3,1,7,6,2,4] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [5,4,4,2,2] => 1

[5,3,1,7,6,4,2] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [5,4,4,2,2] => 1

[5,3,2,1,4,6,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2,1] => 1

[5,3,2,1,6,4,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2,1] => 1

[5,3,2,1,6,7,4] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2,1] => 1

[5,3,2,4,1,6,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2,1] => 1

[5,3,2,4,6,1,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2,1] => 1

[5,3,2,4,6,7,1] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2,1] => 1

[5,3,2,6,1,4,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2,1] => 1

[5,3,2,6,1,7,4] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2,1] => 1

[5,3,2,6,4,1,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2,1] => 1

[5,3,2,6,4,7,1] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2,1] => 1

[5,3,2,6,7,1,4] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2,1] => 1

[5,3,2,6,7,4,1] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2,1] => 1

[5,3,4,1,2,6,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 0

[5,3,4,1,2,7,6] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [5,4,4,2,2] => 1

[5,3,4,1,6,2,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 0

[5,3,4,1,6,7,2] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 0

[5,3,4,1,7,2,6] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [5,4,4,2,2] => 1

[5,3,4,1,7,6,2] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [5,4,4,2,2] => 1

[5,3,4,2,1,6,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2,1] => 1

[5,3,4,2,6,1,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2,1] => 1

[5,3,4,2,6,7,1] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2,1] => 1

[5,3,4,6,1,2,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 0

[5,3,4,6,1,7,2] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 0

[5,3,4,6,2,1,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2,1] => 1

[5,3,4,6,2,7,1] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2,1] => 1

[5,3,4,6,7,1,2] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 0

[5,3,4,6,7,2,1] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2,1] => 1

[5,3,4,7,1,2,6] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [5,4,4,2,2] => 1

[5,3,4,7,1,6,2] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [5,4,4,2,2] => 1

[5,3,4,7,6,1,2] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [5,4,4,2,2] => 1

[5,3,6,1,2,4,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 0

[5,3,6,1,2,7,4] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 0

[5,3,6,1,4,2,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 0

[5,3,6,1,4,7,2] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 0

[5,3,6,1,7,2,4] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 0

[5,3,6,1,7,4,2] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 0

[5,3,6,2,1,4,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2,1] => 1

[5,3,6,2,1,7,4] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2,1] => 1

[5,3,6,2,4,1,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2,1] => 1

[5,3,6,2,4,7,1] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2,1] => 1

[5,3,6,2,7,1,4] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2,1] => 1

[5,3,6,2,7,4,1] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2,1] => 1

[5,3,6,4,1,2,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 0

[5,3,6,4,1,7,2] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 0

[5,3,6,4,2,1,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2,1] => 1

[5,3,6,4,2,7,1] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2,1] => 1

[5,3,6,4,7,1,2] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 0

[5,3,6,4,7,2,1] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2,1] => 1

[5,3,6,7,1,2,4] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 0

[5,3,6,7,1,4,2] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 0

[5,3,6,7,2,1,4] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2,1] => 1

[5,3,6,7,2,4,1] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2,1] => 1

[5,3,6,7,4,1,2] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 0

[5,3,6,7,4,2,1] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2,1] => 1

[5,3,7,1,2,4,6] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [5,4,4,2,2] => 1

[5,3,7,1,2,6,4] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [5,4,4,2,2] => 1

[5,3,7,1,4,2,6] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [5,4,4,2,2] => 1

[5,3,7,1,4,6,2] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [5,4,4,2,2] => 1

[5,3,7,1,6,2,4] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [5,4,4,2,2] => 1

[5,3,7,1,6,4,2] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [5,4,4,2,2] => 1

[5,3,7,4,1,2,6] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [5,4,4,2,2] => 1

[5,3,7,4,1,6,2] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [5,4,4,2,2] => 1

[5,3,7,4,6,1,2] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [5,4,4,2,2] => 1

[5,3,7,6,1,2,4] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [5,4,4,2,2] => 1

[5,3,7,6,1,4,2] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [5,4,4,2,2] => 1

[5,3,7,6,4,1,2] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [5,4,4,2,2] => 1

[5,4,1,2,3,6,7] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3] => 1

[5,4,1,2,3,7,6] => [[[.,[.,[.,.]]],.],[[.,.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [5,4,4,3] => 2

[5,4,1,2,6,3,7] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3] => 1

[5,4,1,2,6,7,3] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3] => 1

[5,4,1,2,7,3,6] => [[[.,[.,[.,.]]],.],[[.,.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [5,4,4,3] => 2

[5,4,1,2,7,6,3] => [[[.,[.,[.,.]]],.],[[.,.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [5,4,4,3] => 2

[5,4,1,3,2,6,7] => [[[.,[[.,.],.]],.],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1] => 2

[5,4,1,3,2,7,6] => [[[.,[[.,.],.]],.],[[.,.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [5,4,4,3,1] => 3

[5,4,1,3,6,2,7] => [[[.,[[.,.],.]],.],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1] => 2

[5,4,1,3,6,7,2] => [[[.,[[.,.],.]],.],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1] => 2

[5,4,1,3,7,2,6] => [[[.,[[.,.],.]],.],[[.,.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [5,4,4,3,1] => 3

[5,4,1,3,7,6,2] => [[[.,[[.,.],.]],.],[[.,.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [5,4,4,3,1] => 3

[5,4,1,6,2,3,7] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3] => 1

[5,4,1,6,2,7,3] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3] => 1

[5,4,1,6,3,2,7] => [[[.,[[.,.],.]],.],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1] => 2

[5,4,1,6,3,7,2] => [[[.,[[.,.],.]],.],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1] => 2

[5,4,1,6,7,2,3] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3] => 1

[5,4,1,6,7,3,2] => [[[.,[[.,.],.]],.],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1] => 2

[5,4,1,7,2,3,6] => [[[.,[.,[.,.]]],.],[[.,.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [5,4,4,3] => 2

[5,4,1,7,2,6,3] => [[[.,[.,[.,.]]],.],[[.,.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [5,4,4,3] => 2

[5,4,1,7,3,2,6] => [[[.,[[.,.],.]],.],[[.,.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [5,4,4,3,1] => 3

[5,4,1,7,3,6,2] => [[[.,[[.,.],.]],.],[[.,.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [5,4,4,3,1] => 3

[5,4,1,7,6,2,3] => [[[.,[.,[.,.]]],.],[[.,.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [5,4,4,3] => 2

[5,4,1,7,6,3,2] => [[[.,[[.,.],.]],.],[[.,.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [5,4,4,3,1] => 3

[5,4,2,1,3,6,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1,1] => 1

[5,4,2,1,6,3,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1,1] => 1

[5,4,2,1,6,7,3] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1,1] => 1

[5,4,2,3,1,6,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1,1] => 1

[5,4,2,3,6,1,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1,1] => 1

[5,4,2,3,6,7,1] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1,1] => 1

[5,4,2,6,1,3,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1,1] => 1

[5,4,2,6,1,7,3] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1,1] => 1

[5,4,2,6,3,1,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1,1] => 1

[5,4,2,6,3,7,1] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1,1] => 1

[5,4,2,6,7,1,3] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1,1] => 1

[5,4,2,6,7,3,1] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1,1] => 1

[5,4,3,1,2,6,7] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [4,4,4,3,2] => 2

[5,4,3,1,6,2,7] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [4,4,4,3,2] => 2

[5,4,3,1,6,7,2] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [4,4,4,3,2] => 2

[5,4,3,2,1,6,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [4,4,4,3,2,1] => 3

[5,4,3,2,1,7,6] => [[[[[.,.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,4,3,2,1] => 4

[5,4,3,2,6,1,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [4,4,4,3,2,1] => 3

[5,4,3,2,6,7,1] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [4,4,4,3,2,1] => 3

[5,4,3,2,7,1,6] => [[[[[.,.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,4,3,2,1] => 4

[5,4,3,2,7,6,1] => [[[[[.,.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,4,3,2,1] => 4

[5,4,3,6,1,2,7] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [4,4,4,3,2] => 2

[5,4,3,6,1,7,2] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [4,4,4,3,2] => 2

[5,4,3,6,2,1,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [4,4,4,3,2,1] => 3

[5,4,3,6,2,7,1] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [4,4,4,3,2,1] => 3

[5,4,3,6,7,1,2] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [4,4,4,3,2] => 2

[5,4,3,6,7,2,1] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [4,4,4,3,2,1] => 3

[5,4,3,7,2,1,6] => [[[[[.,.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,4,3,2,1] => 4

[5,4,3,7,2,6,1] => [[[[[.,.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,4,3,2,1] => 4

[5,4,3,7,6,2,1] => [[[[[.,.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,4,3,2,1] => 4

[5,4,6,1,2,3,7] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3] => 1

[5,4,6,1,2,7,3] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3] => 1

[5,4,6,1,3,2,7] => [[[.,[[.,.],.]],.],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1] => 2

[5,4,6,1,3,7,2] => [[[.,[[.,.],.]],.],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1] => 2

[5,4,6,1,7,2,3] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3] => 1

[5,4,6,1,7,3,2] => [[[.,[[.,.],.]],.],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1] => 2

[5,4,6,2,1,3,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1,1] => 1

[5,4,6,2,1,7,3] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1,1] => 1

[5,4,6,2,3,1,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1,1] => 1

[5,4,6,2,3,7,1] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1,1] => 1

[5,4,6,2,7,1,3] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1,1] => 1

[5,4,6,2,7,3,1] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1,1] => 1

[5,4,6,3,1,2,7] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [4,4,4,3,2] => 2

[5,4,6,3,1,7,2] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [4,4,4,3,2] => 2

[5,4,6,3,2,1,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [4,4,4,3,2,1] => 3

[5,4,6,3,2,7,1] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [4,4,4,3,2,1] => 3

[5,4,6,3,7,1,2] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [4,4,4,3,2] => 2

[5,4,6,3,7,2,1] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [4,4,4,3,2,1] => 3

[5,4,6,7,1,2,3] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3] => 1

[5,4,6,7,1,3,2] => [[[.,[[.,.],.]],.],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1] => 2

[5,4,6,7,2,1,3] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1,1] => 1

[5,4,6,7,2,3,1] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1,1] => 1

[5,4,6,7,3,1,2] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [4,4,4,3,2] => 2

[5,4,6,7,3,2,1] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [4,4,4,3,2,1] => 3

[5,4,7,1,2,3,6] => [[[.,[.,[.,.]]],.],[[.,.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [5,4,4,3] => 2

[5,4,7,1,2,6,3] => [[[.,[.,[.,.]]],.],[[.,.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [5,4,4,3] => 2

[5,4,7,1,3,2,6] => [[[.,[[.,.],.]],.],[[.,.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [5,4,4,3,1] => 3

[5,4,7,1,3,6,2] => [[[.,[[.,.],.]],.],[[.,.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [5,4,4,3,1] => 3

[5,4,7,1,6,2,3] => [[[.,[.,[.,.]]],.],[[.,.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [5,4,4,3] => 2

[5,4,7,1,6,3,2] => [[[.,[[.,.],.]],.],[[.,.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [5,4,4,3,1] => 3

[5,4,7,3,2,1,6] => [[[[[.,.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,4,3,2,1] => 4

[5,4,7,3,2,6,1] => [[[[[.,.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,4,3,2,1] => 4

[5,4,7,3,6,2,1] => [[[[[.,.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,4,3,2,1] => 4

[5,4,7,6,1,2,3] => [[[.,[.,[.,.]]],.],[[.,.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [5,4,4,3] => 2

[5,4,7,6,1,3,2] => [[[.,[[.,.],.]],.],[[.,.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [5,4,4,3,1] => 3

[5,4,7,6,3,2,1] => [[[[[.,.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,4,3,2,1] => 4

[5,6,1,2,3,4,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,4,4] => 0

[5,6,1,2,3,7,4] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,4,4] => 0

[5,6,1,2,4,3,7] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1] => 1

[5,6,1,2,4,7,3] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1] => 1

[5,6,1,2,7,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,4,4] => 0

[5,6,1,2,7,4,3] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1] => 1

[5,6,1,3,2,4,7] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1] => 0

[5,6,1,3,2,7,4] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1] => 0

[5,6,1,3,4,2,7] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1] => 0

[5,6,1,3,4,7,2] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1] => 0

[5,6,1,3,7,2,4] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1] => 0

[5,6,1,3,7,4,2] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1] => 0

[5,6,1,4,2,3,7] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2] => 1

[5,6,1,4,2,7,3] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2] => 1

[5,6,1,4,3,2,7] => [[.,[[[.,.],.],.]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1] => 2

[5,6,1,4,3,7,2] => [[.,[[[.,.],.],.]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1] => 2

[5,6,1,4,7,2,3] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2] => 1

[5,6,1,4,7,3,2] => [[.,[[[.,.],.],.]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1] => 2

[5,6,1,7,2,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,4,4] => 0

[5,6,1,7,2,4,3] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1] => 1

[5,6,1,7,3,2,4] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1] => 0

[5,6,1,7,3,4,2] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1] => 0

[5,6,1,7,4,2,3] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2] => 1

[5,6,1,7,4,3,2] => [[.,[[[.,.],.],.]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1] => 2

[5,6,2,1,3,4,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => 0

[5,6,2,1,3,7,4] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => 0

[5,6,2,1,4,3,7] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1,1] => 1

[5,6,2,1,4,7,3] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1,1] => 1

[5,6,2,1,7,3,4] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => 0

[5,6,2,1,7,4,3] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1,1] => 1

[5,6,2,3,1,4,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => 0

[5,6,2,3,1,7,4] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => 0

[5,6,2,3,4,1,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => 0

[5,6,2,3,4,7,1] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => 0

[5,6,2,3,7,1,4] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => 0

[5,6,2,3,7,4,1] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => 0

[5,6,2,4,1,3,7] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1,1] => 1

[5,6,2,4,1,7,3] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1,1] => 1

[5,6,2,4,3,1,7] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1,1] => 1

[5,6,2,4,3,7,1] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1,1] => 1

[5,6,2,4,7,1,3] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1,1] => 1

[5,6,2,4,7,3,1] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1,1] => 1

[5,6,2,7,1,3,4] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => 0

[5,6,2,7,1,4,3] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1,1] => 1

[5,6,2,7,3,1,4] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => 0

[5,6,2,7,3,4,1] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => 0

[5,6,2,7,4,1,3] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1,1] => 1

[5,6,2,7,4,3,1] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1,1] => 1

[5,6,3,1,2,4,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 0

[5,6,3,1,2,7,4] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 0

[5,6,3,1,4,2,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 0

[5,6,3,1,4,7,2] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 0

[5,6,3,1,7,2,4] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 0

[5,6,3,1,7,4,2] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 0

[5,6,3,2,1,4,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2,1] => 1

[5,6,3,2,1,7,4] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2,1] => 1

[5,6,3,2,4,1,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2,1] => 1

[5,6,3,2,4,7,1] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2,1] => 1

[5,6,3,2,7,1,4] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2,1] => 1

[5,6,3,2,7,4,1] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2,1] => 1

[5,6,3,4,1,2,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 0

[5,6,3,4,1,7,2] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 0

[5,6,3,4,2,1,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2,1] => 1

[5,6,3,4,2,7,1] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2,1] => 1

[5,6,3,4,7,1,2] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 0

[5,6,3,4,7,2,1] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2,1] => 1

[5,6,3,7,1,2,4] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 0

[5,6,3,7,1,4,2] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 0

[5,6,3,7,2,1,4] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2,1] => 1

[5,6,3,7,2,4,1] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2,1] => 1

[5,6,3,7,4,1,2] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 0

[5,6,3,7,4,2,1] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2,1] => 1

[5,6,4,1,2,3,7] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3] => 1

[5,6,4,1,2,7,3] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3] => 1

[5,6,4,1,3,2,7] => [[[.,[[.,.],.]],.],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1] => 2

[5,6,4,1,3,7,2] => [[[.,[[.,.],.]],.],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1] => 2

[5,6,4,1,7,2,3] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3] => 1

[5,6,4,1,7,3,2] => [[[.,[[.,.],.]],.],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1] => 2

[5,6,4,2,1,3,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1,1] => 1

[5,6,4,2,1,7,3] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1,1] => 1

[5,6,4,2,3,1,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1,1] => 1

[5,6,4,2,3,7,1] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1,1] => 1

[5,6,4,2,7,1,3] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1,1] => 1

[5,6,4,2,7,3,1] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1,1] => 1

[5,6,4,3,1,2,7] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [4,4,4,3,2] => 2

[5,6,4,3,1,7,2] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [4,4,4,3,2] => 2

[5,6,4,3,2,1,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [4,4,4,3,2,1] => 3

[5,6,4,3,2,7,1] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [4,4,4,3,2,1] => 3

[5,6,4,3,7,1,2] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [4,4,4,3,2] => 2

[5,6,4,3,7,2,1] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [4,4,4,3,2,1] => 3

[5,6,4,7,1,2,3] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3] => 1

[5,6,4,7,1,3,2] => [[[.,[[.,.],.]],.],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1] => 2

[5,6,4,7,2,1,3] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1,1] => 1

[5,6,4,7,2,3,1] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1,1] => 1

[5,6,4,7,3,1,2] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [4,4,4,3,2] => 2

[5,6,4,7,3,2,1] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [4,4,4,3,2,1] => 3

[5,6,7,1,2,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,4,4] => 0

[5,6,7,1,2,4,3] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1] => 1

[5,6,7,1,3,2,4] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1] => 0

[5,6,7,1,3,4,2] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1] => 0

[5,6,7,1,4,2,3] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2] => 1

[5,6,7,1,4,3,2] => [[.,[[[.,.],.],.]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1] => 2

[5,6,7,2,1,3,4] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => 0

[5,6,7,2,1,4,3] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1,1] => 1

[5,6,7,2,3,1,4] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => 0

[5,6,7,2,3,4,1] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => 0

[5,6,7,2,4,1,3] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1,1] => 1

[5,6,7,2,4,3,1] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1,1] => 1

[5,6,7,3,1,2,4] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 0

[5,6,7,3,1,4,2] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 0

[5,6,7,3,2,1,4] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2,1] => 1

[5,6,7,3,2,4,1] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2,1] => 1

[5,6,7,3,4,1,2] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 0

[5,6,7,3,4,2,1] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2,1] => 1

[5,6,7,4,1,2,3] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3] => 1

[5,6,7,4,1,3,2] => [[[.,[[.,.],.]],.],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1] => 2

[5,6,7,4,2,1,3] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1,1] => 1

[5,6,7,4,2,3,1] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1,1] => 1

[5,6,7,4,3,1,2] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [4,4,4,3,2] => 2

[5,6,7,4,3,2,1] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [4,4,4,3,2,1] => 3

[5,7,1,2,3,4,6] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [5,4,4] => 1

[5,7,1,2,3,6,4] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [5,4,4] => 1

[5,7,1,2,4,3,6] => [[.,[.,[[.,.],.]]],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1] => 2

[5,7,1,2,4,6,3] => [[.,[.,[[.,.],.]]],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1] => 2

[5,7,1,2,6,3,4] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [5,4,4] => 1

[5,7,1,2,6,4,3] => [[.,[.,[[.,.],.]]],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1] => 2

[5,7,1,3,2,4,6] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1] => 1

[5,7,1,3,2,6,4] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1] => 1

[5,7,1,3,4,2,6] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1] => 1

[5,7,1,3,4,6,2] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1] => 1

[5,7,1,3,6,2,4] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1] => 1

[5,7,1,3,6,4,2] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1] => 1

[5,7,1,4,2,3,6] => [[.,[[.,[.,.]],.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2] => 2

[5,7,1,4,2,6,3] => [[.,[[.,[.,.]],.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2] => 2

[5,7,1,4,3,2,6] => [[.,[[[.,.],.],.]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1] => 3

[5,7,1,4,3,6,2] => [[.,[[[.,.],.],.]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1] => 3

[5,7,1,4,6,2,3] => [[.,[[.,[.,.]],.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2] => 2

[5,7,1,4,6,3,2] => [[.,[[[.,.],.],.]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1] => 3

[5,7,1,6,2,3,4] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [5,4,4] => 1

[5,7,1,6,2,4,3] => [[.,[.,[[.,.],.]]],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1] => 2

[5,7,1,6,3,2,4] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1] => 1

[5,7,1,6,3,4,2] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1] => 1

[5,7,1,6,4,2,3] => [[.,[[.,[.,.]],.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2] => 2

[5,7,1,6,4,3,2] => [[.,[[[.,.],.],.]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1] => 3

[5,7,2,1,3,4,6] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1,1] => 1

[5,7,2,1,3,6,4] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1,1] => 1

[5,7,2,1,4,3,6] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1,1] => 2

[5,7,2,1,4,6,3] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1,1] => 2

[5,7,2,1,6,3,4] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1,1] => 1

[5,7,2,1,6,4,3] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1,1] => 2

[5,7,2,3,1,4,6] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1,1] => 1

[5,7,2,3,1,6,4] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1,1] => 1

[5,7,2,3,4,1,6] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1,1] => 1

[5,7,2,3,4,6,1] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1,1] => 1

[5,7,2,3,6,1,4] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1,1] => 1

[5,7,2,3,6,4,1] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1,1] => 1

[5,7,2,4,1,3,6] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1,1] => 2

[5,7,2,4,1,6,3] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1,1] => 2

[5,7,2,4,3,1,6] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1,1] => 2

[5,7,2,4,3,6,1] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1,1] => 2

[5,7,2,4,6,1,3] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1,1] => 2

[5,7,2,4,6,3,1] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1,1] => 2

[5,7,2,6,1,3,4] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1,1] => 1

[5,7,2,6,1,4,3] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1,1] => 2

[5,7,2,6,3,1,4] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1,1] => 1

[5,7,2,6,3,4,1] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1,1] => 1

[5,7,2,6,4,1,3] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1,1] => 2

[5,7,2,6,4,3,1] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1,1] => 2

[5,7,3,1,2,4,6] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [5,4,4,2,2] => 1

[5,7,3,1,2,6,4] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [5,4,4,2,2] => 1

[5,7,3,1,4,2,6] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [5,4,4,2,2] => 1

[5,7,3,1,4,6,2] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [5,4,4,2,2] => 1

[5,7,3,1,6,2,4] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [5,4,4,2,2] => 1

[5,7,3,1,6,4,2] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [5,4,4,2,2] => 1

[5,7,3,4,1,2,6] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [5,4,4,2,2] => 1

[5,7,3,4,1,6,2] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [5,4,4,2,2] => 1

[5,7,3,4,6,1,2] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [5,4,4,2,2] => 1

[5,7,3,6,1,2,4] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [5,4,4,2,2] => 1

[5,7,3,6,1,4,2] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [5,4,4,2,2] => 1

[5,7,3,6,4,1,2] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [5,4,4,2,2] => 1

[5,7,4,1,2,3,6] => [[[.,[.,[.,.]]],.],[[.,.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [5,4,4,3] => 2

[5,7,4,1,2,6,3] => [[[.,[.,[.,.]]],.],[[.,.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [5,4,4,3] => 2

[5,7,4,1,3,2,6] => [[[.,[[.,.],.]],.],[[.,.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [5,4,4,3,1] => 3

[5,7,4,1,3,6,2] => [[[.,[[.,.],.]],.],[[.,.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [5,4,4,3,1] => 3

[5,7,4,1,6,2,3] => [[[.,[.,[.,.]]],.],[[.,.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [5,4,4,3] => 2

[5,7,4,1,6,3,2] => [[[.,[[.,.],.]],.],[[.,.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [5,4,4,3,1] => 3

[5,7,4,3,2,1,6] => [[[[[.,.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,4,3,2,1] => 4

[5,7,4,3,2,6,1] => [[[[[.,.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,4,3,2,1] => 4

[5,7,4,3,6,2,1] => [[[[[.,.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,4,3,2,1] => 4

[5,7,4,6,1,2,3] => [[[.,[.,[.,.]]],.],[[.,.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [5,4,4,3] => 2

[5,7,4,6,1,3,2] => [[[.,[[.,.],.]],.],[[.,.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [5,4,4,3,1] => 3

[5,7,4,6,3,2,1] => [[[[[.,.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,4,3,2,1] => 4

[5,7,6,1,2,3,4] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [5,4,4] => 1

[5,7,6,1,2,4,3] => [[.,[.,[[.,.],.]]],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1] => 2

[5,7,6,1,3,2,4] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1] => 1

[5,7,6,1,3,4,2] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1] => 1

[5,7,6,1,4,2,3] => [[.,[[.,[.,.]],.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2] => 2

[5,7,6,1,4,3,2] => [[.,[[[.,.],.],.]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1] => 3

[5,7,6,2,1,3,4] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1,1] => 1

[5,7,6,2,1,4,3] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1,1] => 2

[5,7,6,2,3,1,4] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1,1] => 1

[5,7,6,2,3,4,1] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1,1] => 1

[5,7,6,2,4,1,3] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1,1] => 2

[5,7,6,2,4,3,1] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1,1] => 2

[5,7,6,3,1,2,4] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [5,4,4,2,2] => 1

[5,7,6,3,1,4,2] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [5,4,4,2,2] => 1

[5,7,6,3,4,1,2] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [5,4,4,2,2] => 1

[5,7,6,4,1,2,3] => [[[.,[.,[.,.]]],.],[[.,.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [5,4,4,3] => 2

[5,7,6,4,1,3,2] => [[[.,[[.,.],.]],.],[[.,.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [5,4,4,3,1] => 3

[5,7,6,4,3,2,1] => [[[[[.,.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,4,3,2,1] => 4

[6,1,2,3,4,5,7] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => 0

[6,1,2,3,4,7,5] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => 0

[6,1,2,3,5,4,7] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,5,1] => 1

[6,1,2,3,5,7,4] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,5,1] => 1

[6,1,2,3,7,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => 0

[6,1,2,3,7,5,4] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,5,1] => 1

[6,1,2,4,3,5,7] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1] => 0

[6,1,2,4,3,7,5] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1] => 0

[6,1,2,4,5,3,7] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1] => 0

[6,1,2,4,5,7,3] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1] => 0

[6,1,2,4,7,3,5] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1] => 0

[6,1,2,4,7,5,3] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1] => 0

[6,1,2,5,3,4,7] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,5,2] => 1

[6,1,2,5,3,7,4] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,5,2] => 1

[6,1,2,5,4,3,7] => [[.,[.,[[[.,.],.],.]]],[.,.]] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1] => 2

[6,1,2,5,4,7,3] => [[.,[.,[[[.,.],.],.]]],[.,.]] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1] => 2

[6,1,2,5,7,3,4] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,5,2] => 1

[6,1,2,5,7,4,3] => [[.,[.,[[[.,.],.],.]]],[.,.]] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1] => 2

[6,1,2,7,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => 0

[6,1,2,7,3,5,4] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,5,1] => 1

[6,1,2,7,4,3,5] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1] => 0

[6,1,2,7,4,5,3] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1] => 0

[6,1,2,7,5,3,4] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,5,2] => 1

[6,1,2,7,5,4,3] => [[.,[.,[[[.,.],.],.]]],[.,.]] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1] => 2

[6,1,3,2,4,5,7] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1] => 0

[6,1,3,2,4,7,5] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1] => 0

[6,1,3,2,5,4,7] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1,1] => 1

[6,1,3,2,5,7,4] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1,1] => 1

[6,1,3,2,7,4,5] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1] => 0

[6,1,3,2,7,5,4] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1,1] => 1

[6,1,3,4,2,5,7] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1] => 0

[6,1,3,4,2,7,5] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1] => 0

[6,1,3,4,5,2,7] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1] => 0

[6,1,3,4,5,7,2] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1] => 0

[6,1,3,4,7,2,5] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1] => 0

[6,1,3,4,7,5,2] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1] => 0

[6,1,3,5,2,4,7] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1,1] => 1

[6,1,3,5,2,7,4] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1,1] => 1

[6,1,3,5,4,2,7] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1,1] => 1

[6,1,3,5,4,7,2] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1,1] => 1

[6,1,3,5,7,2,4] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1,1] => 1

[6,1,3,5,7,4,2] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1,1] => 1

[6,1,3,7,2,4,5] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1] => 0

[6,1,3,7,2,5,4] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1,1] => 1

[6,1,3,7,4,2,5] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1] => 0

[6,1,3,7,4,5,2] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1] => 0

[6,1,3,7,5,2,4] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1,1] => 1

[6,1,3,7,5,4,2] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1,1] => 1

[6,1,4,2,3,5,7] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2] => 0

[6,1,4,2,3,7,5] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2] => 0

[6,1,4,2,5,3,7] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2] => 0

[6,1,4,2,5,7,3] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2] => 0

[6,1,4,2,7,3,5] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2] => 0

[6,1,4,2,7,5,3] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2] => 0

[6,1,4,3,2,5,7] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1] => 1

[6,1,4,3,2,7,5] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1] => 1

[6,1,4,3,5,2,7] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1] => 1

[6,1,4,3,5,7,2] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1] => 1

[6,1,4,3,7,2,5] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1] => 1

[6,1,4,3,7,5,2] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1] => 1

[6,1,4,5,2,3,7] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2] => 0

[6,1,4,5,2,7,3] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2] => 0

[6,1,4,5,3,2,7] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1] => 1

[6,1,4,5,3,7,2] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1] => 1

[6,1,4,5,7,2,3] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2] => 0

[6,1,4,5,7,3,2] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1] => 1

[6,1,4,7,2,3,5] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2] => 0

[6,1,4,7,2,5,3] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2] => 0

[6,1,4,7,3,2,5] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1] => 1

[6,1,4,7,3,5,2] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1] => 1

[6,1,4,7,5,2,3] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2] => 0

[6,1,4,7,5,3,2] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1] => 1

[6,1,5,2,3,4,7] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [5,5,3] => 1

[6,1,5,2,3,7,4] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [5,5,3] => 1

[6,1,5,2,4,3,7] => [[.,[[.,[[.,.],.]],.]],[.,.]] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1] => 2

[6,1,5,2,4,7,3] => [[.,[[.,[[.,.],.]],.]],[.,.]] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1] => 2

[6,1,5,2,7,3,4] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [5,5,3] => 1

[6,1,5,2,7,4,3] => [[.,[[.,[[.,.],.]],.]],[.,.]] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1] => 2

[6,1,5,3,2,4,7] => [[.,[[[.,.],[.,.]],.]],[.,.]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1,1] => 1

[6,1,5,3,2,7,4] => [[.,[[[.,.],[.,.]],.]],[.,.]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1,1] => 1

[6,1,5,3,4,2,7] => [[.,[[[.,.],[.,.]],.]],[.,.]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1,1] => 1

[6,1,5,3,4,7,2] => [[.,[[[.,.],[.,.]],.]],[.,.]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1,1] => 1

[6,1,5,3,7,2,4] => [[.,[[[.,.],[.,.]],.]],[.,.]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1,1] => 1

[6,1,5,3,7,4,2] => [[.,[[[.,.],[.,.]],.]],[.,.]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1,1] => 1

[6,1,5,4,2,3,7] => [[.,[[[.,[.,.]],.],.]],[.,.]] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2] => 2

[6,1,5,4,2,7,3] => [[.,[[[.,[.,.]],.],.]],[.,.]] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2] => 2

[6,1,5,4,3,2,7] => [[.,[[[[.,.],.],.],.]],[.,.]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2,1] => 3

[6,1,5,4,3,7,2] => [[.,[[[[.,.],.],.],.]],[.,.]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2,1] => 3

[6,1,5,4,7,2,3] => [[.,[[[.,[.,.]],.],.]],[.,.]] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2] => 2

[6,1,5,4,7,3,2] => [[.,[[[[.,.],.],.],.]],[.,.]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2,1] => 3

[6,1,5,7,2,3,4] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [5,5,3] => 1

[6,1,5,7,2,4,3] => [[.,[[.,[[.,.],.]],.]],[.,.]] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1] => 2

[6,1,5,7,3,2,4] => [[.,[[[.,.],[.,.]],.]],[.,.]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1,1] => 1

[6,1,5,7,3,4,2] => [[.,[[[.,.],[.,.]],.]],[.,.]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1,1] => 1

[6,1,5,7,4,2,3] => [[.,[[[.,[.,.]],.],.]],[.,.]] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2] => 2

[6,1,5,7,4,3,2] => [[.,[[[[.,.],.],.],.]],[.,.]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2,1] => 3

[6,1,7,2,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => 0

[6,1,7,2,3,5,4] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,5,1] => 1

[6,1,7,2,4,3,5] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1] => 0

[6,1,7,2,4,5,3] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1] => 0

[6,1,7,2,5,3,4] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,5,2] => 1

[6,1,7,2,5,4,3] => [[.,[.,[[[.,.],.],.]]],[.,.]] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1] => 2

[6,1,7,3,2,4,5] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1] => 0

[6,1,7,3,2,5,4] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1,1] => 1

[6,1,7,3,4,2,5] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1] => 0

[6,1,7,3,4,5,2] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1] => 0

[6,1,7,3,5,2,4] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1,1] => 1

[6,1,7,3,5,4,2] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1,1] => 1

[6,1,7,4,2,3,5] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2] => 0

[6,1,7,4,2,5,3] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2] => 0

[6,1,7,4,3,2,5] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1] => 1

[6,1,7,4,3,5,2] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1] => 1

[6,1,7,4,5,2,3] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2] => 0

[6,1,7,4,5,3,2] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1] => 1

[6,1,7,5,2,3,4] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [5,5,3] => 1

[6,1,7,5,2,4,3] => [[.,[[.,[[.,.],.]],.]],[.,.]] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1] => 2

[6,1,7,5,3,2,4] => [[.,[[[.,.],[.,.]],.]],[.,.]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1,1] => 1

[6,1,7,5,3,4,2] => [[.,[[[.,.],[.,.]],.]],[.,.]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1,1] => 1

[6,1,7,5,4,2,3] => [[.,[[[.,[.,.]],.],.]],[.,.]] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2] => 2

[6,1,7,5,4,3,2] => [[.,[[[[.,.],.],.],.]],[.,.]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2,1] => 3

[6,2,1,3,4,5,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1,1] => 0

[6,2,1,3,4,7,5] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1,1] => 0

[6,2,1,3,5,4,7] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1,1,1] => 1

[6,2,1,3,5,7,4] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1,1,1] => 1

[6,2,1,3,7,4,5] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1,1] => 0

[6,2,1,3,7,5,4] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1,1,1] => 1

[6,2,1,4,3,5,7] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1,1] => 0

[6,2,1,4,3,7,5] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1,1] => 0

[6,2,1,4,5,3,7] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1,1] => 0

[6,2,1,4,5,7,3] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1,1] => 0

[6,2,1,4,7,3,5] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1,1] => 0

[6,2,1,4,7,5,3] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1,1] => 0

[6,2,1,5,3,4,7] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1,1,1] => 1

[6,2,1,5,3,7,4] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1,1,1] => 1

[6,2,1,5,4,3,7] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2,1,1] => 2

[6,2,1,5,4,7,3] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2,1,1] => 2

[6,2,1,5,7,3,4] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1,1,1] => 1

[6,2,1,5,7,4,3] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2,1,1] => 2

[6,2,1,7,3,4,5] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1,1] => 0

[6,2,1,7,3,5,4] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1,1,1] => 1

[6,2,1,7,4,3,5] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1,1] => 0

[6,2,1,7,4,5,3] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1,1] => 0

[6,2,1,7,5,3,4] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1,1,1] => 1

[6,2,1,7,5,4,3] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2,1,1] => 2

[6,2,3,1,4,5,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1,1] => 0

[6,2,3,1,4,7,5] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1,1] => 0

[6,2,3,1,5,4,7] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1,1,1] => 1

[6,2,3,1,5,7,4] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1,1,1] => 1

[6,2,3,1,7,4,5] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1,1] => 0

[6,2,3,1,7,5,4] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1,1,1] => 1

[6,2,3,4,1,5,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1,1] => 0

[6,2,3,4,1,7,5] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1,1] => 0

[6,2,3,4,5,1,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1,1] => 0

[6,2,3,4,5,7,1] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1,1] => 0

[6,2,3,4,7,1,5] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1,1] => 0

[6,2,3,4,7,5,1] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1,1] => 0

[6,2,3,5,1,4,7] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1,1,1] => 1

[6,2,3,5,1,7,4] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1,1,1] => 1

[6,2,3,5,4,1,7] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1,1,1] => 1

[6,2,3,5,4,7,1] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1,1,1] => 1

[6,2,3,5,7,1,4] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1,1,1] => 1

[6,2,3,5,7,4,1] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1,1,1] => 1

[6,2,3,7,1,4,5] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1,1] => 0

[6,2,3,7,1,5,4] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1,1,1] => 1

[6,2,3,7,4,1,5] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1,1] => 0

[6,2,3,7,4,5,1] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1,1] => 0

[6,2,3,7,5,1,4] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1,1,1] => 1

[6,2,3,7,5,4,1] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1,1,1] => 1

[6,2,4,1,3,5,7] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1,1] => 0

[6,2,4,1,3,7,5] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1,1] => 0

[6,2,4,1,5,3,7] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1,1] => 0

[6,2,4,1,5,7,3] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1,1] => 0

[6,2,4,1,7,3,5] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1,1] => 0

[6,2,4,1,7,5,3] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1,1] => 0

[6,2,4,3,1,5,7] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1,1] => 0

[6,2,4,3,1,7,5] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1,1] => 0

[6,2,4,3,5,1,7] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1,1] => 0

[6,2,4,3,5,7,1] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1,1] => 0

[6,2,4,3,7,1,5] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1,1] => 0

[6,2,4,3,7,5,1] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1,1] => 0

[6,2,4,5,1,3,7] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1,1] => 0

[6,2,4,5,1,7,3] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1,1] => 0

[6,2,4,5,3,1,7] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1,1] => 0

[6,2,4,5,3,7,1] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1,1] => 0

[6,2,4,5,7,1,3] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1,1] => 0

[6,2,4,5,7,3,1] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1,1] => 0

[6,2,4,7,1,3,5] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1,1] => 0

[6,2,4,7,1,5,3] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1,1] => 0

[6,2,4,7,3,1,5] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1,1] => 0

[6,2,4,7,3,5,1] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1,1] => 0

[6,2,4,7,5,1,3] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1,1] => 0

[6,2,4,7,5,3,1] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1,1] => 0

[6,2,5,1,3,4,7] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1,1,1] => 1

[6,2,5,1,3,7,4] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1,1,1] => 1

[6,2,5,1,4,3,7] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2,1,1] => 2

[6,2,5,1,4,7,3] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2,1,1] => 2

[6,2,5,1,7,3,4] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1,1,1] => 1

[6,2,5,1,7,4,3] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2,1,1] => 2

[6,2,5,3,1,4,7] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1,1,1] => 1

[6,2,5,3,1,7,4] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1,1,1] => 1

[6,2,5,3,4,1,7] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1,1,1] => 1

[6,2,5,3,4,7,1] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1,1,1] => 1

[6,2,5,3,7,1,4] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1,1,1] => 1

[6,2,5,3,7,4,1] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1,1,1] => 1

[6,2,5,4,1,3,7] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2,1,1] => 2

[6,2,5,4,1,7,3] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2,1,1] => 2

[6,2,5,4,3,1,7] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2,1,1] => 2

[6,2,5,4,3,7,1] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2,1,1] => 2

[6,2,5,4,7,1,3] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2,1,1] => 2

[6,2,5,4,7,3,1] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2,1,1] => 2

[6,2,5,7,1,3,4] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1,1,1] => 1

[6,2,5,7,1,4,3] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2,1,1] => 2

[6,2,5,7,3,1,4] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1,1,1] => 1

[6,2,5,7,3,4,1] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1,1,1] => 1

[6,2,5,7,4,1,3] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2,1,1] => 2

[6,2,5,7,4,3,1] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2,1,1] => 2

[6,2,7,1,3,4,5] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1,1] => 0

[6,2,7,1,3,5,4] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1,1,1] => 1

[6,2,7,1,4,3,5] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1,1] => 0

[6,2,7,1,4,5,3] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1,1] => 0

[6,2,7,1,5,3,4] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1,1,1] => 1

[6,2,7,1,5,4,3] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2,1,1] => 2

[6,2,7,3,1,4,5] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1,1] => 0

[6,2,7,3,1,5,4] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1,1,1] => 1

[6,2,7,3,4,1,5] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1,1] => 0

[6,2,7,3,4,5,1] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1,1] => 0

[6,2,7,3,5,1,4] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1,1,1] => 1

[6,2,7,3,5,4,1] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1,1,1] => 1

[6,2,7,4,1,3,5] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1,1] => 0

[6,2,7,4,1,5,3] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1,1] => 0

[6,2,7,4,3,1,5] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1,1] => 0

[6,2,7,4,3,5,1] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1,1] => 0

[6,2,7,4,5,1,3] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1,1] => 0

[6,2,7,4,5,3,1] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1,1] => 0

[6,2,7,5,1,3,4] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1,1,1] => 1

[6,2,7,5,1,4,3] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2,1,1] => 2

[6,2,7,5,3,1,4] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1,1,1] => 1

[6,2,7,5,3,4,1] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1,1,1] => 1

[6,2,7,5,4,1,3] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2,1,1] => 2

[6,2,7,5,4,3,1] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2,1,1] => 2

[6,3,1,2,4,5,7] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 0

[6,3,1,2,4,7,5] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 0

[6,3,1,2,5,4,7] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [5,5,3,2,2] => 1

[6,3,1,2,5,7,4] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [5,5,3,2,2] => 1

[6,3,1,2,7,4,5] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 0

[6,3,1,2,7,5,4] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [5,5,3,2,2] => 1

[6,3,1,4,2,5,7] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 0

[6,3,1,4,2,7,5] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 0

[6,3,1,4,5,2,7] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 0

[6,3,1,4,5,7,2] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 0

[6,3,1,4,7,2,5] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 0

[6,3,1,4,7,5,2] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 0

[6,3,1,5,2,4,7] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [5,5,3,2,2] => 1

[6,3,1,5,2,7,4] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [5,5,3,2,2] => 1

[6,3,1,5,4,2,7] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [5,5,3,2,2] => 1

[6,3,1,5,4,7,2] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [5,5,3,2,2] => 1

[6,3,1,5,7,2,4] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [5,5,3,2,2] => 1

[6,3,1,5,7,4,2] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [5,5,3,2,2] => 1

[6,3,1,7,2,4,5] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 0

[6,3,1,7,2,5,4] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [5,5,3,2,2] => 1

[6,3,1,7,4,2,5] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 0

[6,3,1,7,4,5,2] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 0

[6,3,1,7,5,2,4] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [5,5,3,2,2] => 1

[6,3,1,7,5,4,2] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [5,5,3,2,2] => 1

[6,3,2,1,4,5,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2,1] => 1

[6,3,2,1,4,7,5] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2,1] => 1

[6,3,2,1,7,4,5] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2,1] => 1

[6,3,2,4,1,5,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2,1] => 1

[6,3,2,4,1,7,5] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2,1] => 1

[6,3,2,4,5,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2,1] => 1

[6,3,2,4,5,7,1] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2,1] => 1

[6,3,2,4,7,1,5] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2,1] => 1

[6,3,2,4,7,5,1] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2,1] => 1

[6,3,2,7,1,4,5] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2,1] => 1

[6,3,2,7,4,1,5] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2,1] => 1

[6,3,2,7,4,5,1] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2,1] => 1

[6,3,4,1,2,5,7] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 0

[6,3,4,1,2,7,5] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 0

[6,3,4,1,5,2,7] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 0

[6,3,4,1,5,7,2] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 0

[6,3,4,1,7,2,5] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 0

[6,3,4,1,7,5,2] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 0

[6,3,4,2,1,5,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2,1] => 1

[6,3,4,2,1,7,5] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2,1] => 1

[6,3,4,2,5,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2,1] => 1

[6,3,4,2,5,7,1] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2,1] => 1

[6,3,4,2,7,1,5] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2,1] => 1

[6,3,4,2,7,5,1] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2,1] => 1

[6,3,4,5,1,2,7] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 0

[6,3,4,5,1,7,2] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 0

[6,3,4,5,2,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2,1] => 1

[6,3,4,5,2,7,1] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2,1] => 1

[6,3,4,5,7,1,2] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 0

[6,3,4,5,7,2,1] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2,1] => 1

[6,3,4,7,1,2,5] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 0

[6,3,4,7,1,5,2] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 0

[6,3,4,7,2,1,5] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2,1] => 1

[6,3,4,7,2,5,1] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2,1] => 1

[6,3,4,7,5,1,2] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 0

[6,3,4,7,5,2,1] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2,1] => 1

[6,3,5,1,2,4,7] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [5,5,3,2,2] => 1

[6,3,5,1,2,7,4] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [5,5,3,2,2] => 1

[6,3,5,1,4,2,7] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [5,5,3,2,2] => 1

[6,3,5,1,4,7,2] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [5,5,3,2,2] => 1

[6,3,5,1,7,2,4] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [5,5,3,2,2] => 1

[6,3,5,1,7,4,2] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [5,5,3,2,2] => 1

[6,3,5,4,1,2,7] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [5,5,3,2,2] => 1

[6,3,5,4,1,7,2] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [5,5,3,2,2] => 1

[6,3,5,4,7,1,2] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [5,5,3,2,2] => 1

[6,3,5,7,1,2,4] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [5,5,3,2,2] => 1

[6,3,5,7,1,4,2] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [5,5,3,2,2] => 1

[6,3,5,7,4,1,2] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [5,5,3,2,2] => 1

[6,3,7,1,2,4,5] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 0

[6,3,7,1,2,5,4] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [5,5,3,2,2] => 1

[6,3,7,1,4,2,5] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 0

[6,3,7,1,4,5,2] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 0

[6,3,7,1,5,2,4] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [5,5,3,2,2] => 1

[6,3,7,1,5,4,2] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [5,5,3,2,2] => 1

[6,3,7,2,1,4,5] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2,1] => 1

[6,3,7,2,4,1,5] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2,1] => 1

[6,3,7,2,4,5,1] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2,1] => 1

[6,3,7,4,1,2,5] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 0

[6,3,7,4,1,5,2] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 0

[6,3,7,4,2,1,5] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2,1] => 1

[6,3,7,4,2,5,1] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2,1] => 1

[6,3,7,4,5,1,2] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 0

[6,3,7,4,5,2,1] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2,1] => 1

[6,3,7,5,1,2,4] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [5,5,3,2,2] => 1

[6,3,7,5,1,4,2] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [5,5,3,2,2] => 1

[6,3,7,5,4,1,2] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [5,5,3,2,2] => 1

[6,4,1,2,3,5,7] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 0

[6,4,1,2,3,7,5] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 0

[6,4,1,2,5,3,7] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 0

[6,4,1,2,5,7,3] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 0

[6,4,1,2,7,3,5] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 0

[6,4,1,2,7,5,3] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 0

[6,4,1,3,2,5,7] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1] => 1

[6,4,1,3,2,7,5] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1] => 1

[6,4,1,3,5,2,7] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1] => 1

[6,4,1,3,5,7,2] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1] => 1

[6,4,1,3,7,2,5] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1] => 1

[6,4,1,3,7,5,2] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1] => 1

[6,4,1,5,2,3,7] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 0

[6,4,1,5,2,7,3] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 0

[6,4,1,5,3,2,7] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1] => 1

[6,4,1,5,3,7,2] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1] => 1

[6,4,1,5,7,2,3] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 0

[6,4,1,5,7,3,2] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1] => 1

[6,4,1,7,2,3,5] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 0

[6,4,1,7,2,5,3] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 0

[6,4,1,7,3,2,5] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1] => 1

[6,4,1,7,3,5,2] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1] => 1

[6,4,1,7,5,2,3] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 0

[6,4,1,7,5,3,2] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1] => 1

[6,4,2,1,3,5,7] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 0

[6,4,2,1,3,7,5] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 0

[6,4,2,1,5,3,7] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 0

[6,4,2,1,5,7,3] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 0

[6,4,2,1,7,3,5] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 0

[6,4,2,1,7,5,3] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 0

[6,4,2,3,1,5,7] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 0

[6,4,2,3,1,7,5] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 0

[6,4,2,3,5,1,7] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 0

[6,4,2,3,5,7,1] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 0

[6,4,2,3,7,1,5] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 0

[6,4,2,3,7,5,1] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 0

[6,4,2,5,1,3,7] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 0

[6,4,2,5,1,7,3] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 0

[6,4,2,5,3,1,7] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 0

[6,4,2,5,3,7,1] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 0

[6,4,2,5,7,1,3] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 0

[6,4,2,5,7,3,1] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 0

[6,4,2,7,1,3,5] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 0

[6,4,2,7,1,5,3] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 0

[6,4,2,7,3,1,5] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 0

[6,4,2,7,3,5,1] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 0

[6,4,2,7,5,1,3] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 0

[6,4,2,7,5,3,1] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 0

[6,4,3,1,2,5,7] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2] => 1

[6,4,3,1,2,7,5] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2] => 1

[6,4,3,1,5,2,7] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2] => 1

[6,4,3,1,5,7,2] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2] => 1

[6,4,3,1,7,2,5] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2] => 1

[6,4,3,1,7,5,2] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2] => 1

[6,4,3,2,1,5,7] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2,1] => 2

[6,4,3,2,1,7,5] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2,1] => 2

[6,4,3,2,5,1,7] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2,1] => 2

[6,4,3,2,5,7,1] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2,1] => 2

[6,4,3,2,7,1,5] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2,1] => 2

[6,4,3,2,7,5,1] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2,1] => 2

[6,4,3,5,1,2,7] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2] => 1

[6,4,3,5,1,7,2] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2] => 1

[6,4,3,5,2,1,7] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2,1] => 2

[6,4,3,5,2,7,1] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2,1] => 2

[6,4,3,5,7,1,2] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2] => 1

[6,4,3,5,7,2,1] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2,1] => 2

[6,4,3,7,1,2,5] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2] => 1

[6,4,3,7,1,5,2] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2] => 1

[6,4,3,7,2,1,5] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2,1] => 2

[6,4,3,7,2,5,1] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2,1] => 2

[6,4,3,7,5,1,2] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2] => 1

[6,4,3,7,5,2,1] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2,1] => 2

[6,4,5,1,2,3,7] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 0

[6,4,5,1,2,7,3] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 0

[6,4,5,1,3,2,7] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1] => 1

[6,4,5,1,3,7,2] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1] => 1

[6,4,5,1,7,2,3] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 0

[6,4,5,1,7,3,2] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1] => 1

[6,4,5,2,1,3,7] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 0

[6,4,5,2,1,7,3] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 0

[6,4,5,2,3,1,7] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 0

[6,4,5,2,3,7,1] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 0

[6,4,5,2,7,1,3] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 0

[6,4,5,2,7,3,1] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 0

[6,4,5,3,1,2,7] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2] => 1

[6,4,5,3,1,7,2] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2] => 1

[6,4,5,3,2,1,7] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2,1] => 2

[6,4,5,3,2,7,1] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2,1] => 2

[6,4,5,3,7,1,2] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2] => 1

[6,4,5,3,7,2,1] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2,1] => 2

[6,4,5,7,1,2,3] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 0

[6,4,5,7,1,3,2] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1] => 1

[6,4,5,7,2,1,3] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 0

[6,4,5,7,2,3,1] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 0

[6,4,5,7,3,1,2] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2] => 1

[6,4,5,7,3,2,1] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2,1] => 2

[6,4,7,1,2,3,5] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 0

[6,4,7,1,2,5,3] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 0

[6,4,7,1,3,2,5] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1] => 1

[6,4,7,1,3,5,2] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1] => 1

[6,4,7,1,5,2,3] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 0

[6,4,7,1,5,3,2] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1] => 1

[6,4,7,2,1,3,5] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 0

[6,4,7,2,1,5,3] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 0

[6,4,7,2,3,1,5] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 0

[6,4,7,2,3,5,1] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 0

[6,4,7,2,5,1,3] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 0

[6,4,7,2,5,3,1] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 0

[6,4,7,3,1,2,5] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2] => 1

[6,4,7,3,1,5,2] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2] => 1

[6,4,7,3,2,1,5] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2,1] => 2

[6,4,7,3,2,5,1] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2,1] => 2

[6,4,7,3,5,1,2] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2] => 1

[6,4,7,3,5,2,1] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2,1] => 2

[6,4,7,5,1,2,3] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 0

[6,4,7,5,1,3,2] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1] => 1

[6,4,7,5,2,1,3] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 0

[6,4,7,5,2,3,1] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 0

[6,4,7,5,3,1,2] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2] => 1

[6,4,7,5,3,2,1] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2,1] => 2

[6,5,1,2,3,4,7] => [[[.,[.,[.,[.,.]]]],.],[.,.]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [5,5,4] => 1

[6,5,1,2,3,7,4] => [[[.,[.,[.,[.,.]]]],.],[.,.]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [5,5,4] => 1

[6,5,1,2,4,3,7] => [[[.,[.,[[.,.],.]]],.],[.,.]] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1] => 2

[6,5,1,2,4,7,3] => [[[.,[.,[[.,.],.]]],.],[.,.]] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1] => 2

[6,5,1,2,7,3,4] => [[[.,[.,[.,[.,.]]]],.],[.,.]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [5,5,4] => 1

[6,5,1,2,7,4,3] => [[[.,[.,[[.,.],.]]],.],[.,.]] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1] => 2

[6,5,1,3,2,4,7] => [[[.,[[.,.],[.,.]]],.],[.,.]] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1,1] => 1

[6,5,1,3,2,7,4] => [[[.,[[.,.],[.,.]]],.],[.,.]] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1,1] => 1

[6,5,1,3,4,2,7] => [[[.,[[.,.],[.,.]]],.],[.,.]] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1,1] => 1

[6,5,1,3,4,7,2] => [[[.,[[.,.],[.,.]]],.],[.,.]] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1,1] => 1

[6,5,1,3,7,2,4] => [[[.,[[.,.],[.,.]]],.],[.,.]] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1,1] => 1

[6,5,1,3,7,4,2] => [[[.,[[.,.],[.,.]]],.],[.,.]] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1,1] => 1

[6,5,1,4,2,3,7] => [[[.,[[.,[.,.]],.]],.],[.,.]] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [5,5,4,2] => 2

[6,5,1,4,2,7,3] => [[[.,[[.,[.,.]],.]],.],[.,.]] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [5,5,4,2] => 2

[6,5,1,4,3,2,7] => [[[.,[[[.,.],.],.]],.],[.,.]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [5,5,4,2,1] => 3

[6,5,1,4,3,7,2] => [[[.,[[[.,.],.],.]],.],[.,.]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [5,5,4,2,1] => 3

[6,5,1,4,7,2,3] => [[[.,[[.,[.,.]],.]],.],[.,.]] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [5,5,4,2] => 2

[6,5,1,4,7,3,2] => [[[.,[[[.,.],.],.]],.],[.,.]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [5,5,4,2,1] => 3

[6,5,1,7,2,3,4] => [[[.,[.,[.,[.,.]]]],.],[.,.]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [5,5,4] => 1

[6,5,1,7,2,4,3] => [[[.,[.,[[.,.],.]]],.],[.,.]] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1] => 2

[6,5,1,7,3,2,4] => [[[.,[[.,.],[.,.]]],.],[.,.]] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1,1] => 1

[6,5,1,7,3,4,2] => [[[.,[[.,.],[.,.]]],.],[.,.]] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1,1] => 1

[6,5,1,7,4,2,3] => [[[.,[[.,[.,.]],.]],.],[.,.]] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [5,5,4,2] => 2

[6,5,1,7,4,3,2] => [[[.,[[[.,.],.],.]],.],[.,.]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [5,5,4,2,1] => 3

[6,5,2,1,3,4,7] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1,1,1] => 1

[6,5,2,1,3,7,4] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1,1,1] => 1

[6,5,2,1,7,3,4] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1,1,1] => 1

[6,5,2,3,1,4,7] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1,1,1] => 1

[6,5,2,3,1,7,4] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1,1,1] => 1

[6,5,2,3,4,1,7] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1,1,1] => 1

[6,5,2,3,4,7,1] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1,1,1] => 1

[6,5,2,3,7,1,4] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1,1,1] => 1

[6,5,2,3,7,4,1] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1,1,1] => 1

[6,5,2,7,1,3,4] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1,1,1] => 1

[6,5,2,7,3,1,4] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1,1,1] => 1

[6,5,2,7,3,4,1] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1,1,1] => 1

[6,5,3,1,2,4,7] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2] => 1

[6,5,3,1,2,7,4] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2] => 1

[6,5,3,1,4,2,7] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2] => 1

[6,5,3,1,4,7,2] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2] => 1

[6,5,3,1,7,2,4] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2] => 1

[6,5,3,1,7,4,2] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2] => 1

[6,5,3,2,1,4,7] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2,1] => 2

[6,5,3,2,1,7,4] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2,1] => 2

[6,5,3,2,4,1,7] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2,1] => 2

[6,5,3,2,4,7,1] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2,1] => 2

[6,5,3,2,7,1,4] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2,1] => 2

[6,5,3,2,7,4,1] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2,1] => 2

[6,5,3,4,1,2,7] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2] => 1

[6,5,3,4,1,7,2] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2] => 1

[6,5,3,4,2,1,7] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2,1] => 2

[6,5,3,4,2,7,1] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2,1] => 2

[6,5,3,4,7,1,2] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2] => 1

[6,5,3,4,7,2,1] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2,1] => 2

[6,5,3,7,1,2,4] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2] => 1

[6,5,3,7,1,4,2] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2] => 1

[6,5,3,7,2,1,4] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2,1] => 2

[6,5,3,7,2,4,1] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2,1] => 2

[6,5,3,7,4,1,2] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2] => 1

[6,5,3,7,4,2,1] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2,1] => 2

[6,5,4,1,2,3,7] => [[[[.,[.,[.,.]]],.],.],[.,.]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3] => 2

[6,5,4,1,2,7,3] => [[[[.,[.,[.,.]]],.],.],[.,.]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3] => 2

[6,5,4,1,7,2,3] => [[[[.,[.,[.,.]]],.],.],[.,.]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3] => 2

[6,5,4,2,1,3,7] => [[[[[.,.],[.,.]],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3,1,1] => 2

[6,5,4,2,1,7,3] => [[[[[.,.],[.,.]],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3,1,1] => 2

[6,5,4,2,3,1,7] => [[[[[.,.],[.,.]],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3,1,1] => 2

[6,5,4,2,3,7,1] => [[[[[.,.],[.,.]],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3,1,1] => 2

[6,5,4,2,7,1,3] => [[[[[.,.],[.,.]],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3,1,1] => 2

[6,5,4,2,7,3,1] => [[[[[.,.],[.,.]],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3,1,1] => 2

[6,5,4,3,1,2,7] => [[[[[.,[.,.]],.],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [5,5,4,3,2] => 3

[6,5,4,3,1,7,2] => [[[[[.,[.,.]],.],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [5,5,4,3,2] => 3

[6,5,4,3,2,1,7] => [[[[[[.,.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [5,5,4,3,2,1] => 4

[6,5,4,3,2,7,1] => [[[[[[.,.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [5,5,4,3,2,1] => 4

[6,5,4,3,7,1,2] => [[[[[.,[.,.]],.],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [5,5,4,3,2] => 3

[6,5,4,3,7,2,1] => [[[[[[.,.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [5,5,4,3,2,1] => 4

[6,5,4,7,1,2,3] => [[[[.,[.,[.,.]]],.],.],[.,.]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3] => 2

[6,5,4,7,2,1,3] => [[[[[.,.],[.,.]],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3,1,1] => 2

[6,5,4,7,2,3,1] => [[[[[.,.],[.,.]],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3,1,1] => 2

[6,5,4,7,3,1,2] => [[[[[.,[.,.]],.],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [5,5,4,3,2] => 3

[6,5,4,7,3,2,1] => [[[[[[.,.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [5,5,4,3,2,1] => 4

[6,5,7,1,2,3,4] => [[[.,[.,[.,[.,.]]]],.],[.,.]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [5,5,4] => 1

[6,5,7,1,2,4,3] => [[[.,[.,[[.,.],.]]],.],[.,.]] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1] => 2

[6,5,7,1,3,2,4] => [[[.,[[.,.],[.,.]]],.],[.,.]] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1,1] => 1

[6,5,7,1,3,4,2] => [[[.,[[.,.],[.,.]]],.],[.,.]] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1,1] => 1

[6,5,7,1,4,2,3] => [[[.,[[.,[.,.]],.]],.],[.,.]] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [5,5,4,2] => 2

[6,5,7,1,4,3,2] => [[[.,[[[.,.],.],.]],.],[.,.]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [5,5,4,2,1] => 3

[6,5,7,2,1,3,4] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1,1,1] => 1

[6,5,7,2,3,1,4] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1,1,1] => 1

[6,5,7,2,3,4,1] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1,1,1] => 1

[6,5,7,3,1,2,4] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2] => 1

[6,5,7,3,1,4,2] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2] => 1

[6,5,7,3,2,1,4] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2,1] => 2

[6,5,7,3,2,4,1] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2,1] => 2

[6,5,7,3,4,1,2] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2] => 1

[6,5,7,3,4,2,1] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2,1] => 2

[6,5,7,4,1,2,3] => [[[[.,[.,[.,.]]],.],.],[.,.]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3] => 2

[6,5,7,4,2,1,3] => [[[[[.,.],[.,.]],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3,1,1] => 2

[6,5,7,4,2,3,1] => [[[[[.,.],[.,.]],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3,1,1] => 2

[6,5,7,4,3,1,2] => [[[[[.,[.,.]],.],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [5,5,4,3,2] => 3

[6,5,7,4,3,2,1] => [[[[[[.,.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [5,5,4,3,2,1] => 4

[6,7,1,2,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => 0

[6,7,1,2,3,5,4] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,5,1] => 1

[6,7,1,2,4,3,5] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1] => 0

[6,7,1,2,4,5,3] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1] => 0

[6,7,1,2,5,3,4] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,5,2] => 1

[6,7,1,2,5,4,3] => [[.,[.,[[[.,.],.],.]]],[.,.]] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1] => 2

[6,7,1,3,2,4,5] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1] => 0

[6,7,1,3,2,5,4] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1,1] => 1

[6,7,1,3,4,2,5] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1] => 0

[6,7,1,3,4,5,2] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1] => 0

[6,7,1,3,5,2,4] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1,1] => 1

[6,7,1,3,5,4,2] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1,1] => 1

[6,7,1,4,2,3,5] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2] => 0

[6,7,1,4,2,5,3] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2] => 0

[6,7,1,4,3,2,5] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1] => 1

[6,7,1,4,3,5,2] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1] => 1

[6,7,1,4,5,2,3] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2] => 0

[6,7,1,4,5,3,2] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1] => 1

[6,7,1,5,2,3,4] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [5,5,3] => 1

[6,7,1,5,2,4,3] => [[.,[[.,[[.,.],.]],.]],[.,.]] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1] => 2

[6,7,1,5,3,2,4] => [[.,[[[.,.],[.,.]],.]],[.,.]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1,1] => 1

[6,7,1,5,3,4,2] => [[.,[[[.,.],[.,.]],.]],[.,.]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1,1] => 1

[6,7,1,5,4,2,3] => [[.,[[[.,[.,.]],.],.]],[.,.]] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2] => 2

[6,7,1,5,4,3,2] => [[.,[[[[.,.],.],.],.]],[.,.]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2,1] => 3

[6,7,2,1,3,4,5] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1,1] => 0

[6,7,2,1,3,5,4] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1,1,1] => 1

[6,7,2,1,4,3,5] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1,1] => 0

[6,7,2,1,4,5,3] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1,1] => 0

[6,7,2,1,5,3,4] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1,1,1] => 1

[6,7,2,1,5,4,3] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2,1,1] => 2

[6,7,2,3,1,4,5] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1,1] => 0

[6,7,2,3,1,5,4] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1,1,1] => 1

[6,7,2,3,4,1,5] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1,1] => 0

[6,7,2,3,4,5,1] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1,1] => 0

[6,7,2,3,5,1,4] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1,1,1] => 1

[6,7,2,3,5,4,1] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1,1,1] => 1

[6,7,2,4,1,3,5] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1,1] => 0

[6,7,2,4,1,5,3] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1,1] => 0

[6,7,2,4,3,1,5] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1,1] => 0

[6,7,2,4,3,5,1] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1,1] => 0

[6,7,2,4,5,1,3] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1,1] => 0

[6,7,2,4,5,3,1] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1,1] => 0

[6,7,2,5,1,3,4] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1,1,1] => 1

[6,7,2,5,1,4,3] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2,1,1] => 2

[6,7,2,5,3,1,4] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1,1,1] => 1

[6,7,2,5,3,4,1] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1,1,1] => 1

[6,7,2,5,4,1,3] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2,1,1] => 2

[6,7,2,5,4,3,1] => [[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2,1,1] => 2

[6,7,3,1,2,4,5] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 0

[6,7,3,1,2,5,4] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [5,5,3,2,2] => 1

[6,7,3,1,4,2,5] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 0

[6,7,3,1,4,5,2] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 0

[6,7,3,1,5,2,4] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [5,5,3,2,2] => 1

[6,7,3,1,5,4,2] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [5,5,3,2,2] => 1

[6,7,3,2,1,4,5] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2,1] => 1

[6,7,3,2,4,1,5] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2,1] => 1

[6,7,3,2,4,5,1] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2,1] => 1

[6,7,3,4,1,2,5] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 0

[6,7,3,4,1,5,2] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 0

[6,7,3,4,2,1,5] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2,1] => 1

[6,7,3,4,2,5,1] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2,1] => 1

[6,7,3,4,5,1,2] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 0

[6,7,3,4,5,2,1] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2,1] => 1

[6,7,3,5,1,2,4] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [5,5,3,2,2] => 1

[6,7,3,5,1,4,2] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [5,5,3,2,2] => 1

[6,7,3,5,4,1,2] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [5,5,3,2,2] => 1

[6,7,4,1,2,3,5] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 0

[6,7,4,1,2,5,3] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 0

[6,7,4,1,3,2,5] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1] => 1

[6,7,4,1,3,5,2] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1] => 1

[6,7,4,1,5,2,3] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 0

[6,7,4,1,5,3,2] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1] => 1

[6,7,4,2,1,3,5] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 0

[6,7,4,2,1,5,3] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 0

[6,7,4,2,3,1,5] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 0

[6,7,4,2,3,5,1] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 0

[6,7,4,2,5,1,3] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 0

[6,7,4,2,5,3,1] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 0

[6,7,4,3,1,2,5] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2] => 1

[6,7,4,3,1,5,2] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2] => 1

[6,7,4,3,2,1,5] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2,1] => 2

[6,7,4,3,2,5,1] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2,1] => 2

[6,7,4,3,5,1,2] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2] => 1

[6,7,4,3,5,2,1] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2,1] => 2

[6,7,4,5,1,2,3] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 0

[6,7,4,5,1,3,2] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1] => 1

[6,7,4,5,2,1,3] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 0

[6,7,4,5,2,3,1] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 0

[6,7,4,5,3,1,2] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2] => 1

[6,7,4,5,3,2,1] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2,1] => 2

[6,7,5,1,2,3,4] => [[[.,[.,[.,[.,.]]]],.],[.,.]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [5,5,4] => 1

[6,7,5,1,2,4,3] => [[[.,[.,[[.,.],.]]],.],[.,.]] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1] => 2

[6,7,5,1,3,2,4] => [[[.,[[.,.],[.,.]]],.],[.,.]] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1,1] => 1

[6,7,5,1,3,4,2] => [[[.,[[.,.],[.,.]]],.],[.,.]] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1,1] => 1

[6,7,5,1,4,2,3] => [[[.,[[.,[.,.]],.]],.],[.,.]] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [5,5,4,2] => 2

[6,7,5,1,4,3,2] => [[[.,[[[.,.],.],.]],.],[.,.]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [5,5,4,2,1] => 3

[6,7,5,2,1,3,4] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1,1,1] => 1

[6,7,5,2,3,1,4] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1,1,1] => 1

[6,7,5,2,3,4,1] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1,1,1] => 1

[6,7,5,3,1,2,4] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2] => 1

[6,7,5,3,1,4,2] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2] => 1

[6,7,5,3,2,1,4] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2,1] => 2

[6,7,5,3,2,4,1] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2,1] => 2

[6,7,5,3,4,1,2] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2] => 1

[6,7,5,3,4,2,1] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2,1] => 2

[6,7,5,4,1,2,3] => [[[[.,[.,[.,.]]],.],.],[.,.]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3] => 2

[6,7,5,4,2,1,3] => [[[[[.,.],[.,.]],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3,1,1] => 2

[6,7,5,4,2,3,1] => [[[[[.,.],[.,.]],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3,1,1] => 2

[6,7,5,4,3,1,2] => [[[[[.,[.,.]],.],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [5,5,4,3,2] => 3

[6,7,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [5,5,4,3,2,1] => 4

[7,1,2,3,4,5,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],.] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 1

[7,1,2,3,4,6,5] => [[.,[.,[.,[.,[[.,.],.]]]]],.] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1] => 2

[7,1,2,3,5,4,6] => [[.,[.,[.,[[.,.],[.,.]]]]],.] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,1,1] => 1

[7,1,2,3,5,6,4] => [[.,[.,[.,[[.,.],[.,.]]]]],.] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,1,1] => 1

[7,1,2,3,6,4,5] => [[.,[.,[.,[[.,[.,.]],.]]]],.] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,2] => 2

[7,1,2,3,6,5,4] => [[.,[.,[.,[[[.,.],.],.]]]],.] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,2,1] => 3

[7,1,2,4,3,5,6] => [[.,[.,[[.,.],[.,[.,.]]]]],.] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1] => 1

[7,1,2,4,3,6,5] => [[.,[.,[[.,.],[[.,.],.]]]],.] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1] => 2

[7,1,2,4,5,3,6] => [[.,[.,[[.,.],[.,[.,.]]]]],.] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1] => 1

[7,1,2,4,5,6,3] => [[.,[.,[[.,.],[.,[.,.]]]]],.] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1] => 1

[7,1,2,4,6,3,5] => [[.,[.,[[.,.],[[.,.],.]]]],.] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1] => 2

[7,1,2,4,6,5,3] => [[.,[.,[[.,.],[[.,.],.]]]],.] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1] => 2

[7,1,2,5,3,4,6] => [[.,[.,[[.,[.,.]],[.,.]]]],.] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,2,2] => 1

[7,1,2,5,3,6,4] => [[.,[.,[[.,[.,.]],[.,.]]]],.] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,2,2] => 1

[7,1,2,5,4,3,6] => [[.,[.,[[[.,.],.],[.,.]]]],.] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1] => 2

[7,1,2,5,4,6,3] => [[.,[.,[[[.,.],.],[.,.]]]],.] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1] => 2

[7,1,2,5,6,3,4] => [[.,[.,[[.,[.,.]],[.,.]]]],.] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,2,2] => 1

[7,1,2,5,6,4,3] => [[.,[.,[[[.,.],.],[.,.]]]],.] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1] => 2

[7,1,2,6,3,4,5] => [[.,[.,[[.,[.,[.,.]]],.]]],.] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,3] => 2

[7,1,2,6,3,5,4] => [[.,[.,[[.,[[.,.],.]],.]]],.] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,1] => 3

[7,1,2,6,4,3,5] => [[.,[.,[[[.,.],[.,.]],.]]],.] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1] => 2

[7,1,2,6,4,5,3] => [[.,[.,[[[.,.],[.,.]],.]]],.] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1] => 2

[7,1,2,6,5,3,4] => [[.,[.,[[[.,[.,.]],.],.]]],.] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [6,3,2] => 3

[7,1,2,6,5,4,3] => [[.,[.,[[[[.,.],.],.],.]]],.] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1] => 4

[7,1,3,2,4,5,6] => [[.,[[.,.],[.,[.,[.,.]]]]],.] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1,1] => 1

[7,1,3,2,4,6,5] => [[.,[[.,.],[.,[[.,.],.]]]],.] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1,1] => 2

[7,1,3,2,5,4,6] => [[.,[[.,.],[[.,.],[.,.]]]],.] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1,1] => 1

[7,1,3,2,5,6,4] => [[.,[[.,.],[[.,.],[.,.]]]],.] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1,1] => 1

[7,1,3,2,6,4,5] => [[.,[[.,.],[[.,[.,.]],.]]],.] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1,1] => 2

[7,1,3,2,6,5,4] => [[.,[[.,.],[[[.,.],.],.]]],.] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,1] => 3

[7,1,3,4,2,5,6] => [[.,[[.,.],[.,[.,[.,.]]]]],.] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1,1] => 1

[7,1,3,4,2,6,5] => [[.,[[.,.],[.,[[.,.],.]]]],.] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1,1] => 2

[7,1,3,4,5,2,6] => [[.,[[.,.],[.,[.,[.,.]]]]],.] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1,1] => 1

[7,1,3,4,5,6,2] => [[.,[[.,.],[.,[.,[.,.]]]]],.] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1,1] => 1

[7,1,3,4,6,2,5] => [[.,[[.,.],[.,[[.,.],.]]]],.] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1,1] => 2

[7,1,3,4,6,5,2] => [[.,[[.,.],[.,[[.,.],.]]]],.] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1,1] => 2

[7,1,3,5,2,4,6] => [[.,[[.,.],[[.,.],[.,.]]]],.] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1,1] => 1

[7,1,3,5,2,6,4] => [[.,[[.,.],[[.,.],[.,.]]]],.] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1,1] => 1

[7,1,3,5,4,2,6] => [[.,[[.,.],[[.,.],[.,.]]]],.] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1,1] => 1

[7,1,3,5,4,6,2] => [[.,[[.,.],[[.,.],[.,.]]]],.] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1,1] => 1

[7,1,3,5,6,2,4] => [[.,[[.,.],[[.,.],[.,.]]]],.] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1,1] => 1

[7,1,3,5,6,4,2] => [[.,[[.,.],[[.,.],[.,.]]]],.] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1,1] => 1

[7,1,3,6,2,4,5] => [[.,[[.,.],[[.,[.,.]],.]]],.] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1,1] => 2

[7,1,3,6,2,5,4] => [[.,[[.,.],[[[.,.],.],.]]],.] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,1] => 3

[7,1,3,6,4,2,5] => [[.,[[.,.],[[.,[.,.]],.]]],.] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1,1] => 2

[7,1,3,6,4,5,2] => [[.,[[.,.],[[.,[.,.]],.]]],.] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1,1] => 2

[7,1,3,6,5,2,4] => [[.,[[.,.],[[[.,.],.],.]]],.] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,1] => 3

[7,1,3,6,5,4,2] => [[.,[[.,.],[[[.,.],.],.]]],.] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,1] => 3

[7,1,4,2,3,5,6] => [[.,[[.,[.,.]],[.,[.,.]]]],.] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2] => 1

[7,1,4,2,3,6,5] => [[.,[[.,[.,.]],[[.,.],.]]],.] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [6,3,2,2] => 2

[7,1,4,2,5,3,6] => [[.,[[.,[.,.]],[.,[.,.]]]],.] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2] => 1

[7,1,4,2,5,6,3] => [[.,[[.,[.,.]],[.,[.,.]]]],.] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2] => 1

[7,1,4,2,6,3,5] => [[.,[[.,[.,.]],[[.,.],.]]],.] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [6,3,2,2] => 2

[7,1,4,2,6,5,3] => [[.,[[.,[.,.]],[[.,.],.]]],.] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [6,3,2,2] => 2

[7,1,4,3,2,5,6] => [[.,[[[.,.],.],[.,[.,.]]]],.] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2,1] => 2

[7,1,4,3,2,6,5] => [[.,[[[.,.],.],[[.,.],.]]],.] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,2,1] => 3

[7,1,4,3,5,2,6] => [[.,[[[.,.],.],[.,[.,.]]]],.] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2,1] => 2

[7,1,4,3,5,6,2] => [[.,[[[.,.],.],[.,[.,.]]]],.] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2,1] => 2

[7,1,4,3,6,2,5] => [[.,[[[.,.],.],[[.,.],.]]],.] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,2,1] => 3

[7,1,4,3,6,5,2] => [[.,[[[.,.],.],[[.,.],.]]],.] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,2,1] => 3

[7,1,4,5,2,3,6] => [[.,[[.,[.,.]],[.,[.,.]]]],.] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2] => 1

[7,1,4,5,2,6,3] => [[.,[[.,[.,.]],[.,[.,.]]]],.] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2] => 1

[7,1,4,5,3,2,6] => [[.,[[[.,.],.],[.,[.,.]]]],.] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2,1] => 2

[7,1,4,5,3,6,2] => [[.,[[[.,.],.],[.,[.,.]]]],.] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2,1] => 2

[7,1,4,5,6,2,3] => [[.,[[.,[.,.]],[.,[.,.]]]],.] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2] => 1

[7,1,4,5,6,3,2] => [[.,[[[.,.],.],[.,[.,.]]]],.] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2,1] => 2

[7,1,4,6,2,3,5] => [[.,[[.,[.,.]],[[.,.],.]]],.] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [6,3,2,2] => 2

[7,1,4,6,2,5,3] => [[.,[[.,[.,.]],[[.,.],.]]],.] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [6,3,2,2] => 2

[7,1,4,6,3,2,5] => [[.,[[[.,.],.],[[.,.],.]]],.] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,2,1] => 3

[7,1,4,6,3,5,2] => [[.,[[[.,.],.],[[.,.],.]]],.] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,2,1] => 3

[7,1,4,6,5,2,3] => [[.,[[.,[.,.]],[[.,.],.]]],.] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [6,3,2,2] => 2

[7,1,4,6,5,3,2] => [[.,[[[.,.],.],[[.,.],.]]],.] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,2,1] => 3

[7,1,5,2,3,4,6] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [6,3,3] => 1

[7,1,5,2,3,6,4] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [6,3,3] => 1

[7,1,5,2,4,3,6] => [[.,[[.,[[.,.],.]],[.,.]]],.] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [6,3,3,1] => 2

[7,1,5,2,4,6,3] => [[.,[[.,[[.,.],.]],[.,.]]],.] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [6,3,3,1] => 2

[7,1,5,2,6,3,4] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [6,3,3] => 1

[7,1,5,2,6,4,3] => [[.,[[.,[[.,.],.]],[.,.]]],.] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [6,3,3,1] => 2

[7,1,5,3,2,4,6] => [[.,[[[.,.],[.,.]],[.,.]]],.] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [6,3,3,1,1] => 1

[7,1,5,3,2,6,4] => [[.,[[[.,.],[.,.]],[.,.]]],.] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [6,3,3,1,1] => 1

[7,1,5,3,4,2,6] => [[.,[[[.,.],[.,.]],[.,.]]],.] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [6,3,3,1,1] => 1

[7,1,5,3,4,6,2] => [[.,[[[.,.],[.,.]],[.,.]]],.] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [6,3,3,1,1] => 1

[7,1,5,3,6,2,4] => [[.,[[[.,.],[.,.]],[.,.]]],.] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [6,3,3,1,1] => 1

[7,1,5,3,6,4,2] => [[.,[[[.,.],[.,.]],[.,.]]],.] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [6,3,3,1,1] => 1

[7,1,5,4,2,3,6] => [[.,[[[.,[.,.]],.],[.,.]]],.] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [6,3,3,2] => 2

[7,1,5,4,2,6,3] => [[.,[[[.,[.,.]],.],[.,.]]],.] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [6,3,3,2] => 2

[7,1,5,4,3,2,6] => [[.,[[[[.,.],.],.],[.,.]]],.] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [6,3,3,2,1] => 3

[7,1,5,4,3,6,2] => [[.,[[[[.,.],.],.],[.,.]]],.] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [6,3,3,2,1] => 3

[7,1,5,4,6,2,3] => [[.,[[[.,[.,.]],.],[.,.]]],.] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [6,3,3,2] => 2

[7,1,5,4,6,3,2] => [[.,[[[[.,.],.],.],[.,.]]],.] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [6,3,3,2,1] => 3

[7,1,5,6,2,3,4] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [6,3,3] => 1

[7,1,5,6,2,4,3] => [[.,[[.,[[.,.],.]],[.,.]]],.] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [6,3,3,1] => 2

[7,1,5,6,3,2,4] => [[.,[[[.,.],[.,.]],[.,.]]],.] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [6,3,3,1,1] => 1

[7,1,5,6,3,4,2] => [[.,[[[.,.],[.,.]],[.,.]]],.] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [6,3,3,1,1] => 1

[7,1,5,6,4,2,3] => [[.,[[[.,[.,.]],.],[.,.]]],.] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [6,3,3,2] => 2

[7,1,5,6,4,3,2] => [[.,[[[[.,.],.],.],[.,.]]],.] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [6,3,3,2,1] => 3

[7,1,6,2,3,4,5] => [[.,[[.,[.,[.,[.,.]]]],.]],.] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [6,4] => 2

[7,1,6,2,3,5,4] => [[.,[[.,[.,[[.,.],.]]],.]],.] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [6,4,1] => 3

[7,1,6,2,4,3,5] => [[.,[[.,[[.,.],[.,.]]],.]],.] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [6,4,1,1] => 2

[7,1,6,2,4,5,3] => [[.,[[.,[[.,.],[.,.]]],.]],.] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [6,4,1,1] => 2

[7,1,6,2,5,3,4] => [[.,[[.,[[.,[.,.]],.]],.]],.] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [6,4,2] => 3

[7,1,6,2,5,4,3] => [[.,[[.,[[[.,.],.],.]],.]],.] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1] => 4

[7,1,6,3,2,4,5] => [[.,[[[.,.],[.,[.,.]]],.]],.] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,1,1] => 2

[7,1,6,3,2,5,4] => [[.,[[[.,.],[[.,.],.]],.]],.] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,1] => 3

[7,1,6,3,4,2,5] => [[.,[[[.,.],[.,[.,.]]],.]],.] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,1,1] => 2

[7,1,6,3,4,5,2] => [[.,[[[.,.],[.,[.,.]]],.]],.] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,1,1] => 2

[7,1,6,3,5,2,4] => [[.,[[[.,.],[[.,.],.]],.]],.] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,1] => 3

[7,1,6,3,5,4,2] => [[.,[[[.,.],[[.,.],.]],.]],.] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,1] => 3

[7,1,6,4,2,3,5] => [[.,[[[.,[.,.]],[.,.]],.]],.] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [6,4,2,2] => 2

[7,1,6,4,2,5,3] => [[.,[[[.,[.,.]],[.,.]],.]],.] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [6,4,2,2] => 2

[7,1,6,4,3,2,5] => [[.,[[[[.,.],.],[.,.]],.]],.] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,2,1] => 3

[7,1,6,4,3,5,2] => [[.,[[[[.,.],.],[.,.]],.]],.] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,2,1] => 3

[7,1,6,4,5,2,3] => [[.,[[[.,[.,.]],[.,.]],.]],.] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [6,4,2,2] => 2

[7,1,6,4,5,3,2] => [[.,[[[[.,.],.],[.,.]],.]],.] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,2,1] => 3

[7,1,6,5,2,3,4] => [[.,[[[.,[.,[.,.]]],.],.]],.] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [6,4,3] => 3

[7,1,6,5,2,4,3] => [[.,[[[.,[[.,.],.]],.],.]],.] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1] => 4

[7,1,6,5,3,2,4] => [[.,[[[[.,.],[.,.]],.],.]],.] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,1] => 3

[7,1,6,5,3,4,2] => [[.,[[[[.,.],[.,.]],.],.]],.] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,1] => 3

[7,1,6,5,4,2,3] => [[.,[[[[.,[.,.]],.],.],.]],.] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2] => 4

[7,1,6,5,4,3,2] => [[.,[[[[[.,.],.],.],.],.]],.] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2,1] => 5

[7,2,1,3,4,5,6] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1,1,1] => 1

[7,2,1,3,4,6,5] => [[[.,.],[.,[.,[[.,.],.]]]],.] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1,1,1] => 2

[7,2,1,3,5,4,6] => [[[.,.],[.,[[.,.],[.,.]]]],.] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1,1,1] => 1

[7,2,1,3,5,6,4] => [[[.,.],[.,[[.,.],[.,.]]]],.] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1,1,1] => 1

[7,2,1,3,6,4,5] => [[[.,.],[.,[[.,[.,.]],.]]],.] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1,1,1] => 2

[7,2,1,3,6,5,4] => [[[.,.],[.,[[[.,.],.],.]]],.] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,1,1] => 3

[7,2,1,4,3,5,6] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2,1,1] => 1

[7,2,1,4,3,6,5] => [[[.,.],[[.,.],[[.,.],.]]],.] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,2,1,1] => 2

[7,2,1,4,5,3,6] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2,1,1] => 1

[7,2,1,4,5,6,3] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2,1,1] => 1

[7,2,1,4,6,3,5] => [[[.,.],[[.,.],[[.,.],.]]],.] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,2,1,1] => 2

[7,2,1,4,6,5,3] => [[[.,.],[[.,.],[[.,.],.]]],.] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,2,1,1] => 2

[7,2,1,5,3,4,6] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,3,1,1,1] => 1

[7,2,1,5,3,6,4] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,3,1,1,1] => 1

[7,2,1,5,4,3,6] => [[[.,.],[[[.,.],.],[.,.]]],.] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,3,2,1,1] => 2

[7,2,1,5,4,6,3] => [[[.,.],[[[.,.],.],[.,.]]],.] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,3,2,1,1] => 2

[7,2,1,5,6,3,4] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,3,1,1,1] => 1

[7,2,1,5,6,4,3] => [[[.,.],[[[.,.],.],[.,.]]],.] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,3,2,1,1] => 2

[7,2,1,6,3,4,5] => [[[.,.],[[.,[.,[.,.]]],.]],.] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,1,1,1] => 2

[7,2,1,6,3,5,4] => [[[.,.],[[.,[[.,.],.]],.]],.] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,1,1] => 3

[7,2,1,6,4,3,5] => [[[.,.],[[[.,.],[.,.]],.]],.] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,2,1,1] => 2

[7,2,1,6,4,5,3] => [[[.,.],[[[.,.],[.,.]],.]],.] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,2,1,1] => 2

[7,2,1,6,5,3,4] => [[[.,.],[[[.,[.,.]],.],.]],.] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,1,1] => 3

[7,2,1,6,5,4,3] => [[[.,.],[[[[.,.],.],.],.]],.] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2,1,1] => 4

[7,2,3,1,4,5,6] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1,1,1] => 1

[7,2,3,1,4,6,5] => [[[.,.],[.,[.,[[.,.],.]]]],.] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1,1,1] => 2

[7,2,3,1,5,4,6] => [[[.,.],[.,[[.,.],[.,.]]]],.] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1,1,1] => 1

[7,2,3,1,5,6,4] => [[[.,.],[.,[[.,.],[.,.]]]],.] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1,1,1] => 1

[7,2,3,1,6,4,5] => [[[.,.],[.,[[.,[.,.]],.]]],.] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1,1,1] => 2

[7,2,3,1,6,5,4] => [[[.,.],[.,[[[.,.],.],.]]],.] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,1,1] => 3

[7,2,3,4,1,5,6] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1,1,1] => 1

[7,2,3,4,1,6,5] => [[[.,.],[.,[.,[[.,.],.]]]],.] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1,1,1] => 2

[7,2,3,4,5,1,6] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1,1,1] => 1

[7,2,3,4,5,6,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1,1,1] => 1

[7,2,3,4,6,1,5] => [[[.,.],[.,[.,[[.,.],.]]]],.] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1,1,1] => 2

[7,2,3,4,6,5,1] => [[[.,.],[.,[.,[[.,.],.]]]],.] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1,1,1] => 2

[7,2,3,5,1,4,6] => [[[.,.],[.,[[.,.],[.,.]]]],.] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1,1,1] => 1

[7,2,3,5,1,6,4] => [[[.,.],[.,[[.,.],[.,.]]]],.] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1,1,1] => 1

[7,2,3,5,4,1,6] => [[[.,.],[.,[[.,.],[.,.]]]],.] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1,1,1] => 1

[7,2,3,5,4,6,1] => [[[.,.],[.,[[.,.],[.,.]]]],.] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1,1,1] => 1

[7,2,3,5,6,1,4] => [[[.,.],[.,[[.,.],[.,.]]]],.] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1,1,1] => 1

[7,2,3,5,6,4,1] => [[[.,.],[.,[[.,.],[.,.]]]],.] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1,1,1] => 1

[7,2,3,6,1,4,5] => [[[.,.],[.,[[.,[.,.]],.]]],.] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1,1,1] => 2

[7,2,3,6,1,5,4] => [[[.,.],[.,[[[.,.],.],.]]],.] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,1,1] => 3

[7,2,3,6,4,1,5] => [[[.,.],[.,[[.,[.,.]],.]]],.] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1,1,1] => 2

[7,2,3,6,4,5,1] => [[[.,.],[.,[[.,[.,.]],.]]],.] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1,1,1] => 2

[7,2,3,6,5,1,4] => [[[.,.],[.,[[[.,.],.],.]]],.] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,1,1] => 3

[7,2,3,6,5,4,1] => [[[.,.],[.,[[[.,.],.],.]]],.] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,1,1] => 3

[7,2,4,1,3,5,6] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2,1,1] => 1

[7,2,4,1,3,6,5] => [[[.,.],[[.,.],[[.,.],.]]],.] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,2,1,1] => 2

[7,2,4,1,5,3,6] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2,1,1] => 1

[7,2,4,1,5,6,3] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2,1,1] => 1

[7,2,4,1,6,3,5] => [[[.,.],[[.,.],[[.,.],.]]],.] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,2,1,1] => 2

[7,2,4,1,6,5,3] => [[[.,.],[[.,.],[[.,.],.]]],.] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,2,1,1] => 2

[7,2,4,3,1,5,6] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2,1,1] => 1

[7,2,4,3,1,6,5] => [[[.,.],[[.,.],[[.,.],.]]],.] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,2,1,1] => 2

[7,2,4,3,5,1,6] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2,1,1] => 1

[7,2,4,3,5,6,1] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2,1,1] => 1

[7,2,4,3,6,1,5] => [[[.,.],[[.,.],[[.,.],.]]],.] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,2,1,1] => 2

[7,2,4,3,6,5,1] => [[[.,.],[[.,.],[[.,.],.]]],.] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,2,1,1] => 2

[7,2,4,5,1,3,6] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2,1,1] => 1

[7,2,4,5,1,6,3] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2,1,1] => 1

[7,2,4,5,3,1,6] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2,1,1] => 1

[7,2,4,5,3,6,1] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2,1,1] => 1

[7,2,4,5,6,1,3] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2,1,1] => 1

[7,2,4,5,6,3,1] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2,1,1] => 1

[7,2,4,6,1,3,5] => [[[.,.],[[.,.],[[.,.],.]]],.] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,2,1,1] => 2

[7,2,4,6,1,5,3] => [[[.,.],[[.,.],[[.,.],.]]],.] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,2,1,1] => 2

[7,2,4,6,3,1,5] => [[[.,.],[[.,.],[[.,.],.]]],.] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,2,1,1] => 2

[7,2,4,6,3,5,1] => [[[.,.],[[.,.],[[.,.],.]]],.] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,2,1,1] => 2

[7,2,4,6,5,1,3] => [[[.,.],[[.,.],[[.,.],.]]],.] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,2,1,1] => 2

[7,2,4,6,5,3,1] => [[[.,.],[[.,.],[[.,.],.]]],.] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,2,1,1] => 2

[7,2,5,1,3,4,6] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,3,1,1,1] => 1

[7,2,5,1,3,6,4] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,3,1,1,1] => 1

[7,2,5,1,4,3,6] => [[[.,.],[[[.,.],.],[.,.]]],.] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,3,2,1,1] => 2

[7,2,5,1,4,6,3] => [[[.,.],[[[.,.],.],[.,.]]],.] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,3,2,1,1] => 2

[7,2,5,1,6,3,4] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,3,1,1,1] => 1

[7,2,5,1,6,4,3] => [[[.,.],[[[.,.],.],[.,.]]],.] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,3,2,1,1] => 2

[7,2,5,3,1,4,6] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,3,1,1,1] => 1

[7,2,5,3,1,6,4] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,3,1,1,1] => 1

[7,2,5,3,4,1,6] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,3,1,1,1] => 1

[7,2,5,3,4,6,1] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,3,1,1,1] => 1

[7,2,5,3,6,1,4] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,3,1,1,1] => 1

[7,2,5,3,6,4,1] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,3,1,1,1] => 1

[7,2,5,4,1,3,6] => [[[.,.],[[[.,.],.],[.,.]]],.] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,3,2,1,1] => 2

[7,2,5,4,1,6,3] => [[[.,.],[[[.,.],.],[.,.]]],.] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,3,2,1,1] => 2

[7,2,5,4,3,1,6] => [[[.,.],[[[.,.],.],[.,.]]],.] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,3,2,1,1] => 2

[7,2,5,4,3,6,1] => [[[.,.],[[[.,.],.],[.,.]]],.] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,3,2,1,1] => 2

[7,2,5,4,6,1,3] => [[[.,.],[[[.,.],.],[.,.]]],.] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,3,2,1,1] => 2

[7,2,5,4,6,3,1] => [[[.,.],[[[.,.],.],[.,.]]],.] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,3,2,1,1] => 2

[7,2,5,6,1,3,4] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,3,1,1,1] => 1

[7,2,5,6,1,4,3] => [[[.,.],[[[.,.],.],[.,.]]],.] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,3,2,1,1] => 2

[7,2,5,6,3,1,4] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,3,1,1,1] => 1

[7,2,5,6,3,4,1] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,3,1,1,1] => 1

[7,2,5,6,4,1,3] => [[[.,.],[[[.,.],.],[.,.]]],.] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,3,2,1,1] => 2

[7,2,5,6,4,3,1] => [[[.,.],[[[.,.],.],[.,.]]],.] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,3,2,1,1] => 2

[7,2,6,1,3,4,5] => [[[.,.],[[.,[.,[.,.]]],.]],.] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,1,1,1] => 2

[7,2,6,1,3,5,4] => [[[.,.],[[.,[[.,.],.]],.]],.] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,1,1] => 3

[7,2,6,1,4,3,5] => [[[.,.],[[[.,.],[.,.]],.]],.] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,2,1,1] => 2

[7,2,6,1,4,5,3] => [[[.,.],[[[.,.],[.,.]],.]],.] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,2,1,1] => 2

[7,2,6,1,5,3,4] => [[[.,.],[[[.,[.,.]],.],.]],.] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,1,1] => 3

[7,2,6,1,5,4,3] => [[[.,.],[[[[.,.],.],.],.]],.] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2,1,1] => 4

[7,2,6,3,1,4,5] => [[[.,.],[[.,[.,[.,.]]],.]],.] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,1,1,1] => 2

[7,2,6,3,1,5,4] => [[[.,.],[[.,[[.,.],.]],.]],.] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,1,1] => 3

[7,2,6,3,4,1,5] => [[[.,.],[[.,[.,[.,.]]],.]],.] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,1,1,1] => 2

[7,2,6,3,4,5,1] => [[[.,.],[[.,[.,[.,.]]],.]],.] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,1,1,1] => 2

[7,2,6,3,5,1,4] => [[[.,.],[[.,[[.,.],.]],.]],.] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,1,1] => 3

[7,2,6,3,5,4,1] => [[[.,.],[[.,[[.,.],.]],.]],.] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,1,1] => 3

[7,2,6,4,1,3,5] => [[[.,.],[[[.,.],[.,.]],.]],.] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,2,1,1] => 2

[7,2,6,4,1,5,3] => [[[.,.],[[[.,.],[.,.]],.]],.] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,2,1,1] => 2

[7,2,6,4,3,1,5] => [[[.,.],[[[.,.],[.,.]],.]],.] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,2,1,1] => 2

[7,2,6,4,3,5,1] => [[[.,.],[[[.,.],[.,.]],.]],.] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,2,1,1] => 2

[7,2,6,4,5,1,3] => [[[.,.],[[[.,.],[.,.]],.]],.] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,2,1,1] => 2

[7,2,6,4,5,3,1] => [[[.,.],[[[.,.],[.,.]],.]],.] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,2,1,1] => 2

[7,2,6,5,1,3,4] => [[[.,.],[[[.,[.,.]],.],.]],.] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,1,1] => 3

[7,2,6,5,1,4,3] => [[[.,.],[[[[.,.],.],.],.]],.] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2,1,1] => 4

[7,2,6,5,3,1,4] => [[[.,.],[[[.,[.,.]],.],.]],.] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,1,1] => 3

[7,2,6,5,3,4,1] => [[[.,.],[[[.,[.,.]],.],.]],.] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,1,1] => 3

[7,2,6,5,4,1,3] => [[[.,.],[[[[.,.],.],.],.]],.] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2,1,1] => 4

[7,2,6,5,4,3,1] => [[[.,.],[[[[.,.],.],.],.]],.] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2,1,1] => 4

[7,3,1,2,4,5,6] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2] => 1

[7,3,1,2,4,6,5] => [[[.,[.,.]],[.,[[.,.],.]]],.] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,2,2] => 2

[7,3,1,2,5,4,6] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [6,3,3,2,2] => 1

[7,3,1,2,5,6,4] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [6,3,3,2,2] => 1

[7,3,1,2,6,4,5] => [[[.,[.,.]],[[.,[.,.]],.]],.] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,2,2] => 2

[7,3,1,2,6,5,4] => [[[.,[.,.]],[[[.,.],.],.]],.] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,2] => 3

[7,3,1,4,2,5,6] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2] => 1

[7,3,1,4,2,6,5] => [[[.,[.,.]],[.,[[.,.],.]]],.] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,2,2] => 2

[7,3,1,4,5,2,6] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2] => 1

[7,3,1,4,5,6,2] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2] => 1

[7,3,1,4,6,2,5] => [[[.,[.,.]],[.,[[.,.],.]]],.] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,2,2] => 2

[7,3,1,4,6,5,2] => [[[.,[.,.]],[.,[[.,.],.]]],.] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,2,2] => 2

[7,3,1,5,2,4,6] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [6,3,3,2,2] => 1

[7,3,1,5,2,6,4] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [6,3,3,2,2] => 1

[7,3,1,5,4,2,6] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [6,3,3,2,2] => 1

[7,3,1,5,4,6,2] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [6,3,3,2,2] => 1

[7,3,1,5,6,2,4] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [6,3,3,2,2] => 1

[7,3,1,5,6,4,2] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [6,3,3,2,2] => 1

[7,3,1,6,2,4,5] => [[[.,[.,.]],[[.,[.,.]],.]],.] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,2,2] => 2

[7,3,1,6,2,5,4] => [[[.,[.,.]],[[[.,.],.],.]],.] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,2] => 3

[7,3,1,6,4,2,5] => [[[.,[.,.]],[[.,[.,.]],.]],.] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,2,2] => 2

[7,3,1,6,4,5,2] => [[[.,[.,.]],[[.,[.,.]],.]],.] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,2,2] => 2

[7,3,1,6,5,2,4] => [[[.,[.,.]],[[[.,.],.],.]],.] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,2] => 3

[7,3,1,6,5,4,2] => [[[.,[.,.]],[[[.,.],.],.]],.] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,2] => 3

[7,3,2,1,4,5,6] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2,1] => 2

[7,3,2,1,4,6,5] => [[[[.,.],.],[.,[[.,.],.]]],.] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,2,2,1] => 3

[7,3,2,1,5,4,6] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,3,2,2,1] => 2

[7,3,2,1,5,6,4] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,3,2,2,1] => 2

[7,3,2,1,6,4,5] => [[[[.,.],.],[[.,[.,.]],.]],.] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,2,2,1] => 3

[7,3,2,4,1,5,6] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2,1] => 2

[7,3,2,4,1,6,5] => [[[[.,.],.],[.,[[.,.],.]]],.] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,2,2,1] => 3

[7,3,2,4,5,1,6] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2,1] => 2

[7,3,2,4,5,6,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2,1] => 2

[7,3,2,4,6,1,5] => [[[[.,.],.],[.,[[.,.],.]]],.] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,2,2,1] => 3

[7,3,2,4,6,5,1] => [[[[.,.],.],[.,[[.,.],.]]],.] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,2,2,1] => 3

[7,3,2,5,1,4,6] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,3,2,2,1] => 2

[7,3,2,5,1,6,4] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,3,2,2,1] => 2

[7,3,2,5,4,1,6] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,3,2,2,1] => 2

[7,3,2,5,4,6,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,3,2,2,1] => 2

[7,3,2,5,6,1,4] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,3,2,2,1] => 2

[7,3,2,5,6,4,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,3,2,2,1] => 2

[7,3,2,6,1,4,5] => [[[[.,.],.],[[.,[.,.]],.]],.] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,2,2,1] => 3

[7,3,2,6,4,1,5] => [[[[.,.],.],[[.,[.,.]],.]],.] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,2,2,1] => 3

[7,3,2,6,4,5,1] => [[[[.,.],.],[[.,[.,.]],.]],.] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,2,2,1] => 3

[7,3,4,1,2,5,6] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2] => 1

[7,3,4,1,2,6,5] => [[[.,[.,.]],[.,[[.,.],.]]],.] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,2,2] => 2

[7,3,4,1,5,2,6] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2] => 1

[7,3,4,1,5,6,2] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2] => 1

[7,3,4,1,6,2,5] => [[[.,[.,.]],[.,[[.,.],.]]],.] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,2,2] => 2

[7,3,4,1,6,5,2] => [[[.,[.,.]],[.,[[.,.],.]]],.] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,2,2] => 2

[7,3,4,2,1,5,6] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2,1] => 2

[7,3,4,2,1,6,5] => [[[[.,.],.],[.,[[.,.],.]]],.] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,2,2,1] => 3

[7,3,4,2,5,1,6] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2,1] => 2

[7,3,4,2,5,6,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2,1] => 2

[7,3,4,2,6,1,5] => [[[[.,.],.],[.,[[.,.],.]]],.] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,2,2,1] => 3

[7,3,4,2,6,5,1] => [[[[.,.],.],[.,[[.,.],.]]],.] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,2,2,1] => 3

[7,3,4,5,1,2,6] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2] => 1

[7,3,4,5,1,6,2] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2] => 1

[7,3,4,5,2,1,6] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2,1] => 2

[7,3,4,5,2,6,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2,1] => 2

[7,3,4,5,6,1,2] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2] => 1

[7,3,4,5,6,2,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2,1] => 2

[7,3,4,6,1,2,5] => [[[.,[.,.]],[.,[[.,.],.]]],.] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,2,2] => 2

[7,3,4,6,1,5,2] => [[[.,[.,.]],[.,[[.,.],.]]],.] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,2,2] => 2

[7,3,4,6,2,1,5] => [[[[.,.],.],[.,[[.,.],.]]],.] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,2,2,1] => 3

[7,3,4,6,2,5,1] => [[[[.,.],.],[.,[[.,.],.]]],.] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,2,2,1] => 3

[7,3,4,6,5,1,2] => [[[.,[.,.]],[.,[[.,.],.]]],.] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,2,2] => 2

[7,3,4,6,5,2,1] => [[[[.,.],.],[.,[[.,.],.]]],.] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,2,2,1] => 3

[7,3,5,1,2,4,6] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [6,3,3,2,2] => 1

[7,3,5,1,2,6,4] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [6,3,3,2,2] => 1

[7,3,5,1,4,2,6] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [6,3,3,2,2] => 1

[7,3,5,1,4,6,2] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [6,3,3,2,2] => 1

[7,3,5,1,6,2,4] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [6,3,3,2,2] => 1

[7,3,5,1,6,4,2] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [6,3,3,2,2] => 1

[7,3,5,2,1,4,6] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,3,2,2,1] => 2

[7,3,5,2,1,6,4] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,3,2,2,1] => 2

[7,3,5,2,4,1,6] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,3,2,2,1] => 2

[7,3,5,2,4,6,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,3,2,2,1] => 2

[7,3,5,2,6,1,4] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,3,2,2,1] => 2

[7,3,5,2,6,4,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,3,2,2,1] => 2

[7,3,5,4,1,2,6] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [6,3,3,2,2] => 1

[7,3,5,4,1,6,2] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [6,3,3,2,2] => 1

[7,3,5,4,2,1,6] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,3,2,2,1] => 2

[7,3,5,4,2,6,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,3,2,2,1] => 2

[7,3,5,4,6,1,2] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [6,3,3,2,2] => 1

[7,3,5,4,6,2,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,3,2,2,1] => 2

[7,3,5,6,1,2,4] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [6,3,3,2,2] => 1

[7,3,5,6,1,4,2] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [6,3,3,2,2] => 1

[7,3,5,6,2,1,4] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,3,2,2,1] => 2

[7,3,5,6,2,4,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,3,2,2,1] => 2

[7,3,5,6,4,1,2] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [6,3,3,2,2] => 1

[7,3,5,6,4,2,1] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,3,2,2,1] => 2

[7,3,6,1,2,4,5] => [[[.,[.,.]],[[.,[.,.]],.]],.] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,2,2] => 2

[7,3,6,1,2,5,4] => [[[.,[.,.]],[[[.,.],.],.]],.] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,2] => 3

[7,3,6,1,4,2,5] => [[[.,[.,.]],[[.,[.,.]],.]],.] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,2,2] => 2

[7,3,6,1,4,5,2] => [[[.,[.,.]],[[.,[.,.]],.]],.] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,2,2] => 2

[7,3,6,1,5,2,4] => [[[.,[.,.]],[[[.,.],.],.]],.] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,2] => 3

[7,3,6,1,5,4,2] => [[[.,[.,.]],[[[.,.],.],.]],.] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,2] => 3

[7,3,6,2,1,4,5] => [[[[.,.],.],[[.,[.,.]],.]],.] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,2,2,1] => 3

[7,3,6,2,4,1,5] => [[[[.,.],.],[[.,[.,.]],.]],.] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,2,2,1] => 3

[7,3,6,2,4,5,1] => [[[[.,.],.],[[.,[.,.]],.]],.] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,2,2,1] => 3

[7,3,6,4,1,2,5] => [[[.,[.,.]],[[.,[.,.]],.]],.] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,2,2] => 2

[7,3,6,4,1,5,2] => [[[.,[.,.]],[[.,[.,.]],.]],.] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,2,2] => 2

[7,3,6,4,2,1,5] => [[[[.,.],.],[[.,[.,.]],.]],.] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,2,2,1] => 3

[7,3,6,4,2,5,1] => [[[[.,.],.],[[.,[.,.]],.]],.] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,2,2,1] => 3

[7,3,6,4,5,1,2] => [[[.,[.,.]],[[.,[.,.]],.]],.] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,2,2] => 2

[7,3,6,4,5,2,1] => [[[[.,.],.],[[.,[.,.]],.]],.] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,2,2,1] => 3

[7,3,6,5,1,2,4] => [[[.,[.,.]],[[[.,.],.],.]],.] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,2] => 3

[7,3,6,5,1,4,2] => [[[.,[.,.]],[[[.,.],.],.]],.] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,2] => 3

[7,3,6,5,4,1,2] => [[[.,[.,.]],[[[.,.],.],.]],.] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,2] => 3

[7,4,1,2,3,5,6] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => 1

[7,4,1,2,3,6,5] => [[[.,[.,[.,.]]],[[.,.],.]],.] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [6,4,3,3] => 2

[7,4,1,2,5,3,6] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => 1

[7,4,1,2,5,6,3] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => 1

[7,4,1,2,6,3,5] => [[[.,[.,[.,.]]],[[.,.],.]],.] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [6,4,3,3] => 2

[7,4,1,2,6,5,3] => [[[.,[.,[.,.]]],[[.,.],.]],.] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [6,4,3,3] => 2

[7,4,1,3,2,5,6] => [[[.,[[.,.],.]],[.,[.,.]]],.] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1] => 2

[7,4,1,3,2,6,5] => [[[.,[[.,.],.]],[[.,.],.]],.] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,3,1] => 3

[7,4,1,3,5,2,6] => [[[.,[[.,.],.]],[.,[.,.]]],.] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1] => 2

[7,4,1,3,5,6,2] => [[[.,[[.,.],.]],[.,[.,.]]],.] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1] => 2

[7,4,1,3,6,2,5] => [[[.,[[.,.],.]],[[.,.],.]],.] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,3,1] => 3

[7,4,1,3,6,5,2] => [[[.,[[.,.],.]],[[.,.],.]],.] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,3,1] => 3

[7,4,1,5,2,3,6] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => 1

[7,4,1,5,2,6,3] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => 1

[7,4,1,5,3,2,6] => [[[.,[[.,.],.]],[.,[.,.]]],.] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1] => 2

[7,4,1,5,3,6,2] => [[[.,[[.,.],.]],[.,[.,.]]],.] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1] => 2

[7,4,1,5,6,2,3] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => 1

[7,4,1,5,6,3,2] => [[[.,[[.,.],.]],[.,[.,.]]],.] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1] => 2

[7,4,1,6,2,3,5] => [[[.,[.,[.,.]]],[[.,.],.]],.] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [6,4,3,3] => 2

[7,4,1,6,2,5,3] => [[[.,[.,[.,.]]],[[.,.],.]],.] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [6,4,3,3] => 2

[7,4,1,6,3,2,5] => [[[.,[[.,.],.]],[[.,.],.]],.] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,3,1] => 3

[7,4,1,6,3,5,2] => [[[.,[[.,.],.]],[[.,.],.]],.] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,3,1] => 3

[7,4,1,6,5,2,3] => [[[.,[.,[.,.]]],[[.,.],.]],.] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [6,4,3,3] => 2

[7,4,1,6,5,3,2] => [[[.,[[.,.],.]],[[.,.],.]],.] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,3,1] => 3

[7,4,2,1,3,5,6] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1,1] => 1

[7,4,2,1,5,3,6] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1,1] => 1

[7,4,2,1,5,6,3] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1,1] => 1

[7,4,2,3,1,5,6] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1,1] => 1

[7,4,2,3,5,1,6] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1,1] => 1

[7,4,2,3,5,6,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1,1] => 1

[7,4,2,5,1,3,6] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1,1] => 1

[7,4,2,5,1,6,3] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1,1] => 1

[7,4,2,5,3,1,6] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1,1] => 1

[7,4,2,5,3,6,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1,1] => 1

[7,4,2,5,6,1,3] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1,1] => 1

[7,4,2,5,6,3,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1,1] => 1

[7,4,3,1,2,5,6] => [[[[.,[.,.]],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [6,3,3,3,2] => 2

[7,4,3,1,5,2,6] => [[[[.,[.,.]],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [6,3,3,3,2] => 2

[7,4,3,1,5,6,2] => [[[[.,[.,.]],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [6,3,3,3,2] => 2

[7,4,3,2,1,5,6] => [[[[[.,.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,3,3,2,1] => 3

[7,4,3,2,5,1,6] => [[[[[.,.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,3,3,2,1] => 3

[7,4,3,2,5,6,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,3,3,2,1] => 3

[7,4,3,5,1,2,6] => [[[[.,[.,.]],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [6,3,3,3,2] => 2

[7,4,3,5,1,6,2] => [[[[.,[.,.]],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [6,3,3,3,2] => 2

[7,4,3,5,2,1,6] => [[[[[.,.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,3,3,2,1] => 3

[7,4,3,5,2,6,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,3,3,2,1] => 3

[7,4,3,5,6,1,2] => [[[[.,[.,.]],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [6,3,3,3,2] => 2

[7,4,3,5,6,2,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,3,3,2,1] => 3

[7,4,5,1,2,3,6] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => 1

[7,4,5,1,2,6,3] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => 1

[7,4,5,1,3,2,6] => [[[.,[[.,.],.]],[.,[.,.]]],.] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1] => 2

[7,4,5,1,3,6,2] => [[[.,[[.,.],.]],[.,[.,.]]],.] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1] => 2

[7,4,5,1,6,2,3] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => 1

[7,4,5,1,6,3,2] => [[[.,[[.,.],.]],[.,[.,.]]],.] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1] => 2

[7,4,5,2,1,3,6] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1,1] => 1

[7,4,5,2,1,6,3] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1,1] => 1

[7,4,5,2,3,1,6] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1,1] => 1

[7,4,5,2,3,6,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1,1] => 1

[7,4,5,2,6,1,3] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1,1] => 1

[7,4,5,2,6,3,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1,1] => 1

[7,4,5,3,1,2,6] => [[[[.,[.,.]],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [6,3,3,3,2] => 2

[7,4,5,3,1,6,2] => [[[[.,[.,.]],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [6,3,3,3,2] => 2

[7,4,5,3,2,1,6] => [[[[[.,.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,3,3,2,1] => 3

[7,4,5,3,2,6,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,3,3,2,1] => 3

[7,4,5,3,6,1,2] => [[[[.,[.,.]],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [6,3,3,3,2] => 2

[7,4,5,3,6,2,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,3,3,2,1] => 3

[7,4,5,6,1,2,3] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => 1

[7,4,5,6,1,3,2] => [[[.,[[.,.],.]],[.,[.,.]]],.] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1] => 2

[7,4,5,6,2,1,3] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1,1] => 1

[7,4,5,6,2,3,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1,1] => 1

[7,4,5,6,3,1,2] => [[[[.,[.,.]],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [6,3,3,3,2] => 2

[7,4,5,6,3,2,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,3,3,2,1] => 3

[7,4,6,1,2,3,5] => [[[.,[.,[.,.]]],[[.,.],.]],.] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [6,4,3,3] => 2

[7,4,6,1,2,5,3] => [[[.,[.,[.,.]]],[[.,.],.]],.] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [6,4,3,3] => 2

[7,4,6,1,3,2,5] => [[[.,[[.,.],.]],[[.,.],.]],.] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,3,1] => 3

[7,4,6,1,3,5,2] => [[[.,[[.,.],.]],[[.,.],.]],.] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,3,1] => 3

[7,4,6,1,5,2,3] => [[[.,[.,[.,.]]],[[.,.],.]],.] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [6,4,3,3] => 2

[7,4,6,1,5,3,2] => [[[.,[[.,.],.]],[[.,.],.]],.] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,3,1] => 3

[7,4,6,5,1,2,3] => [[[.,[.,[.,.]]],[[.,.],.]],.] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [6,4,3,3] => 2

[7,4,6,5,1,3,2] => [[[.,[[.,.],.]],[[.,.],.]],.] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,3,1] => 3

[7,5,1,2,3,4,6] => [[[.,[.,[.,[.,.]]]],[.,.]],.] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [6,4,4] => 1

[7,5,1,2,3,6,4] => [[[.,[.,[.,[.,.]]]],[.,.]],.] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [6,4,4] => 1

[7,5,1,2,4,3,6] => [[[.,[.,[[.,.],.]]],[.,.]],.] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1] => 2

[7,5,1,2,4,6,3] => [[[.,[.,[[.,.],.]]],[.,.]],.] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1] => 2

[7,5,1,2,6,3,4] => [[[.,[.,[.,[.,.]]]],[.,.]],.] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [6,4,4] => 1

[7,5,1,2,6,4,3] => [[[.,[.,[[.,.],.]]],[.,.]],.] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1] => 2

[7,5,1,3,2,4,6] => [[[.,[[.,.],[.,.]]],[.,.]],.] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1] => 1

[7,5,1,3,2,6,4] => [[[.,[[.,.],[.,.]]],[.,.]],.] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1] => 1

[7,5,1,3,4,2,6] => [[[.,[[.,.],[.,.]]],[.,.]],.] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1] => 1

[7,5,1,3,4,6,2] => [[[.,[[.,.],[.,.]]],[.,.]],.] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1] => 1

[7,5,1,3,6,2,4] => [[[.,[[.,.],[.,.]]],[.,.]],.] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1] => 1

[7,5,1,3,6,4,2] => [[[.,[[.,.],[.,.]]],[.,.]],.] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1] => 1

[7,5,1,4,2,3,6] => [[[.,[[.,[.,.]],.]],[.,.]],.] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [6,4,4,2] => 2

[7,5,1,4,2,6,3] => [[[.,[[.,[.,.]],.]],[.,.]],.] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [6,4,4,2] => 2

[7,5,1,4,3,2,6] => [[[.,[[[.,.],.],.]],[.,.]],.] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [6,4,4,2,1] => 3

[7,5,1,4,3,6,2] => [[[.,[[[.,.],.],.]],[.,.]],.] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [6,4,4,2,1] => 3

[7,5,1,4,6,2,3] => [[[.,[[.,[.,.]],.]],[.,.]],.] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [6,4,4,2] => 2

[7,5,1,4,6,3,2] => [[[.,[[[.,.],.],.]],[.,.]],.] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [6,4,4,2,1] => 3

[7,5,1,6,2,3,4] => [[[.,[.,[.,[.,.]]]],[.,.]],.] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [6,4,4] => 1

[7,5,1,6,2,4,3] => [[[.,[.,[[.,.],.]]],[.,.]],.] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1] => 2

[7,5,1,6,3,2,4] => [[[.,[[.,.],[.,.]]],[.,.]],.] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1] => 1

[7,5,1,6,3,4,2] => [[[.,[[.,.],[.,.]]],[.,.]],.] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1] => 1

[7,5,1,6,4,2,3] => [[[.,[[.,[.,.]],.]],[.,.]],.] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [6,4,4,2] => 2

[7,5,1,6,4,3,2] => [[[.,[[[.,.],.],.]],[.,.]],.] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [6,4,4,2,1] => 3

[7,5,2,1,3,4,6] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1,1] => 1

[7,5,2,1,3,6,4] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1,1] => 1

[7,5,2,1,6,3,4] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1,1] => 1

[7,5,2,3,1,4,6] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1,1] => 1

[7,5,2,3,1,6,4] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1,1] => 1

[7,5,2,3,4,1,6] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1,1] => 1

[7,5,2,3,4,6,1] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1,1] => 1

[7,5,2,3,6,1,4] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1,1] => 1

[7,5,2,3,6,4,1] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1,1] => 1

[7,5,2,6,1,3,4] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1,1] => 1

[7,5,2,6,3,1,4] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1,1] => 1

[7,5,2,6,3,4,1] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1,1] => 1

[7,5,3,1,2,4,6] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 1

[7,5,3,1,2,6,4] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 1

[7,5,3,1,4,2,6] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 1

[7,5,3,1,4,6,2] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 1

[7,5,3,1,6,2,4] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 1

[7,5,3,1,6,4,2] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 1

[7,5,3,2,1,4,6] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2,1] => 2

[7,5,3,2,1,6,4] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2,1] => 2

[7,5,3,2,4,1,6] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2,1] => 2

[7,5,3,2,4,6,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2,1] => 2

[7,5,3,2,6,1,4] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2,1] => 2

[7,5,3,2,6,4,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2,1] => 2

[7,5,3,4,1,2,6] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 1

[7,5,3,4,1,6,2] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 1

[7,5,3,4,2,1,6] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2,1] => 2

[7,5,3,4,2,6,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2,1] => 2

[7,5,3,4,6,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 1

[7,5,3,4,6,2,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2,1] => 2

[7,5,3,6,1,2,4] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 1

[7,5,3,6,1,4,2] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 1

[7,5,3,6,2,1,4] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2,1] => 2

[7,5,3,6,2,4,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2,1] => 2

[7,5,3,6,4,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 1

[7,5,3,6,4,2,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2,1] => 2

[7,5,4,1,2,3,6] => [[[[.,[.,[.,.]]],.],[.,.]],.] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3] => 2

[7,5,4,1,2,6,3] => [[[[.,[.,[.,.]]],.],[.,.]],.] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3] => 2

[7,5,4,1,6,2,3] => [[[[.,[.,[.,.]]],.],[.,.]],.] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3] => 2

[7,5,4,2,1,3,6] => [[[[[.,.],[.,.]],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3,1,1] => 2

[7,5,4,2,1,6,3] => [[[[[.,.],[.,.]],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3,1,1] => 2

[7,5,4,2,3,1,6] => [[[[[.,.],[.,.]],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3,1,1] => 2

[7,5,4,2,3,6,1] => [[[[[.,.],[.,.]],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3,1,1] => 2

[7,5,4,2,6,1,3] => [[[[[.,.],[.,.]],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3,1,1] => 2

[7,5,4,2,6,3,1] => [[[[[.,.],[.,.]],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3,1,1] => 2

[7,5,4,3,1,2,6] => [[[[[.,[.,.]],.],.],[.,.]],.] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [6,4,4,3,2] => 3

[7,5,4,3,1,6,2] => [[[[[.,[.,.]],.],.],[.,.]],.] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [6,4,4,3,2] => 3

[7,5,4,3,2,1,6] => [[[[[[.,.],.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [6,4,4,3,2,1] => 4

[7,5,4,3,2,6,1] => [[[[[[.,.],.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [6,4,4,3,2,1] => 4

[7,5,4,3,6,1,2] => [[[[[.,[.,.]],.],.],[.,.]],.] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [6,4,4,3,2] => 3

[7,5,4,3,6,2,1] => [[[[[[.,.],.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [6,4,4,3,2,1] => 4

[7,5,4,6,1,2,3] => [[[[.,[.,[.,.]]],.],[.,.]],.] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3] => 2

[7,5,4,6,2,1,3] => [[[[[.,.],[.,.]],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3,1,1] => 2

[7,5,4,6,2,3,1] => [[[[[.,.],[.,.]],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3,1,1] => 2

[7,5,4,6,3,1,2] => [[[[[.,[.,.]],.],.],[.,.]],.] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [6,4,4,3,2] => 3

[7,5,4,6,3,2,1] => [[[[[[.,.],.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [6,4,4,3,2,1] => 4

[7,5,6,1,2,3,4] => [[[.,[.,[.,[.,.]]]],[.,.]],.] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [6,4,4] => 1

[7,5,6,1,2,4,3] => [[[.,[.,[[.,.],.]]],[.,.]],.] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1] => 2

[7,5,6,1,3,2,4] => [[[.,[[.,.],[.,.]]],[.,.]],.] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1] => 1

[7,5,6,1,3,4,2] => [[[.,[[.,.],[.,.]]],[.,.]],.] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1] => 1

[7,5,6,1,4,2,3] => [[[.,[[.,[.,.]],.]],[.,.]],.] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [6,4,4,2] => 2

[7,5,6,1,4,3,2] => [[[.,[[[.,.],.],.]],[.,.]],.] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [6,4,4,2,1] => 3

[7,5,6,2,1,3,4] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1,1] => 1

[7,5,6,2,3,1,4] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1,1] => 1

[7,5,6,2,3,4,1] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1,1] => 1

[7,5,6,3,1,2,4] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 1

[7,5,6,3,1,4,2] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 1

[7,5,6,3,2,1,4] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2,1] => 2

[7,5,6,3,2,4,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2,1] => 2

[7,5,6,3,4,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 1

[7,5,6,3,4,2,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2,1] => 2

[7,5,6,4,1,2,3] => [[[[.,[.,[.,.]]],.],[.,.]],.] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3] => 2

[7,5,6,4,2,1,3] => [[[[[.,.],[.,.]],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3,1,1] => 2

[7,5,6,4,2,3,1] => [[[[[.,.],[.,.]],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3,1,1] => 2

[7,5,6,4,3,1,2] => [[[[[.,[.,.]],.],.],[.,.]],.] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [6,4,4,3,2] => 3

[7,5,6,4,3,2,1] => [[[[[[.,.],.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [6,4,4,3,2,1] => 4

[7,6,1,2,3,4,5] => [[[.,[.,[.,[.,[.,.]]]]],.],.] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,5] => 2

[7,6,1,2,3,5,4] => [[[.,[.,[.,[[.,.],.]]]],.],.] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [6,5,1] => 3

[7,6,1,2,4,3,5] => [[[.,[.,[[.,.],[.,.]]]],.],.] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [6,5,1,1] => 2

[7,6,1,2,4,5,3] => [[[.,[.,[[.,.],[.,.]]]],.],.] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [6,5,1,1] => 2

[7,6,1,2,5,3,4] => [[[.,[.,[[.,[.,.]],.]]],.],.] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [6,5,2] => 3

[7,6,1,2,5,4,3] => [[[.,[.,[[[.,.],.],.]]],.],.] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1] => 4

[7,6,1,3,2,4,5] => [[[.,[[.,.],[.,[.,.]]]],.],.] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,1,1] => 2

[7,6,1,3,2,5,4] => [[[.,[[.,.],[[.,.],.]]],.],.] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,1] => 3

[7,6,1,3,4,2,5] => [[[.,[[.,.],[.,[.,.]]]],.],.] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,1,1] => 2

[7,6,1,3,4,5,2] => [[[.,[[.,.],[.,[.,.]]]],.],.] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,1,1] => 2

[7,6,1,3,5,2,4] => [[[.,[[.,.],[[.,.],.]]],.],.] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,1] => 3

[7,6,1,3,5,4,2] => [[[.,[[.,.],[[.,.],.]]],.],.] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,1] => 3

[7,6,1,4,2,3,5] => [[[.,[[.,[.,.]],[.,.]]],.],.] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [6,5,2,2] => 2

[7,6,1,4,2,5,3] => [[[.,[[.,[.,.]],[.,.]]],.],.] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [6,5,2,2] => 2

[7,6,1,4,3,2,5] => [[[.,[[[.,.],.],[.,.]]],.],.] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,2,1] => 3

[7,6,1,4,3,5,2] => [[[.,[[[.,.],.],[.,.]]],.],.] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,2,1] => 3

[7,6,1,4,5,2,3] => [[[.,[[.,[.,.]],[.,.]]],.],.] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [6,5,2,2] => 2

[7,6,1,4,5,3,2] => [[[.,[[[.,.],.],[.,.]]],.],.] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,2,1] => 3

[7,6,1,5,2,3,4] => [[[.,[[.,[.,[.,.]]],.]],.],.] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [6,5,3] => 3

[7,6,1,5,2,4,3] => [[[.,[[.,[[.,.],.]],.]],.],.] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1] => 4

[7,6,1,5,3,2,4] => [[[.,[[[.,.],[.,.]],.]],.],.] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,1] => 3

[7,6,1,5,3,4,2] => [[[.,[[[.,.],[.,.]],.]],.],.] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,1] => 3

[7,6,1,5,4,2,3] => [[[.,[[[.,[.,.]],.],.]],.],.] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2] => 4

[7,6,1,5,4,3,2] => [[[.,[[[[.,.],.],.],.]],.],.] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2,1] => 5

[7,6,2,1,3,4,5] => [[[[.,.],[.,[.,[.,.]]]],.],.] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,1,1,1] => 2

[7,6,2,1,3,5,4] => [[[[.,.],[.,[[.,.],.]]],.],.] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,1,1] => 3

[7,6,2,1,4,3,5] => [[[[.,.],[[.,.],[.,.]]],.],.] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,2,1,1] => 2

[7,6,2,1,4,5,3] => [[[[.,.],[[.,.],[.,.]]],.],.] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,2,1,1] => 2

[7,6,2,1,5,3,4] => [[[[.,.],[[.,[.,.]],.]],.],.] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,1,1] => 3

[7,6,2,3,1,4,5] => [[[[.,.],[.,[.,[.,.]]]],.],.] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,1,1,1] => 2

[7,6,2,3,1,5,4] => [[[[.,.],[.,[[.,.],.]]],.],.] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,1,1] => 3

[7,6,2,3,4,1,5] => [[[[.,.],[.,[.,[.,.]]]],.],.] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,1,1,1] => 2

[7,6,2,3,4,5,1] => [[[[.,.],[.,[.,[.,.]]]],.],.] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,1,1,1] => 2

[7,6,2,3,5,1,4] => [[[[.,.],[.,[[.,.],.]]],.],.] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,1,1] => 3

[7,6,2,3,5,4,1] => [[[[.,.],[.,[[.,.],.]]],.],.] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,1,1] => 3

[7,6,2,4,1,3,5] => [[[[.,.],[[.,.],[.,.]]],.],.] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,2,1,1] => 2

[7,6,2,4,1,5,3] => [[[[.,.],[[.,.],[.,.]]],.],.] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,2,1,1] => 2

[7,6,2,4,3,1,5] => [[[[.,.],[[.,.],[.,.]]],.],.] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,2,1,1] => 2

[7,6,2,4,3,5,1] => [[[[.,.],[[.,.],[.,.]]],.],.] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,2,1,1] => 2

[7,6,2,4,5,1,3] => [[[[.,.],[[.,.],[.,.]]],.],.] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,2,1,1] => 2

[7,6,2,4,5,3,1] => [[[[.,.],[[.,.],[.,.]]],.],.] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,2,1,1] => 2

[7,6,2,5,1,3,4] => [[[[.,.],[[.,[.,.]],.]],.],.] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,1,1] => 3

[7,6,2,5,3,1,4] => [[[[.,.],[[.,[.,.]],.]],.],.] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,1,1] => 3

[7,6,2,5,3,4,1] => [[[[.,.],[[.,[.,.]],.]],.],.] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,1,1] => 3

[7,6,3,1,2,4,5] => [[[[.,[.,.]],[.,[.,.]]],.],.] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2] => 2

[7,6,3,1,4,2,5] => [[[[.,[.,.]],[.,[.,.]]],.],.] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2] => 2

[7,6,3,1,4,5,2] => [[[[.,[.,.]],[.,[.,.]]],.],.] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2] => 2

[7,6,3,2,1,4,5] => [[[[[.,.],.],[.,[.,.]]],.],.] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2,1] => 3

[7,6,3,2,4,1,5] => [[[[[.,.],.],[.,[.,.]]],.],.] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2,1] => 3

[7,6,3,2,4,5,1] => [[[[[.,.],.],[.,[.,.]]],.],.] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2,1] => 3

[7,6,3,4,1,2,5] => [[[[.,[.,.]],[.,[.,.]]],.],.] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2] => 2

[7,6,3,4,1,5,2] => [[[[.,[.,.]],[.,[.,.]]],.],.] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2] => 2

[7,6,3,4,2,1,5] => [[[[[.,.],.],[.,[.,.]]],.],.] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2,1] => 3

[7,6,3,4,2,5,1] => [[[[[.,.],.],[.,[.,.]]],.],.] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2,1] => 3

[7,6,3,4,5,1,2] => [[[[.,[.,.]],[.,[.,.]]],.],.] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2] => 2

[7,6,3,4,5,2,1] => [[[[[.,.],.],[.,[.,.]]],.],.] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2,1] => 3

[7,6,4,1,2,3,5] => [[[[.,[.,[.,.]]],[.,.]],.],.] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3] => 2

[7,6,4,1,2,5,3] => [[[[.,[.,[.,.]]],[.,.]],.],.] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3] => 2

[7,6,4,1,5,2,3] => [[[[.,[.,[.,.]]],[.,.]],.],.] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3] => 2

[7,6,4,2,1,3,5] => [[[[[.,.],[.,.]],[.,.]],.],.] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3,1,1] => 2

[7,6,4,2,1,5,3] => [[[[[.,.],[.,.]],[.,.]],.],.] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3,1,1] => 2

[7,6,4,2,3,1,5] => [[[[[.,.],[.,.]],[.,.]],.],.] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3,1,1] => 2

[7,6,4,2,3,5,1] => [[[[[.,.],[.,.]],[.,.]],.],.] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3,1,1] => 2

[7,6,4,2,5,1,3] => [[[[[.,.],[.,.]],[.,.]],.],.] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3,1,1] => 2

[7,6,4,2,5,3,1] => [[[[[.,.],[.,.]],[.,.]],.],.] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3,1,1] => 2

[7,6,4,3,1,2,5] => [[[[[.,[.,.]],.],[.,.]],.],.] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,3,2] => 3

[7,6,4,3,1,5,2] => [[[[[.,[.,.]],.],[.,.]],.],.] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,3,2] => 3

[7,6,4,3,2,1,5] => [[[[[[.,.],.],.],[.,.]],.],.] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,3,2,1] => 4

[7,6,4,3,2,5,1] => [[[[[[.,.],.],.],[.,.]],.],.] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,3,2,1] => 4

[7,6,4,3,5,1,2] => [[[[[.,[.,.]],.],[.,.]],.],.] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,3,2] => 3

[7,6,4,3,5,2,1] => [[[[[[.,.],.],.],[.,.]],.],.] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,3,2,1] => 4

[7,6,4,5,1,2,3] => [[[[.,[.,[.,.]]],[.,.]],.],.] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3] => 2

[7,6,4,5,2,1,3] => [[[[[.,.],[.,.]],[.,.]],.],.] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3,1,1] => 2

[7,6,4,5,2,3,1] => [[[[[.,.],[.,.]],[.,.]],.],.] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3,1,1] => 2

[7,6,4,5,3,1,2] => [[[[[.,[.,.]],.],[.,.]],.],.] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,3,2] => 3

[7,6,4,5,3,2,1] => [[[[[[.,.],.],.],[.,.]],.],.] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,3,2,1] => 4

[7,6,5,1,2,3,4] => [[[[.,[.,[.,[.,.]]]],.],.],.] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [6,5,4] => 3

[7,6,5,1,2,4,3] => [[[[.,[.,[[.,.],.]]],.],.],.] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1] => 4

[7,6,5,1,3,2,4] => [[[[.,[[.,.],[.,.]]],.],.],.] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,1] => 3

[7,6,5,1,3,4,2] => [[[[.,[[.,.],[.,.]]],.],.],.] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,1] => 3

[7,6,5,1,4,2,3] => [[[[.,[[.,[.,.]],.]],.],.],.] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [6,5,4,2] => 4

[7,6,5,2,1,3,4] => [[[[[.,.],[.,[.,.]]],.],.],.] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,1,1] => 3

[7,6,5,2,3,1,4] => [[[[[.,.],[.,[.,.]]],.],.],.] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,1,1] => 3

[7,6,5,2,3,4,1] => [[[[[.,.],[.,[.,.]]],.],.],.] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,1,1] => 3

[7,6,5,3,1,2,4] => [[[[[.,[.,.]],[.,.]],.],.],.] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,2] => 3

[7,6,5,3,1,4,2] => [[[[[.,[.,.]],[.,.]],.],.],.] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,2] => 3

[7,6,5,3,2,1,4] => [[[[[[.,.],.],[.,.]],.],.],.] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,2,1] => 4

[7,6,5,3,2,4,1] => [[[[[[.,.],.],[.,.]],.],.],.] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,2,1] => 4

[7,6,5,3,4,1,2] => [[[[[.,[.,.]],[.,.]],.],.],.] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,2] => 3

[7,6,5,3,4,2,1] => [[[[[[.,.],.],[.,.]],.],.],.] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,2,1] => 4

[7,6,5,4,1,2,3] => [[[[[.,[.,[.,.]]],.],.],.],.] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3] => 4

[7,6,5,4,1,3,2] => [[[[[.,[[.,.],.]],.],.],.],.] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1] => 5

[7,6,5,4,2,1,3] => [[[[[[.,.],[.,.]],.],.],.],.] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1,1] => 4

[7,6,5,4,2,3,1] => [[[[[[.,.],[.,.]],.],.],.],.] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1,1] => 4

[7,6,5,4,3,1,2] => [[[[[[.,[.,.]],.],.],.],.],.] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2] => 5

[7,6,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],.] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1] => 6

[8,7,6,5,4,3,2,1] => [[[[[[[[.,.],.],.],.],.],.],.],.] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1] => 7

[7,8,6,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [6,6,5,4,3,2,1] => 5

[7,6,8,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [6,6,5,4,3,2,1] => 5

[6,7,8,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,5,5,4,3,2,1] => 4

[7,6,5,8,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [6,6,5,4,3,2,1] => 5

[6,7,5,8,4,3,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,5,5,4,3,2,1] => 4

[6,5,7,8,4,3,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,5,5,4,3,2,1] => 4

[5,6,7,8,4,3,2,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3,2,1] => 3

[7,6,5,4,8,3,2,1] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [6,6,5,4,3,2,1] => 5

[6,7,5,4,8,3,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,5,5,4,3,2,1] => 4

[6,5,7,4,8,3,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,5,5,4,3,2,1] => 4

[5,6,7,4,8,3,2,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3,2,1] => 3

[6,5,4,7,8,3,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,5,5,4,3,2,1] => 4

[5,6,4,7,8,3,2,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3,2,1] => 3

[5,4,6,7,8,3,2,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3,2,1] => 3

[4,5,6,7,8,3,2,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,2,1] => 2

[7,6,5,4,3,8,2,1] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [6,6,5,4,3,2,1] => 5

[6,7,5,4,3,8,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,5,5,4,3,2,1] => 4

[6,5,7,4,3,8,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,5,5,4,3,2,1] => 4

[5,6,7,4,3,8,2,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3,2,1] => 3

[6,5,4,7,3,8,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,5,5,4,3,2,1] => 4

[5,4,6,7,3,8,2,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3,2,1] => 3

[4,5,6,7,3,8,2,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,2,1] => 2

[6,5,4,3,7,8,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,5,5,4,3,2,1] => 4

[5,4,3,6,7,8,2,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3,2,1] => 3

[4,3,5,6,7,8,2,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,2,1] => 2

[3,4,5,6,7,8,2,1] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2,1] => 1

[4,5,6,7,8,2,3,1] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1,1] => 0

[7,8,2,3,4,5,6,1] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1,1,1] => 0

[8,2,3,4,5,6,7,1] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1,1,1,1] => 1

[7,6,5,4,3,2,8,1] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [6,6,5,4,3,2,1] => 5

[6,7,5,4,3,2,8,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,5,5,4,3,2,1] => 4

[6,5,7,4,3,2,8,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,5,5,4,3,2,1] => 4

[5,6,7,4,3,2,8,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3,2,1] => 3

[6,5,4,7,3,2,8,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,5,5,4,3,2,1] => 4

[4,5,6,7,3,2,8,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,2,1] => 2

[6,5,4,3,7,2,8,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,5,5,4,3,2,1] => 4

[5,4,6,3,7,2,8,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3,2,1] => 3

[4,5,6,3,7,2,8,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,2,1] => 2

[5,4,3,6,7,2,8,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3,2,1] => 3

[4,5,3,6,7,2,8,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,2,1] => 2

[4,3,5,6,7,2,8,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,2,1] => 2

[3,4,5,6,7,2,8,1] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2,1] => 1

[4,5,6,7,2,3,8,1] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1,1] => 0

[7,2,3,4,5,6,8,1] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1,1,1] => 0

[6,5,4,3,2,7,8,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,5,5,4,3,2,1] => 4

[5,4,6,3,2,7,8,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3,2,1] => 3

[4,5,6,3,2,7,8,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,2,1] => 2

[5,4,3,6,2,7,8,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3,2,1] => 3

[4,3,5,6,2,7,8,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,2,1] => 2

[3,4,5,6,2,7,8,1] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2,1] => 1

[4,5,6,2,3,7,8,1] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1,1] => 0

[5,4,3,2,6,7,8,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3,2,1] => 3

[4,5,3,2,6,7,8,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,2,1] => 2

[4,3,5,2,6,7,8,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,2,1] => 2

[3,4,5,2,6,7,8,1] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2,1] => 1

[4,5,2,3,6,7,8,1] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1,1] => 0

[4,3,2,5,6,7,8,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,2,1] => 2

[3,4,2,5,6,7,8,1] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2,1] => 1

[4,2,3,5,6,7,8,1] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1,1] => 0

[3,2,4,5,6,7,8,1] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2,1] => 1

[2,3,4,5,6,7,8,1] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 0

[8,7,6,5,4,3,1,2] => [[[[[[[.,[.,.]],.],.],.],.],.],.] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,2] => 6

[4,5,6,7,8,3,1,2] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,2] => 1

[8,7,3,4,5,6,1,2] => [[[[.,[.,.]],[.,[.,[.,.]]]],.],.] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,2,2,2] => 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] => [6,6,2,2,2,2] => 0

[8,3,4,5,6,7,1,2] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2,2] => 1

[4,5,6,7,3,8,1,2] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,2] => 1

[7,3,4,5,6,8,1,2] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,2,2] => 0

[4,5,6,3,7,8,1,2] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,2] => 1

[4,5,3,6,7,8,1,2] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,2] => 1

[4,3,5,6,7,8,1,2] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,2] => 1

[3,4,5,6,7,8,1,2] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2] => 0

[4,5,6,7,8,2,1,3] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1,1] => 0

[5,6,7,8,4,1,2,3] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3] => 1

[5,6,7,4,8,1,2,3] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3] => 1

[5,6,4,7,8,1,2,3] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3] => 1

[5,4,6,7,8,1,2,3] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3] => 1

[4,5,6,7,8,1,2,3] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => 0

[7,8,6,5,1,2,3,4] => [[[[.,[.,[.,[.,.]]]],.],.],[.,.]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [6,6,5,4] => 2

[7,6,8,5,1,2,3,4] => [[[[.,[.,[.,[.,.]]]],.],.],[.,.]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [6,6,5,4] => 2

[7,6,5,8,1,2,3,4] => [[[[.,[.,[.,[.,.]]]],.],.],[.,.]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [6,6,5,4] => 2

[5,6,7,8,1,2,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 0

[8,7,6,1,2,3,4,5] => [[[[.,[.,[.,[.,[.,.]]]]],.],.],.] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [7,6,5] => 3

[7,8,6,1,2,3,4,5] => [[[.,[.,[.,[.,[.,.]]]]],.],[.,.]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [6,6,5] => 1

[8,6,7,1,2,3,4,5] => [[[.,[.,[.,[.,[.,.]]]]],[.,.]],.] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [7,5,5] => 1

[7,6,8,1,2,3,4,5] => [[[.,[.,[.,[.,[.,.]]]]],.],[.,.]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [6,6,5] => 1

[6,7,8,1,2,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => 0

[7,8,2,3,4,5,1,6] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1,1,1] => 0

[8,7,3,4,5,1,2,6] => [[[[.,[.,.]],[.,[.,[.,.]]]],.],.] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,2,2,2] => 2

[7,8,3,4,5,1,2,6] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,2,2] => 0

[7,8,2,3,4,1,5,6] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1,1,1] => 0

[8,7,3,4,1,2,5,6] => [[[[.,[.,.]],[.,[.,[.,.]]]],.],.] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,2,2,2] => 2

[7,8,3,4,1,2,5,6] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,2,2] => 0

[7,8,2,3,1,4,5,6] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1,1,1] => 0

[7,8,3,1,2,4,5,6] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,2,2] => 0

[7,8,2,1,3,4,5,6] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1,1,1] => 0

[8,7,1,2,3,4,5,6] => [[[.,[.,[.,[.,[.,[.,.]]]]]],.],.] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [7,6] => 2

[7,8,1,2,3,4,5,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,6] => 0

[8,2,3,4,5,6,1,7] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1,1,1,1] => 1

[8,3,4,5,6,1,2,7] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2,2] => 1

[8,6,1,2,3,4,5,7] => [[[.,[.,[.,[.,[.,.]]]]],[.,.]],.] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [7,5,5] => 1

[8,2,3,4,5,1,6,7] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1,1,1,1] => 1

[8,3,4,5,1,2,6,7] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2,2] => 1

[8,2,3,4,1,5,6,7] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1,1,1,1] => 1

[8,3,4,1,2,5,6,7] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2,2] => 1

[8,2,3,1,4,5,6,7] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1,1,1,1] => 1

[8,3,1,2,4,5,6,7] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2,2] => 1

[8,2,1,3,4,5,6,7] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1,1,1,1] => 1

[8,1,2,3,4,5,6,7] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 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] => [6,6,5,4,3,2,1] => 5

[6,7,5,4,3,2,1,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,5,5,4,3,2,1] => 4

[6,5,7,4,3,2,1,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,5,5,4,3,2,1] => 4

[5,6,7,4,3,2,1,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3,2,1] => 3

[6,5,4,7,3,2,1,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,5,5,4,3,2,1] => 4

[5,6,4,7,3,2,1,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3,2,1] => 3

[5,4,6,7,3,2,1,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3,2,1] => 3

[4,5,6,7,3,2,1,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,2,1] => 2

[6,5,4,3,7,2,1,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,5,5,4,3,2,1] => 4

[5,6,4,3,7,2,1,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3,2,1] => 3

[5,4,6,3,7,2,1,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3,2,1] => 3

[5,4,3,6,7,2,1,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3,2,1] => 3

[3,4,5,6,7,2,1,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2,1] => 1

[4,5,6,7,2,3,1,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1,1] => 0

[7,2,3,4,5,6,1,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1,1,1] => 0

[6,5,4,3,2,7,1,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,5,5,4,3,2,1] => 4

[5,6,4,3,2,7,1,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3,2,1] => 3

[5,4,6,3,2,7,1,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3,2,1] => 3

[5,4,3,6,2,7,1,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3,2,1] => 3

[4,5,3,6,2,7,1,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,2,1] => 2

[4,3,5,6,2,7,1,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,2,1] => 2

[3,4,5,6,2,7,1,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2,1] => 1

[5,4,3,2,6,7,1,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3,2,1] => 3

[3,4,5,2,6,7,1,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2,1] => 1

[4,5,2,3,6,7,1,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1,1] => 0

[4,3,2,5,6,7,1,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,2,1] => 2

[3,4,2,5,6,7,1,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2,1] => 1

[4,2,3,5,6,7,1,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1,1] => 0

[3,2,4,5,6,7,1,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2,1] => 1

[2,3,4,5,6,7,1,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 0

[4,5,6,7,3,1,2,8] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,2] => 1

[4,3,5,6,7,1,2,8] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,2] => 1

[3,4,5,6,7,1,2,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2] => 0

[4,5,6,7,2,1,3,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1,1] => 0

[5,6,7,4,1,2,3,8] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3] => 1

[5,6,4,7,1,2,3,8] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3] => 1

[5,4,6,7,1,2,3,8] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3] => 1

[4,5,6,7,1,2,3,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => 0

[7,6,5,1,2,3,4,8] => [[[[.,[.,[.,[.,.]]]],.],.],[.,.]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [6,6,5,4] => 2

[5,6,7,1,2,3,4,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 0

[7,6,1,2,3,4,5,8] => [[[.,[.,[.,[.,[.,.]]]]],.],[.,.]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [6,6,5] => 1

[6,7,1,2,3,4,5,8] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => 0

[7,2,3,4,5,1,6,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1,1,1] => 0

[7,2,3,4,1,5,6,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1,1,1] => 0

[7,3,4,1,2,5,6,8] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,2,2] => 0

[7,2,3,1,4,5,6,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1,1,1] => 0

[7,3,1,2,4,5,6,8] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,2,2] => 0

[7,2,1,3,4,5,6,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1,1,1] => 0

[7,1,2,3,4,5,6,8] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,6] => 0

[6,5,4,3,2,1,7,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,5,5,4,3,2,1] => 4

[5,6,4,3,2,1,7,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3,2,1] => 3

[5,4,6,3,2,1,7,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3,2,1] => 3

[4,5,6,3,2,1,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,2,1] => 2

[5,4,3,6,2,1,7,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3,2,1] => 3

[3,4,5,6,2,1,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2,1] => 1

[5,4,3,2,6,1,7,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3,2,1] => 3

[4,5,3,2,6,1,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,2,1] => 2

[4,3,5,2,6,1,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,2,1] => 2

[3,4,5,2,6,1,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2,1] => 1

[4,3,2,5,6,1,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,2,1] => 2

[3,4,2,5,6,1,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2,1] => 1

[4,2,3,5,6,1,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1,1] => 0

[3,2,4,5,6,1,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2,1] => 1

[2,3,4,5,6,1,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 0

[4,3,5,6,1,2,7,8] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,2] => 1

[3,4,5,6,1,2,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2] => 0

[4,5,6,2,1,3,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1,1] => 0

[4,5,6,1,2,3,7,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => 0

[6,1,2,3,4,5,7,8] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => 0

[5,4,3,2,1,6,7,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3,2,1] => 3

[4,5,3,2,1,6,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,2,1] => 2

[4,3,5,2,1,6,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,2,1] => 2

[3,4,5,2,1,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2,1] => 1

[4,5,2,3,1,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1,1] => 0

[4,3,2,5,1,6,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,2,1] => 2

[3,4,2,5,1,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2,1] => 1

[4,2,3,5,1,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1,1] => 0

[3,2,4,5,1,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2,1] => 1

[2,3,4,5,1,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 0

[4,3,5,1,2,6,7,8] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,2] => 1

[3,4,5,1,2,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2] => 0

[4,5,2,1,3,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1,1] => 0

[5,4,1,2,3,6,7,8] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3] => 1

[4,5,1,2,3,6,7,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => 0

[5,1,2,3,4,6,7,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 0

[4,3,2,1,5,6,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,2,1] => 2

[3,4,2,1,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2,1] => 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] => [3,3,3,3,3,1,1] => 0

[3,2,4,1,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2,1] => 1

[2,3,4,1,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 0

[4,3,1,2,5,6,7,8] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,2] => 1

[3,4,1,2,5,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2] => 0

[4,2,1,3,5,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1,1] => 0

[4,1,2,3,5,6,7,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => 0

[3,2,1,4,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2,1] => 1

[2,3,1,4,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 0

[3,1,2,4,5,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2] => 0

[2,1,3,4,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 0

[1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [] => 0

[6,8,7,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,5,4,3,2,1] => 5

[5,8,7,6,4,3,2,1] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,4,3,2,1] => 5

[6,5,8,7,4,3,2,1] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,5,4,3,2,1] => 5

[5,6,8,7,4,3,2,1] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [5,4,4,4,3,2,1] => 4

[4,8,7,6,5,3,2,1] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,3,2,1] => 5

[5,6,4,8,7,3,2,1] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [5,4,4,4,3,2,1] => 4

[3,8,7,6,5,4,2,1] => [[[.,.],.],[[[[[.,.],.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,2,1] => 5

[3,5,6,7,8,4,2,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => 1

[4,3,8,7,6,5,2,1] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,3,2,1] => 5

[3,4,6,7,8,5,2,1] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2,1] => 1

[5,4,3,8,7,6,2,1] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,4,3,2,1] => 5

[3,4,5,7,8,6,2,1] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2,1] => 1

[6,5,4,3,8,7,2,1] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,5,4,3,2,1] => 5

[5,6,4,3,8,7,2,1] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [5,4,4,4,3,2,1] => 4

[5,4,3,6,8,7,2,1] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [5,4,4,4,3,2,1] => 4

[3,4,5,6,8,7,2,1] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,2,1] => 2

[3,5,6,7,4,8,2,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => 1

[3,4,6,7,5,8,2,1] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2,1] => 1

[3,4,5,7,6,8,2,1] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2,1] => 1

[3,5,6,4,7,8,2,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => 1

[3,4,6,5,7,8,2,1] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2,1] => 1

[3,5,4,6,7,8,2,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => 1

[2,8,7,6,5,4,3,1] => [[.,.],[[[[[[.,.],.],.],.],.],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,1,1] => 5

[2,5,6,7,8,4,3,1] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1,1] => 1

[2,4,7,8,6,5,3,1] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1,1] => 1

[2,4,6,8,7,5,3,1] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,6,7,8,5,3,1] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[2,4,5,7,8,6,3,1] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1,1] => 0

[2,5,6,4,8,7,3,1] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1,1] => 2

[2,4,6,5,8,7,3,1] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,5,6,8,7,3,1] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,1,1] => 1

[2,5,6,7,4,8,3,1] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1,1] => 1

[2,4,6,7,5,8,3,1] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[2,5,6,4,7,8,3,1] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1,1] => 1

[2,4,6,5,7,8,3,1] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[2,5,4,6,7,8,3,1] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1,1] => 1

[2,4,5,6,7,8,3,1] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1,1] => 0

[3,2,8,7,6,5,4,1] => [[[.,.],.],[[[[[.,.],.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,2,1] => 5

[3,2,5,6,7,8,4,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => 1

[2,3,8,7,6,5,4,1] => [[.,.],[.,[[[[[.,.],.],.],.],.]]] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,1,1] => 4

[2,3,6,7,8,5,4,1] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1,1] => 1

[2,3,5,8,7,6,4,1] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1,1,1] => 2

[2,3,5,7,8,6,4,1] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1,1] => 0

[2,3,6,5,8,7,4,1] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1,1] => 2

[2,3,5,6,8,7,4,1] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1,1,1] => 1

[2,3,7,6,5,8,4,1] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1,1,1] => 2

[2,3,5,7,6,8,4,1] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1,1] => 0

[2,3,5,6,7,8,4,1] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1,1] => 0

[4,3,2,8,7,6,5,1] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,3,2,1] => 5

[2,4,3,6,8,7,5,1] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,3,6,7,8,5,1] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[2,3,4,8,7,6,5,1] => [[.,.],[.,[.,[[[[.,.],.],.],.]]]] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1,1,1] => 3

[2,3,4,7,8,6,5,1] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1,1,1] => 1

[2,3,4,6,8,7,5,1] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1,1] => 1

[2,3,4,7,6,8,5,1] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1,1,1] => 1

[2,3,4,6,7,8,5,1] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1,1] => 0

[5,4,3,2,8,7,6,1] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,4,3,2,1] => 5

[3,4,5,2,7,8,6,1] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2,1] => 1

[2,4,5,3,8,7,6,1] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,1,1] => 2

[2,4,5,3,7,8,6,1] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1,1] => 0

[2,3,5,4,8,7,6,1] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1,1,1] => 2

[2,3,5,4,7,8,6,1] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1,1] => 0

[3,4,2,5,8,7,6,1] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,2,1] => 3

[3,4,2,5,7,8,6,1] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2,1] => 1

[3,2,4,5,7,8,6,1] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2,1] => 1

[2,3,4,5,8,7,6,1] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1,1] => 2

[2,3,4,5,7,8,6,1] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1,1] => 0

[6,5,4,3,2,8,7,1] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,5,4,3,2,1] => 5

[5,4,6,3,2,8,7,1] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [5,4,4,4,3,2,1] => 4

[5,4,3,6,2,8,7,1] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [5,4,4,4,3,2,1] => 4

[3,4,5,6,2,8,7,1] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,2,1] => 2

[2,4,6,5,3,8,7,1] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,5,6,3,8,7,1] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,1,1] => 1

[2,3,5,6,4,8,7,1] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1,1,1] => 1

[3,4,2,6,5,8,7,1] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2,1] => 2

[2,4,3,6,5,8,7,1] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[3,2,4,6,5,8,7,1] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2,1] => 2

[2,3,4,6,5,8,7,1] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1,1] => 1

[5,4,3,2,6,8,7,1] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [5,4,4,4,3,2,1] => 4

[2,5,4,3,6,8,7,1] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1,1] => 2

[2,4,5,3,6,8,7,1] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,1,1] => 1

[3,4,2,5,6,8,7,1] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,2,1] => 2

[2,4,3,5,6,8,7,1] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,1,1] => 1

[3,2,4,5,6,8,7,1] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,2,1] => 2

[2,3,4,5,6,8,7,1] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => 1

[3,5,6,7,4,2,8,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => 1

[3,4,6,7,5,2,8,1] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2,1] => 1

[3,4,5,7,6,2,8,1] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2,1] => 1

[3,5,6,4,7,2,8,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => 1

[3,4,6,5,7,2,8,1] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2,1] => 1

[3,5,4,6,7,2,8,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => 1

[2,5,6,7,4,3,8,1] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1,1] => 1

[2,4,6,7,5,3,8,1] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[2,4,6,5,7,3,8,1] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[2,5,4,6,7,3,8,1] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1,1] => 1

[2,4,5,6,7,3,8,1] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1,1] => 0

[3,2,5,6,7,4,8,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => 1

[2,3,7,6,5,4,8,1] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1,1,1] => 2

[2,3,5,7,6,4,8,1] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1,1] => 0

[2,3,5,6,7,4,8,1] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1,1] => 0

[3,4,2,6,7,5,8,1] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2,1] => 1

[2,4,3,7,6,5,8,1] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1,1] => 1

[2,4,3,6,7,5,8,1] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[2,3,4,7,6,5,8,1] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1,1,1] => 1

[2,3,4,6,7,5,8,1] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1,1] => 0

[3,4,5,2,7,6,8,1] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2,1] => 1

[2,3,5,4,7,6,8,1] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1,1] => 0

[3,4,2,5,7,6,8,1] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2,1] => 1

[2,4,3,5,7,6,8,1] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1,1] => 0

[3,2,4,5,7,6,8,1] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2,1] => 1

[2,3,4,5,7,6,8,1] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1,1] => 0

[3,5,6,4,2,7,8,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => 1

[3,4,6,5,2,7,8,1] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2,1] => 1

[3,5,4,6,2,7,8,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => 1

[2,5,6,4,3,7,8,1] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1,1] => 1

[2,4,6,5,3,7,8,1] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[2,4,5,6,3,7,8,1] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1,1] => 0

[3,2,5,6,4,7,8,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => 1

[2,3,6,5,4,7,8,1] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1,1] => 1

[2,3,5,6,4,7,8,1] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1,1] => 0

[3,4,2,6,5,7,8,1] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2,1] => 1

[2,4,3,6,5,7,8,1] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[2,3,4,6,5,7,8,1] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1,1] => 0

[3,5,4,2,6,7,8,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => 1

[2,5,4,3,6,7,8,1] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1,1] => 1

[2,4,5,3,6,7,8,1] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1,1] => 0

[3,2,5,4,6,7,8,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => 1

[2,3,5,4,6,7,8,1] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1,1] => 0

[2,4,3,5,6,7,8,1] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1,1] => 0

[1,8,7,6,5,4,3,2] => [.,[[[[[[[.,.],.],.],.],.],.],.]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,1] => 6

[1,7,8,6,5,4,3,2] => [.,[[[[[[.,.],.],.],.],.],[.,.]]] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3,2,1] => 4

[1,6,8,7,5,4,3,2] => [.,[[[[[.,.],.],.],.],[[.,.],.]]] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3,2,1] => 4

[1,7,6,8,5,4,3,2] => [.,[[[[[[.,.],.],.],.],.],[.,.]]] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3,2,1] => 4

[1,6,7,8,5,4,3,2] => [.,[[[[[.,.],.],.],.],[.,[.,.]]]] => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,2,1] => 3

[1,5,8,7,6,4,3,2] => [.,[[[[.,.],.],.],[[[.,.],.],.]]] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,2,1] => 4

[1,6,5,8,7,4,3,2] => [.,[[[[[.,.],.],.],.],[[.,.],.]]] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3,2,1] => 4

[1,7,6,5,8,4,3,2] => [.,[[[[[[.,.],.],.],.],.],[.,.]]] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3,2,1] => 4

[1,6,7,5,8,4,3,2] => [.,[[[[[.,.],.],.],.],[.,[.,.]]]] => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,2,1] => 3

[1,5,7,6,8,4,3,2] => [.,[[[[.,.],.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2,1] => 2

[1,6,5,7,8,4,3,2] => [.,[[[[[.,.],.],.],.],[.,[.,.]]]] => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,2,1] => 3

[1,5,6,7,8,4,3,2] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1] => 2

[1,4,8,7,6,5,3,2] => [.,[[[.,.],.],[[[[.,.],.],.],.]]] => [1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,2,1] => 4

[1,4,7,8,6,5,3,2] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1] => 2

[1,4,6,8,7,5,3,2] => [.,[[[.,.],.],[[.,.],[[.,.],.]]]] => [1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1] => 2

[1,4,6,7,8,5,3,2] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1] => 1

[1,5,4,7,8,6,3,2] => [.,[[[[.,.],.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2,1] => 2

[1,4,5,8,7,6,3,2] => [.,[[[.,.],.],[.,[[[.,.],.],.]]]] => [1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,1] => 3

[1,4,6,5,8,7,3,2] => [.,[[[.,.],.],[[.,.],[[.,.],.]]]] => [1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1] => 2

[1,7,6,5,4,8,3,2] => [.,[[[[[[.,.],.],.],.],.],[.,.]]] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3,2,1] => 4

[1,4,7,6,5,8,3,2] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1] => 2

[1,4,6,7,5,8,3,2] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1] => 1

[1,6,5,4,7,8,3,2] => [.,[[[[[.,.],.],.],.],[.,[.,.]]]] => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,2,1] => 3

[1,5,6,4,7,8,3,2] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1] => 2

[1,5,4,6,7,8,3,2] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1] => 2

[1,4,5,6,7,8,3,2] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1] => 1

[1,3,8,7,6,5,4,2] => [.,[[.,.],[[[[[.,.],.],.],.],.]]] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,1] => 4

[1,3,7,8,6,5,4,2] => [.,[[.,.],[[[[.,.],.],.],[.,.]]]] => [1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1,1] => 2

[1,3,6,8,7,5,4,2] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]] => [1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1] => 2

[1,3,6,7,8,5,4,2] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1] => 1

[1,3,5,8,7,6,4,2] => [.,[[.,.],[[.,.],[[[.,.],.],.]]]] => [1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1,1] => 2

[1,3,5,7,8,6,4,2] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1] => 0

[1,3,5,6,8,7,4,2] => [.,[[.,.],[[.,.],[.,[[.,.],.]]]]] => [1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1,1] => 1

[1,3,6,7,5,8,4,2] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1] => 1

[1,3,6,5,7,8,4,2] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1] => 1

[1,3,5,6,7,8,4,2] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1] => 0

[1,4,3,8,7,6,5,2] => [.,[[[.,.],.],[[[[.,.],.],.],.]]] => [1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,2,1] => 4

[1,4,3,7,8,6,5,2] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1] => 2

[1,4,3,6,8,7,5,2] => [.,[[[.,.],.],[[.,.],[[.,.],.]]]] => [1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1] => 2

[1,4,3,7,6,8,5,2] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1] => 2

[1,4,3,6,7,8,5,2] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1] => 1

[1,3,4,8,7,6,5,2] => [.,[[.,.],[.,[[[[.,.],.],.],.]]]] => [1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1,1] => 3

[1,3,4,7,6,8,5,2] => [.,[[.,.],[.,[[[.,.],.],[.,.]]]]] => [1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1,1] => 1

[1,3,4,6,7,8,5,2] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1] => 0

[1,5,4,3,8,7,6,2] => [.,[[[[.,.],.],.],[[[.,.],.],.]]] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,2,1] => 4

[1,4,5,3,8,7,6,2] => [.,[[[.,.],.],[.,[[[.,.],.],.]]]] => [1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,1] => 3

[1,4,5,3,7,8,6,2] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]] => [1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1] => 1

[1,3,5,4,8,7,6,2] => [.,[[.,.],[[.,.],[[[.,.],.],.]]]] => [1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1,1] => 2

[1,4,3,5,8,7,6,2] => [.,[[[.,.],.],[.,[[[.,.],.],.]]]] => [1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,1] => 3

[1,4,3,5,7,8,6,2] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]] => [1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1] => 1

[1,3,4,5,8,7,6,2] => [.,[[.,.],[.,[.,[[[.,.],.],.]]]]] => [1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1] => 2

[1,3,4,5,7,8,6,2] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1] => 0

[1,6,5,4,3,8,7,2] => [.,[[[[[.,.],.],.],.],[[.,.],.]]] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3,2,1] => 4

[1,5,6,4,3,8,7,2] => [.,[[[[.,.],.],.],[.,[[.,.],.]]]] => [1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1] => 3

[1,4,6,5,3,8,7,2] => [.,[[[.,.],.],[[.,.],[[.,.],.]]]] => [1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1] => 2

[1,4,5,6,3,8,7,2] => [.,[[[.,.],.],[.,[.,[[.,.],.]]]]] => [1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,1] => 2

[1,3,6,5,4,8,7,2] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]] => [1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1] => 2

[1,4,3,6,5,8,7,2] => [.,[[[.,.],.],[[.,.],[[.,.],.]]]] => [1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1] => 2

[1,5,4,3,6,8,7,2] => [.,[[[[.,.],.],.],[.,[[.,.],.]]]] => [1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1] => 3

[1,4,5,3,6,8,7,2] => [.,[[[.,.],.],[.,[.,[[.,.],.]]]]] => [1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,1] => 2

[1,3,4,5,6,8,7,2] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1] => 1

[1,7,6,5,4,3,8,2] => [.,[[[[[[.,.],.],.],.],.],[.,.]]] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3,2,1] => 4

[1,6,7,5,4,3,8,2] => [.,[[[[[.,.],.],.],.],[.,[.,.]]]] => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,2,1] => 3

[1,6,5,7,4,3,8,2] => [.,[[[[[.,.],.],.],.],[.,[.,.]]]] => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,2,1] => 3

[1,5,6,7,4,3,8,2] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1] => 2

[1,4,6,7,5,3,8,2] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1] => 1

[1,5,6,4,7,3,8,2] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1] => 2

[1,4,6,5,7,3,8,2] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1] => 1

[1,5,4,6,7,3,8,2] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1] => 2

[1,4,5,6,7,3,8,2] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1] => 1

[1,3,6,5,7,4,8,2] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1] => 1

[1,3,5,6,7,4,8,2] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1] => 0

[1,3,4,7,6,5,8,2] => [.,[[.,.],[.,[[[.,.],.],[.,.]]]]] => [1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1,1] => 1

[1,3,4,6,7,5,8,2] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1] => 0

[1,3,5,4,7,6,8,2] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1] => 0

[1,3,4,5,7,6,8,2] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1] => 0

[1,5,4,6,3,7,8,2] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1] => 2

[1,4,3,6,5,7,8,2] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1] => 1

[1,3,4,6,5,7,8,2] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1] => 0

[1,5,4,3,6,7,8,2] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1] => 2

[1,4,5,3,6,7,8,2] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1] => 1

[1,4,3,5,6,7,8,2] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1] => 1

[1,3,4,5,6,7,8,2] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 0

[2,1,8,7,6,5,4,3] => [[.,.],[[[[[[.,.],.],.],.],.],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,1,1] => 5

[2,1,5,6,8,7,4,3] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1,1] => 2

[2,1,5,6,7,8,4,3] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1,1] => 1

[2,1,4,7,8,6,5,3] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1,1] => 1

[2,1,4,6,8,7,5,3] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,1,4,6,7,8,5,3] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[2,1,4,5,8,7,6,3] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,1,1] => 2

[2,1,4,5,7,8,6,3] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1,1] => 0

[2,1,5,6,4,8,7,3] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1,1] => 2

[2,1,4,6,5,8,7,3] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,1,5,4,6,8,7,3] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1,1] => 2

[2,1,4,5,6,8,7,3] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,1,1] => 1

[2,1,5,6,7,4,8,3] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1,1] => 1

[2,1,4,7,6,5,8,3] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1,1] => 1

[2,1,4,6,7,5,8,3] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[2,1,5,6,4,7,8,3] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1,1] => 1

[2,1,5,4,6,7,8,3] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1,1] => 1

[2,1,4,5,6,7,8,3] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1,1] => 0

[1,2,8,7,6,5,4,3] => [.,[.,[[[[[[.,.],.],.],.],.],.]]] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1] => 5

[1,2,7,8,6,5,4,3] => [.,[.,[[[[[.,.],.],.],.],[.,.]]]] => [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1] => 3

[1,2,7,6,8,5,4,3] => [.,[.,[[[[[.,.],.],.],.],[.,.]]]] => [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1] => 3

[1,2,6,7,8,5,4,3] => [.,[.,[[[[.,.],.],.],[.,[.,.]]]]] => [1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1] => 2

[1,2,5,8,7,6,4,3] => [.,[.,[[[.,.],.],[[[.,.],.],.]]]] => [1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1] => 3

[1,2,6,5,8,7,4,3] => [.,[.,[[[[.,.],.],.],[[.,.],.]]]] => [1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1] => 3

[1,2,5,6,8,7,4,3] => [.,[.,[[[.,.],.],[.,[[.,.],.]]]]] => [1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1] => 2

[1,2,7,6,5,8,4,3] => [.,[.,[[[[[.,.],.],.],.],[.,.]]]] => [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1] => 3

[1,2,5,7,6,8,4,3] => [.,[.,[[[.,.],.],[[.,.],[.,.]]]]] => [1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1] => 1

[1,2,6,5,7,8,4,3] => [.,[.,[[[[.,.],.],.],[.,[.,.]]]]] => [1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1] => 2

[1,2,5,6,7,8,4,3] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]] => [1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1] => 1

[1,2,4,8,7,6,5,3] => [.,[.,[[.,.],[[[[.,.],.],.],.]]]] => [1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1] => 3

[1,2,4,7,8,6,5,3] => [.,[.,[[.,.],[[[.,.],.],[.,.]]]]] => [1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1] => 1

[1,2,4,6,8,7,5,3] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => [1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1] => 1

[1,2,4,6,7,8,5,3] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1] => 0

[1,2,5,4,8,7,6,3] => [.,[.,[[[.,.],.],[[[.,.],.],.]]]] => [1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1] => 3

[1,2,5,4,7,8,6,3] => [.,[.,[[[.,.],.],[[.,.],[.,.]]]]] => [1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1] => 1

[1,2,4,5,8,7,6,3] => [.,[.,[[.,.],[.,[[[.,.],.],.]]]]] => [1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1] => 2

[1,2,4,5,7,8,6,3] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1] => 0

[1,2,6,5,4,8,7,3] => [.,[.,[[[[.,.],.],.],[[.,.],.]]]] => [1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1] => 3

[1,2,4,6,5,8,7,3] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => [1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1] => 1

[1,2,5,4,6,8,7,3] => [.,[.,[[[.,.],.],[.,[[.,.],.]]]]] => [1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1] => 2

[1,2,4,5,6,8,7,3] => [.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1] => 1

[1,2,7,6,5,4,8,3] => [.,[.,[[[[[.,.],.],.],.],[.,.]]]] => [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1] => 3

[1,2,5,7,6,4,8,3] => [.,[.,[[[.,.],.],[[.,.],[.,.]]]]] => [1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1] => 1

[1,2,5,6,7,4,8,3] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]] => [1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1] => 1

[1,2,4,7,6,5,8,3] => [.,[.,[[.,.],[[[.,.],.],[.,.]]]]] => [1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1] => 1

[1,2,5,4,7,6,8,3] => [.,[.,[[[.,.],.],[[.,.],[.,.]]]]] => [1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1] => 1

[1,2,6,5,4,7,8,3] => [.,[.,[[[[.,.],.],.],[.,[.,.]]]]] => [1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1] => 2

[1,2,5,6,4,7,8,3] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]] => [1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1] => 1

[1,2,5,4,6,7,8,3] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]] => [1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1] => 1

[1,2,4,5,6,7,8,3] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1] => 0

[3,2,1,8,7,6,5,4] => [[[.,.],.],[[[[[.,.],.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,2,1] => 5

[3,2,1,5,6,7,8,4] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => 1

[2,3,1,8,7,6,5,4] => [[.,.],[.,[[[[[.,.],.],.],.],.]]] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,1,1] => 4

[2,3,1,7,8,6,5,4] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1,1,1] => 2

[2,3,1,6,8,7,5,4] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1,1] => 2

[2,3,1,7,6,8,5,4] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1,1,1] => 2

[2,3,1,6,7,8,5,4] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1,1] => 1

[2,3,1,5,7,8,6,4] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1,1] => 0

[2,3,1,6,5,8,7,4] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1,1] => 2

[2,3,1,7,6,5,8,4] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1,1,1] => 2

[2,3,1,6,7,5,8,4] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1,1] => 1

[2,3,1,5,7,6,8,4] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1,1] => 0

[2,3,1,5,6,7,8,4] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1,1] => 0

[1,3,2,8,7,6,5,4] => [.,[[.,.],[[[[[.,.],.],.],.],.]]] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,1] => 4

[1,3,2,6,8,7,5,4] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]] => [1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1] => 2

[1,3,2,7,6,8,5,4] => [.,[[.,.],[[[[.,.],.],.],[.,.]]]] => [1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1,1] => 2

[1,3,2,6,7,8,5,4] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1] => 1

[1,3,2,5,8,7,6,4] => [.,[[.,.],[[.,.],[[[.,.],.],.]]]] => [1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1,1] => 2

[1,3,2,5,7,8,6,4] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1] => 0

[1,3,2,6,5,8,7,4] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]] => [1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1] => 2

[1,3,2,5,6,8,7,4] => [.,[[.,.],[[.,.],[.,[[.,.],.]]]]] => [1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1,1] => 1

[1,3,2,7,6,5,8,4] => [.,[[.,.],[[[[.,.],.],.],[.,.]]]] => [1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1,1] => 2

[1,3,2,6,7,5,8,4] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1] => 1

[1,3,2,6,5,7,8,4] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1] => 1

[1,3,2,5,6,7,8,4] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1] => 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] => [5,4,3,2,1,1,1] => 4

[2,1,3,7,8,6,5,4] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1,1,1] => 2

[2,1,3,6,8,7,5,4] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1,1] => 2

[2,1,3,6,7,8,5,4] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1,1] => 1

[2,1,3,6,5,8,7,4] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1,1] => 2

[2,1,3,5,6,7,8,4] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1,1] => 0

[1,2,3,8,7,6,5,4] => [.,[.,[.,[[[[[.,.],.],.],.],.]]]] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1] => 4

[1,2,3,7,8,6,5,4] => [.,[.,[.,[[[[.,.],.],.],[.,.]]]]] => [1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1] => 2

[1,2,3,6,8,7,5,4] => [.,[.,[.,[[[.,.],.],[[.,.],.]]]]] => [1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1] => 2

[1,2,3,7,6,8,5,4] => [.,[.,[.,[[[[.,.],.],.],[.,.]]]]] => [1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1] => 2

[1,2,3,6,7,8,5,4] => [.,[.,[.,[[[.,.],.],[.,[.,.]]]]]] => [1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1] => 1

[1,2,3,5,8,7,6,4] => [.,[.,[.,[[.,.],[[[.,.],.],.]]]]] => [1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1] => 2

[1,2,3,5,7,8,6,4] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1] => 0

[1,2,3,6,5,8,7,4] => [.,[.,[.,[[[.,.],.],[[.,.],.]]]]] => [1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1] => 2

[1,2,3,5,6,8,7,4] => [.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] => [1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1] => 1

[1,2,3,7,6,5,8,4] => [.,[.,[.,[[[[.,.],.],.],[.,.]]]]] => [1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1] => 2

[1,2,3,6,7,5,8,4] => [.,[.,[.,[[[.,.],.],[.,[.,.]]]]]] => [1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1] => 1

[1,2,3,5,7,6,8,4] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1] => 0

[1,2,3,6,5,7,8,4] => [.,[.,[.,[[[.,.],.],[.,[.,.]]]]]] => [1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1] => 1

[1,2,3,5,6,7,8,4] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1] => 0

[4,3,2,1,8,7,6,5] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,3,2,1] => 5

[3,4,2,1,6,8,7,5] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2,1] => 2

[3,4,2,1,6,7,8,5] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2,1] => 1

[2,4,3,1,7,8,6,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1,1] => 1

[2,4,3,1,6,8,7,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,3,1,7,6,8,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1,1] => 1

[2,4,3,1,6,7,8,5] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[3,2,4,1,6,8,7,5] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2,1] => 2

[3,2,4,1,6,7,8,5] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2,1] => 1

[2,3,4,1,8,7,6,5] => [[.,.],[.,[.,[[[[.,.],.],.],.]]]] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1,1,1] => 3

[2,3,4,1,7,8,6,5] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1,1,1] => 1

[2,3,4,1,6,8,7,5] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1,1] => 1

[2,3,4,1,7,6,8,5] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1,1,1] => 1

[2,3,4,1,6,7,8,5] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1,1] => 0

[1,4,3,2,8,7,6,5] => [.,[[[.,.],.],[[[[.,.],.],.],.]]] => [1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,2,1] => 4

[1,4,3,2,6,8,7,5] => [.,[[[.,.],.],[[.,.],[[.,.],.]]]] => [1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1] => 2

[1,4,3,2,7,6,8,5] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1] => 2

[1,4,3,2,6,7,8,5] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1] => 1

[1,3,4,2,8,7,6,5] => [.,[[.,.],[.,[[[[.,.],.],.],.]]]] => [1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1,1] => 3

[1,3,4,2,7,8,6,5] => [.,[[.,.],[.,[[[.,.],.],[.,.]]]]] => [1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1,1] => 1

[1,3,4,2,6,8,7,5] => [.,[[.,.],[.,[[.,.],[[.,.],.]]]]] => [1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1] => 1

[1,3,4,2,7,6,8,5] => [.,[[.,.],[.,[[[.,.],.],[.,.]]]]] => [1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1,1] => 1

[1,3,4,2,6,7,8,5] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1] => 0

[2,1,4,3,7,8,6,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1,1] => 1

[2,1,4,3,6,8,7,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,1,4,3,7,6,8,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1,1] => 1

[2,1,4,3,6,7,8,5] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[1,2,4,3,8,7,6,5] => [.,[.,[[.,.],[[[[.,.],.],.],.]]]] => [1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1] => 3

[1,2,4,3,7,8,6,5] => [.,[.,[[.,.],[[[.,.],.],[.,.]]]]] => [1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1] => 1

[1,2,4,3,6,8,7,5] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => [1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1] => 1

[1,2,4,3,7,6,8,5] => [.,[.,[[.,.],[[[.,.],.],[.,.]]]]] => [1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1] => 1

[1,2,4,3,6,7,8,5] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1] => 0

[3,2,1,4,6,8,7,5] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2,1] => 2

[3,2,1,4,6,7,8,5] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2,1] => 1

[2,3,1,4,8,7,6,5] => [[.,.],[.,[.,[[[[.,.],.],.],.]]]] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1,1,1] => 3

[2,3,1,4,7,8,6,5] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1,1,1] => 1

[2,3,1,4,7,6,8,5] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1,1,1] => 1

[2,3,1,4,6,7,8,5] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1,1] => 0

[1,3,2,4,8,7,6,5] => [.,[[.,.],[.,[[[[.,.],.],.],.]]]] => [1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1,1] => 3

[1,3,2,4,6,8,7,5] => [.,[[.,.],[.,[[.,.],[[.,.],.]]]]] => [1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1] => 1

[1,3,2,4,7,6,8,5] => [.,[[.,.],[.,[[[.,.],.],[.,.]]]]] => [1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1,1] => 1

[1,3,2,4,6,7,8,5] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1] => 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] => [4,3,2,1,1,1,1] => 3

[2,1,3,4,7,8,6,5] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1,1,1] => 1

[2,1,3,4,7,6,8,5] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1,1,1] => 1

[2,1,3,4,6,7,8,5] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1,1] => 0

[1,2,3,4,8,7,6,5] => [.,[.,[.,[.,[[[[.,.],.],.],.]]]]] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,2,1] => 3

[1,2,3,4,7,8,6,5] => [.,[.,[.,[.,[[[.,.],.],[.,.]]]]]] => [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [2,2,1] => 1

[1,2,3,4,6,8,7,5] => [.,[.,[.,[.,[[.,.],[[.,.],.]]]]]] => [1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [2,1,1] => 1

[1,2,3,4,7,6,8,5] => [.,[.,[.,[.,[[[.,.],.],[.,.]]]]]] => [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [2,2,1] => 1

[1,2,3,4,6,7,8,5] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,1] => 0

[5,4,3,2,1,8,7,6] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,4,3,2,1] => 5

[3,4,5,2,1,8,7,6] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,2,1] => 3

[2,4,5,3,1,8,7,6] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,1,1] => 2

[2,4,5,3,1,7,8,6] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1,1] => 0

[2,3,5,4,1,8,7,6] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1,1,1] => 2

[3,4,2,5,1,8,7,6] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,2,1] => 3

[3,4,2,5,1,7,8,6] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2,1] => 1

[2,4,3,5,1,8,7,6] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,1,1] => 2

[2,4,3,5,1,7,8,6] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1,1] => 0

[3,2,4,5,1,8,7,6] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,2,1] => 3

[2,3,4,5,1,8,7,6] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1,1] => 2

[2,3,4,5,1,7,8,6] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1,1] => 0

[1,5,4,3,2,8,7,6] => [.,[[[[.,.],.],.],[[[.,.],.],.]]] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,2,1] => 4

[1,5,4,3,2,7,8,6] => [.,[[[[.,.],.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2,1] => 2

[1,4,5,3,2,8,7,6] => [.,[[[.,.],.],[.,[[[.,.],.],.]]]] => [1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,1] => 3

[1,4,5,3,2,7,8,6] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]] => [1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1] => 1

[1,3,5,4,2,7,8,6] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1] => 0

[1,3,4,5,2,8,7,6] => [.,[[.,.],[.,[.,[[[.,.],.],.]]]]] => [1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1] => 2

[1,3,4,5,2,7,8,6] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1] => 0

[2,1,4,5,3,8,7,6] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,1,1] => 2

[1,2,5,4,3,8,7,6] => [.,[.,[[[.,.],.],[[[.,.],.],.]]]] => [1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1] => 3

[1,2,5,4,3,7,8,6] => [.,[.,[[[.,.],.],[[.,.],[.,.]]]]] => [1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1] => 1

[1,2,4,5,3,8,7,6] => [.,[.,[[.,.],[.,[[[.,.],.],.]]]]] => [1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1] => 2

[1,2,4,5,3,7,8,6] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1] => 0

[1,3,2,5,4,8,7,6] => [.,[[.,.],[[.,.],[[[.,.],.],.]]]] => [1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1,1] => 2

[1,3,2,5,4,7,8,6] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1] => 0

[2,1,3,5,4,8,7,6] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1,1,1] => 2

[2,1,3,5,4,7,8,6] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1,1] => 0

[1,2,3,5,4,8,7,6] => [.,[.,[.,[[.,.],[[[.,.],.],.]]]]] => [1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1] => 2

[1,2,3,5,4,7,8,6] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1] => 0

[2,4,3,1,5,8,7,6] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,1,1] => 2

[3,2,4,1,5,8,7,6] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,2,1] => 3

[3,2,4,1,5,7,8,6] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2,1] => 1

[2,3,4,1,5,8,7,6] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1,1] => 2

[2,3,4,1,5,7,8,6] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1,1] => 0

[1,4,3,2,5,8,7,6] => [.,[[[.,.],.],[.,[[[.,.],.],.]]]] => [1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,1] => 3

[1,4,3,2,5,7,8,6] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]] => [1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1] => 1

[1,3,4,2,5,7,8,6] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1] => 0

[2,1,4,3,5,8,7,6] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,1,1] => 2

[2,1,4,3,5,7,8,6] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1,1] => 0

[1,2,4,3,5,8,7,6] => [.,[.,[[.,.],[.,[[[.,.],.],.]]]]] => [1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1] => 2

[1,2,4,3,5,7,8,6] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1] => 0

[3,2,1,4,5,8,7,6] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,2,1] => 3

[3,2,1,4,5,7,8,6] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2,1] => 1

[2,3,1,4,5,7,8,6] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1,1] => 0

[1,3,2,4,5,8,7,6] => [.,[[.,.],[.,[.,[[[.,.],.],.]]]]] => [1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1] => 2

[1,3,2,4,5,7,8,6] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1] => 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] => [3,2,1,1,1,1,1] => 2

[2,1,3,4,5,7,8,6] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1,1] => 0

[1,2,3,4,5,8,7,6] => [.,[.,[.,[.,[.,[[[.,.],.],.]]]]]] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => 2

[1,2,3,4,5,7,8,6] => [.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1] => 0

[6,5,4,3,2,1,8,7] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,5,4,3,2,1] => 5

[5,6,4,3,2,1,8,7] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [5,4,4,4,3,2,1] => 4

[5,4,6,3,2,1,8,7] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [5,4,4,4,3,2,1] => 4

[3,4,6,5,2,1,8,7] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2,1] => 2

[5,4,3,6,2,1,8,7] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [5,4,4,4,3,2,1] => 4

[3,4,5,6,2,1,8,7] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,2,1] => 2

[2,5,6,4,3,1,8,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1,1] => 2

[2,4,6,5,3,1,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,3,6,5,4,1,8,7] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1,1] => 2

[2,3,5,6,4,1,8,7] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1,1,1] => 1

[3,4,2,6,5,1,8,7] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2,1] => 2

[2,4,3,6,5,1,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[5,4,3,2,6,1,8,7] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [5,4,4,4,3,2,1] => 4

[3,4,5,2,6,1,8,7] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,2,1] => 2

[2,5,4,3,6,1,8,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1,1] => 2

[2,4,5,3,6,1,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,1,1] => 1

[3,4,2,5,6,1,8,7] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,2,1] => 2

[2,4,3,5,6,1,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,1,1] => 1

[2,3,4,5,6,1,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => 1

[1,6,5,4,3,2,8,7] => [.,[[[[[.,.],.],.],.],[[.,.],.]]] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3,2,1] => 4

[1,5,6,4,3,2,8,7] => [.,[[[[.,.],.],.],[.,[[.,.],.]]]] => [1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1] => 3

[1,5,4,6,3,2,8,7] => [.,[[[[.,.],.],.],[.,[[.,.],.]]]] => [1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1] => 3

[1,3,6,5,4,2,8,7] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]] => [1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1] => 2

[1,3,4,5,6,2,8,7] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1] => 1

[2,1,5,6,4,3,8,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1,1] => 2

[2,1,4,6,5,3,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,1,5,4,6,3,8,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1,1] => 2

[2,1,4,5,6,3,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,1,1] => 1

[1,2,4,5,6,3,8,7] => [.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1] => 1

[2,3,1,6,5,4,8,7] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1,1] => 2

[1,3,2,6,5,4,8,7] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]] => [1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1] => 2

[1,3,2,5,6,4,8,7] => [.,[[.,.],[[.,.],[.,[[.,.],.]]]]] => [1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1,1] => 1

[2,1,3,6,5,4,8,7] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1,1] => 2

[2,1,3,5,6,4,8,7] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1,1,1] => 1

[1,2,3,6,5,4,8,7] => [.,[.,[.,[[[.,.],.],[[.,.],.]]]]] => [1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1] => 2

[1,2,3,5,6,4,8,7] => [.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] => [1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1] => 1

[3,4,2,1,6,5,8,7] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2,1] => 2

[2,4,3,1,6,5,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[3,2,4,1,6,5,8,7] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2,1] => 2

[2,3,4,1,6,5,8,7] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1,1] => 1

[1,3,4,2,6,5,8,7] => [.,[[.,.],[.,[[.,.],[[.,.],.]]]]] => [1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1] => 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] => [4,3,3,2,2,1,1] => 1

[1,2,4,3,6,5,8,7] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => [1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1] => 1

[2,3,1,4,6,5,8,7] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1,1] => 1

[1,3,2,4,6,5,8,7] => [.,[[.,.],[.,[[.,.],[[.,.],.]]]]] => [1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1] => 1

[2,1,3,4,6,5,8,7] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1,1] => 1

[1,2,3,4,6,5,8,7] => [.,[.,[.,[.,[[.,.],[[.,.],.]]]]]] => [1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [2,1,1] => 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] => [5,4,4,4,3,2,1] => 4

[3,4,5,2,1,6,8,7] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,2,1] => 2

[2,5,4,3,1,6,8,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1,1] => 2

[2,4,5,3,1,6,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,1,1] => 1

[2,3,5,4,1,6,8,7] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1,1,1] => 1

[2,4,3,5,1,6,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,1,1] => 1

[2,3,4,5,1,6,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => 1

[1,4,5,3,2,6,8,7] => [.,[[[.,.],.],[.,[.,[[.,.],.]]]]] => [1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,1] => 2

[1,3,5,4,2,6,8,7] => [.,[[.,.],[[.,.],[.,[[.,.],.]]]]] => [1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1,1] => 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] => [4,3,3,3,2,1,1] => 2

[2,1,4,5,3,6,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,1,1] => 1

[1,2,5,4,3,6,8,7] => [.,[.,[[[.,.],.],[.,[[.,.],.]]]]] => [1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1] => 2

[2,1,3,5,4,6,8,7] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1,1,1] => 1

[1,2,3,5,4,6,8,7] => [.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] => [1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1] => 1

[3,2,4,1,5,6,8,7] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,2,1] => 2

[2,3,4,1,5,6,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => 1

[1,4,3,2,5,6,8,7] => [.,[[[.,.],.],[.,[.,[[.,.],.]]]]] => [1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,1] => 2

[1,3,4,2,5,6,8,7] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1] => 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] => [3,2,2,2,2,1,1] => 1

[1,2,4,3,5,6,8,7] => [.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1] => 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] => [3,2,2,2,2,2,1] => 2

[2,3,1,4,5,6,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => 1

[1,3,2,4,5,6,8,7] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1] => 1

[2,1,3,4,5,6,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => 1

[1,2,3,4,5,6,8,7] => [.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1] => 1

[3,5,6,7,4,2,1,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => 1

[3,5,6,4,7,2,1,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => 1

[2,5,6,7,4,3,1,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1,1] => 1

[2,4,6,7,5,3,1,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[2,5,6,4,7,3,1,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1,1] => 1

[2,5,4,6,7,3,1,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1,1] => 1

[2,4,5,6,7,3,1,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1,1] => 0

[3,2,5,6,7,4,1,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => 1

[2,3,7,6,5,4,1,8] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1,1,1] => 2

[2,3,6,7,5,4,1,8] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1,1] => 1

[2,3,5,7,6,4,1,8] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1,1] => 0

[2,3,6,5,7,4,1,8] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1,1] => 1

[2,3,5,6,7,4,1,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1,1] => 0

[3,4,2,6,7,5,1,8] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2,1] => 1

[3,2,4,6,7,5,1,8] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2,1] => 1

[2,3,4,7,6,5,1,8] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1,1,1] => 1

[2,3,4,6,7,5,1,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1,1] => 0

[3,4,5,2,7,6,1,8] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2,1] => 1

[3,4,2,5,7,6,1,8] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2,1] => 1

[2,3,4,5,7,6,1,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1,1] => 0

[3,5,6,4,2,7,1,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => 1

[3,4,6,5,2,7,1,8] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2,1] => 1

[3,5,4,6,2,7,1,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => 1

[2,5,4,6,3,7,1,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1,1] => 1

[2,4,5,6,3,7,1,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1,1] => 0

[2,3,5,6,4,7,1,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1,1] => 0

[3,4,2,6,5,7,1,8] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2,1] => 1

[2,4,3,6,5,7,1,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[2,3,4,6,5,7,1,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1,1] => 0

[3,5,4,2,6,7,1,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => 1

[2,5,4,3,6,7,1,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1,1] => 1

[2,3,5,4,6,7,1,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1,1] => 0

[2,4,3,5,6,7,1,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1,1] => 0

[1,7,6,5,4,3,2,8] => [.,[[[[[[.,.],.],.],.],.],[.,.]]] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3,2,1] => 4

[1,6,7,5,4,3,2,8] => [.,[[[[[.,.],.],.],.],[.,[.,.]]]] => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,2,1] => 3

[1,6,5,7,4,3,2,8] => [.,[[[[[.,.],.],.],.],[.,[.,.]]]] => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,2,1] => 3

[1,5,6,7,4,3,2,8] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1] => 2

[1,4,7,6,5,3,2,8] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1] => 2

[1,4,6,7,5,3,2,8] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1] => 1

[1,5,6,4,7,3,2,8] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1] => 2

[1,4,6,5,7,3,2,8] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1] => 1

[1,5,4,6,7,3,2,8] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1] => 2

[1,4,5,6,7,3,2,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1] => 1

[1,3,6,7,5,4,2,8] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1] => 1

[1,3,5,7,6,4,2,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1] => 0

[1,3,6,5,7,4,2,8] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1] => 1

[1,3,5,6,7,4,2,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1] => 0

[1,3,4,6,7,5,2,8] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1] => 0

[1,3,5,4,7,6,2,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1] => 0

[1,4,3,5,7,6,2,8] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]] => [1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1] => 1

[1,3,4,5,7,6,2,8] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1] => 0

[1,5,4,6,3,7,2,8] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1] => 2

[1,4,5,6,3,7,2,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1] => 1

[1,3,6,5,4,7,2,8] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1] => 1

[1,3,5,6,4,7,2,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1] => 0

[1,4,3,6,5,7,2,8] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1] => 1

[1,3,4,6,5,7,2,8] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1] => 0

[1,5,4,3,6,7,2,8] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1] => 2

[1,4,5,3,6,7,2,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1] => 1

[1,4,3,5,6,7,2,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1] => 1

[1,3,4,5,6,7,2,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 0

[2,1,5,6,7,4,3,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1,1] => 1

[2,1,5,4,6,7,3,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1,1] => 1

[2,1,4,5,6,7,3,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1,1] => 0

[1,2,7,6,5,4,3,8] => [.,[.,[[[[[.,.],.],.],.],[.,.]]]] => [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1] => 3

[1,2,6,7,5,4,3,8] => [.,[.,[[[[.,.],.],.],[.,[.,.]]]]] => [1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1] => 2

[1,2,5,7,6,4,3,8] => [.,[.,[[[.,.],.],[[.,.],[.,.]]]]] => [1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1] => 1

[1,2,5,6,7,4,3,8] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]] => [1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1] => 1

[1,2,4,6,7,5,3,8] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1] => 0

[1,2,5,6,4,7,3,8] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]] => [1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1] => 1

[1,2,4,6,5,7,3,8] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1] => 0

[1,2,5,4,6,7,3,8] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]] => [1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1] => 1

[1,2,4,5,6,7,3,8] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1] => 0

[2,3,1,6,7,5,4,8] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1,1] => 1

[2,3,1,6,5,7,4,8] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1,1] => 1

[2,3,1,5,6,7,4,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1,1] => 0

[1,3,2,7,6,5,4,8] => [.,[[.,.],[[[[.,.],.],.],[.,.]]]] => [1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1,1] => 2

[1,3,2,6,7,5,4,8] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1] => 1

[1,3,2,5,7,6,4,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1] => 0

[1,3,2,6,5,7,4,8] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1] => 1

[1,3,2,5,6,7,4,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1] => 0

[2,1,3,6,7,5,4,8] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1,1] => 1

[1,2,3,7,6,5,4,8] => [.,[.,[.,[[[[.,.],.],.],[.,.]]]]] => [1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1] => 2

[1,2,3,6,7,5,4,8] => [.,[.,[.,[[[.,.],.],[.,[.,.]]]]]] => [1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1] => 1

[1,2,3,5,7,6,4,8] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1] => 0

[1,2,3,6,5,7,4,8] => [.,[.,[.,[[[.,.],.],[.,[.,.]]]]]] => [1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1] => 1

[1,2,3,5,6,7,4,8] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1] => 0

[3,2,4,1,6,7,5,8] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2,1] => 1

[2,3,4,1,7,6,5,8] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1,1,1] => 1

[2,3,4,1,6,7,5,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1,1] => 0

[1,4,3,2,7,6,5,8] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1] => 2

[1,4,3,2,6,7,5,8] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1] => 1

[1,3,4,2,6,7,5,8] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1] => 0

[2,1,4,3,6,7,5,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[1,2,4,3,6,7,5,8] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1] => 0

[2,3,1,4,6,7,5,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1,1] => 0

[1,3,2,4,7,6,5,8] => [.,[[.,.],[.,[[[.,.],.],[.,.]]]]] => [1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1,1] => 1

[1,3,2,4,6,7,5,8] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1] => 0

[1,2,3,4,7,6,5,8] => [.,[.,[.,[.,[[[.,.],.],[.,.]]]]]] => [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [2,2,1] => 1

[1,2,3,4,6,7,5,8] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,1] => 0

[3,4,5,2,1,7,6,8] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2,1] => 1

[2,4,5,3,1,7,6,8] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1,1] => 0

[2,3,5,4,1,7,6,8] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1,1] => 0

[3,4,2,5,1,7,6,8] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2,1] => 1

[2,4,3,5,1,7,6,8] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1,1] => 0

[2,3,4,5,1,7,6,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1,1] => 0

[1,5,4,3,2,7,6,8] => [.,[[[[.,.],.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2,1] => 2

[1,4,5,3,2,7,6,8] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]] => [1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1] => 1

[1,3,5,4,2,7,6,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1] => 0

[1,4,3,5,2,7,6,8] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]] => [1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1] => 1

[1,3,4,5,2,7,6,8] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1] => 0

[1,2,4,5,3,7,6,8] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1] => 0

[2,3,1,5,4,7,6,8] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1,1] => 0

[1,3,2,5,4,7,6,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1] => 0

[1,2,3,5,4,7,6,8] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1] => 0

[3,2,4,1,5,7,6,8] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2,1] => 1

[2,3,4,1,5,7,6,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1,1] => 0

[1,4,3,2,5,7,6,8] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]] => [1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1] => 1

[1,3,4,2,5,7,6,8] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1] => 0

[1,2,4,3,5,7,6,8] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1] => 0

[3,2,1,4,5,7,6,8] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2,1] => 1

[2,3,1,4,5,7,6,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1,1] => 0

[1,3,2,4,5,7,6,8] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1] => 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] => [2,2,1,1,1,1,1] => 0

[1,2,3,4,5,7,6,8] => [.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1] => 0

[2,4,6,5,3,1,7,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[2,4,5,6,3,1,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1,1] => 0

[2,3,6,5,4,1,7,8] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1,1] => 1

[2,3,5,6,4,1,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1,1] => 0

[2,4,3,6,5,1,7,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[2,3,4,6,5,1,7,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1,1] => 0

[3,5,4,2,6,1,7,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => 1

[2,3,5,4,6,1,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1,1] => 0

[1,6,5,4,3,2,7,8] => [.,[[[[[.,.],.],.],.],[.,[.,.]]]] => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,2,1] => 3

[1,5,6,4,3,2,7,8] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1] => 2

[1,4,6,5,3,2,7,8] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1] => 1

[1,5,4,6,3,2,7,8] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1] => 2

[1,4,5,6,3,2,7,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1] => 1

[1,3,5,6,4,2,7,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1] => 0

[1,4,3,6,5,2,7,8] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1] => 1

[1,5,4,3,6,2,7,8] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1] => 2

[1,4,5,3,6,2,7,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1] => 1

[1,4,3,5,6,2,7,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1] => 1

[1,3,4,5,6,2,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 0

[2,1,5,6,4,3,7,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1,1] => 1

[2,1,4,6,5,3,7,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[1,2,6,5,4,3,7,8] => [.,[.,[[[[.,.],.],.],[.,[.,.]]]]] => [1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1] => 2

[1,2,5,6,4,3,7,8] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]] => [1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1] => 1

[1,2,4,6,5,3,7,8] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1] => 0

[1,2,4,5,6,3,7,8] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1] => 0

[3,2,1,5,6,4,7,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => 1

[2,3,1,6,5,4,7,8] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1,1] => 1

[2,3,1,5,6,4,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1,1] => 0

[1,3,2,6,5,4,7,8] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1] => 1

[1,3,2,5,6,4,7,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1] => 0

[1,2,3,6,5,4,7,8] => [.,[.,[.,[[[.,.],.],[.,[.,.]]]]]] => [1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1] => 1

[1,2,3,5,6,4,7,8] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1] => 0

[2,4,3,1,6,5,7,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[3,2,4,1,6,5,7,8] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2,1] => 1

[2,3,4,1,6,5,7,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1,1] => 0

[2,1,4,3,6,5,7,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[1,2,4,3,6,5,7,8] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1] => 0

[1,3,2,4,6,5,7,8] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1] => 0

[2,1,3,4,6,5,7,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1,1] => 0

[1,2,3,4,6,5,7,8] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,1] => 0

[3,5,4,2,1,6,7,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => 1

[2,5,4,3,1,6,7,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1,1] => 1

[2,4,5,3,1,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1,1] => 0

[3,2,5,4,1,6,7,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => 1

[2,3,5,4,1,6,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1,1] => 0

[2,4,3,5,1,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1,1] => 0

[1,5,4,3,2,6,7,8] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1] => 2

[1,4,5,3,2,6,7,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1] => 1

[1,4,3,5,2,6,7,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1] => 1

[1,3,4,5,2,6,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 0

[2,1,5,4,3,6,7,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1,1] => 1

[2,1,4,5,3,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1,1] => 0

[1,2,5,4,3,6,7,8] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]] => [1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1] => 1

[1,2,4,5,3,6,7,8] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1] => 0

[3,2,1,5,4,6,7,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => 1

[2,3,1,5,4,6,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1,1] => 0

[1,3,2,5,4,6,7,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1] => 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] => [2,2,2,2,1,1,1] => 0

[1,2,3,5,4,6,7,8] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1] => 0

[2,4,3,1,5,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1,1] => 0

[1,4,3,2,5,6,7,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1] => 1

[1,3,4,2,5,6,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 0

[2,1,4,3,5,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1,1] => 0

[1,2,4,3,5,6,7,8] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1] => 0

[1,3,2,4,5,6,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 0

[1,2,3,4,8,6,7,5] => [.,[.,[.,[.,[[[.,.],[.,.]],.]]]]] => [1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [3,1,1] => 1

[1,2,3,5,8,6,7,4] => [.,[.,[.,[[.,.],[[.,[.,.]],.]]]]] => [1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1] => 1

[1,2,3,7,5,6,4,8] => [.,[.,[.,[[[.,.],[.,.]],[.,.]]]]] => [1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1] => 0

[1,2,3,7,5,6,8,4] => [.,[.,[.,[[[.,.],[.,.]],[.,.]]]]] => [1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1] => 0

[1,2,3,8,5,6,7,4] => [.,[.,[.,[[[.,.],[.,[.,.]]],.]]]] => [1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1] => 1

[1,2,3,8,5,7,6,4] => [.,[.,[.,[[[.,.],[[.,.],.]],.]]]] => [1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1] => 2

[1,2,3,8,6,5,7,4] => [.,[.,[.,[[[[.,.],.],[.,.]],.]]]] => [1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1] => 2

[1,2,3,8,6,7,5,4] => [.,[.,[.,[[[[.,.],.],[.,.]],.]]]] => [1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1] => 2

[1,2,4,3,8,6,7,5] => [.,[.,[[.,.],[[[.,.],[.,.]],.]]]] => [1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1] => 1

[1,2,4,5,8,6,7,3] => [.,[.,[[.,.],[.,[[.,[.,.]],.]]]]] => [1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1] => 1

[1,2,4,7,5,6,8,3] => [.,[.,[[.,.],[[.,[.,.]],[.,.]]]]] => [1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1] => 0

[1,2,4,8,5,6,7,3] => [.,[.,[[.,.],[[.,[.,[.,.]]],.]]]] => [1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1] => 1

[1,2,4,8,6,5,7,3] => [.,[.,[[.,.],[[[.,.],[.,.]],.]]]] => [1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1] => 1

[1,2,5,4,8,6,7,3] => [.,[.,[[[.,.],.],[[.,[.,.]],.]]]] => [1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1] => 2

[1,2,6,4,5,3,7,8] => [.,[.,[[[.,.],[.,.]],[.,[.,.]]]]] => [1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1] => 0

[1,2,6,4,5,7,8,3] => [.,[.,[[[.,.],[.,.]],[.,[.,.]]]]] => [1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1] => 0

[1,2,7,4,5,6,8,3] => [.,[.,[[[.,.],[.,[.,.]]],[.,.]]]] => [1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1] => 0

[1,2,8,4,5,6,7,3] => [.,[.,[[[.,.],[.,[.,[.,.]]]],.]]] => [1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1] => 1

[1,2,8,4,6,7,5,3] => [.,[.,[[[.,.],[[.,.],[.,.]]],.]]] => [1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1] => 1

[1,2,8,4,7,6,5,3] => [.,[.,[[[.,.],[[[.,.],.],.]],.]]] => [1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,1] => 3

[1,2,7,5,4,6,3,8] => [.,[.,[[[[.,.],.],[.,.]],[.,.]]]] => [1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1] => 1

[1,2,7,5,4,6,8,3] => [.,[.,[[[[.,.],.],[.,.]],[.,.]]]] => [1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1] => 1

[1,2,8,5,4,6,7,3] => [.,[.,[[[[.,.],.],[.,[.,.]]],.]]] => [1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1] => 2

[1,2,8,5,4,7,6,3] => [.,[.,[[[[.,.],.],[[.,.],.]],.]]] => [1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1] => 3

[1,2,8,5,6,4,7,3] => [.,[.,[[[[.,.],.],[.,[.,.]]],.]]] => [1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1] => 2

[1,2,8,5,6,7,4,3] => [.,[.,[[[[.,.],.],[.,[.,.]]],.]]] => [1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1] => 2

[1,2,8,6,5,4,7,3] => [.,[.,[[[[[.,.],.],.],[.,.]],.]]] => [1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1] => 3

[1,2,8,6,5,7,4,3] => [.,[.,[[[[[.,.],.],.],[.,.]],.]]] => [1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1] => 3

[1,2,8,7,5,6,4,3] => [.,[.,[[[[[.,.],.],[.,.]],.],.]]] => [1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,1] => 3

[1,3,2,4,8,6,7,5] => [.,[[.,.],[.,[[[.,.],[.,.]],.]]]] => [1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1,1] => 1

[1,3,2,7,5,6,8,4] => [.,[[.,.],[[[.,.],[.,.]],[.,.]]]] => [1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1] => 0

[1,3,2,8,5,7,6,4] => [.,[[.,.],[[[.,.],[[.,.],.]],.]]] => [1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1,1] => 2

[1,3,2,8,6,5,7,4] => [.,[[.,.],[[[[.,.],.],[.,.]],.]]] => [1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1,1] => 2

[1,3,2,8,6,7,5,4] => [.,[[.,.],[[[[.,.],.],[.,.]],.]]] => [1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1,1] => 2

[1,3,4,2,8,6,7,5] => [.,[[.,.],[.,[[[.,.],[.,.]],.]]]] => [1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1,1] => 1

[1,3,4,5,8,6,7,2] => [.,[[.,.],[.,[.,[[.,[.,.]],.]]]]] => [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1] => 1

[1,3,4,8,5,6,7,2] => [.,[[.,.],[.,[[.,[.,[.,.]]],.]]]] => [1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1] => 1

[1,3,6,4,5,2,8,7] => [.,[[.,.],[[.,[.,.]],[[.,.],.]]]] => [1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1] => 1

[1,3,6,4,5,7,2,8] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => [1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1] => 0

[1,3,6,4,5,7,8,2] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => [1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1] => 0

[1,3,6,4,5,8,7,2] => [.,[[.,.],[[.,[.,.]],[[.,.],.]]]] => [1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1] => 1

[1,3,7,4,5,6,2,8] => [.,[[.,.],[[.,[.,[.,.]]],[.,.]]]] => [1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1,1] => 0

[1,3,7,4,5,6,8,2] => [.,[[.,.],[[.,[.,[.,.]]],[.,.]]]] => [1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1,1] => 0

[1,3,8,4,5,6,7,2] => [.,[[.,.],[[.,[.,[.,[.,.]]]],.]]] => [1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1,1] => 1

[1,3,8,4,6,5,7,2] => [.,[[.,.],[[.,[[.,.],[.,.]]],.]]] => [1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1,1] => 1

[1,3,8,4,6,7,5,2] => [.,[[.,.],[[.,[[.,.],[.,.]]],.]]] => [1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1,1] => 1

[1,3,8,5,4,6,7,2] => [.,[[.,.],[[[.,.],[.,[.,.]]],.]]] => [1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1,1] => 1

[1,3,8,5,4,7,6,2] => [.,[[.,.],[[[.,.],[[.,.],.]],.]]] => [1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1,1] => 2

[1,3,8,5,6,7,4,2] => [.,[[.,.],[[[.,.],[.,[.,.]]],.]]] => [1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1,1] => 1

[1,3,8,5,7,6,4,2] => [.,[[.,.],[[[.,.],[[.,.],.]],.]]] => [1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1,1] => 2

[1,3,8,6,5,7,4,2] => [.,[[.,.],[[[[.,.],.],[.,.]],.]]] => [1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1,1] => 2

[1,3,8,7,5,6,4,2] => [.,[[.,.],[[[[.,.],[.,.]],.],.]]] => [1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,1,1] => 2

[1,4,3,2,8,6,7,5] => [.,[[[.,.],.],[[[.,.],[.,.]],.]]] => [1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1] => 2

[1,4,3,5,8,6,7,2] => [.,[[[.,.],.],[.,[[.,[.,.]],.]]]] => [1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,1] => 2

[1,4,3,8,5,6,7,2] => [.,[[[.,.],.],[[.,[.,[.,.]]],.]]] => [1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,1] => 2

[1,4,3,8,5,7,6,2] => [.,[[[.,.],.],[[.,[[.,.],.]],.]]] => [1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,1] => 3

[1,4,3,8,6,5,7,2] => [.,[[[.,.],.],[[[.,.],[.,.]],.]]] => [1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1] => 2

[1,4,3,8,6,7,5,2] => [.,[[[.,.],.],[[[.,.],[.,.]],.]]] => [1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1] => 2

[1,5,3,4,2,6,7,8] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => [1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1] => 0

[1,5,3,4,2,7,8,6] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1] => 0

[1,5,3,4,2,8,7,6] => [.,[[[.,.],[.,.]],[[[.,.],.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1,1] => 2

[1,5,3,4,6,2,8,7] => [.,[[[.,.],[.,.]],[.,[[.,.],.]]]] => [1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1] => 1

[1,5,3,4,6,7,2,8] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => [1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1] => 0

[1,5,3,4,6,7,8,2] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => [1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1] => 0

[1,5,3,4,8,6,7,2] => [.,[[[.,.],[.,.]],[[.,[.,.]],.]]] => [1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1] => 1

[1,6,3,4,5,2,7,8] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]] => [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1] => 0

[1,6,3,4,5,8,7,2] => [.,[[[.,.],[.,[.,.]]],[[.,.],.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1] => 1

[1,7,3,4,5,6,2,8] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1,1] => 0

[1,7,3,4,5,6,8,2] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1,1] => 0

[1,8,3,4,5,6,7,2] => [.,[[[.,.],[.,[.,[.,[.,.]]]]],.]] => [1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1,1] => 1

[1,8,3,4,6,7,5,2] => [.,[[[.,.],[.,[[.,.],[.,.]]]],.]] => [1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1,1,1] => 1

[1,8,3,4,7,6,5,2] => [.,[[[.,.],[.,[[[.,.],.],.]]],.]] => [1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,1,1] => 3

[1,6,3,5,4,2,7,8] => [.,[[[.,.],[[.,.],.]],[.,[.,.]]]] => [1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1] => 1

[1,6,3,5,4,8,7,2] => [.,[[[.,.],[[.,.],.]],[[.,.],.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,1,1] => 2

[1,7,3,5,4,6,2,8] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]] => [1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1] => 0

[1,8,3,5,4,6,7,2] => [.,[[[.,.],[[.,.],[.,[.,.]]]],.]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,1,1] => 1

[1,8,3,5,6,4,7,2] => [.,[[[.,.],[[.,.],[.,[.,.]]]],.]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,1,1] => 1

[1,8,3,5,6,7,4,2] => [.,[[[.,.],[[.,.],[.,[.,.]]]],.]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,1,1] => 1

[1,8,3,5,7,6,4,2] => [.,[[[.,.],[[.,.],[[.,.],.]]],.]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,1,1] => 2

[1,7,3,6,5,4,2,8] => [.,[[[.,.],[[[.,.],.],.]],[.,.]]] => [1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,1,1] => 2

[1,7,3,6,5,4,8,2] => [.,[[[.,.],[[[.,.],.],.]],[.,.]]] => [1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,1,1] => 2

[1,8,3,6,5,4,7,2] => [.,[[[.,.],[[[.,.],.],[.,.]]],.]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,1,1] => 2

[1,8,3,7,5,6,4,2] => [.,[[[.,.],[[[.,.],[.,.]],.]],.]] => [1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,1,1] => 2

[1,8,3,7,6,5,4,2] => [.,[[[.,.],[[[[.,.],.],.],.]],.]] => [1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,1,1] => 4

[1,6,4,3,5,2,7,8] => [.,[[[[.,.],.],[.,.]],[.,[.,.]]]] => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2,1] => 1

[1,8,4,3,5,6,7,2] => [.,[[[[.,.],.],[.,[.,[.,.]]]],.]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,1] => 2

[1,8,4,3,5,7,6,2] => [.,[[[[.,.],.],[.,[[.,.],.]]],.]] => [1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2,1] => 3

[1,8,4,3,6,5,7,2] => [.,[[[[.,.],.],[[.,.],[.,.]]],.]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,2,1] => 2

[1,8,4,3,6,7,5,2] => [.,[[[[.,.],.],[[.,.],[.,.]]],.]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,2,1] => 2

[1,6,4,5,3,2,7,8] => [.,[[[[.,.],.],[.,.]],[.,[.,.]]]] => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2,1] => 1

[1,7,4,5,3,6,8,2] => [.,[[[[.,.],.],[.,[.,.]]],[.,.]]] => [1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2,1] => 1

[1,8,4,5,3,6,7,2] => [.,[[[[.,.],.],[.,[.,[.,.]]]],.]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,1] => 2

[1,7,4,5,6,3,8,2] => [.,[[[[.,.],.],[.,[.,.]]],[.,.]]] => [1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2,1] => 1

[1,8,4,5,6,3,7,2] => [.,[[[[.,.],.],[.,[.,[.,.]]]],.]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,1] => 2

[1,8,4,5,6,7,3,2] => [.,[[[[.,.],.],[.,[.,[.,.]]]],.]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,1] => 2

[1,8,4,6,5,3,7,2] => [.,[[[[.,.],.],[[.,.],[.,.]]],.]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,2,1] => 2

[1,8,4,6,5,7,3,2] => [.,[[[[.,.],.],[[.,.],[.,.]]],.]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,2,1] => 2

[1,7,5,4,3,6,2,8] => [.,[[[[[.,.],.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,2,1] => 2

[1,7,5,4,3,6,8,2] => [.,[[[[[.,.],.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,2,1] => 2

[1,8,5,4,3,6,7,2] => [.,[[[[[.,.],.],.],[.,[.,.]]],.]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,2,1] => 3

[1,8,5,4,6,3,7,2] => [.,[[[[[.,.],.],.],[.,[.,.]]],.]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,2,1] => 3

[1,8,5,4,6,7,3,2] => [.,[[[[[.,.],.],.],[.,[.,.]]],.]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,2,1] => 3

[1,7,6,4,5,3,2,8] => [.,[[[[[.,.],.],[.,.]],.],[.,.]]] => [1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,2,1] => 2

[1,8,6,4,5,3,7,2] => [.,[[[[[.,.],.],[.,.]],[.,.]],.]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2,2,1] => 2

[1,8,6,4,5,7,3,2] => [.,[[[[[.,.],.],[.,.]],[.,.]],.]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2,2,1] => 2

[1,8,7,4,5,6,3,2] => [.,[[[[[.,.],.],[.,[.,.]]],.],.]] => [1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,2,1] => 3

[1,8,6,5,4,3,7,2] => [.,[[[[[[.,.],.],.],.],[.,.]],.]] => [1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3,2,1] => 4

[1,8,6,5,4,7,3,2] => [.,[[[[[[.,.],.],.],.],[.,.]],.]] => [1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3,2,1] => 4

[1,8,7,5,4,6,3,2] => [.,[[[[[[.,.],.],.],[.,.]],.],.]] => [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3,2,1] => 4

[1,8,7,5,6,4,3,2] => [.,[[[[[[.,.],.],.],[.,.]],.],.]] => [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3,2,1] => 4

[2,1,3,4,8,6,7,5] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1,1,1] => 1

[2,1,3,5,8,6,7,4] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1,1,1] => 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] => [5,2,2,2,1,1,1] => 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] => [5,3,2,2,1,1,1] => 2

[2,1,3,8,6,5,7,4] => [[.,.],[.,[[[[.,.],.],[.,.]],.]]] => [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1,1,1] => 2

[2,1,3,8,6,7,5,4] => [[.,.],[.,[[[[.,.],.],[.,.]],.]]] => [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1,1,1] => 2

[2,1,4,3,8,6,7,5] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1,1] => 1

[2,1,4,5,8,6,7,3] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,1,1] => 1

[2,1,4,8,5,6,7,3] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,1,1] => 1

[2,1,4,8,5,7,6,3] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,1,1] => 2

[2,1,4,8,6,5,7,3] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1,1] => 1

[2,1,4,8,6,7,5,3] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1,1] => 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] => [6,2,2,2,2,1,1] => 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] => [6,3,2,2,2,1,1] => 2

[2,3,1,7,5,6,4,8] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1,1] => 0

[2,3,1,8,5,6,7,4] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1,1,1] => 1

[2,3,1,8,6,7,5,4] => [[.,.],[.,[[[[.,.],.],[.,.]],.]]] => [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1,1,1] => 2

[2,3,4,1,8,6,7,5] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1,1,1] => 1

[2,3,4,5,8,6,7,1] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1,1] => 1

[2,3,4,7,5,6,1,8] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1,1] => 0

[2,3,4,7,5,6,8,1] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1,1] => 0

[2,3,4,8,5,6,7,1] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1,1] => 1

[2,3,4,8,5,7,6,1] => [[.,.],[.,[.,[[.,[[.,.],.]],.]]]] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1,1,1] => 2

[2,3,4,8,6,5,7,1] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1,1,1] => 1

[2,3,4,8,6,7,5,1] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1,1,1] => 1

[2,3,5,4,8,6,7,1] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1,1,1] => 1

[2,3,6,4,5,1,7,8] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1,1] => 0

[2,3,6,4,5,1,8,7] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1,1] => 1

[2,3,6,4,5,7,8,1] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1,1] => 0

[2,3,6,4,5,8,7,1] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1,1] => 1

[2,3,7,4,5,6,8,1] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1,1,1] => 0

[2,3,8,4,5,6,7,1] => [[.,.],[.,[[.,[.,[.,[.,.]]]],.]]] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1,1,1] => 1

[2,3,7,4,6,5,8,1] => [[.,.],[.,[[.,[[.,.],.]],[.,.]]]] => [1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1,1,1] => 1

[2,3,8,4,6,7,5,1] => [[.,.],[.,[[.,[[.,.],[.,.]]],.]]] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1,1,1] => 1

[2,3,7,5,4,6,1,8] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1,1] => 0

[2,3,7,5,4,6,8,1] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1,1] => 0

[2,3,8,5,4,6,7,1] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1,1,1] => 1

[2,3,7,5,6,4,1,8] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1,1] => 0

[2,3,7,5,6,4,8,1] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1,1] => 0

[2,3,8,5,6,4,7,1] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1,1,1] => 1

[2,3,8,5,6,7,4,1] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1,1,1] => 1

[2,3,8,5,7,6,4,1] => [[.,.],[.,[[[.,.],[[.,.],.]],.]]] => [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1,1,1] => 2

[2,3,8,6,5,4,7,1] => [[.,.],[.,[[[[.,.],.],[.,.]],.]]] => [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1,1,1] => 2

[2,4,3,5,8,6,7,1] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,1,1] => 1

[2,4,3,7,5,6,8,1] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => 0

[2,4,3,8,5,6,7,1] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,1,1] => 1

[2,4,3,8,5,7,6,1] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,1,1] => 2

[2,4,3,8,6,5,7,1] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1,1] => 1

[2,5,3,4,1,6,7,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1,1] => 0

[2,5,3,4,6,7,1,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1,1] => 0

[2,5,3,4,6,7,8,1] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1,1] => 0

[2,5,3,4,6,8,7,1] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1,1] => 1

[2,5,3,4,7,6,8,1] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[2,5,3,4,8,6,7,1] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1,1] => 1

[2,6,3,4,5,1,7,8] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1,1] => 0

[2,6,3,4,5,7,8,1] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1,1] => 0

[2,6,3,4,5,8,7,1] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1,1] => 1

[2,7,3,4,5,6,1,8] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1,1,1] => 0

[2,8,3,4,5,6,7,1] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1,1,1] => 1

[2,8,3,4,5,7,6,1] => [[.,.],[[.,[.,[.,[[.,.],.]]]],.]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1,1,1,1] => 2

[2,7,3,5,4,6,8,1] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1,1] => 0

[2,8,3,5,4,7,6,1] => [[.,.],[[.,[[.,.],[[.,.],.]]],.]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,1,1,1] => 2

[2,7,3,5,6,4,8,1] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1,1] => 0

[2,8,3,5,6,7,4,1] => [[.,.],[[.,[[.,.],[.,[.,.]]]],.]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,1,1,1] => 1

[2,8,3,5,7,6,4,1] => [[.,.],[[.,[[.,.],[[.,.],.]]],.]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,1,1,1] => 2

[2,8,3,7,5,6,4,1] => [[.,.],[[.,[[[.,.],[.,.]],.]],.]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,1,1,1] => 2

[2,8,4,3,5,6,7,1] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,1,1] => 1

[2,8,4,3,5,7,6,1] => [[.,.],[[[.,.],[.,[[.,.],.]]],.]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2,1,1] => 2

[2,8,4,5,3,6,7,1] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,1,1] => 1

[2,8,4,5,6,3,7,1] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,1,1] => 1

[2,8,4,5,6,7,3,1] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,1,1] => 1

[3,2,4,5,8,6,7,1] => [[[.,.],.],[.,[.,[[.,[.,.]],.]]]] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,2,1] => 2

[3,2,4,7,5,6,8,1] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2,1] => 1

[3,2,4,8,5,6,7,1] => [[[.,.],.],[.,[[.,[.,[.,.]]],.]]] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,2,1] => 2

[3,2,8,4,5,6,7,1] => [[[.,.],.],[[.,[.,[.,[.,.]]]],.]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,2,1] => 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] => [7,2,1,1,1,1,1] => 2

[8,2,3,5,4,6,7,1] => [[[.,.],[.,[[.,.],[.,[.,.]]]]],.] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,1,1,1] => 1

[8,2,3,5,6,7,4,1] => [[[.,.],[.,[[.,.],[.,[.,.]]]]],.] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,1,1,1] => 1

[8,2,3,5,7,6,4,1] => [[[.,.],[.,[[.,.],[[.,.],.]]]],.] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,1,1,1] => 2

[8,2,4,5,6,7,3,1] => [[[.,.],[[.,.],[.,[.,[.,.]]]]],.] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2,1,1] => 1

[4,3,2,8,5,6,7,1] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [6,3,3,3,3,2,1] => 3

[4,3,2,8,5,7,6,1] => [[[[.,.],.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,3,3,2,1] => 4

[5,4,3,2,8,6,7,1] => [[[[[.,.],.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,4,4,3,2,1] => 4

[2,4,1,3,6,5,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,1,4,6,3,5,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,1,6,3,5,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,6,1,3,5,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,1,4,3,6,8,5,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,1,3,6,8,5,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,1,4,6,3,8,5,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,1,6,3,8,5,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,6,1,3,8,5,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,1,4,6,8,3,5,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,1,6,8,3,5,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,6,1,8,3,5,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,6,8,1,3,5,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,1,3,6,5,7,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[2,1,4,6,3,5,7,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[2,4,1,6,3,5,7,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[2,4,6,1,3,5,7,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[2,1,4,6,3,7,5,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[2,4,1,6,3,7,5,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[2,4,6,1,3,7,5,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[2,4,6,7,1,3,5,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[2,4,1,3,6,7,8,5] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[2,1,4,6,3,7,8,5] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[2,4,1,6,3,7,8,5] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[2,1,4,6,7,3,8,5] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[2,4,1,6,7,3,8,5] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[2,4,6,1,7,3,8,5] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[2,4,6,7,1,3,8,5] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[2,1,4,6,7,8,3,5] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[2,4,1,6,7,8,3,5] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[2,4,6,7,8,1,3,5] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[2,1,4,3,7,5,8,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => 0

[2,4,1,3,7,5,8,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => 0

[2,1,4,7,3,5,8,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => 0

[2,4,1,7,3,5,8,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => 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] => [4,4,2,2,2,1,1] => 0

[2,4,1,3,7,8,5,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => 0

[2,4,1,7,3,8,5,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => 0

[2,1,4,7,8,3,5,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => 0

[2,4,1,7,8,3,5,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => 0

[2,4,7,1,8,3,5,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => 0

[2,4,7,8,1,3,5,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => 0

[2,4,1,5,3,7,6,8] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1,1] => 0

[2,4,5,1,3,7,6,8] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1,1] => 0

[2,4,5,1,7,3,6,8] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1,1] => 0

[2,4,1,3,5,7,8,6] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1,1] => 0

[2,4,1,5,3,7,8,6] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1,1] => 0

[2,4,5,1,3,7,8,6] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1,1] => 0

[2,1,4,5,7,3,8,6] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1,1] => 0

[2,4,1,5,7,3,8,6] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1,1] => 0

[2,4,5,1,7,3,8,6] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1,1] => 0

[2,1,4,5,7,8,3,6] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1,1] => 0

[2,4,5,1,7,8,3,6] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1,1] => 0

[2,4,5,7,1,8,3,6] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1,1] => 0

[2,4,5,7,8,1,3,6] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1,1] => 0

[2,1,4,3,8,5,6,7] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,1,1] => 1

[2,4,1,3,8,5,6,7] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,1,1] => 1

[2,1,4,8,3,5,6,7] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,1,1] => 1

[2,4,1,8,3,5,6,7] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,1,1] => 1

[2,4,8,1,3,5,6,7] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,1,1] => 1

[2,1,4,3,5,8,6,7] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,1,1] => 1

[2,4,1,5,3,8,6,7] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,1,1] => 1

[2,1,4,5,8,3,6,7] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,1,1] => 1

[2,4,1,5,8,3,6,7] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,1,1] => 1

[2,4,5,1,8,3,6,7] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,1,1] => 1

[2,4,1,5,3,6,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,1,1] => 1

[2,4,1,5,6,3,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,1,1] => 1

[2,4,5,1,6,3,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,1,1] => 1

[2,4,5,6,1,3,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,1,1] => 1

[2,1,4,5,6,8,3,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,1,1] => 1

[2,4,1,5,6,8,3,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,1,1] => 1

[2,4,5,1,6,8,3,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,1,1] => 1

[2,4,5,6,1,8,3,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,1,1] => 1

[2,4,5,6,8,1,3,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,1,1] => 1

[2,4,1,3,5,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1,1] => 0

[2,4,1,5,3,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1,1] => 0

[2,4,5,1,3,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1,1] => 0

[2,4,1,5,6,3,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1,1] => 0

[2,4,5,1,6,3,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1,1] => 0

[2,4,5,6,1,3,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1,1] => 0

[2,4,1,5,6,7,3,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1,1] => 0

[2,4,5,6,1,7,3,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1,1] => 0

[2,4,5,6,7,1,3,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1,1] => 0

[2,4,1,5,6,7,8,3] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1,1] => 0

[2,4,5,1,6,7,8,3] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1,1] => 0

[2,4,5,6,1,7,8,3] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1,1] => 0

[2,4,5,6,7,1,8,3] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1,1] => 0

[2,4,5,6,7,8,1,3] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1,1] => 0

[2,1,5,3,6,4,8,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1,1] => 1

[2,5,1,3,6,4,8,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1,1] => 1

[2,1,5,6,3,4,8,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1,1] => 1

[2,5,1,6,3,4,8,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1,1] => 1

[2,5,6,1,3,4,8,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1,1] => 1

[2,1,5,3,6,8,4,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1,1] => 1

[2,5,1,3,6,8,4,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1,1] => 1

[2,5,6,1,3,8,4,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1,1] => 1

[2,1,5,6,8,3,4,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1,1] => 1

[2,5,1,6,8,3,4,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1,1] => 1

[2,5,6,8,1,3,4,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1,1] => 1

[2,5,1,3,6,4,7,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1,1] => 0

[2,1,5,6,3,4,7,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1,1] => 0

[2,5,1,6,3,4,7,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1,1] => 0

[2,1,5,3,6,7,4,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1,1] => 0

[2,1,5,6,3,7,4,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1,1] => 0

[2,5,1,6,3,7,4,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1,1] => 0

[2,5,6,1,3,7,4,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1,1] => 0

[2,1,5,6,7,3,4,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1,1] => 0

[2,5,1,6,7,3,4,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1,1] => 0

[2,5,6,1,7,3,4,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1,1] => 0

[2,1,5,3,6,7,8,4] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1,1] => 0

[2,5,1,3,6,7,8,4] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1,1] => 0

[2,1,5,6,3,7,8,4] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1,1] => 0

[2,5,1,6,3,7,8,4] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1,1] => 0

[2,5,6,1,3,7,8,4] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1,1] => 0

[2,1,5,6,7,3,8,4] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1,1] => 0

[2,5,1,6,7,3,8,4] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1,1] => 0

[2,5,6,7,1,3,8,4] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1,1] => 0

[2,1,5,6,7,8,3,4] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1,1] => 0

[2,5,1,6,7,8,3,4] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1,1] => 0

[2,5,6,1,7,8,3,4] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1,1] => 0

[2,5,6,7,1,8,3,4] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1,1] => 0

[2,5,6,7,8,1,3,4] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1,1] => 0

[2,1,5,3,7,4,8,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[2,5,1,3,7,4,8,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[2,1,5,7,3,4,8,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[2,5,1,7,3,4,8,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[2,5,7,1,3,4,8,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[2,1,5,3,7,8,4,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[2,5,1,3,7,8,4,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 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] => [4,4,3,3,1,1,1] => 0

[2,1,5,7,8,3,4,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[2,5,1,7,8,3,4,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[2,5,7,1,8,3,4,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[2,5,7,8,1,3,4,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[2,1,5,7,3,4,6,8] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[2,3,5,1,4,7,6,8] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1,1] => 0

[2,3,5,7,1,4,6,8] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1,1] => 0

[2,3,5,1,7,4,8,6] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1,1] => 0

[2,3,5,7,1,4,8,6] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1,1] => 0

[2,3,1,5,7,8,4,6] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1,1] => 0

[2,3,5,7,1,8,4,6] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1,1] => 0

[2,3,5,7,8,1,4,6] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1,1] => 0

[2,1,5,3,8,4,6,7] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1,1] => 1

[2,5,1,3,8,4,6,7] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1,1] => 1

[2,1,5,8,3,4,6,7] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1,1] => 1

[2,5,1,8,3,4,6,7] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1,1] => 1

[2,5,8,1,3,4,6,7] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1,1] => 1

[2,3,5,1,4,8,6,7] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1,1,1] => 1

[2,1,3,5,8,4,6,7] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1,1,1] => 1

[2,3,5,1,8,4,6,7] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1,1,1] => 1

[2,3,5,8,1,4,6,7] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1,1,1] => 1

[2,1,5,3,4,6,8,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1,1] => 1

[2,3,5,1,6,4,8,7] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1,1,1] => 1

[2,3,5,6,1,4,8,7] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1,1,1] => 1

[2,1,3,5,6,8,4,7] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1,1,1] => 1

[2,3,1,5,6,8,4,7] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1,1,1] => 1

[2,3,5,1,6,8,4,7] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1,1,1] => 1

[2,3,5,6,1,8,4,7] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1,1,1] => 1

[2,3,5,6,8,1,4,7] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1,1,1] => 1

[2,1,5,3,4,6,7,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1,1] => 0

[2,5,1,3,4,6,7,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1,1] => 0

[2,3,5,1,4,6,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1,1] => 0

[2,3,5,6,1,4,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1,1] => 0

[2,3,5,6,1,7,4,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1,1] => 0

[2,3,5,6,7,1,4,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1,1] => 0

[2,3,5,1,6,7,8,4] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1,1] => 0

[2,3,5,6,1,7,8,4] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1,1] => 0

[2,3,5,6,7,1,8,4] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1,1] => 0

[2,3,5,6,7,8,1,4] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1,1] => 0

[2,1,6,3,7,4,8,5] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1,1] => 0

[2,6,1,3,7,4,8,5] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1,1] => 0

[2,1,6,7,3,4,8,5] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1,1] => 0

[2,6,1,7,3,4,8,5] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1,1] => 0

[2,6,7,1,3,4,8,5] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1,1] => 0

[2,1,6,3,7,8,4,5] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1,1] => 0

[2,6,1,3,7,8,4,5] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1,1] => 0

[2,6,1,7,3,8,4,5] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1,1] => 0

[2,6,7,1,3,8,4,5] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1,1] => 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] => [4,4,4,1,1,1,1] => 0

[2,6,1,7,8,3,4,5] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1,1] => 0

[2,6,7,1,8,3,4,5] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1,1] => 0

[2,6,7,8,1,3,4,5] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1,1] => 0

[2,6,1,7,3,4,5,8] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1,1] => 0

[2,6,7,1,3,4,5,8] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1,1] => 0

[2,6,1,3,4,7,5,8] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1,1] => 0

[2,3,1,6,4,7,5,8] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1,1] => 0

[2,3,6,1,4,7,5,8] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1,1] => 0

[2,1,6,3,4,7,8,5] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1,1] => 0

[2,6,1,3,4,7,8,5] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1,1] => 0

[2,3,6,1,4,7,8,5] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1,1] => 0

[2,1,3,6,7,4,8,5] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1,1] => 0

[2,1,3,6,7,8,4,5] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1,1] => 0

[2,3,1,6,7,8,4,5] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1,1] => 0

[2,3,6,1,7,8,4,5] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1,1] => 0

[2,3,6,7,1,8,4,5] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1,1] => 0

[2,3,6,7,8,1,4,5] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1,1] => 0

[2,1,6,3,8,4,5,7] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1,1] => 1

[2,6,1,3,8,4,5,7] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1,1] => 1

[2,1,6,8,3,4,5,7] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1,1] => 1

[2,6,1,8,3,4,5,7] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1,1] => 1

[2,6,8,1,3,4,5,7] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1,1] => 1

[2,1,6,3,4,8,5,7] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1,1] => 1

[2,6,1,3,4,8,5,7] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1,1] => 1

[2,1,3,6,4,8,5,7] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1,1] => 1

[2,3,1,6,4,8,5,7] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1,1] => 1

[2,3,6,1,4,8,5,7] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1,1] => 1

[2,3,1,6,8,4,5,7] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1,1] => 1

[2,3,6,1,8,4,5,7] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1,1] => 1

[2,1,6,3,4,5,8,7] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1,1] => 1

[2,6,1,3,4,5,8,7] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1,1] => 1

[2,1,3,6,4,5,8,7] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1,1] => 1

[2,3,6,1,4,5,8,7] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1,1] => 1

[2,3,4,1,6,8,5,7] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1,1] => 1

[2,3,4,6,1,8,5,7] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1,1] => 1

[2,3,4,6,8,1,5,7] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1,1] => 1

[2,6,1,3,4,5,7,8] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1,1] => 0

[2,1,3,6,4,5,7,8] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1,1] => 0

[2,3,1,6,4,5,7,8] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1,1] => 0

[2,3,6,1,4,5,7,8] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1,1] => 0

[2,3,4,6,1,5,7,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1,1] => 0

[2,3,4,6,1,7,5,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1,1] => 0

[2,3,4,6,7,1,5,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1,1] => 0

[2,3,4,6,1,7,8,5] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1,1] => 0

[2,3,4,6,7,8,1,5] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1,1] => 0

[2,1,7,3,8,4,5,6] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1,1,1] => 0

[2,7,1,3,8,4,5,6] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1,1,1] => 0

[2,1,7,8,3,4,5,6] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1,1,1] => 0

[2,7,1,8,3,4,5,6] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1,1,1] => 0

[2,7,8,1,3,4,5,6] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1,1,1] => 0

[2,1,7,3,4,8,5,6] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1,1,1] => 0

[2,1,3,7,4,8,5,6] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1,1,1] => 0

[2,3,1,7,4,8,5,6] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1,1,1] => 0

[2,3,7,1,4,8,5,6] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1,1,1] => 0

[2,1,3,7,8,4,5,6] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1,1,1] => 0

[2,3,1,7,8,4,5,6] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1,1,1] => 0

[2,3,7,8,1,4,5,6] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1,1,1] => 0

[2,1,7,3,4,5,8,6] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1,1,1] => 0

[2,7,1,3,4,5,8,6] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1,1,1] => 0

[2,3,1,7,4,5,8,6] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1,1,1] => 0

[2,3,7,1,4,5,8,6] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1,1,1] => 0

[2,1,3,4,7,5,8,6] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1,1] => 0

[2,3,4,1,7,5,8,6] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1,1] => 0

[2,3,4,7,1,5,8,6] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1,1] => 0

[2,1,3,4,7,8,5,6] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1,1] => 0

[2,3,1,4,7,8,5,6] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1,1] => 0

[2,3,4,1,7,8,5,6] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1,1] => 0

[2,3,4,7,1,8,5,6] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1,1] => 0

[2,3,4,7,8,1,5,6] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1,1] => 0

[2,1,7,3,4,5,6,8] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1,1,1] => 0

[2,7,1,3,4,5,6,8] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1,1,1] => 0

[2,3,7,1,4,5,6,8] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1,1,1] => 0

[2,1,3,4,7,5,6,8] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1,1] => 0

[2,3,1,4,7,5,6,8] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1,1] => 0

[2,3,4,1,7,5,6,8] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1,1] => 0

[2,3,4,7,1,5,6,8] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1,1] => 0

[2,3,4,5,7,1,6,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1,1] => 0

[2,3,4,5,7,1,8,6] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1,1] => 0

[2,3,4,5,7,8,1,6] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1,1] => 0

[2,1,8,3,4,5,6,7] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1,1,1] => 1

[2,8,1,3,4,5,6,7] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1,1,1] => 1

[2,1,3,8,4,5,6,7] => [[.,.],[.,[[.,[.,[.,[.,.]]]],.]]] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1,1,1] => 1

[2,3,1,8,4,5,6,7] => [[.,.],[.,[[.,[.,[.,[.,.]]]],.]]] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1,1,1] => 1

[2,3,8,1,4,5,6,7] => [[.,.],[.,[[.,[.,[.,[.,.]]]],.]]] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1,1,1] => 1

[2,1,3,4,8,5,6,7] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1,1] => 1

[2,3,1,4,8,5,6,7] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1,1] => 1

[2,3,4,1,8,5,6,7] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1,1] => 1

[2,3,4,8,1,5,6,7] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1,1] => 1

[2,1,3,4,5,8,6,7] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1,1] => 1

[2,3,1,4,5,8,6,7] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1,1] => 1

[2,3,4,1,5,8,6,7] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1,1] => 1

[2,3,4,5,1,8,6,7] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1,1] => 1

[2,3,4,5,8,1,6,7] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1,1] => 1

[2,3,4,5,6,8,1,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => 1

[3,1,4,2,6,5,8,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2] => 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] => [4,3,3,2,2,2] => 1

[3,1,4,6,2,5,8,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2] => 1

[3,4,1,6,2,5,8,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2] => 1

[3,4,6,1,2,5,8,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2] => 1

[3,1,4,2,6,8,5,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2] => 1

[3,4,1,2,6,8,5,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2] => 1

[3,1,4,6,2,8,5,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2] => 1

[3,4,1,6,2,8,5,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2] => 1

[3,1,4,6,8,2,5,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2] => 1

[3,4,1,6,8,2,5,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2] => 1

[3,4,6,8,1,2,5,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2] => 1

[3,1,4,2,6,5,7,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2] => 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] => [3,3,3,2,2,2] => 0

[3,1,4,2,6,7,5,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2] => 0

[3,4,1,2,6,7,5,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2] => 0

[3,4,1,6,2,7,5,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2] => 0

[3,4,6,1,2,7,5,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2] => 0

[3,4,1,6,7,2,5,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2] => 0

[3,4,6,7,1,2,5,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2] => 0

[3,1,4,2,6,7,8,5] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2] => 0

[3,4,1,2,6,7,8,5] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2] => 0

[3,1,4,6,2,7,8,5] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2] => 0

[3,4,1,6,2,7,8,5] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2] => 0

[3,4,6,1,2,7,8,5] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2] => 0

[3,1,4,6,7,2,8,5] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2] => 0

[3,4,1,6,7,2,8,5] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2] => 0

[3,4,6,1,7,2,8,5] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2] => 0

[3,4,6,7,1,2,8,5] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2] => 0

[3,1,4,6,7,8,2,5] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2] => 0

[3,4,1,6,7,8,2,5] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2] => 0

[3,4,6,1,7,8,2,5] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2] => 0

[3,4,6,7,1,8,2,5] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2] => 0

[3,4,6,7,8,1,2,5] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2] => 0

[3,1,4,2,7,5,8,6] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2] => 0

[3,4,1,2,7,5,8,6] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2] => 0

[3,1,4,7,2,5,8,6] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2] => 0

[3,4,7,1,2,5,8,6] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2] => 0

[3,1,4,2,7,8,5,6] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2] => 0

[3,4,1,2,7,8,5,6] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2] => 0

[3,4,7,1,8,2,5,6] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2] => 0

[3,4,7,8,1,2,5,6] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2] => 0

[3,1,4,2,7,5,6,8] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2] => 0

[3,4,1,2,7,5,6,8] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2] => 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] => [3,3,2,2,2,2] => 0

[3,1,4,5,2,7,6,8] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2] => 0

[3,4,1,5,2,7,6,8] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2] => 0

[3,4,1,5,7,2,6,8] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2] => 0

[3,4,5,7,1,2,6,8] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2] => 0

[3,1,4,2,5,7,8,6] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2] => 0

[3,4,1,2,5,7,8,6] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2] => 0

[3,1,4,5,2,7,8,6] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2] => 0

[3,4,5,1,2,7,8,6] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2] => 0

[3,1,4,5,7,2,8,6] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2] => 0

[3,4,1,5,7,2,8,6] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2] => 0

[3,4,5,7,1,2,8,6] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2] => 0

[3,1,4,5,7,8,2,6] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2] => 0

[3,4,1,5,7,8,2,6] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2] => 0

[3,4,5,1,7,8,2,6] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2] => 0

[3,4,5,7,1,8,2,6] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2] => 0

[3,4,5,7,8,1,2,6] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2] => 0

[3,1,4,2,8,5,6,7] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,2] => 1

[3,4,1,2,8,5,6,7] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,2] => 1

[3,1,4,8,2,5,6,7] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,2] => 1

[3,4,1,8,2,5,6,7] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,2] => 1

[3,4,8,1,2,5,6,7] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,2] => 1

[3,1,4,2,5,8,6,7] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,2] => 1

[3,4,1,2,5,8,6,7] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,2] => 1

[3,4,1,5,2,8,6,7] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,2] => 1

[3,4,5,1,2,8,6,7] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,2] => 1

[3,1,4,5,8,2,6,7] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,2] => 1

[3,4,1,5,8,2,6,7] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,2] => 1

[3,4,5,8,1,2,6,7] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,2] => 1

[3,4,1,2,5,6,8,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,2] => 1

[3,4,5,1,2,6,8,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,2] => 1

[3,1,4,5,6,2,8,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,2] => 1

[3,4,1,5,6,2,8,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,2] => 1

[3,4,5,1,6,2,8,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,2] => 1

[3,4,5,6,1,2,8,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,2] => 1

[3,1,4,5,6,8,2,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,2] => 1

[3,4,1,5,6,8,2,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,2] => 1

[3,4,5,6,1,8,2,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,2] => 1

[3,4,5,6,8,1,2,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,2] => 1

[3,1,4,2,5,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2] => 0

[3,1,4,5,2,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2] => 0

[3,4,1,5,2,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2] => 0

[3,4,1,5,6,2,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2] => 0

[3,4,5,1,6,2,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2] => 0

[3,1,4,5,6,7,2,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2] => 0

[3,4,1,5,6,7,2,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2] => 0

[3,4,5,1,6,7,2,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2] => 0

[3,4,5,6,1,7,2,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2] => 0

[3,1,4,5,6,7,8,2] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2] => 0

[3,4,1,5,6,7,8,2] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2] => 0

[3,4,5,1,6,7,8,2] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2] => 0

[3,4,5,6,1,7,8,2] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2] => 0

[3,4,5,6,7,1,8,2] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2] => 0

[3,1,5,2,6,4,8,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,2] => 1

[3,5,1,2,6,4,8,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,2] => 1

[3,1,5,6,2,4,8,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,2] => 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] => [4,3,3,3,2,2] => 1

[3,5,6,1,2,4,8,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,2] => 1

[3,1,5,2,6,8,4,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,2] => 1

[3,5,1,2,6,8,4,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,2] => 1

[3,1,5,6,2,8,4,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,2] => 1

[3,5,6,1,2,8,4,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,2] => 1

[3,1,5,6,8,2,4,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,2] => 1

[3,5,1,6,8,2,4,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,2] => 1

[3,5,6,1,8,2,4,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,2] => 1

[3,5,6,8,1,2,4,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,2] => 1

[3,1,5,6,2,4,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 0

[3,5,1,6,2,4,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 0

[3,5,6,1,2,4,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 0

[3,5,1,2,6,7,4,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 0

[3,5,1,6,2,7,4,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 0

[3,5,6,1,2,7,4,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 0

[3,5,1,6,7,2,4,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 0

[3,5,6,1,7,2,4,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 0

[3,5,6,7,1,2,4,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 0

[3,1,5,2,6,7,8,4] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 0

[3,5,1,2,6,7,8,4] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 0

[3,1,5,6,2,7,8,4] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 0

[3,5,1,6,2,7,8,4] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 0

[3,5,6,1,2,7,8,4] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 0

[3,1,5,6,7,2,8,4] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 0

[3,5,1,6,7,2,8,4] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 0

[3,5,6,1,7,2,8,4] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 0

[3,5,6,7,1,2,8,4] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 0

[3,1,5,6,7,8,2,4] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 0

[3,5,1,6,7,8,2,4] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 0

[3,5,6,1,7,8,2,4] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 0

[3,5,6,7,1,8,2,4] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 0

[3,5,6,7,8,1,2,4] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 0

[1,3,5,2,4,7,6,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1] => 0

[1,3,2,5,7,4,6,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1] => 0

[1,3,5,2,7,4,6,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1] => 0

[1,3,5,7,2,4,6,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1] => 0

[1,3,5,2,7,4,8,6] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1] => 0

[1,3,5,7,2,4,8,6] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1] => 0

[1,3,2,5,7,8,4,6] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1] => 0

[1,3,5,2,7,8,4,6] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1] => 0

[1,3,5,7,2,8,4,6] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1] => 0

[1,3,5,7,8,2,4,6] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1] => 0

[1,3,2,5,4,8,6,7] => [.,[[.,.],[[.,.],[[.,[.,.]],.]]]] => [1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1,1] => 1

[1,3,5,2,4,8,6,7] => [.,[[.,.],[[.,.],[[.,[.,.]],.]]]] => [1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1,1] => 1

[1,3,2,5,8,4,6,7] => [.,[[.,.],[[.,.],[[.,[.,.]],.]]]] => [1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1,1] => 1

[1,3,5,2,8,4,6,7] => [.,[[.,.],[[.,.],[[.,[.,.]],.]]]] => [1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1,1] => 1

[1,3,5,8,2,4,6,7] => [.,[[.,.],[[.,.],[[.,[.,.]],.]]]] => [1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1,1] => 1

[3,5,1,2,4,6,8,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,2] => 1

[3,1,2,5,4,6,8,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,2] => 1

[1,3,5,2,4,6,8,7] => [.,[[.,.],[[.,.],[.,[[.,.],.]]]]] => [1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1,1] => 1

[1,3,5,2,6,4,8,7] => [.,[[.,.],[[.,.],[.,[[.,.],.]]]]] => [1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1,1] => 1

[1,3,5,6,2,4,8,7] => [.,[[.,.],[[.,.],[.,[[.,.],.]]]]] => [1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1,1] => 1

[3,1,2,5,6,8,4,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,2] => 1

[1,3,5,2,6,8,4,7] => [.,[[.,.],[[.,.],[.,[[.,.],.]]]]] => [1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1,1] => 1

[1,3,5,6,2,8,4,7] => [.,[[.,.],[[.,.],[.,[[.,.],.]]]]] => [1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1,1] => 1

[1,3,5,6,8,2,4,7] => [.,[[.,.],[[.,.],[.,[[.,.],.]]]]] => [1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1,1] => 1

[3,5,1,2,4,6,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 0

[1,3,5,2,4,6,7,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1] => 0

[1,3,5,6,2,4,7,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1] => 0

[3,1,2,5,6,7,4,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 0

[1,3,5,2,6,7,4,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1] => 0

[1,3,5,6,2,7,4,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1] => 0

[1,3,5,6,7,2,4,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1] => 0

[3,1,2,5,6,7,8,4] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 0

[1,3,5,6,2,7,8,4] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1] => 0

[1,3,5,6,7,2,8,4] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1] => 0

[1,3,5,6,7,8,2,4] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1] => 0

[1,3,2,6,4,7,5,8] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => [1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1] => 0

[1,3,6,2,4,7,5,8] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => [1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1] => 0

[1,3,2,6,7,4,5,8] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => [1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1] => 0

[1,3,6,2,7,4,5,8] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => [1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1] => 0

[1,3,6,2,4,7,8,5] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => [1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1] => 0

[1,3,2,6,7,4,8,5] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => [1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1] => 0

[1,3,6,2,7,4,8,5] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => [1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1] => 0

[1,3,6,7,2,4,8,5] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => [1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1] => 0

[1,3,2,6,7,8,4,5] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => [1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1] => 0

[1,3,6,2,7,8,4,5] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => [1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1] => 0

[1,3,6,7,8,2,4,5] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => [1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1] => 0

[1,3,2,6,4,8,5,7] => [.,[[.,.],[[.,[.,.]],[[.,.],.]]]] => [1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1] => 1

[1,3,6,2,4,8,5,7] => [.,[[.,.],[[.,[.,.]],[[.,.],.]]]] => [1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1] => 1

[1,3,2,6,8,4,5,7] => [.,[[.,.],[[.,[.,.]],[[.,.],.]]]] => [1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1] => 1

[1,3,6,2,4,5,8,7] => [.,[[.,.],[[.,[.,.]],[[.,.],.]]]] => [1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1] => 1

[3,1,2,4,6,5,8,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2] => 1

[1,3,4,6,2,5,8,7] => [.,[[.,.],[.,[[.,.],[[.,.],.]]]]] => [1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1] => 1

[3,1,2,4,6,8,5,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2] => 1

[1,3,2,4,6,8,5,7] => [.,[[.,.],[.,[[.,.],[[.,.],.]]]]] => [1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1] => 1

[1,3,4,6,8,2,5,7] => [.,[[.,.],[.,[[.,.],[[.,.],.]]]]] => [1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1] => 1

[1,3,2,6,4,5,7,8] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => [1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1] => 0

[1,3,6,2,4,5,7,8] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => [1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1] => 0

[1,3,4,6,2,5,7,8] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1] => 0

[3,1,2,4,6,7,5,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2] => 0

[1,3,4,6,2,7,5,8] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1] => 0

[1,3,4,6,7,2,5,8] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1] => 0

[3,1,2,4,6,7,8,5] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2] => 0

[1,3,4,6,7,2,8,5] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1] => 0

[1,3,2,7,4,8,5,6] => [.,[[.,.],[[.,[.,[.,.]]],[.,.]]]] => [1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1,1] => 0

[1,3,7,2,4,8,5,6] => [.,[[.,.],[[.,[.,[.,.]]],[.,.]]]] => [1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1,1] => 0

[1,3,7,2,8,4,5,6] => [.,[[.,.],[[.,[.,[.,.]]],[.,.]]]] => [1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1,1] => 0

[1,3,7,8,2,4,5,6] => [.,[[.,.],[[.,[.,[.,.]]],[.,.]]]] => [1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1,1] => 0

[1,3,7,2,4,5,8,6] => [.,[[.,.],[[.,[.,[.,.]]],[.,.]]]] => [1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1,1] => 0

[3,1,2,4,7,5,8,6] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2] => 0

[1,3,2,4,7,5,8,6] => [.,[[.,.],[.,[[.,[.,.]],[.,.]]]]] => [1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1] => 0

[1,3,4,2,7,5,8,6] => [.,[[.,.],[.,[[.,[.,.]],[.,.]]]]] => [1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1] => 0

[1,3,4,7,2,5,8,6] => [.,[[.,.],[.,[[.,[.,.]],[.,.]]]]] => [1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1] => 0

[3,1,2,4,7,8,5,6] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2] => 0

[1,3,2,4,7,8,5,6] => [.,[[.,.],[.,[[.,[.,.]],[.,.]]]]] => [1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1] => 0

[1,3,4,2,7,8,5,6] => [.,[[.,.],[.,[[.,[.,.]],[.,.]]]]] => [1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1] => 0

[1,3,4,7,8,2,5,6] => [.,[[.,.],[.,[[.,[.,.]],[.,.]]]]] => [1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1] => 0

[1,3,2,7,4,5,6,8] => [.,[[.,.],[[.,[.,[.,.]]],[.,.]]]] => [1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1,1] => 0

[1,3,7,2,4,5,6,8] => [.,[[.,.],[[.,[.,[.,.]]],[.,.]]]] => [1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1,1] => 0

[3,1,2,4,7,5,6,8] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2] => 0

[1,3,4,7,2,5,6,8] => [.,[[.,.],[.,[[.,[.,.]],[.,.]]]]] => [1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1] => 0

[3,1,2,4,5,7,6,8] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2] => 0

[1,3,4,5,7,2,6,8] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1] => 0

[3,1,2,4,5,7,8,6] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2] => 0

[1,3,4,5,7,8,2,6] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1] => 0

[3,1,8,2,4,5,6,7] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,2] => 1

[3,8,1,2,4,5,6,7] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,2] => 1

[3,1,2,8,4,5,6,7] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,2] => 1

[1,3,2,8,4,5,6,7] => [.,[[.,.],[[.,[.,[.,[.,.]]]],.]]] => [1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1,1] => 1

[1,3,8,2,4,5,6,7] => [.,[[.,.],[[.,[.,[.,[.,.]]]],.]]] => [1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1,1] => 1

[3,1,2,4,8,5,6,7] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,2] => 1

[1,3,2,4,8,5,6,7] => [.,[[.,.],[.,[[.,[.,[.,.]]],.]]]] => [1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1] => 1

[1,3,4,2,8,5,6,7] => [.,[[.,.],[.,[[.,[.,[.,.]]],.]]]] => [1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1] => 1

[1,3,4,8,2,5,6,7] => [.,[[.,.],[.,[[.,[.,[.,.]]],.]]]] => [1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1] => 1

[3,1,2,4,5,8,6,7] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,2] => 1

[1,3,2,4,5,8,6,7] => [.,[[.,.],[.,[.,[[.,[.,.]],.]]]]] => [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1] => 1

[1,3,4,2,5,8,6,7] => [.,[[.,.],[.,[.,[[.,[.,.]],.]]]]] => [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1] => 1

[1,3,4,5,2,8,6,7] => [.,[[.,.],[.,[.,[[.,[.,.]],.]]]]] => [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1] => 1

[1,3,4,5,8,2,6,7] => [.,[[.,.],[.,[.,[[.,[.,.]],.]]]]] => [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1] => 1

[3,1,2,4,5,6,8,7] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,2] => 1

[1,3,4,5,6,8,2,7] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1] => 1

[4,1,5,2,6,3,8,7] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3] => 1

[4,5,1,2,6,3,8,7] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3] => 1

[4,1,5,6,2,3,8,7] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3] => 1

[4,5,1,6,2,3,8,7] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3] => 1

[4,5,6,1,2,3,8,7] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3] => 1

[4,1,5,2,6,8,3,7] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3] => 1

[4,5,1,2,6,8,3,7] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3] => 1

[4,1,5,6,2,8,3,7] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3] => 1

[4,5,1,6,2,8,3,7] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3] => 1

[4,5,6,1,2,8,3,7] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3] => 1

[4,1,5,6,8,2,3,7] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3] => 1

[4,5,1,6,8,2,3,7] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3] => 1

[4,5,6,1,8,2,3,7] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3] => 1

[4,5,6,8,1,2,3,7] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3] => 1

[4,1,5,2,6,3,7,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => 0

[4,1,5,6,2,3,7,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => 0

[4,5,1,6,2,3,7,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => 0

[4,5,1,2,6,7,3,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => 0

[4,5,1,6,2,7,3,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => 0

[4,5,6,1,2,7,3,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => 0

[4,1,5,6,7,2,3,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => 0

[4,5,1,6,7,2,3,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => 0

[4,5,6,1,7,2,3,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => 0

[4,1,5,2,6,7,8,3] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => 0

[4,5,1,2,6,7,8,3] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => 0

[4,5,1,6,2,7,8,3] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => 0

[4,5,6,1,2,7,8,3] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => 0

[4,1,5,6,7,2,8,3] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => 0

[4,5,1,6,7,2,8,3] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => 0

[4,5,6,1,7,2,8,3] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => 0

[4,5,6,7,1,2,8,3] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => 0

[4,1,5,6,7,8,2,3] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => 0

[4,5,1,6,7,8,2,3] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => 0

[4,5,6,1,7,8,2,3] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => 0

[4,5,6,7,1,8,2,3] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => 0

[4,1,5,2,7,3,8,6] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [4,4,3,3,3] => 0

[4,5,1,2,7,3,8,6] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [4,4,3,3,3] => 0

[4,5,1,7,2,3,8,6] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [4,4,3,3,3] => 0

[4,1,5,2,7,8,3,6] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [4,4,3,3,3] => 0

[4,5,1,2,7,8,3,6] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [4,4,3,3,3] => 0

[4,1,5,7,2,8,3,6] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [4,4,3,3,3] => 0

[4,5,1,7,2,8,3,6] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [4,4,3,3,3] => 0

[4,5,7,1,2,8,3,6] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [4,4,3,3,3] => 0

[4,5,1,7,8,2,3,6] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [4,4,3,3,3] => 0

[4,5,7,8,1,2,3,6] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [4,4,3,3,3] => 0

[4,1,5,2,7,3,6,8] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [4,4,3,3,3] => 0

[4,5,1,2,7,3,6,8] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [4,4,3,3,3] => 0

[4,1,5,2,3,7,6,8] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [4,4,3,3,3] => 0

[4,5,1,2,3,7,6,8] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [4,4,3,3,3] => 0

[4,1,2,5,3,7,6,8] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [4,4,3,3,3] => 0

[1,4,2,5,3,7,6,8] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2] => 0

[1,4,5,2,3,7,6,8] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2] => 0

[4,1,2,5,7,3,6,8] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [4,4,3,3,3] => 0

[1,4,2,5,7,3,6,8] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2] => 0

[1,4,5,2,7,3,6,8] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2] => 0

[1,4,5,7,2,3,6,8] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2] => 0

[4,1,5,2,3,7,8,6] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [4,4,3,3,3] => 0

[4,1,2,5,3,7,8,6] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [4,4,3,3,3] => 0

[1,4,5,2,3,7,8,6] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2] => 0

[4,1,2,5,7,3,8,6] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [4,4,3,3,3] => 0

[1,4,2,5,7,3,8,6] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2] => 0

[1,4,5,2,7,3,8,6] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2] => 0

[1,4,5,7,2,3,8,6] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2] => 0

[4,1,2,5,7,8,3,6] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [4,4,3,3,3] => 0

[1,4,2,5,7,8,3,6] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2] => 0

[1,4,5,2,7,8,3,6] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2] => 0

[1,4,5,7,8,2,3,6] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2] => 0

[4,1,5,2,8,3,6,7] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [5,3,3,3,3] => 1

[4,5,1,2,8,3,6,7] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [5,3,3,3,3] => 1

[4,5,1,8,2,3,6,7] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [5,3,3,3,3] => 1

[4,5,8,1,2,3,6,7] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [5,3,3,3,3] => 1

[4,1,5,2,3,8,6,7] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [5,3,3,3,3] => 1

[4,5,1,2,3,8,6,7] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [5,3,3,3,3] => 1

[4,1,2,5,3,8,6,7] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [5,3,3,3,3] => 1

[1,4,2,5,3,8,6,7] => [.,[[.,[.,.]],[.,[[.,[.,.]],.]]]] => [1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2] => 1

[1,4,5,2,3,8,6,7] => [.,[[.,[.,.]],[.,[[.,[.,.]],.]]]] => [1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2] => 1

[4,1,2,5,8,3,6,7] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [5,3,3,3,3] => 1

[1,4,2,5,8,3,6,7] => [.,[[.,[.,.]],[.,[[.,[.,.]],.]]]] => [1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2] => 1

[1,4,5,2,8,3,6,7] => [.,[[.,[.,.]],[.,[[.,[.,.]],.]]]] => [1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2] => 1

[1,4,2,5,3,6,8,7] => [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => [1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2] => 1

[4,1,2,5,6,3,8,7] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3] => 1

[1,4,5,2,6,3,8,7] => [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => [1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2] => 1

[4,1,2,5,6,8,3,7] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3] => 1

[1,4,2,5,6,8,3,7] => [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => [1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2] => 1

[1,4,5,2,6,8,3,7] => [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => [1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2] => 1

[1,4,5,6,8,2,3,7] => [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => [1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2] => 1

[4,1,5,2,3,6,7,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => 0

[4,1,2,5,3,6,7,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => 0

[1,4,2,5,3,6,7,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2] => 0

[1,4,5,2,3,6,7,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2] => 0

[4,1,2,5,6,3,7,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => 0

[1,4,5,2,6,3,7,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2] => 0

[1,4,5,6,2,3,7,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2] => 0

[4,1,2,5,6,7,3,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => 0

[1,4,2,5,6,7,3,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2] => 0

[1,4,5,2,6,7,3,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2] => 0

[1,4,5,6,2,7,3,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2] => 0

[1,4,5,6,7,2,3,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2] => 0

[4,1,2,5,6,7,8,3] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => 0

[1,4,2,5,6,7,8,3] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2] => 0

[1,4,5,2,6,7,8,3] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2] => 0

[1,4,5,6,2,7,8,3] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2] => 0

[1,4,5,6,7,2,8,3] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2] => 0

[1,4,5,6,7,8,2,3] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2] => 0

[4,1,6,2,7,3,8,5] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[4,1,6,7,2,3,8,5] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[4,6,7,1,2,3,8,5] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[4,6,1,2,7,8,3,5] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[4,6,1,7,2,8,3,5] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[4,6,7,1,2,8,3,5] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[4,1,6,7,8,2,3,5] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[4,6,1,7,8,2,3,5] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[4,6,7,1,8,2,3,5] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[4,6,7,8,1,2,3,5] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[4,1,6,2,7,3,5,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[4,1,6,7,2,3,5,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[4,6,1,7,2,3,5,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[4,6,7,1,2,3,5,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[4,1,6,2,3,7,5,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[4,6,1,2,3,7,5,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[4,1,2,6,3,7,5,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[1,4,2,6,3,7,5,8] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2] => 0

[4,1,2,6,7,3,5,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[1,4,2,6,7,3,5,8] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2] => 0

[1,4,6,2,7,3,5,8] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2] => 0

[1,4,6,7,2,3,5,8] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2] => 0

[4,1,6,2,3,7,8,5] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[4,1,2,6,3,7,8,5] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[1,4,6,2,3,7,8,5] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2] => 0

[4,1,2,6,7,3,8,5] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[1,4,6,2,7,3,8,5] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2] => 0

[1,4,2,6,7,8,3,5] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2] => 0

[1,4,6,2,7,8,3,5] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2] => 0

[1,4,6,7,2,8,3,5] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2] => 0

[1,4,6,7,8,2,3,5] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2] => 0

[1,4,2,6,3,8,5,7] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2] => 1

[1,4,6,2,3,8,5,7] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2] => 1

[1,4,2,6,8,3,5,7] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2] => 1

[1,4,6,2,8,3,5,7] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2] => 1

[1,4,6,8,2,3,5,7] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2] => 1

[1,4,2,6,3,5,8,7] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2] => 1

[1,4,6,2,3,5,8,7] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2] => 1

[1,4,2,3,6,5,8,7] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2] => 1

[1,2,4,6,3,5,8,7] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => [1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1] => 1

[1,2,4,3,6,8,5,7] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => [1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1] => 1

[1,2,4,6,3,8,5,7] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => [1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1] => 1

[1,2,4,6,8,3,5,7] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => [1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1] => 1

[4,1,6,2,3,5,7,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[4,6,1,2,3,5,7,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[1,4,2,6,3,5,7,8] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2] => 0

[1,4,6,2,3,5,7,8] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2] => 0

[4,1,2,3,6,5,7,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[1,4,2,3,6,5,7,8] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2] => 0

[1,2,4,6,3,5,7,8] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1] => 0

[4,1,2,3,6,7,5,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[1,4,2,3,6,7,5,8] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2] => 0

[1,2,4,6,3,7,5,8] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1] => 0

[4,1,2,3,6,7,8,5] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[1,4,2,3,6,7,8,5] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2] => 0

[1,2,4,6,7,8,3,5] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1] => 0

[1,4,2,7,3,8,5,6] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2] => 0

[1,4,7,2,3,8,5,6] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2] => 0

[1,4,2,7,8,3,5,6] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2] => 0

[1,4,7,2,8,3,5,6] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2] => 0

[1,4,7,8,2,3,5,6] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2] => 0

[1,4,2,7,3,5,8,6] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2] => 0

[1,4,7,2,3,5,8,6] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2] => 0

[1,4,2,3,7,5,8,6] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2] => 0

[1,2,4,3,7,5,8,6] => [.,[.,[[.,.],[[.,[.,.]],[.,.]]]]] => [1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1] => 0

[1,2,4,7,3,5,8,6] => [.,[.,[[.,.],[[.,[.,.]],[.,.]]]]] => [1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1] => 0

[1,4,2,3,7,8,5,6] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2] => 0

[1,2,4,3,7,8,5,6] => [.,[.,[[.,.],[[.,[.,.]],[.,.]]]]] => [1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1] => 0

[1,2,4,7,3,8,5,6] => [.,[.,[[.,.],[[.,[.,.]],[.,.]]]]] => [1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1] => 0

[1,2,4,7,8,3,5,6] => [.,[.,[[.,.],[[.,[.,.]],[.,.]]]]] => [1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1] => 0

[1,4,2,7,3,5,6,8] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2] => 0

[1,4,7,2,3,5,6,8] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2] => 0

[1,4,2,3,7,5,6,8] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2] => 0

[1,2,4,3,7,5,6,8] => [.,[.,[[.,.],[[.,[.,.]],[.,.]]]]] => [1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1] => 0

[1,2,4,7,3,5,6,8] => [.,[.,[[.,.],[[.,[.,.]],[.,.]]]]] => [1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1] => 0

[4,1,2,3,5,7,6,8] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [4,4,3,3,3] => 0

[1,4,2,3,5,7,6,8] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2] => 0

[1,2,4,5,7,3,6,8] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1] => 0

[4,1,2,3,5,7,8,6] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [4,4,3,3,3] => 0

[1,4,2,3,5,7,8,6] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2] => 0

[1,2,4,5,7,3,8,6] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1] => 0

[1,2,4,5,7,8,3,6] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1] => 0

[1,4,2,8,3,5,6,7] => [.,[[.,[.,.]],[[.,[.,[.,.]]],.]]] => [1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2] => 1

[1,4,8,2,3,5,6,7] => [.,[[.,[.,.]],[[.,[.,[.,.]]],.]]] => [1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2] => 1

[1,4,2,3,8,5,6,7] => [.,[[.,[.,.]],[[.,[.,[.,.]]],.]]] => [1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2] => 1

[1,2,4,3,8,5,6,7] => [.,[.,[[.,.],[[.,[.,[.,.]]],.]]]] => [1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1] => 1

[1,2,4,8,3,5,6,7] => [.,[.,[[.,.],[[.,[.,[.,.]]],.]]]] => [1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1] => 1

[4,1,2,3,5,8,6,7] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [5,3,3,3,3] => 1

[1,4,2,3,5,8,6,7] => [.,[[.,[.,.]],[.,[[.,[.,.]],.]]]] => [1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2] => 1

[1,2,4,3,5,8,6,7] => [.,[.,[[.,.],[.,[[.,[.,.]],.]]]]] => [1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1] => 1

[1,2,4,5,3,8,6,7] => [.,[.,[[.,.],[.,[[.,[.,.]],.]]]]] => [1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1] => 1

[1,2,4,5,8,3,6,7] => [.,[.,[[.,.],[.,[[.,[.,.]],.]]]]] => [1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1] => 1

[4,1,2,3,5,6,8,7] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3] => 1

[1,4,2,3,5,6,8,7] => [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => [1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2] => 1

[1,2,4,5,6,8,3,7] => [.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1] => 1

[1,4,2,3,5,6,7,8] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2] => 0

[5,1,6,2,7,3,8,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 0

[5,6,1,2,7,3,8,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 0

[5,1,6,7,2,3,8,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 0

[5,6,1,7,2,3,8,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 0

[5,6,7,1,2,3,8,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 0

[5,6,1,2,7,8,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 0

[5,1,6,7,2,8,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 0

[5,6,7,1,2,8,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 0

[5,1,6,7,8,2,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 0

[5,6,1,7,8,2,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 0

[5,6,7,1,8,2,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 0

[5,1,6,2,7,3,4,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 0

[5,6,1,7,2,3,4,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 0

[5,1,6,2,3,7,4,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 0

[5,1,2,6,3,7,4,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 0

[1,5,2,6,3,7,4,8] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3] => 0

[5,1,2,6,7,3,4,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 0

[1,5,2,6,7,3,4,8] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3] => 0

[1,5,6,7,2,3,4,8] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3] => 0

[5,1,6,2,3,7,8,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 0

[5,6,1,2,3,7,8,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 0

[5,1,2,6,3,7,8,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 0

[1,5,2,6,3,7,8,4] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3] => 0

[1,5,6,2,3,7,8,4] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3] => 0

[5,1,2,6,7,3,8,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 0

[1,5,6,7,2,3,8,4] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3] => 0

[5,1,2,6,7,8,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 0

[1,5,2,6,7,8,3,4] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3] => 0

[1,5,6,2,7,8,3,4] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3] => 0

[1,5,6,7,2,8,3,4] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3] => 0

[1,5,6,7,8,2,3,4] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3] => 0

[5,1,6,2,8,3,4,7] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [5,4,4,4] => 1

[5,6,1,2,8,3,4,7] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [5,4,4,4] => 1

[5,6,1,8,2,3,4,7] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [5,4,4,4] => 1

[5,6,8,1,2,3,4,7] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [5,4,4,4] => 1

[5,1,6,2,3,8,4,7] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [5,4,4,4] => 1

[5,6,1,2,3,8,4,7] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [5,4,4,4] => 1

[5,1,2,6,3,8,4,7] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [5,4,4,4] => 1

[1,5,2,6,3,8,4,7] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3] => 1

[1,5,6,2,3,8,4,7] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3] => 1

[5,1,2,6,8,3,4,7] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [5,4,4,4] => 1

[1,5,2,6,8,3,4,7] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3] => 1

[1,5,6,2,8,3,4,7] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3] => 1

[1,5,6,8,2,3,4,7] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3] => 1

[5,1,6,2,3,4,8,7] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [5,4,4,4] => 1

[5,6,1,2,3,4,8,7] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [5,4,4,4] => 1

[5,1,2,6,3,4,8,7] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [5,4,4,4] => 1

[1,5,2,6,3,4,8,7] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3] => 1

[1,5,6,2,3,4,8,7] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3] => 1

[1,5,2,3,6,4,8,7] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3] => 1

[1,2,5,3,6,4,8,7] => [.,[.,[[.,[.,.]],[.,[[.,.],.]]]]] => [1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2] => 1

[1,2,5,6,3,4,8,7] => [.,[.,[[.,[.,.]],[.,[[.,.],.]]]]] => [1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2] => 1

[5,1,2,3,6,8,4,7] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [5,4,4,4] => 1

[1,5,2,3,6,8,4,7] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3] => 1

[1,2,5,6,3,8,4,7] => [.,[.,[[.,[.,.]],[.,[[.,.],.]]]]] => [1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2] => 1

[1,2,5,6,8,3,4,7] => [.,[.,[[.,[.,.]],[.,[[.,.],.]]]]] => [1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2] => 1

[5,1,6,2,3,4,7,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 0

[5,1,2,6,3,4,7,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 0

[1,5,2,6,3,4,7,8] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3] => 0

[1,5,6,2,3,4,7,8] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3] => 0

[5,1,2,3,6,4,7,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 0

[1,5,2,3,6,4,7,8] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3] => 0

[1,2,5,3,6,4,7,8] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => [1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2] => 0

[1,2,5,6,3,4,7,8] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => [1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2] => 0

[5,1,2,3,6,7,4,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 0

[1,5,2,3,6,7,4,8] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3] => 0

[1,2,5,6,3,7,4,8] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => [1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2] => 0

[5,1,2,3,6,7,8,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 0

[1,5,2,3,6,7,8,4] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3] => 0

[1,2,5,3,6,7,8,4] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => [1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2] => 0

[1,2,5,6,3,7,8,4] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => [1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2] => 0

[1,2,5,6,7,3,8,4] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => [1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2] => 0

[1,2,5,6,7,8,3,4] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => [1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2] => 0

[5,1,7,2,8,3,4,6] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4] => 0

[5,7,1,2,8,3,4,6] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4] => 0

[5,1,7,8,2,3,4,6] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4] => 0

[5,7,1,8,2,3,4,6] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4] => 0

[5,7,8,1,2,3,4,6] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4] => 0

[5,1,7,2,3,8,4,6] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4] => 0

[5,7,1,2,3,8,4,6] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4] => 0

[5,1,2,7,3,8,4,6] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4] => 0

[1,5,2,7,3,8,4,6] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3] => 0

[1,5,7,2,3,8,4,6] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3] => 0

[5,1,2,7,8,3,4,6] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4] => 0

[1,5,2,7,8,3,4,6] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3] => 0

[1,5,7,2,8,3,4,6] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3] => 0

[1,5,7,8,2,3,4,6] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3] => 0

[5,1,7,2,3,4,8,6] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4] => 0

[5,7,1,2,3,4,8,6] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4] => 0

[5,1,2,7,3,4,8,6] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4] => 0

[1,5,2,7,3,4,8,6] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3] => 0

[1,5,7,2,3,4,8,6] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3] => 0

[5,1,2,3,7,4,8,6] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4] => 0

[1,5,2,3,7,4,8,6] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3] => 0

[1,2,5,3,7,4,8,6] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => [1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2] => 0

[1,2,5,7,3,4,8,6] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => [1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2] => 0

[5,1,2,3,7,8,4,6] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4] => 0

[1,5,2,3,7,8,4,6] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3] => 0

[1,2,5,3,7,8,4,6] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => [1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2] => 0

[1,2,5,7,3,8,4,6] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => [1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2] => 0

[1,2,5,7,8,3,4,6] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => [1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2] => 0

[5,1,7,2,3,4,6,8] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4] => 0

[5,7,1,2,3,4,6,8] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4] => 0

[5,1,2,7,3,4,6,8] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4] => 0

[1,5,2,7,3,4,6,8] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3] => 0

[1,5,2,3,7,4,6,8] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3] => 0

[1,2,5,3,7,4,6,8] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => [1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2] => 0

[1,2,5,7,3,4,6,8] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => [1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2] => 0

[1,5,2,3,4,7,6,8] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3] => 0

[1,2,5,3,4,7,6,8] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => [1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2] => 0

[1,2,3,5,7,4,6,8] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1] => 0

[5,1,2,3,4,7,8,6] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4] => 0

[1,5,2,3,4,7,8,6] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3] => 0

[1,2,5,3,4,7,8,6] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => [1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2] => 0

[1,2,3,5,7,4,8,6] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1] => 0

[1,2,3,5,7,8,4,6] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1] => 0

[5,1,8,2,3,4,6,7] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [6,4,4,4] => 1

[5,8,1,2,3,4,6,7] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [6,4,4,4] => 1

[5,1,2,8,3,4,6,7] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [6,4,4,4] => 1

[1,5,2,8,3,4,6,7] => [.,[[.,[.,[.,.]]],[[.,[.,.]],.]]] => [1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3] => 1

[1,5,8,2,3,4,6,7] => [.,[[.,[.,[.,.]]],[[.,[.,.]],.]]] => [1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3] => 1

[5,1,2,3,8,4,6,7] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [6,4,4,4] => 1

[1,5,2,3,8,4,6,7] => [.,[[.,[.,[.,.]]],[[.,[.,.]],.]]] => [1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3] => 1

[1,2,5,3,8,4,6,7] => [.,[.,[[.,[.,.]],[[.,[.,.]],.]]]] => [1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2] => 1

[1,2,5,8,3,4,6,7] => [.,[.,[[.,[.,.]],[[.,[.,.]],.]]]] => [1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2] => 1

[5,1,2,3,4,8,6,7] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [6,4,4,4] => 1

[1,5,2,3,4,8,6,7] => [.,[[.,[.,[.,.]]],[[.,[.,.]],.]]] => [1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3] => 1

[1,2,5,3,4,8,6,7] => [.,[.,[[.,[.,.]],[[.,[.,.]],.]]]] => [1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2] => 1

[1,2,3,5,4,8,6,7] => [.,[.,[.,[[.,.],[[.,[.,.]],.]]]]] => [1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1] => 1

[1,2,3,5,8,4,6,7] => [.,[.,[.,[[.,.],[[.,[.,.]],.]]]]] => [1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1] => 1

[5,1,2,3,4,6,8,7] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [5,4,4,4] => 1

[1,5,2,3,4,6,8,7] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3] => 1

[1,2,5,3,4,6,8,7] => [.,[.,[[.,[.,.]],[.,[[.,.],.]]]]] => [1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2] => 1

[1,2,3,5,6,8,4,7] => [.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] => [1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1] => 1

[1,5,2,3,4,6,7,8] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3] => 0

[1,2,5,3,4,6,7,8] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => [1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2] => 0

[6,1,7,2,8,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => 0

[6,7,1,2,8,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => 0

[6,1,7,8,2,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => 0

[6,7,1,8,2,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => 0

[6,1,7,2,3,8,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => 0

[6,7,1,2,3,8,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => 0

[6,1,2,7,3,8,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => 0

[1,6,2,7,3,8,4,5] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [4,4,4] => 0

[1,6,7,2,3,8,4,5] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [4,4,4] => 0

[6,1,2,7,8,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => 0

[1,6,2,7,8,3,4,5] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [4,4,4] => 0

[1,6,7,2,8,3,4,5] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [4,4,4] => 0

[1,6,7,8,2,3,4,5] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [4,4,4] => 0

[6,1,7,2,3,4,8,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => 0

[6,7,1,2,3,4,8,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => 0

[6,1,2,7,3,4,8,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => 0

[1,6,2,7,3,4,8,5] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [4,4,4] => 0

[1,6,7,2,3,4,8,5] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [4,4,4] => 0

[6,1,2,3,7,4,8,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => 0

[1,6,2,3,7,4,8,5] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [4,4,4] => 0

[1,2,6,3,7,4,8,5] => [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [3,3,3] => 0

[1,2,6,7,3,4,8,5] => [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [3,3,3] => 0

[6,1,2,3,7,8,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => 0

[1,6,2,3,7,8,4,5] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [4,4,4] => 0

[1,2,6,3,7,8,4,5] => [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [3,3,3] => 0

[1,2,6,7,3,8,4,5] => [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [3,3,3] => 0

[1,2,6,7,8,3,4,5] => [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [3,3,3] => 0

[6,1,7,2,3,4,5,8] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => 0

[6,1,2,7,3,4,5,8] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => 0

[1,6,2,7,3,4,5,8] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [4,4,4] => 0

[1,6,7,2,3,4,5,8] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [4,4,4] => 0

[6,1,2,3,7,4,5,8] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => 0

[1,6,2,3,7,4,5,8] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [4,4,4] => 0

[1,2,6,3,7,4,5,8] => [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [3,3,3] => 0

[1,2,6,7,3,4,5,8] => [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [3,3,3] => 0

[6,1,2,3,4,7,5,8] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => 0

[1,6,2,3,4,7,5,8] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [4,4,4] => 0

[1,2,6,3,4,7,5,8] => [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [3,3,3] => 0

[1,2,3,6,4,7,5,8] => [.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [2,2,2] => 0

[1,2,3,6,7,4,5,8] => [.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [2,2,2] => 0

[6,1,2,3,4,7,8,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => 0

[1,6,2,3,4,7,8,5] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [4,4,4] => 0

[1,2,6,3,4,7,8,5] => [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [3,3,3] => 0

[1,2,3,6,4,7,8,5] => [.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [2,2,2] => 0

[1,2,3,6,7,4,8,5] => [.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [2,2,2] => 0

[1,2,3,6,7,8,4,5] => [.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [2,2,2] => 0

[6,1,8,2,3,4,5,7] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [6,5,5] => 1

[6,8,1,2,3,4,5,7] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [6,5,5] => 1

[6,1,2,8,3,4,5,7] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [6,5,5] => 1

[1,6,2,8,3,4,5,7] => [.,[[.,[.,[.,[.,.]]]],[[.,.],.]]] => [1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,4,4] => 1

[1,6,8,2,3,4,5,7] => [.,[[.,[.,[.,[.,.]]]],[[.,.],.]]] => [1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,4,4] => 1

[6,1,2,3,8,4,5,7] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [6,5,5] => 1

[1,6,2,3,8,4,5,7] => [.,[[.,[.,[.,[.,.]]]],[[.,.],.]]] => [1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,4,4] => 1

[1,2,6,3,8,4,5,7] => [.,[.,[[.,[.,[.,.]]],[[.,.],.]]]] => [1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [4,3,3] => 1

[1,2,6,8,3,4,5,7] => [.,[.,[[.,[.,[.,.]]],[[.,.],.]]]] => [1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [4,3,3] => 1

[6,1,2,3,4,8,5,7] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [6,5,5] => 1

[1,6,2,3,4,8,5,7] => [.,[[.,[.,[.,[.,.]]]],[[.,.],.]]] => [1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,4,4] => 1

[1,2,6,3,4,8,5,7] => [.,[.,[[.,[.,[.,.]]],[[.,.],.]]]] => [1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [4,3,3] => 1

[1,2,3,6,4,8,5,7] => [.,[.,[.,[[.,[.,.]],[[.,.],.]]]]] => [1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [3,2,2] => 1

[1,2,3,6,8,4,5,7] => [.,[.,[.,[[.,[.,.]],[[.,.],.]]]]] => [1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [3,2,2] => 1

[6,1,2,3,4,5,8,7] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [6,5,5] => 1

[1,6,2,3,4,5,8,7] => [.,[[.,[.,[.,[.,.]]]],[[.,.],.]]] => [1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,4,4] => 1

[1,2,6,3,4,5,8,7] => [.,[.,[[.,[.,[.,.]]],[[.,.],.]]]] => [1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [4,3,3] => 1

[1,2,3,6,4,5,8,7] => [.,[.,[.,[[.,[.,.]],[[.,.],.]]]]] => [1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [3,2,2] => 1

[1,2,3,4,6,8,5,7] => [.,[.,[.,[.,[[.,.],[[.,.],.]]]]]] => [1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [2,1,1] => 1

[1,6,2,3,4,5,7,8] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [4,4,4] => 0

[1,2,6,3,4,5,7,8] => [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [3,3,3] => 0

[1,2,3,6,4,5,7,8] => [.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [2,2,2] => 0

[7,1,8,2,3,4,5,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,6] => 0

[7,1,2,8,3,4,5,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,6] => 0

[1,7,2,8,3,4,5,6] => [.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]] => [1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [5,5] => 0

[1,7,8,2,3,4,5,6] => [.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]] => [1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [5,5] => 0

[7,1,2,3,8,4,5,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,6] => 0

[1,7,2,3,8,4,5,6] => [.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]] => [1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [5,5] => 0

[1,2,7,3,8,4,5,6] => [.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]] => [1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [4,4] => 0

[1,2,7,8,3,4,5,6] => [.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]] => [1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [4,4] => 0

[7,1,2,3,4,8,5,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,6] => 0

[1,7,2,3,4,8,5,6] => [.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]] => [1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [5,5] => 0

[1,2,7,3,4,8,5,6] => [.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]] => [1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [4,4] => 0

[1,2,3,7,4,8,5,6] => [.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [3,3] => 0

[1,2,3,7,8,4,5,6] => [.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [3,3] => 0

[7,1,2,3,4,5,8,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,6] => 0

[1,7,2,3,4,5,8,6] => [.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]] => [1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [5,5] => 0

[1,2,7,3,4,5,8,6] => [.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]] => [1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [4,4] => 0

[1,2,3,7,4,5,8,6] => [.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [3,3] => 0

[1,2,3,4,7,5,8,6] => [.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [2,2] => 0

[1,2,3,4,7,8,5,6] => [.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [2,2] => 0

[1,7,2,3,4,5,6,8] => [.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]] => [1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [5,5] => 0

[1,2,7,3,4,5,6,8] => [.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]] => [1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [4,4] => 0

[1,2,3,7,4,5,6,8] => [.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [3,3] => 0

[1,2,3,4,7,5,6,8] => [.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [2,2] => 0

[1,8,2,3,4,5,6,7] => [.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 1

[1,2,8,3,4,5,6,7] => [.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [5] => 1

[1,2,3,8,4,5,6,7] => [.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4] => 1

[1,2,3,4,8,5,6,7] => [.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => 1

[1,2,3,4,5,8,6,7] => [.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => 1

[2,1,10,9,8,7,6,5,4,3] => [[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,2,1,1] => 7

[10,9,8,7,6,5,4,3,2,1] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,3,2,1] => 9

[3,2,5,1,4,6,7,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => 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] => [3,3,3,3,3,1,1] => 0

[3,2,8,1,4,5,6,7] => [[[.,.],.],[[.,[.,[.,[.,.]]]],.]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,2,1] => 2

[7,2,8,1,3,4,5,6] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1,1,1] => 0

[7,3,8,1,2,4,5,6] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,2,2] => 0

[8,2,4,1,3,5,6,7] => [[[.,.],[[.,.],[.,[.,[.,.]]]]],.] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2,1,1] => 1

[7,3,4,8,1,2,5,6] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,2,2] => 0

[3,8,2,7,1,4,5,6] => [[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,2,2,1] => 3

[4,3,2,8,1,5,6,7] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [6,3,3,3,3,2,1] => 3

[4,3,8,2,7,1,5,6] => [[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,3,3,2,1] => 4

[5,4,3,2,8,1,6,7] => [[[[[.,.],.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,4,4,3,2,1] => 4

[4,8,3,7,2,6,1,5] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,3,2,1] => 5

[5,4,3,8,2,7,1,6] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,4,3,2,1] => 5

[6,5,4,3,2,8,1,7] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,5,4,3,2,1] => 5

[8,1,2,3,4,7,5,6] => [[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,2] => 2

[8,1,2,3,6,4,5,7] => [[.,[.,[.,[[.,[.,.]],[.,.]]]]],.] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [7,2,2] => 1

[8,1,2,3,7,4,5,6] => [[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,3] => 2

[7,1,2,3,6,4,8,5] => [[.,[.,[.,[[.,[.,.]],.]]]],[.,.]] => [1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [6,6,2] => 1

[8,1,2,3,6,7,4,5] => [[.,[.,[.,[[.,[.,.]],[.,.]]]]],.] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [7,2,2] => 1

[8,1,2,5,3,4,6,7] => [[.,[.,[[.,[.,.]],[.,[.,.]]]]],.] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2] => 1

[7,1,2,5,3,4,8,6] => [[.,[.,[[.,[.,.]],[.,.]]]],[.,.]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2] => 0

[8,1,2,6,3,4,5,7] => [[.,[.,[[.,[.,[.,.]]],[.,.]]]],.] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [7,3,3] => 1

[7,1,2,6,3,4,8,5] => [[.,[.,[[.,[.,[.,.]]],.]]],[.,.]] => [1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [6,6,3] => 1

[8,1,2,5,3,7,4,6] => [[.,[.,[[.,[.,.]],[[.,.],.]]]],.] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2] => 2

[8,1,2,6,3,7,4,5] => [[.,[.,[[.,[.,[.,.]]],[.,.]]]],.] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [7,3,3] => 1

[6,1,2,5,3,7,8,4] => [[.,[.,[[.,[.,.]],.]]],[.,[.,.]]] => [1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [5,5,5,2] => 1

[8,1,2,5,6,3,4,7] => [[.,[.,[[.,[.,.]],[.,[.,.]]]]],.] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2] => 1

[8,1,2,5,7,3,4,6] => [[.,[.,[[.,[.,.]],[[.,.],.]]]],.] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2] => 2

[8,1,2,7,6,3,4,5] => [[.,[.,[[[.,[.,[.,.]]],.],.]]],.] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [7,4,3] => 3

[7,1,2,5,6,3,8,4] => [[.,[.,[[.,[.,.]],[.,.]]]],[.,.]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2] => 0

[8,1,2,5,6,7,3,4] => [[.,[.,[[.,[.,.]],[.,[.,.]]]]],.] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2] => 1

[8,1,4,2,3,5,6,7] => [[.,[[.,[.,.]],[.,[.,[.,.]]]]],.] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2] => 1

[8,1,4,2,3,7,5,6] => [[.,[[.,[.,.]],[[.,[.,.]],.]]],.] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,2,2] => 2

[8,1,5,2,3,4,6,7] => [[.,[[.,[.,[.,.]]],[.,[.,.]]]],.] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [7,3,3,3] => 1

[8,1,7,2,3,4,5,6] => [[.,[[.,[.,[.,[.,[.,.]]]]],.]],.] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [7,5] => 2

[8,1,5,2,3,7,4,6] => [[.,[[.,[.,[.,.]]],[[.,.],.]]],.] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [7,4,3,3] => 2

[6,1,8,2,3,7,4,5] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [6,5,5] => 1

[8,1,4,2,6,3,5,7] => [[.,[[.,[.,.]],[[.,.],[.,.]]]],.] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2,2] => 1

[8,1,4,2,7,3,5,6] => [[.,[[.,[.,.]],[[.,[.,.]],.]]],.] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,2,2] => 2

[8,1,5,2,6,3,4,7] => [[.,[[.,[.,[.,.]]],[.,[.,.]]]],.] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [7,3,3,3] => 1

[8,1,5,2,7,3,4,6] => [[.,[[.,[.,[.,.]]],[[.,.],.]]],.] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [7,4,3,3] => 2

[7,1,8,2,6,3,4,5] => [[.,[.,[[.,[.,[.,.]]],.]]],[.,.]] => [1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [6,6,3] => 1

[8,1,4,2,6,7,3,5] => [[.,[[.,[.,.]],[[.,.],[.,.]]]],.] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2,2] => 1

[8,1,5,2,6,7,3,4] => [[.,[[.,[.,[.,.]]],[.,[.,.]]]],.] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [7,3,3,3] => 1

[5,1,4,2,6,7,8,3] => [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,2] => 1

[3,1,4,8,2,7,5,6] => [[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,2] => 2

[8,1,4,5,2,3,6,7] => [[.,[[.,[.,.]],[.,[.,[.,.]]]]],.] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2] => 1

[8,1,4,6,2,3,5,7] => [[.,[[.,[.,.]],[[.,.],[.,.]]]],.] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2,2] => 1

[7,1,8,6,2,3,4,5] => [[.,[[.,[.,[.,[.,.]]]],.]],[.,.]] => [1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [6,6,4] => 1

[8,1,4,5,2,7,3,6] => [[.,[[.,[.,.]],[.,[[.,.],.]]]],.] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,2] => 2

[8,1,4,6,2,7,3,5] => [[.,[[.,[.,.]],[[.,.],[.,.]]]],.] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2,2] => 1

[3,1,4,8,6,2,5,7] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,2] => 1

[3,1,4,8,7,2,5,6] => [[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,2] => 2

[3,1,4,7,6,2,8,5] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,2] => 1

[8,1,4,5,6,2,3,7] => [[.,[[.,[.,.]],[.,[.,[.,.]]]]],.] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2] => 1

[8,1,4,5,7,2,3,6] => [[.,[[.,[.,.]],[.,[[.,.],.]]]],.] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,2] => 2

[3,1,4,5,8,7,2,6] => [[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,2] => 2

[3,1,4,8,6,7,2,5] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,2] => 1

[8,1,4,5,6,7,2,3] => [[.,[[.,[.,.]],[.,[.,[.,.]]]]],.] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2] => 1

[2,8,1,3,4,7,5,6] => [[.,.],[[.,[.,[[.,[.,.]],.]]],.]] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1,1,1,1] => 2

[2,8,1,3,6,4,5,7] => [[.,.],[[.,[[.,[.,.]],[.,.]]],.]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1,1,1,1] => 1

[2,8,1,3,7,4,5,6] => [[.,.],[[.,[[.,[.,[.,.]]],.]],.]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,1,1,1,1] => 2

[2,7,1,3,6,4,8,5] => [[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1,1,1,1] => 1

[2,8,1,3,6,7,4,5] => [[.,.],[[.,[[.,[.,.]],[.,.]]],.]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1,1,1,1] => 1

[2,4,1,8,3,7,5,6] => [[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,1,1] => 2

[2,4,1,8,6,3,5,7] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1,1] => 1

[2,4,1,8,7,3,5,6] => [[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,1,1] => 2

[2,4,1,7,6,3,8,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1,1] => 1

[2,8,1,7,6,3,4,5] => [[.,.],[[[[.,[.,[.,.]]],.],.],.]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,1,1,1] => 3

[2,4,1,5,8,7,3,6] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,1,1] => 2

[2,4,1,8,6,7,3,5] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1,1] => 1

[7,3,1,2,4,5,8,6] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,2,2] => 0

[7,6,1,2,3,4,8,5] => [[[.,[.,[.,[.,[.,.]]]]],.],[.,.]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [6,6,5] => 1

[8,6,1,2,3,7,4,5] => [[[.,[.,[.,[.,[.,.]]]]],[.,.]],.] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [7,5,5] => 1

[5,8,1,2,6,3,4,7] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [6,4,4,4] => 1

[8,7,1,2,6,3,4,5] => [[[.,[.,[[.,[.,[.,.]]],.]]],.],.] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [7,6,3] => 3

[5,7,1,2,6,3,8,4] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4] => 0

[5,8,1,2,6,7,3,4] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [6,4,4,4] => 1

[5,4,1,2,6,7,8,3] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3] => 1

[7,3,1,8,2,4,5,6] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,2,2] => 0

[8,7,1,6,2,3,4,5] => [[[.,[[.,[.,[.,[.,.]]]],.]],.],.] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [7,6,4] => 3

[4,3,1,5,6,7,8,2] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,2] => 1

[2,3,8,1,4,7,5,6] => [[.,.],[.,[[.,[[.,[.,.]],.]],.]]] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1,1,1,1] => 2

[2,3,8,1,6,4,5,7] => [[.,.],[.,[[[.,[.,.]],[.,.]],.]]] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1,1,1] => 1

[2,3,8,1,7,4,5,6] => [[.,.],[.,[[[.,[.,[.,.]]],.],.]]] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1,1,1,1] => 2

[2,3,7,1,6,4,8,5] => [[.,.],[.,[[[.,[.,.]],.],[.,.]]]] => [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1,1,1] => 1

[2,3,5,1,8,7,4,6] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1,1,1] => 2

[2,3,8,1,6,7,4,5] => [[.,.],[.,[[[.,[.,.]],[.,.]],.]]] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1,1,1] => 1

[2,8,4,1,3,5,6,7] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,1,1] => 1

[2,8,7,1,3,4,5,6] => [[.,.],[[[.,[.,[.,[.,.]]]],.],.]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,1,1,1,1] => 2

[2,6,8,1,3,7,4,5] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1,1] => 1

[2,5,4,1,6,8,3,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1,1] => 2

[2,5,4,1,6,7,8,3] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1,1] => 1

[7,3,4,1,2,5,8,6] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,2,2] => 0

[2,3,4,8,1,7,5,6] => [[.,.],[.,[.,[[[.,[.,.]],.],.]]]] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1,1,1] => 2

[2,3,8,5,1,4,6,7] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1,1,1] => 1

[2,3,7,5,1,4,8,6] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1,1] => 0

[2,3,8,6,1,4,5,7] => [[.,.],[.,[[[.,[.,.]],[.,.]],.]]] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1,1,1] => 1

[2,3,7,6,1,4,8,5] => [[.,.],[.,[[[.,[.,.]],.],[.,.]]]] => [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1,1,1] => 1

[2,3,6,5,1,8,4,7] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1,1] => 2

[2,3,8,5,1,7,4,6] => [[.,.],[.,[[[.,.],[[.,.],.]],.]]] => [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1,1,1] => 2

[2,3,8,6,1,7,4,5] => [[.,.],[.,[[[.,[.,.]],[.,.]],.]]] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1,1,1] => 1

[2,3,6,5,1,7,8,4] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1,1] => 1

[2,8,4,5,1,3,6,7] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,1,1] => 1

[2,8,4,5,1,7,3,6] => [[.,.],[[[.,.],[.,[[.,.],.]]],.]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2,1,1] => 2

[7,3,4,5,1,2,8,6] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,2,2] => 0

[2,3,4,8,6,1,5,7] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1,1,1] => 1

[2,3,4,8,7,1,5,6] => [[.,.],[.,[.,[[[.,[.,.]],.],.]]]] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1,1,1] => 2

[2,3,4,7,6,1,8,5] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1,1,1] => 1

[2,3,8,5,6,1,4,7] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1,1,1] => 1

[2,3,8,5,7,1,4,6] => [[.,.],[.,[[[.,.],[[.,.],.]],.]]] => [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1,1,1] => 2

[2,3,8,7,6,1,4,5] => [[.,.],[.,[[[[.,[.,.]],.],.],.]]] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,1,1,1] => 3

[2,3,7,5,6,1,8,4] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1,1] => 0

[2,8,4,5,6,1,3,7] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,1,1] => 1

[2,8,4,5,7,1,3,6] => [[.,.],[[[.,.],[.,[[.,.],.]]],.]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2,1,1] => 2

[7,3,4,5,6,1,8,2] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,2,2] => 0

[2,3,4,5,8,7,1,6] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1,1] => 2

[2,3,4,8,6,7,1,5] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1,1,1] => 1

[2,3,8,5,6,7,1,4] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1,1,1] => 1

[2,8,4,5,6,7,1,3] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,1,1] => 1

[9,1,2,3,4,5,6,7,8] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8] => 1

[8,1,2,3,4,5,6,9,7] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,7] => 0

[7,1,2,3,4,5,9,6,8] => [[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [7,6,6] => 1

[9,1,2,3,4,5,8,6,7] => [[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [8,2] => 2

[7,1,2,3,4,5,8,9,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,6,6] => 0

[6,1,2,3,4,7,8,9,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,5,5,5] => 0

[8,1,2,3,9,4,5,6,7] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,7] => 0

[5,1,2,3,6,7,8,9,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,4,4,4,4] => 0

[7,1,2,8,3,4,5,9,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,6,6] => 0

[4,1,2,5,6,7,8,9,3] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3,3] => 0

[7,1,8,9,2,3,4,5,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,6,6] => 0

[3,1,4,5,6,7,8,9,2] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2] => 0

[2,9,1,3,4,5,6,7,8] => [[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1,1,1,1,1,1] => 1

[9,7,1,2,3,4,5,6,8] => [[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [8,6,6] => 1

[8,9,1,2,3,4,5,6,7] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,7] => 0

[9,7,1,2,3,4,8,5,6] => [[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [8,6,6] => 1

[5,6,1,2,3,7,8,9,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,4,4,4,4] => 0

[9,7,8,1,2,3,4,5,6] => [[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [8,6,6] => 1

[6,7,8,1,2,3,4,9,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,5,5,5] => 0

[2,3,4,5,6,7,8,9,1] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1] => 0

[3,5,1,6,4,2,8,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,2] => 1

[4,5,6,1,3,2,8,7] => [[.,[[.,.],.]],[.,[.,[[.,.],.]]]] => [1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3,1] => 2

[3,4,2,1,7,8,5,6] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2,1] => 1

[3,4,1,2,7,8,6,5] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,2] => 1

[4,5,7,1,2,8,6,3] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [4,4,3,3,3] => 0

[2,1,5,7,3,8,6,4] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[2,1,6,7,8,3,5,4] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1,1] => 1

[4,6,7,1,8,2,5,3] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[5,6,7,8,1,2,4,3] => [[.,[.,[[.,.],.]]],[.,[.,[.,.]]]] => [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,1] => 1

[5,6,7,8,1,4,2,3] => [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,2] => 1

[4,6,7,1,8,5,2,3] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[1,6,7,4,5,2,3,8] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2] => 0

[1,5,4,7,6,2,3,8] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2] => 1

[2,5,3,7,1,6,8,4] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[1,5,3,7,2,6,4,8] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1] => 0

[1,6,7,3,2,5,4,8] => [.,[[[.,.],[[.,.],.]],[.,[.,.]]]] => [1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1] => 1

[2,6,7,3,1,5,8,4] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1,1] => 1

[5,8,6,7,1,2,3,4] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [6,4,4,4] => 1

[5,7,6,8,1,2,3,4] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4] => 0

[2,1,4,3,8,7,5,6] => [[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,1,1] => 2

[3,4,1,2,8,7,5,6] => [[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,2] => 2

[2,1,6,8,7,3,4,5] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1,1] => 1

[5,6,8,7,1,2,3,4] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [5,4,4,4] => 1

[5,7,8,6,1,2,3,4] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4] => 0

[2,1,8,7,6,3,4,5] => [[.,.],[[[[.,[.,[.,.]]],.],.],.]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,1,1,1] => 3

[4,3,2,1,8,7,5,6] => [[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,3,3,2,1] => 4

[4,3,2,1,8,5,7,6] => [[[[.,.],.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,3,3,2,1] => 4

[4,3,2,1,8,5,6,7] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [6,3,3,3,3,2,1] => 3

[1,6,8,4,7,2,5,3] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,2] => 1

[1,6,8,3,2,7,5,4] => [.,[[[.,.],[[.,.],.]],[[.,.],.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,1,1] => 2

[7,8,1,2,3,6,5,4] => [[.,[.,[.,[[[.,.],.],.]]]],[.,.]] => [1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [6,6,2,1] => 2

[6,1,8,2,3,7,5,4] => [[.,[.,[.,[[.,.],.]]]],[[.,.],.]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [6,5,5,1] => 2

[1,6,8,2,3,7,5,4] => [.,[[.,[.,[[.,.],.]]],[[.,.],.]]] => [1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1] => 2

[1,5,2,8,3,7,6,4] => [.,[[.,[.,[.,.]]],[[[.,.],.],.]]] => [1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3] => 2

[1,2,5,8,3,7,6,4] => [.,[.,[[.,[.,.]],[[[.,.],.],.]]]] => [1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2] => 2

[1,4,2,3,8,7,6,5] => [.,[[.,[.,.]],[[[[.,.],.],.],.]]] => [1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,2] => 3

[1,5,3,8,2,7,6,4] => [.,[[[.,.],[.,.]],[[[.,.],.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1,1] => 2

[1,5,4,8,7,2,6,3] => [.,[[[.,[.,.]],.],[[[.,.],.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,2] => 3

[1,4,5,8,7,2,6,3] => [.,[[.,[.,.]],[.,[[[.,.],.],.]]]] => [1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2] => 2

[1,3,5,8,2,7,6,4] => [.,[[.,.],[[.,.],[[[.,.],.],.]]]] => [1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1,1] => 2

[3,4,5,8,7,6,1,2] => [[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,2] => 2

[2,4,5,8,7,1,6,3] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,1,1] => 2

[2,3,5,8,1,7,6,4] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1,1,1] => 2

[8,1,3,2,5,4,7,6] => [[.,[[.,.],[[.,.],[[.,.],.]]]],.] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,1,1] => 2

[8,1,4,2,5,3,7,6] => [[.,[[.,[.,.]],[.,[[.,.],.]]]],.] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,2] => 2

[2,1,7,3,5,4,8,6] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1,1] => 0

[2,1,8,3,5,4,7,6] => [[.,.],[[.,[[.,.],[[.,.],.]]],.]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,1,1,1] => 2

[5,1,8,2,6,3,7,4] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [6,4,4,4] => 1

[2,1,8,3,6,4,7,5] => [[.,.],[[.,[[.,[.,.]],[.,.]]],.]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1,1,1,1] => 1

[2,1,7,3,6,4,8,5] => [[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1,1,1,1] => 1

[5,1,7,2,6,3,8,4] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4] => 0

[8,1,5,2,6,3,7,4] => [[.,[[.,[.,[.,.]]],[.,[.,.]]]],.] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [7,3,3,3] => 1

[8,1,4,2,6,3,7,5] => [[.,[[.,[.,.]],[[.,.],[.,.]]]],.] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2,2] => 1

[8,1,3,2,6,4,7,5] => [[.,[[.,.],[[.,[.,.]],[.,.]]]],.] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,3,1,1,1] => 1

[2,1,4,3,8,5,7,6] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,1,1] => 2

[3,1,4,2,8,5,7,6] => [[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,2] => 2

[2,1,6,3,8,4,7,5] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1,1] => 1

[5,1,6,2,8,3,7,4] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [5,4,4,4] => 1

[3,4,2,6,8,1,5,7] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2,1] => 2

[3,5,6,1,4,8,2,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,2] => 1

[4,1,5,6,3,8,2,7] => [[.,[[.,.],.]],[.,[.,[[.,.],.]]]] => [1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3,1] => 2

[4,5,1,6,3,8,2,7] => [[.,[[.,.],.]],[.,[.,[[.,.],.]]]] => [1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3,1] => 2

[3,4,7,8,2,1,5,6] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2,1] => 1

[4,1,5,7,8,2,6,3] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [4,4,3,3,3] => 0

[5,1,6,2,7,8,4,3] => [[.,[.,[[.,.],.]]],[.,[.,[.,.]]]] => [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,1] => 1

[5,6,1,7,2,8,4,3] => [[.,[.,[[.,.],.]]],[.,[.,[.,.]]]] => [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,1] => 1

[5,1,6,7,2,8,4,3] => [[.,[.,[[.,.],.]]],[.,[.,[.,.]]]] => [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,1] => 1

[2,4,5,3,7,1,8,6] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1,1] => 0

[8,2,4,5,6,3,1,7] => [[[.,.],[[.,.],[.,[.,[.,.]]]]],.] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2,1,1] => 1

[8,2,4,5,6,1,3,7] => [[[.,.],[[.,.],[.,[.,[.,.]]]]],.] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2,1,1] => 1

[8,1,2,4,5,6,3,7] => [[.,[.,[[.,.],[.,[.,[.,.]]]]]],.] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1,1] => 1

[8,1,4,5,6,3,2,7] => [[.,[[[.,.],.],[.,[.,[.,.]]]]],.] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2,1] => 2

[1,4,3,6,7,2,8,5] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1] => 1

[1,6,4,7,8,3,5,2] => [.,[[[[.,.],.],[.,.]],[.,[.,.]]]] => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2,1] => 1

[3,5,6,7,8,4,1,2] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 0

[3,1,5,6,7,8,4,2] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 0

[1,5,3,6,7,8,2,4] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => [1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1] => 0

[3,5,6,7,8,2,1,4] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => 1

[3,5,6,7,8,2,4,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => 1

[1,7,3,4,2,5,8,6] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1,1] => 0

[7,8,1,3,4,2,6,5] => [[.,[[.,.],[.,[[.,.],.]]]],[.,.]] => [1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [6,6,2,1,1,1] => 1

[4,6,1,7,8,5,2,3] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[5,1,2,6,7,8,4,3] => [[.,[.,[[.,.],.]]],[.,[.,[.,.]]]] => [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,1] => 1

[2,5,6,7,8,4,1,3] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1,1] => 1

[1,5,2,6,7,8,4,3] => [.,[[.,[[.,.],.]],[.,[.,[.,.]]]]] => [1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1] => 1

[1,6,4,7,8,5,2,3] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2] => 0

[2,6,7,1,3,8,5,4] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1,1] => 1

[1,5,6,3,4,8,7,2] => [.,[[[.,.],[.,.]],[.,[[.,.],.]]]] => [1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1] => 1

[1,7,5,4,8,3,6,2] => [.,[[[[[.,.],.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,2,1] => 2

[1,8,6,7,4,5,3,2] => [.,[[[[[.,.],.],[.,.]],[.,.]],.]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2,2,1] => 2

[6,1,7,8,2,4,5,3] => [[.,[.,[[.,.],[.,.]]]],[.,[.,.]]] => [1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [5,5,5,1,1] => 0

[1,7,6,8,4,3,5,2] => [.,[[[[[.,.],.],[.,.]],.],[.,.]]] => [1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,2,1] => 2

[1,6,7,8,3,4,5,2] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]] => [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1] => 0

[1,5,7,3,8,4,6,2] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1] => 0

[1,4,3,7,8,5,6,2] => [.,[[[.,.],.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1] => 1

[1,5,8,3,7,6,4,2] => [.,[[[.,.],[.,.]],[[[.,.],.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1,1] => 2

[5,6,1,2,3,8,7,4] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [5,4,4,4] => 1

[5,7,1,2,8,3,6,4] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4] => 0

[6,7,1,8,2,3,5,4] => [[.,[.,[.,[[.,.],.]]]],[.,[.,.]]] => [1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,5,5,1] => 1

[1,6,8,7,3,5,4,2] => [.,[[[.,.],[[.,.],.]],[[.,.],.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,1,1] => 2

[1,7,8,6,5,3,4,2] => [.,[[[[[.,.],[.,.]],.],.],[.,.]]] => [1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3,1,1] => 2

[3,2,8,1,7,6,4,5] => [[[.,.],.],[[[[.,[.,.]],.],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,2,2,1] => 4

[1,7,5,3,8,4,6,2] => [.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,1,1] => 0

[8,1,6,7,2,4,5,3] => [[.,[[.,[[.,.],[.,.]]],[.,.]]],.] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [7,4,4,1,1] => 1

[1,8,6,7,3,4,5,2] => [.,[[[[.,.],[.,[.,.]]],[.,.]],.]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,4,1,1,1] => 1

[1,7,6,8,3,4,5,2] => [.,[[[[.,.],[.,[.,.]]],.],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1,1,1] => 1

[1,4,3,8,7,5,6,2] => [.,[[[.,.],.],[[[.,[.,.]],.],.]]] => [1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,1] => 3

[1,5,8,3,7,4,6,2] => [.,[[[.,.],[.,.]],[[[.,.],.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1,1] => 2

[1,6,8,7,3,4,5,2] => [.,[[[.,.],[.,[.,.]]],[[.,.],.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1] => 1

[6,8,1,7,2,3,5,4] => [[.,[.,[.,[[.,.],.]]]],[[.,.],.]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [6,5,5,1] => 2

[6,8,7,1,2,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [6,5,5] => 1

[5,8,6,1,2,3,4,7] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [6,4,4,4] => 1

[5,7,6,1,2,3,4,8] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4] => 0

[7,8,1,6,2,3,5,4] => [[.,[[.,[.,[[.,.],.]]],.]],[.,.]] => [1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [6,6,4,1] => 2

[1,7,8,6,3,4,5,2] => [.,[[[[.,.],[.,[.,.]]],.],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1,1,1] => 1

[1,8,7,6,3,4,5,2] => [.,[[[[[.,.],[.,[.,.]]],.],.],.]] => [1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,1,1] => 3

[3,1,5,4,6,2,8,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,2] => 1

[4,1,5,3,6,2,8,7] => [[.,[[.,.],.]],[.,[.,[[.,.],.]]]] => [1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3,1] => 2

[3,2,4,1,7,5,8,6] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2,1] => 1

[3,1,4,2,7,6,8,5] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,2] => 1

[4,1,5,2,7,6,8,3] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [4,4,3,3,3] => 0

[2,1,5,3,7,6,8,4] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[2,1,6,3,7,5,8,4] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1,1] => 1

[4,1,6,2,7,5,8,3] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[5,1,6,2,7,4,8,3] => [[.,[.,[[.,.],.]]],[.,[.,[.,.]]]] => [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,1] => 1

[5,4,6,1,7,2,8,3] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3] => 1

[5,1,6,4,7,2,8,3] => [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,2] => 1

[4,1,6,5,7,2,8,3] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[2,4,5,7,3,1,8,6] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1,1] => 0

[1,4,6,7,3,2,8,5] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1] => 1

[1,7,4,5,3,2,8,6] => [.,[[[[.,.],.],[.,[.,.]]],[.,.]]] => [1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2,1] => 1

[1,7,3,5,6,8,2,4] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]] => [1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1] => 0

[1,3,6,7,5,8,2,4] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1] => 1

[2,3,5,7,6,8,1,4] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1,1] => 0

[8,1,2,5,6,7,4,3] => [[.,[.,[[[.,.],.],[.,[.,.]]]]],.] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,1] => 2

[1,7,2,5,8,6,4,3] => [.,[[.,[[[.,.],.],[.,.]]],[.,.]]] => [1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1] => 1

[1,7,4,8,2,6,5,3] => [.,[[[.,[.,.]],[[.,.],.]],[.,.]]] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,2] => 1

[2,4,8,3,5,6,7,1] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,1,1] => 1

[3,8,4,2,5,6,7,1] => [[[.,.],.],[[.,[.,[.,[.,.]]]],.]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,2,1] => 2

[2,1,4,8,3,6,7,5] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1,1] => 1

[2,3,8,1,5,6,7,4] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1,1,1] => 1

[4,3,8,2,5,6,7,1] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [6,3,3,3,3,2,1] => 3

[2,8,1,3,5,6,7,4] => [[.,.],[[.,[[.,.],[.,[.,.]]]],.]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,1,1,1] => 1

[8,1,2,3,5,6,7,4] => [[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1] => 1

[2,1,8,3,4,6,7,5] => [[.,.],[[.,[.,[[.,.],[.,.]]]],.]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1,1,1,1] => 1

[3,8,7,4,2,6,1,5] => [[[.,.],.],[[[.,[[.,.],.]],.],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,2,2,1] => 4

[2,4,3,1,8,5,7,6] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,1,1] => 2

[8,1,4,2,5,6,7,3] => [[.,[[.,[.,.]],[.,[.,[.,.]]]]],.] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2] => 1

[2,8,4,1,5,6,7,3] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,1,1] => 1

[3,4,8,1,5,6,7,2] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,2] => 1

[3,4,2,8,5,6,7,1] => [[[.,.],.],[.,[[.,[.,[.,.]]],.]]] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,2,1] => 2

[2,4,1,8,5,6,7,3] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,1,1] => 1

[2,1,5,3,8,6,7,4] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1,1] => 1

[8,3,4,1,5,6,7,2] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2,2] => 1

[3,1,4,8,5,6,7,2] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,2] => 1

[3,8,7,4,5,2,1,6] => [[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,2,2,1] => 3

[5,4,3,8,2,7,6,1] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,4,3,2,1] => 5

[1,4,7,5,8,3,2,6] => [.,[[[.,.],.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1] => 1

[1,4,5,8,7,3,6,2] => [.,[[[.,.],.],[.,[[[.,.],.],.]]]] => [1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,1] => 3

[1,5,4,8,7,3,6,2] => [.,[[[[.,.],.],.],[[[.,.],.],.]]] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,2,1] => 4

[4,8,3,7,6,5,2,1] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,3,2,1] => 5

[1,8,6,5,3,7,4,2] => [.,[[[[[.,.],[.,.]],.],[.,.]],.]] => [1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3,1,1] => 2

[1,5,8,6,3,7,4,2] => [.,[[[.,.],[.,.]],[[.,[.,.]],.]]] => [1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1] => 1

[1,7,6,4,8,3,2,5] => [.,[[[[[.,.],.],[.,.]],.],[.,.]]] => [1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,2,1] => 2

[2,4,8,6,3,7,5,1] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1,1] => 1

[1,6,5,2,3,8,4,7] => [.,[[[.,[.,[.,.]]],.],[[.,.],.]]] => [1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3] => 2

[1,7,5,2,8,3,4,6] => [.,[[[.,[.,[.,.]]],[.,.]],[.,.]]] => [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3] => 0

[1,8,5,2,7,3,4,6] => [.,[[[.,[.,[.,.]]],[[.,.],.]],.]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,3] => 2

[1,8,6,7,2,3,4,5] => [.,[[[.,[.,[.,[.,.]]]],[.,.]],.]] => [1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [6,4,4] => 1

[8,1,6,7,2,3,4,5] => [[.,[[.,[.,[.,[.,.]]]],[.,.]]],.] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [7,4,4] => 1

[7,1,6,8,2,3,4,5] => [[.,[[.,[.,[.,[.,.]]]],.]],[.,.]] => [1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [6,6,4] => 1

[3,2,8,7,1,4,5,6] => [[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,2,2,1] => 3

[1,7,6,8,2,3,4,5] => [.,[[[.,[.,[.,[.,.]]]],.],[.,.]]] => [1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,5,4] => 1

[1,4,2,8,7,3,5,6] => [.,[[.,[.,.]],[[[.,[.,.]],.],.]]] => [1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2] => 2

[1,5,8,2,7,3,4,6] => [.,[[.,[.,[.,.]]],[[[.,.],.],.]]] => [1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3] => 2

[7,6,1,8,2,3,4,5] => [[[.,[.,[.,[.,[.,.]]]]],.],[.,.]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [6,6,5] => 1

[8,6,1,7,2,3,4,5] => [[[.,[.,[.,[.,[.,.]]]]],[.,.]],.] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [7,5,5] => 1

[1,6,8,7,2,3,4,5] => [.,[[.,[.,[.,[.,.]]]],[[.,.],.]]] => [1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,4,4] => 1

[1,7,8,6,2,3,4,5] => [.,[[[.,[.,[.,[.,.]]]],.],[.,.]]] => [1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,5,4] => 1

[7,8,1,6,2,3,4,5] => [[.,[[.,[.,[.,[.,.]]]],.]],[.,.]] => [1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [6,6,4] => 1

[6,8,1,7,2,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [6,5,5] => 1

[3,2,8,1,7,4,5,6] => [[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,2,2,1] => 3

[3,2,1,8,7,4,5,6] => [[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,2,2,1] => 3

[6,1,8,7,2,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [6,5,5] => 1

[8,1,7,6,2,3,4,5] => [[.,[[[.,[.,[.,[.,.]]]],.],.]],.] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [7,5,4] => 3

[1,8,7,6,2,3,4,5] => [.,[[[[.,[.,[.,[.,.]]]],.],.],.]] => [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [6,5,4] => 3

[3,1,4,6,5,2,8,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2] => 1

[3,4,7,8,5,2,1,6] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2,1] => 1

[3,4,8,6,5,7,1,2] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,2] => 1

[2,5,4,6,7,1,8,3] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1,1] => 1

[2,4,6,3,7,5,8,1] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[2,3,8,1,6,7,5,4] => [[.,.],[.,[[[[.,.],.],[.,.]],.]]] => [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1,1,1] => 2

[2,8,1,3,6,5,7,4] => [[.,.],[[.,[[[.,.],.],[.,.]]],.]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,1,1,1] => 2

[4,3,8,7,2,1,6,5] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,3,2,1] => 5

[2,3,4,1,8,5,7,6] => [[.,.],[.,[.,[[.,[[.,.],.]],.]]]] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1,1,1] => 2

[2,4,1,5,8,7,6,3] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,1,1] => 2

[4,1,2,5,8,6,7,3] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [5,3,3,3,3] => 1

[2,1,5,3,6,8,7,4] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1,1] => 1

[3,1,4,5,6,8,7,2] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,2] => 1

[2,5,7,3,8,6,4,1] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[3,4,2,8,5,7,6,1] => [[[.,.],.],[.,[[.,[[.,.],.]],.]]] => [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,2,1] => 3

[3,1,4,8,6,5,7,2] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,2] => 1

[2,4,3,1,8,5,6,7] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,1,1] => 1

[2,4,8,3,5,6,1,7] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,1,1] => 1

[3,4,8,1,7,2,5,6] => [[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,2] => 2

[2,3,8,1,4,6,7,5] => [[.,.],[.,[[.,[[.,.],[.,.]]],.]]] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1,1,1] => 1

[4,3,8,2,5,1,7,6] => [[[[.,.],.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,3,3,2,1] => 4

[2,1,4,8,3,5,7,6] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,1,1] => 2

[2,8,1,3,4,5,7,6] => [[.,.],[[.,[.,[.,[[.,.],.]]]],.]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1,1,1,1] => 2

[4,5,2,6,3,1,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1,1] => 0

[3,1,4,8,6,2,7,5] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,2] => 1

[3,1,4,8,6,5,2,7] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,2] => 1

[4,5,2,6,3,7,1,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1,1] => 0

[4,1,2,5,6,8,7,3] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3] => 1

[4,5,2,6,3,7,8,1] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1,1] => 0

[2,4,8,1,5,7,3,6] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,1,1] => 2

[7,8,3,4,5,1,6,2] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,2,2] => 0

[1,3,8,2,6,4,7,5] => [.,[[.,.],[[[.,[.,.]],[.,.]],.]]] => [1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1,1] => 1

[2,4,7,1,5,3,6,8] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => 0

[1,3,7,6,4,2,8,5] => [.,[[.,.],[[[.,[.,.]],.],[.,.]]]] => [1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1,1] => 1

[1,5,6,8,2,4,7,3] => [.,[[.,[[.,.],.]],[.,[[.,.],.]]]] => [1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1] => 2

[4,5,6,7,2,8,1,3] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1,1] => 0

[1,5,8,6,2,7,3,4] => [.,[[.,[.,[.,.]]],[[.,[.,.]],.]]] => [1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3] => 1

[4,6,5,7,1,2,8,3] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[1,6,2,4,7,8,3,5] => [.,[[.,[[.,.],[.,.]]],[.,[.,.]]]] => [1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1] => 0

[2,1,8,7,6,5,3,4] => [[.,.],[[[[[.,[.,.]],.],.],.],.]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1,1,1] => 4

[3,1,4,7,8,2,6,5] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,2] => 1

[1,6,8,7,5,2,4,3] => [.,[[[.,[[.,.],.]],.],[[.,.],.]]] => [1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3,1] => 3

[2,4,8,7,1,3,5,6] => [[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,1,1] => 2

[2,8,7,6,1,3,4,5] => [[.,.],[[[[.,[.,[.,.]]],.],.],.]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,1,1,1] => 3

[2,3,4,5,6,7,8,1,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1] => 0

[3,4,5,6,7,8,9,1,2] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2] => 0

[2,3,4,5,6,7,8,9,10,1] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1] => 0

[2,3,4,5,6,7,8,9,1,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1] => 0

[2,3,4,5,6,7,1,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1] => 0

[1,6,3,2,8,4,5,7] => [.,[[[.,.],[.,[.,.]]],[[.,.],.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1] => 1

[1,8,6,3,7,2,4,5] => [.,[[[[.,.],[.,[.,.]]],[.,.]],.]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,4,1,1,1] => 1

[1,8,2,7,3,4,5,6] => [.,[[.,[[.,[.,[.,[.,.]]]],.]],.]] => [1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [6,4] => 2

[2,8,1,7,3,4,5,6] => [[.,.],[[[.,[.,[.,[.,.]]]],.],.]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,1,1,1,1] => 2

[8,1,2,7,3,4,5,6] => [[.,[.,[[.,[.,[.,[.,.]]]],.]]],.] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [7,4] => 2

[1,5,3,4,6,8,2,7] => [.,[[[.,.],[.,.]],[.,[[.,.],.]]]] => [1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1] => 1

[2,3,8,7,1,4,5,6] => [[.,.],[.,[[[.,[.,[.,.]]],.],.]]] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1,1,1,1] => 2

[2,1,8,7,3,4,5,6] => [[.,.],[[[.,[.,[.,[.,.]]]],.],.]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,1,1,1,1] => 2

[1,2,8,7,3,4,5,6] => [.,[.,[[[.,[.,[.,[.,.]]]],.],.]]] => [1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [5,4] => 2

[1,3,8,7,2,4,5,6] => [.,[[.,.],[[[.,[.,[.,.]]],.],.]]] => [1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1,1,1] => 2

[1,7,8,3,6,2,4,5] => [.,[[[.,.],[[.,[.,.]],.]],[.,.]]] => [1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1,1,1] => 1

[8,1,4,3,2,5,7,6] => [[.,[[[.,.],.],[.,[[.,.],.]]]],.] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,2,1] => 3

[8,1,4,3,2,5,6,7] => [[.,[[[.,.],.],[.,[.,[.,.]]]]],.] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2,1] => 2

[5,4,3,2,8,6,1,7] => [[[[[.,.],.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,4,4,3,2,1] => 4

[5,4,3,2,8,7,1,6] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,4,3,2,1] => 5

[5,4,3,2,1,8,6,7] => [[[[[.,.],.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,4,4,3,2,1] => 4

[5,4,3,2,8,1,7,6] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,4,3,2,1] => 5

[5,4,3,2,6,8,1,7] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [5,4,4,4,3,2,1] => 4

[7,8,1,2,5,4,6,3] => [[.,[.,[[[.,.],.],[.,.]]]],[.,.]] => [1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,1] => 1

[3,4,7,1,8,2,6,5] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,2] => 1

[1,8,2,4,3,5,6,7] => [.,[[.,[[.,.],[.,[.,[.,.]]]]],.]] => [1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1] => 1

[1,7,2,4,3,5,6,8] => [.,[[.,[[.,.],[.,[.,.]]]],[.,.]]] => [1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1] => 0

[1,6,2,4,3,5,7,8] => [.,[[.,[[.,.],[.,.]]],[.,[.,.]]]] => [1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1] => 0

[1,5,2,4,3,6,7,8] => [.,[[.,[[.,.],.]],[.,[.,[.,.]]]]] => [1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1] => 1

[1,6,2,5,3,4,7,8] => [.,[[.,[[.,[.,.]],.]],[.,[.,.]]]] => [1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2] => 1

[1,7,2,5,3,4,6,8] => [.,[[.,[[.,[.,.]],[.,.]]],[.,.]]] => [1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2] => 0

[1,8,2,5,3,4,6,7] => [.,[[.,[[.,[.,.]],[.,[.,.]]]],.]] => [1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2] => 1

[1,8,2,6,3,4,5,7] => [.,[[.,[[.,[.,[.,.]]],[.,.]]],.]] => [1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [6,3,3] => 1

[1,7,2,6,3,4,5,8] => [.,[[.,[[.,[.,[.,.]]],.]],[.,.]]] => [1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [5,5,3] => 1

[1,8,2,7,3,5,4,6] => [.,[[.,[[.,[[.,.],[.,.]]],.]],.]] => [1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,1] => 2

[1,7,2,8,3,5,4,6] => [.,[[.,[.,[[.,.],[.,.]]]],[.,.]]] => [1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1] => 0

[1,6,2,8,3,5,4,7] => [.,[[.,[.,[[.,.],.]]],[[.,.],.]]] => [1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1] => 2

[1,5,2,8,3,6,4,7] => [.,[[.,[.,[.,.]]],[[.,[.,.]],.]]] => [1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3] => 1

[1,4,2,8,3,6,5,7] => [.,[[.,[.,.]],[[[.,.],[.,.]],.]]] => [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2] => 1

[1,3,2,8,4,6,5,7] => [.,[[.,.],[[.,[[.,.],[.,.]]],.]]] => [1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1,1] => 1

[1,2,3,8,4,6,5,7] => [.,[.,[.,[[.,[[.,.],[.,.]]],.]]]] => [1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [4,1,1] => 1

[1,2,3,7,4,6,5,8] => [.,[.,[.,[[.,[[.,.],.]],[.,.]]]]] => [1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [3,3,1] => 1

[1,3,2,7,4,6,5,8] => [.,[[.,.],[[.,[[.,.],.]],[.,.]]]] => [1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1,1] => 1

[1,4,2,7,3,6,5,8] => [.,[[.,[.,.]],[[[.,.],.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2] => 1

[1,5,2,7,3,6,4,8] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3] => 0

[1,6,2,7,3,5,4,8] => [.,[[.,[.,[[.,.],.]]],[.,[.,.]]]] => [1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1] => 1

[1,7,2,6,3,5,4,8] => [.,[[.,[[.,[[.,.],.]],.]],[.,.]]] => [1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1] => 2

[1,8,2,6,3,5,4,7] => [.,[[.,[[.,[[.,.],.]],[.,.]]],.]] => [1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1] => 2

[1,8,2,5,3,6,4,7] => [.,[[.,[[.,[.,.]],[.,[.,.]]]],.]] => [1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2] => 1

[1,7,2,5,3,6,4,8] => [.,[[.,[[.,[.,.]],[.,.]]],[.,.]]] => [1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2] => 0

[1,6,2,5,3,7,4,8] => [.,[[.,[[.,[.,.]],.]],[.,[.,.]]]] => [1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2] => 1

[1,5,2,4,3,7,6,8] => [.,[[.,[[.,.],.]],[[.,.],[.,.]]]] => [1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1] => 1

[1,6,2,4,3,7,5,8] => [.,[[.,[[.,.],[.,.]]],[.,[.,.]]]] => [1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1] => 0

[1,7,2,4,3,6,5,8] => [.,[[.,[[.,.],[[.,.],.]]],[.,.]]] => [1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1] => 1

[1,8,2,4,3,6,5,7] => [.,[[.,[[.,.],[[.,.],[.,.]]]],.]] => [1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1,1] => 1

[1,8,2,3,4,6,5,7] => [.,[[.,[.,[.,[[.,.],[.,.]]]]],.]] => [1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [6,1,1] => 1

[1,7,2,3,4,6,5,8] => [.,[[.,[.,[.,[[.,.],.]]]],[.,.]]] => [1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [5,5,1] => 1

[1,8,2,3,4,7,5,6] => [.,[[.,[.,[.,[[.,[.,.]],.]]]],.]] => [1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,2] => 2

[1,8,2,4,3,7,5,6] => [.,[[.,[[.,.],[[.,[.,.]],.]]],.]] => [1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1,1] => 2

[1,7,2,4,3,8,5,6] => [.,[[.,[[.,.],[.,[.,.]]]],[.,.]]] => [1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1] => 0

[1,6,2,4,3,8,5,7] => [.,[[.,[[.,.],[.,.]]],[[.,.],.]]] => [1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1] => 1

[1,5,2,4,3,8,6,7] => [.,[[.,[[.,.],.]],[[.,[.,.]],.]]] => [1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1] => 2

[1,6,2,5,3,8,4,7] => [.,[[.,[[.,[.,.]],.]],[[.,.],.]]] => [1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2] => 2

[1,7,2,5,3,8,4,6] => [.,[[.,[[.,[.,.]],[.,.]]],[.,.]]] => [1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2] => 0

[1,8,2,5,3,7,4,6] => [.,[[.,[[.,[.,.]],[[.,.],.]]],.]] => [1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2] => 2

[1,8,2,6,3,7,4,5] => [.,[[.,[[.,[.,[.,.]]],[.,.]]],.]] => [1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [6,3,3] => 1

[1,7,2,6,3,8,4,5] => [.,[[.,[[.,[.,[.,.]]],.]],[.,.]]] => [1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [5,5,3] => 1

[1,2,3,8,4,7,5,6] => [.,[.,[.,[[.,[[.,[.,.]],.]],.]]]] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [4,2] => 2

[1,3,2,8,4,7,5,6] => [.,[[.,.],[[.,[[.,[.,.]],.]],.]]] => [1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1,1,1] => 2

[1,4,2,8,3,7,5,6] => [.,[[.,[.,.]],[[[.,[.,.]],.],.]]] => [1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2] => 2

[1,5,2,8,3,7,4,6] => [.,[[.,[.,[.,.]]],[[[.,.],.],.]]] => [1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3] => 2

[1,6,2,8,3,7,4,5] => [.,[[.,[.,[.,[.,.]]]],[[.,.],.]]] => [1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,4,4] => 1

[1,7,2,8,3,6,4,5] => [.,[[.,[.,[[.,[.,.]],.]]],[.,.]]] => [1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [5,5,2] => 1

[1,8,2,7,3,6,4,5] => [.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => [1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [6,4,2] => 3

[6,7,8,1,2,5,3,4] => [[.,[.,[[.,[.,.]],.]]],[.,[.,.]]] => [1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [5,5,5,2] => 1

[6,7,8,1,2,4,5,3] => [[.,[.,[[.,.],[.,.]]]],[.,[.,.]]] => [1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [5,5,5,1,1] => 0

[6,7,8,1,2,4,3,5] => [[.,[.,[[.,.],[.,.]]]],[.,[.,.]]] => [1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [5,5,5,1,1] => 0

[6,7,8,1,2,3,5,4] => [[.,[.,[.,[[.,.],.]]]],[.,[.,.]]] => [1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,5,5,1] => 1

[1,3,7,5,2,6,4,8] => [.,[[.,.],[[[.,.],[.,.]],[.,.]]]] => [1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1] => 0

[1,3,7,5,4,2,6,8] => [.,[[.,.],[[[.,.],[.,.]],[.,.]]]] => [1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1] => 0

[2,8,4,5,6,1,7,3] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,1,1] => 1

[2,8,4,5,3,7,1,6] => [[.,.],[[[.,.],[.,[[.,.],.]]],.]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2,1,1] => 2

[2,8,4,3,5,6,1,7] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,1,1] => 1

[1,6,3,7,5,2,4,8] => [.,[[[.,.],[[.,.],.]],[.,[.,.]]]] => [1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1] => 1

[3,4,1,2,7,6,8,5] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,2] => 1

[3,4,2,1,7,5,8,6] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2,1] => 1

[1,6,5,7,3,4,2,8] => [.,[[[[.,.],[.,.]],.],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,1,1] => 1

[1,5,2,7,4,6,3,8] => [.,[[.,[[.,.],.]],[[.,.],[.,.]]]] => [1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1] => 1

[7,1,3,8,4,6,2,5] => [[.,[[.,.],[.,[[.,.],.]]]],[.,.]] => [1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [6,6,2,1,1,1] => 1

[2,3,4,8,6,1,7,5] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1,1,1] => 1

[2,3,4,8,6,5,1,7] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1,1,1] => 1

[2,7,3,5,8,6,1,4] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1,1] => 0

[1,5,4,6,2,7,3,8] => [.,[[[.,[.,.]],.],[.,[.,[.,.]]]]] => [1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2] => 1

[3,2,4,1,7,8,5,6] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2,1] => 1

[3,1,4,2,7,8,6,5] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,2] => 1

[3,1,4,6,8,5,7,2] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2] => 1

[2,5,4,6,1,7,8,3] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1,1] => 1

[1,8,3,2,5,4,7,6] => [.,[[[.,.],[[.,.],[[.,.],.]]],.]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,1,1] => 2

[1,8,4,5,2,3,7,6] => [.,[[[.,[.,.]],[.,[[.,.],.]]],.]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2] => 2

[1,8,6,4,3,7,2,5] => [.,[[[[[.,.],.],[.,.]],[.,.]],.]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2,2,1] => 2

[2,3,8,1,5,4,7,6] => [[.,.],[.,[[[.,.],[[.,.],.]],.]]] => [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1,1,1] => 2

[2,4,8,5,1,3,7,6] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,1,1] => 2

[1,8,7,5,6,3,4,2] => [.,[[[[[.,.],[.,.]],[.,.]],.],.]] => [1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3,1,1] => 2

[2,5,8,6,7,1,3,4] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1,1] => 1

[2,4,8,6,1,7,3,5] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1,1] => 1

[1,8,6,5,7,3,2,4] => [.,[[[[[.,.],[.,.]],.],[.,.]],.]] => [1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3,1,1] => 2

[1,8,5,6,7,2,3,4] => [.,[[[.,[.,[.,.]]],[.,[.,.]]],.]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3] => 1

[5,4,6,7,1,8,2,3] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3] => 1

[1,8,4,6,2,7,3,5] => [.,[[[.,[.,.]],[[.,.],[.,.]]],.]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,2] => 1

[1,8,3,2,6,7,4,5] => [.,[[[.,.],[[.,[.,.]],[.,.]]],.]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1,1,1] => 1

[1,8,3,2,7,6,5,4] => [.,[[[.,.],[[[[.,.],.],.],.]],.]] => [1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,1,1] => 4

[1,8,4,7,2,6,5,3] => [.,[[[.,[.,.]],[[[.,.],.],.]],.]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,2] => 3

[3,4,5,8,1,2,7,6] => [[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,2] => 2

[3,4,6,8,1,7,2,5] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2] => 1

[3,5,6,8,7,1,2,4] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,2] => 1

[1,8,5,7,6,2,4,3] => [.,[[[.,[[.,.],.]],[[.,.],.]],.]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,3,1] => 3

[1,8,6,7,5,4,2,3] => [.,[[[[[.,[.,.]],.],.],[.,.]],.]] => [1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3,2] => 3

[3,4,7,8,1,6,5,2] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,2] => 1

[2,3,8,1,7,6,5,4] => [[.,.],[.,[[[[[.,.],.],.],.],.]]] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,1,1] => 4

[1,4,6,2,7,5,8,3] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2] => 0

[1,7,5,2,6,8,4,3] => [.,[[[.,[[.,.],.]],[.,.]],[.,.]]] => [1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,1] => 1

[3,4,6,5,7,1,8,2] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2] => 0

[1,8,4,2,6,7,5,3] => [.,[[[.,[.,.]],[[.,.],[.,.]]],.]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,2] => 1

[1,5,3,2,7,6,8,4] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1] => 0

[2,5,3,1,7,6,8,4] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[2,4,6,1,7,5,8,3] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[4,6,1,2,7,5,8,3] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[1,2,5,3,7,6,8,4] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => [1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2] => 0

[2,3,5,1,7,6,8,4] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1,1] => 0

[1,3,5,2,7,6,8,4] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1] => 0

[1,7,6,2,5,8,3,4] => [.,[[[.,[[.,[.,.]],.]],.],[.,.]]] => [1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2] => 2

[1,8,3,5,7,6,2,4] => [.,[[[.,.],[[.,.],[[.,.],.]]],.]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,1,1] => 2

[1,5,2,3,7,6,8,4] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3] => 0

[1,4,2,3,7,6,8,5] => [.,[[.,[.,.]],[[[.,.],.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2] => 1

[2,4,1,3,7,6,8,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1,1] => 1

[2,5,1,3,7,6,8,4] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[2,8,3,5,7,6,1,4] => [[.,.],[[.,[[.,.],[[.,.],.]]],.]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,1,1,1] => 2

[5,1,2,3,7,6,8,4] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4] => 0

[3,1,2,4,7,6,8,5] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,2] => 1

[8,1,2,4,3,6,5,7] => [[.,[.,[[.,.],[[.,.],[.,.]]]]],.] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1,1] => 1

[8,1,3,5,6,2,7,4] => [[.,[[.,.],[[.,.],[.,[.,.]]]]],.] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,1,1] => 1

[8,1,3,4,2,6,7,5] => [[.,[[.,.],[.,[[.,.],[.,.]]]]],.] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1,1,1] => 1

[8,1,3,2,4,5,7,6] => [[.,[[.,.],[.,[.,[[.,.],.]]]]],.] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,1,1,1] => 2

[2,7,8,3,4,5,6,1] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1,1,1] => 0

[2,6,3,8,4,5,7,1] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1,1] => 1

[2,3,6,7,4,5,8,1] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1,1] => 0

[2,5,6,7,8,3,4,1] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1,1] => 0

[2,4,6,7,3,8,5,1] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[3,4,6,7,2,8,1,5] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2,1] => 1

[3,4,5,2,7,8,1,6] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2,1] => 1

[3,4,2,5,6,8,1,7] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,2,1] => 2

[1,7,3,4,8,6,5,2] => [.,[[[.,.],[.,[[.,.],.]]],[.,.]]] => [1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1,1] => 1

[1,6,8,3,7,4,5,2] => [.,[[[.,.],[.,[.,.]]],[[.,.],.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1] => 1

[1,6,8,3,4,7,5,2] => [.,[[[.,.],[.,[.,.]]],[[.,.],.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1] => 1

[1,8,7,5,3,4,6,2] => [.,[[[[[.,.],[.,.]],[.,.]],.],.]] => [1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3,1,1] => 2

[1,8,7,3,5,4,6,2] => [.,[[[[.,.],[[.,.],[.,.]]],.],.]] => [1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,1,1] => 2

[1,8,7,5,4,3,6,2] => [.,[[[[[[.,.],.],.],[.,.]],.],.]] => [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3,2,1] => 4

[8,1,2,6,5,7,4,3] => [[.,[.,[[[[.,.],.],.],[.,.]]]],.] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2,1] => 3

[1,8,7,4,5,3,6,2] => [.,[[[[[.,.],.],[.,[.,.]]],.],.]] => [1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,2,1] => 3

[1,8,7,4,3,5,6,2] => [.,[[[[[.,.],.],[.,[.,.]]],.],.]] => [1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,2,1] => 3

[1,8,7,3,4,5,6,2] => [.,[[[[.,.],[.,[.,[.,.]]]],.],.]] => [1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,1,1,1] => 2

[2,1,8,7,6,3,5,4] => [[.,.],[[[[.,[[.,.],.]],.],.],.]] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,1,1,1] => 4

[7,3,4,1,8,5,6,2] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,2,2] => 0

[1,6,5,2,7,4,3,8] => [.,[[[.,[[.,.],.]],.],[.,[.,.]]]] => [1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,1] => 2

[1,6,4,2,7,5,3,8] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2] => 0

[1,5,3,2,7,6,4,8] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1] => 0

[2,5,3,1,7,8,6,4] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[4,5,7,1,6,8,2,3] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [4,4,3,3,3] => 0

[7,1,3,4,8,2,5,6] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1,1] => 0

[1,6,2,5,7,3,4,8] => [.,[[.,[[.,[.,.]],.]],[.,[.,.]]]] => [1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2] => 1

[1,6,2,4,7,3,5,8] => [.,[[.,[[.,.],[.,.]]],[.,[.,.]]]] => [1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1] => 0

[7,3,4,1,5,2,8,6] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,2,2] => 0

[3,1,4,2,8,6,7,5] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,2] => 1

[4,1,5,2,8,6,7,3] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [5,3,3,3,3] => 1

[7,3,8,4,5,1,6,2] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,2,2] => 0

[1,3,8,4,7,2,5,6] => [.,[[.,.],[[.,[[.,[.,.]],.]],.]]] => [1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1,1,1] => 2

[4,6,1,2,5,7,3,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[1,4,8,2,5,7,3,6] => [.,[[.,[.,.]],[[.,[[.,.],.]],.]]] => [1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2] => 2

[1,5,8,4,3,2,7,6] => [.,[[[[.,.],.],.],[[[.,.],.],.]]] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,2,1] => 4

[1,4,6,8,3,7,5,2] => [.,[[[.,.],.],[[.,.],[[.,.],.]]]] => [1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1] => 2

[2,4,8,5,3,1,6,7] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,1,1] => 1

[1,6,2,4,7,3,8,5] => [.,[[.,[[.,.],[.,.]]],[.,[.,.]]]] => [1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1] => 0

[1,4,7,2,5,3,8,6] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2] => 0

[1,6,7,5,8,2,4,3] => [.,[[[.,[[.,.],.]],.],[.,[.,.]]]] => [1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,1] => 2

[3,5,6,7,8,1,4,2] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 0

[2,5,7,6,8,1,3,4] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[3,2,8,4,5,6,1,7] => [[[.,.],.],[[.,[.,[.,[.,.]]]],.]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,2,1] => 2

[3,4,7,1,5,2,6,8] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2] => 0

[1,7,3,8,5,2,6,4] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]] => [1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1] => 0

[7,1,3,4,8,2,6,5] => [[.,[[.,.],[.,[[.,.],.]]]],[.,.]] => [1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [6,6,2,1,1,1] => 1

[2,4,5,1,7,8,6,3] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1,1] => 0

[2,6,3,4,5,8,1,7] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1,1] => 1

[1,7,5,2,4,8,3,6] => [.,[[[.,[[.,.],.]],[.,.]],[.,.]]] => [1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,1] => 1

[6,8,1,2,3,4,7,5] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [6,5,5] => 1

[2,5,1,7,8,3,6,4] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[2,5,3,6,8,4,7,1] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1,1] => 1

[2,1,4,7,8,5,6,3] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => 0

[1,4,2,7,5,8,6,3] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2] => 0

[1,5,7,6,4,2,8,3] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2] => 1

[4,5,1,2,7,6,3,8] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [4,4,3,3,3] => 0

[4,5,1,2,6,8,7,3] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3] => 1

[3,5,6,1,8,4,7,2] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,2] => 1

[3,1,4,7,5,6,2,8] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2] => 0

[3,1,4,5,8,6,7,2] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,2] => 1

[3,4,6,8,5,2,7,1] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2,1] => 2

[1,2,7,5,3,8,6,4] => [.,[.,[[[.,[.,.]],[.,.]],[.,.]]]] => [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2] => 0

[1,3,7,2,4,8,6,5] => [.,[[.,.],[[.,[[.,.],.]],[.,.]]]] => [1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1,1] => 1

[2,4,1,7,8,6,5,3] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1,1] => 1

[3,4,7,5,1,8,6,2] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2] => 0

[2,3,7,1,5,8,6,4] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1,1] => 0

[2,1,6,8,3,4,7,5] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1,1] => 1

[2,6,3,7,5,8,1,4] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1,1] => 1

[8,2,3,5,1,6,7,4] => [[[.,.],[.,[[.,.],[.,[.,.]]]]],.] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,1,1,1] => 1

[2,4,8,1,7,3,5,6] => [[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,1,1] => 2

[1,6,2,8,5,3,7,4] => [.,[[.,[[.,[.,.]],.]],[[.,.],.]]] => [1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2] => 2

[1,6,3,7,2,8,4,5] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]] => [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1] => 0

[8,1,3,4,6,2,5,7] => [[.,[[.,.],[.,[[.,.],[.,.]]]]],.] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1,1,1] => 1

[2,4,5,6,8,1,7,3] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,1,1] => 1

[8,1,4,6,2,5,3,7] => [[.,[[.,[.,.]],[[.,.],[.,.]]]],.] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2,2] => 1

[1,8,4,7,2,5,3,6] => [.,[[[.,[.,.]],[[.,[.,.]],.]],.]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,2] => 2

[1,4,8,7,2,6,3,5] => [.,[[.,[.,.]],[[[[.,.],.],.],.]]] => [1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,2] => 3

[1,5,8,7,2,6,3,4] => [.,[[.,[.,[.,.]]],[[[.,.],.],.]]] => [1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3] => 2

[1,5,8,2,7,6,4,3] => [.,[[.,[[.,.],.]],[[[.,.],.],.]]] => [1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1] => 3

[1,4,2,8,7,6,5,3] => [.,[[.,[.,.]],[[[[.,.],.],.],.]]] => [1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,2] => 3

[1,3,8,2,7,6,4,5] => [.,[[.,.],[[[[.,[.,.]],.],.],.]]] => [1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,1,1] => 3

[1,8,3,2,7,5,4,6] => [.,[[[.,.],[[[.,.],[.,.]],.]],.]] => [1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,1,1] => 2

[8,1,3,2,6,5,4,7] => [[.,[[.,.],[[[.,.],.],[.,.]]]],.] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2,1,1] => 2

[2,8,3,1,7,5,4,6] => [[.,.],[[.,[[[.,.],[.,.]],.]],.]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,1,1,1] => 2

[2,3,8,1,7,6,4,5] => [[.,.],[.,[[[[.,[.,.]],.],.],.]]] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,1,1,1] => 3

[2,1,8,3,7,6,4,5] => [[.,.],[[.,[[[.,[.,.]],.],.]],.]] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,1,1,1] => 3

[2,8,1,3,7,5,4,6] => [[.,.],[[.,[[[.,.],[.,.]],.]],.]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,1,1,1] => 2

[8,1,2,3,6,5,4,7] => [[.,[.,[.,[[[.,.],.],[.,.]]]]],.] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1] => 2

[1,8,2,3,7,5,4,6] => [.,[[.,[.,[[[.,.],[.,.]],.]]],.]] => [1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1] => 2

[1,2,8,3,7,6,4,5] => [.,[.,[[.,[[[.,[.,.]],.],.]],.]]] => [1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,3,2] => 3

[1,4,3,6,8,2,5,7] => [.,[[[.,.],.],[[.,.],[[.,.],.]]]] => [1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1] => 2

[1,4,5,2,8,3,7,6] => [.,[[.,[.,.]],[.,[[[.,.],.],.]]]] => [1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2] => 2

[1,4,2,6,5,8,3,7] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2] => 1

[1,5,4,2,6,8,3,7] => [.,[[[.,[.,.]],.],[.,[[.,.],.]]]] => [1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2] => 2

[1,6,4,2,5,8,3,7] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,2] => 1

[1,5,2,6,4,8,3,7] => [.,[[.,[[.,.],.]],[.,[[.,.],.]]]] => [1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1] => 2

[1,2,6,5,4,8,3,7] => [.,[.,[[[[.,.],.],.],[[.,.],.]]]] => [1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1] => 3

[1,2,5,4,7,3,8,6] => [.,[.,[[[.,.],.],[[.,.],[.,.]]]]] => [1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1] => 1

[1,4,7,5,2,8,3,6] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2] => 0

[1,4,5,2,8,7,3,6] => [.,[[.,[.,.]],[.,[[[.,.],.],.]]]] => [1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2] => 2

[1,6,4,2,8,3,7,5] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,2] => 1

[1,4,2,8,3,7,6,5] => [.,[[.,[.,.]],[[[[.,.],.],.],.]]] => [1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,2] => 3

[1,2,5,3,8,7,6,4] => [.,[.,[[.,[.,.]],[[[.,.],.],.]]]] => [1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2] => 2

[1,2,8,6,5,3,7,4] => [.,[.,[[[[.,[.,.]],.],[.,.]],.]]] => [1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2] => 2

[1,5,2,8,6,3,7,4] => [.,[[.,[.,[.,.]]],[[.,[.,.]],.]]] => [1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3] => 1

[1,6,4,2,8,7,3,5] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,2] => 1

[1,7,6,4,2,8,3,5] => [.,[[[[.,[.,.]],[.,.]],.],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,2] => 1

[1,7,5,2,6,3,8,4] => [.,[[[.,[.,[.,.]]],[.,.]],[.,.]]] => [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3] => 0

[1,6,2,7,5,3,8,4] => [.,[[.,[[.,[.,.]],.]],[.,[.,.]]]] => [1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2] => 1

[1,2,7,6,5,3,8,4] => [.,[.,[[[[.,[.,.]],.],.],[.,.]]]] => [1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2] => 2

[1,2,6,5,3,8,7,4] => [.,[.,[[[.,[.,.]],.],[[.,.],.]]]] => [1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2] => 2

[1,5,2,6,3,8,7,4] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3] => 1

[1,5,2,7,6,3,8,4] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3] => 0

[1,6,5,2,7,3,8,4] => [.,[[[.,[.,[.,.]]],.],[.,[.,.]]]] => [1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3] => 1

[1,5,7,4,2,8,3,6] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2] => 1

[7,1,8,3,2,4,6,5] => [[.,[[.,.],[.,[[.,.],.]]]],[.,.]] => [1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [6,6,2,1,1,1] => 1

[1,8,7,3,2,4,6,5] => [.,[[[[.,.],[.,[[.,.],.]]],.],.]] => [1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,1,1] => 3

[1,4,2,8,7,3,6,5] => [.,[[.,[.,.]],[[[[.,.],.],.],.]]] => [1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,2] => 3

[1,7,4,2,8,3,6,5] => [.,[[[.,[.,.]],[[.,.],.]],[.,.]]] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,2] => 1

[1,4,8,5,2,7,3,6] => [.,[[.,[.,.]],[[.,[[.,.],.]],.]]] => [1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2] => 2

[1,8,6,4,2,7,3,5] => [.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2,2] => 1

[1,8,5,2,6,3,7,4] => [.,[[[.,[.,[.,.]]],[.,[.,.]]],.]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3] => 1

[1,5,2,7,3,8,6,4] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3] => 0

[1,2,8,5,3,7,6,4] => [.,[.,[[[.,[.,.]],[[.,.],.]],.]]] => [1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2] => 2

[1,2,6,3,8,7,5,4] => [.,[.,[[.,[[.,.],.]],[[.,.],.]]]] => [1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1] => 2

[1,2,7,6,3,8,5,4] => [.,[.,[[[.,[[.,.],.]],.],[.,.]]]] => [1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1] => 2

[1,6,2,7,3,8,5,4] => [.,[[.,[.,[[.,.],.]]],[.,[.,.]]]] => [1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1] => 1

[1,7,2,8,5,3,6,4] => [.,[[.,[[.,[.,.]],[.,.]]],[.,.]]] => [1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2] => 0

[1,7,4,2,8,6,3,5] => [.,[[[.,[.,.]],[[.,.],.]],[.,.]]] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,2] => 1

[1,8,7,3,2,6,4,5] => [.,[[[[.,.],[[.,[.,.]],.]],.],.]] => [1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1,1,1] => 3

[1,4,2,8,7,6,3,5] => [.,[[.,[.,.]],[[[[.,.],.],.],.]]] => [1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,2] => 3

[1,2,8,7,5,3,6,4] => [.,[.,[[[[.,[.,.]],[.,.]],.],.]]] => [1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2] => 2

[1,2,8,6,3,7,5,4] => [.,[.,[[[.,[[.,.],.]],[.,.]],.]]] => [1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1] => 2

[1,2,7,3,8,6,5,4] => [.,[.,[[.,[[[.,.],.],.]],[.,.]]]] => [1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1] => 2

[8,1,4,5,3,7,6,2] => [[.,[[[.,.],.],[.,[[.,.],.]]]],.] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,2,1] => 3

[8,1,4,5,3,6,7,2] => [[.,[[[.,.],.],[.,[.,[.,.]]]]],.] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2,1] => 2

[2,3,4,1,8,6,5,7] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1,1,1] => 1

[2,3,8,5,1,4,7,6] => [[.,.],[.,[[[.,.],[[.,.],.]],.]]] => [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1,1,1] => 2

[2,3,8,6,1,5,7,4] => [[.,.],[.,[[[[.,.],.],[.,.]],.]]] => [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1,1,1] => 2

[2,3,8,5,6,1,7,4] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1,1,1] => 1

[2,3,8,6,4,1,7,5] => [[.,.],[.,[[[.,[.,.]],[.,.]],.]]] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1,1,1] => 1

[2,3,4,1,8,7,5,6] => [[.,.],[.,[.,[[[.,[.,.]],.],.]]]] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1,1,1] => 2

[2,3,8,1,6,4,7,5] => [[.,.],[.,[[[.,[.,.]],[.,.]],.]]] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1,1,1] => 1

[2,3,8,1,4,5,7,6] => [[.,.],[.,[[.,[.,[[.,.],.]]],.]]] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1,1,1] => 2

[1,2,3,4,5,6,7,9,8] => [.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1] => 1

[2,1,3,4,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1] => 0

[1,2,3,4,5,6,7,8,10,9] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [1] => 1

[2,1,3,4,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1] => 0

[1,2,3,4,5,6,7,8,9,11,10] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]] => [1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [1] => 1

[1,8,2,3,4,5,6,9,7] => [.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [6,6] => 0

[7,1,2,3,4,5,6,9,8] => [[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [7,6,6] => 1

[2,1,9,3,4,5,6,7,8] => [[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1,1,1,1,1,1] => 1

[1,7,6,5,4,2,3,8] => [.,[[[[[.,[.,.]],.],.],.],[.,.]]] => [1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3,2] => 3

[1,8,6,5,2,7,3,4] => [.,[[[[.,[.,[.,.]]],.],[.,.]],.]] => [1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3] => 2

[1,2,7,6,3,4,5,8] => [.,[.,[[[.,[.,[.,.]]],.],[.,.]]]] => [1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [4,4,3] => 1

[1,2,8,3,7,4,5,6] => [.,[.,[[.,[[.,[.,[.,.]]],.]],.]]] => [1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [5,3] => 2

[8,1,7,2,6,3,5,4] => [[.,[[.,[[.,[[.,.],.]],.]],.]],.] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [7,5,3,1] => 4

[7,1,8,2,6,4,3,5] => [[.,[.,[[[.,.],[.,.]],.]]],[.,.]] => [1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [6,6,3,1,1] => 1

[3,2,8,7,1,6,5,4] => [[[.,.],.],[[[[[.,.],.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,2,1] => 5

[1,8,7,2,6,5,3,4] => [.,[[[.,[[[.,[.,.]],.],.]],.],.]] => [1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2] => 4

[1,7,8,2,5,6,3,4] => [.,[[.,[[.,[.,.]],[.,.]]],[.,.]]] => [1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2] => 0

[1,6,8,4,2,7,3,5] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,2] => 1

[1,5,4,8,2,7,3,6] => [.,[[[.,[.,.]],.],[[[.,.],.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,2] => 3

[1,5,4,2,3,6,7,8] => [.,[[[.,[.,.]],.],[.,[.,[.,.]]]]] => [1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2] => 1

[6,7,1,2,4,5,3,8] => [[.,[.,[[.,.],[.,.]]]],[.,[.,.]]] => [1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [5,5,5,1,1] => 0

[1,7,2,3,6,4,5,8] => [.,[[.,[.,[[.,[.,.]],.]]],[.,.]]] => [1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [5,5,2] => 1

[8,7,1,2,3,6,5,4] => [[[.,[.,[.,[[[.,.],.],.]]]],.],.] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [7,6,2,1] => 4

[7,8,1,2,3,5,6,4] => [[.,[.,[.,[[.,.],[.,.]]]]],[.,.]] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1] => 0

[4,1,3,2,5,6,7,8] => [[.,[[.,.],.]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1] => 1

[5,1,2,4,3,6,7,8] => [[.,[.,[[.,.],.]]],[.,[.,[.,.]]]] => [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,1] => 1

[6,1,2,3,5,4,7,8] => [[.,[.,[.,[[.,.],.]]]],[.,[.,.]]] => [1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,5,5,1] => 1

[7,1,2,3,4,6,5,8] => [[.,[.,[.,[.,[[.,.],.]]]]],[.,.]] => [1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [6,6,1] => 1

[8,1,2,3,4,5,7,6] => [[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1] => 2

[3,8,4,5,7,1,2,6] => [[.,[.,.]],[[.,[.,[[.,.],.]]],.]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2,2] => 2

[3,4,8,6,7,1,2,5] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,2] => 1

[4,5,6,7,1,8,3,2] => [[.,[[.,.],.]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1] => 1

[3,5,6,2,7,4,8,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => 1

[3,5,6,1,7,8,4,2] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 0

[2,5,6,1,8,7,4,3] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1,1] => 2

[2,5,6,8,1,7,3,4] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1,1] => 1

[8,2,4,5,1,6,3,7] => [[[.,.],[[.,.],[.,[.,[.,.]]]]],.] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2,1,1] => 1

[1,4,8,6,2,3,7,5] => [.,[[.,[.,.]],[[[.,.],[.,.]],.]]] => [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2] => 1

[1,5,6,8,2,3,7,4] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3] => 1

[1,5,6,2,8,4,7,3] => [.,[[.,[[.,.],.]],[.,[[.,.],.]]]] => [1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1] => 2

[2,5,6,3,4,7,8,1] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1,1] => 0

[1,4,2,6,8,5,7,3] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2] => 1

[8,1,3,2,5,4,6,7] => [[.,[[.,.],[[.,.],[.,[.,.]]]]],.] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,1,1] => 1

[8,2,3,1,5,6,4,7] => [[[.,.],[.,[[.,.],[.,[.,.]]]]],.] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,1,1,1] => 1

[2,8,3,1,5,7,4,6] => [[.,.],[[.,[[.,.],[[.,.],.]]],.]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,1,1,1] => 2

[2,4,1,6,8,7,5,3] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[3,4,1,6,7,8,5,2] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2] => 0

[6,7,1,2,8,4,5,3] => [[.,[.,[[.,.],[.,.]]]],[.,[.,.]]] => [1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [5,5,5,1,1] => 0

[5,1,7,8,2,3,6,4] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4] => 0

[3,1,4,5,7,8,6,2] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2] => 0

[2,1,8,3,4,7,6,5] => [[.,.],[[.,[.,[[[.,.],.],.]]],.]] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,1,1,1] => 3

[8,2,1,3,4,6,5,7] => [[[.,.],[.,[.,[[.,.],[.,.]]]]],.] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1,1,1,1] => 1

[1,8,2,3,4,5,7,6] => [.,[[.,[.,[.,[.,[[.,.],.]]]]],.]] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,1] => 2

[1,2,8,3,4,6,7,5] => [.,[.,[[.,[.,[[.,.],[.,.]]]],.]]] => [1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [5,1,1] => 1

[1,5,7,4,8,3,6,2] => [.,[[[[.,.],.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2,1] => 2

[1,5,7,4,8,6,3,2] => [.,[[[[.,.],.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2,1] => 2

[1,6,7,8,4,5,3,2] => [.,[[[[.,.],.],[.,.]],[.,[.,.]]]] => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2,1] => 1

[1,6,7,8,4,3,5,2] => [.,[[[[.,.],.],[.,.]],[.,[.,.]]]] => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2,1] => 1

[5,7,1,2,8,6,3,4] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4] => 0

[1,5,7,3,8,6,4,2] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1] => 0

[1,6,7,8,3,5,4,2] => [.,[[[.,.],[[.,.],.]],[.,[.,.]]]] => [1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1] => 1

[6,7,1,8,2,5,3,4] => [[.,[.,[[.,[.,.]],.]]],[.,[.,.]]] => [1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [5,5,5,2] => 1

[1,6,7,8,5,3,4,2] => [.,[[[[.,.],[.,.]],.],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,1,1] => 1

[3,4,7,1,8,6,5,2] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,2] => 1

[4,3,8,5,6,7,2,1] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [6,3,3,3,3,2,1] => 3

[4,6,1,2,7,8,5,3] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[6,5,8,4,3,7,2,1] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,5,4,3,2,1] => 5

[1,6,5,2,8,3,4,7] => [.,[[[.,[.,[.,.]]],.],[[.,.],.]]] => [1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3] => 2

[1,7,3,8,4,5,2,6] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1,1] => 0

[1,7,2,8,5,3,4,6] => [.,[[.,[[.,[.,.]],[.,.]]],[.,.]]] => [1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2] => 0

[8,1,2,7,3,4,6,5] => [[.,[.,[[.,[.,[[.,.],.]]],.]]],.] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [7,4,1] => 3

[7,1,2,8,3,5,4,6] => [[.,[.,[.,[[.,.],[.,.]]]]],[.,.]] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1] => 0

[2,3,8,7,4,5,6,1] => [[.,.],[.,[[[.,[.,[.,.]]],.],.]]] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1,1,1,1] => 2

[8,1,7,6,5,2,4,3] => [[.,[[[[.,[[.,.],.]],.],.],.]],.] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,1] => 5

[1,2,8,7,6,3,4,5] => [.,[.,[[[[.,[.,[.,.]]],.],.],.]]] => [1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [5,4,3] => 3

[1,3,8,7,4,6,2,5] => [.,[[.,.],[[[.,[[.,.],.]],.],.]]] => [1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,1,1] => 3

[3,8,7,6,4,5,2,1] => [[[.,.],.],[[[[.,[.,.]],.],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,2,2,1] => 4

[2,8,7,6,5,3,4,1] => [[.,.],[[[[[.,[.,.]],.],.],.],.]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1,1,1] => 4

[1,8,7,6,5,4,2,3] => [.,[[[[[[.,[.,.]],.],.],.],.],.]] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2] => 5

[1,8,6,7,4,5,2,3] => [.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2,2] => 1

[2,7,3,8,5,6,1,4] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1,1] => 0

[1,7,4,8,5,6,2,3] => [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2] => 0

[1,7,3,8,5,6,2,4] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]] => [1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1] => 0

[1,8,5,6,2,7,3,4] => [.,[[[.,[.,[.,.]]],[.,[.,.]]],.]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3] => 1

[1,7,3,8,4,6,2,5] => [.,[[[.,.],[.,[[.,.],.]]],[.,.]]] => [1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1,1] => 1

[2,7,3,8,4,6,1,5] => [[.,.],[[.,[.,[[.,.],.]]],[.,.]]] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1,1,1] => 1

[1,5,2,8,6,7,3,4] => [.,[[.,[.,[.,.]]],[[.,[.,.]],.]]] => [1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3] => 1

[2,5,1,8,6,7,3,4] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1,1] => 1

[1,6,2,8,5,7,3,4] => [.,[[.,[[.,[.,.]],.]],[[.,.],.]]] => [1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2] => 2

[1,6,2,8,4,7,3,5] => [.,[[.,[[.,.],[.,.]]],[[.,.],.]]] => [1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1] => 1

[5,8,1,6,2,7,3,4] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [6,4,4,4] => 1

[1,7,3,6,2,8,4,5] => [.,[[[.,.],[[.,[.,.]],.]],[.,.]]] => [1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1,1,1] => 1

[2,7,3,6,1,8,4,5] => [[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1,1,1,1] => 1

[1,2,3,4,5,6,7,8,9] => [.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [] => 0

[1,2,3,4,5,6,8,9,7] => [.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]] => [1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,1] => 0

[1,3,4,5,6,7,8,9,2] => [.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 0

[1,2,3,4,5,6,7,8,9,10] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [] => 0

[1,2,3,4,5,6,9,8,7] => [.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]] => [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [2,1] => 2

[3,2,4,5,6,7,8,9,1] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2,1] => 1

[4,8,3,7,2,5,1,6] => [[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,3,3,2,1] => 4

[4,8,3,5,2,7,1,6] => [[[[.,.],.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,3,3,2,1] => 4

[4,8,3,5,2,6,1,7] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [6,3,3,3,3,2,1] => 3

[8,1,3,7,4,6,5,2] => [[.,[[.,.],[[.,[[.,.],.]],.]]],.] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,1,1] => 3

[1,6,2,5,4,7,3,8] => [.,[[.,[[[.,.],.],.]],[.,[.,.]]]] => [1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1] => 2

[8,1,3,5,4,7,6,2] => [[.,[[.,.],[[.,.],[[.,.],.]]]],.] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,1,1] => 2

[8,1,3,4,5,6,7,2] => [[.,[[.,.],[.,[.,[.,[.,.]]]]]],.] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1,1,1] => 1

[1,7,2,4,5,6,3,8] => [.,[[.,[[.,.],[.,[.,.]]]],[.,.]]] => [1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1] => 0

[1,2,6,3,5,4,7,8] => [.,[.,[[.,[[.,.],.]],[.,[.,.]]]]] => [1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1] => 1

[3,4,1,2,8,6,5,7] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,2] => 1

[1,7,5,6,3,2,4,8] => [.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,1,1] => 0

[6,1,2,3,8,5,7,4] => [[.,[.,[.,[[.,.],.]]]],[[.,.],.]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [6,5,5,1] => 2

[7,1,2,3,6,5,8,4] => [[.,[.,[.,[[[.,.],.],.]]]],[.,.]] => [1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [6,6,2,1] => 2

[1,5,7,3,2,4,6,8] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1] => 0

[2,4,1,3,8,7,5,6] => [[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,1,1] => 2

[2,8,1,3,6,4,7,5] => [[.,.],[[.,[[.,[.,.]],[.,.]]],.]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1,1,1,1] => 1

[9,8,7,6,5,4,3,2,1] => [[[[[[[[[.,.],.],.],.],.],.],.],.],.] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,3,2,1] => 8

[8,9,7,6,5,4,3,2,1] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,7,6,5,4,3,2,1] => 6

[8,7,9,6,5,4,3,2,1] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,7,6,5,4,3,2,1] => 6

[8,7,6,9,5,4,3,2,1] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,7,6,5,4,3,2,1] => 6

[8,7,6,5,9,4,3,2,1] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,7,6,5,4,3,2,1] => 6

[8,7,6,5,4,9,3,2,1] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,7,6,5,4,3,2,1] => 6

[8,7,6,5,4,3,9,2,1] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,7,6,5,4,3,2,1] => 6

[8,7,6,5,4,3,2,9,1] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,7,6,5,4,3,2,1] => 6

[8,7,6,5,4,3,2,1,9] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,7,6,5,4,3,2,1] => 6

[9,10,8,7,6,5,4,3,2,1] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [8,8,7,6,5,4,3,2,1] => 7

[9,8,10,7,6,5,4,3,2,1] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [8,8,7,6,5,4,3,2,1] => 7

[9,8,7,10,6,5,4,3,2,1] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [8,8,7,6,5,4,3,2,1] => 7

[9,8,7,6,10,5,4,3,2,1] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [8,8,7,6,5,4,3,2,1] => 7

[9,8,7,6,5,10,4,3,2,1] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [8,8,7,6,5,4,3,2,1] => 7

[9,8,7,6,5,4,10,3,2,1] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [8,8,7,6,5,4,3,2,1] => 7

[9,8,7,6,5,4,3,10,2,1] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [8,8,7,6,5,4,3,2,1] => 7

[9,8,7,6,5,4,3,2,10,1] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [8,8,7,6,5,4,3,2,1] => 7

[9,8,7,6,5,4,3,2,1,10] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [8,8,7,6,5,4,3,2,1] => 7

[1,4,2,7,8,6,3,5] => [.,[[.,[.,.]],[[[.,.],.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2] => 1

[1,6,2,4,8,5,3,7] => [.,[[.,[[.,.],[.,.]]],[[.,.],.]]] => [1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1] => 1

[1,6,2,4,7,5,3,8] => [.,[[.,[[.,.],[.,.]]],[.,[.,.]]]] => [1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1] => 0

[1,7,3,8,5,2,4,6] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]] => [1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1] => 0

[1,7,3,2,8,6,4,5] => [.,[[[.,.],[[.,[.,.]],.]],[.,.]]] => [1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1,1,1] => 1

[1,3,6,4,8,5,7,2] => [.,[[.,.],[[.,[.,.]],[[.,.],.]]]] => [1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1] => 1

[1,3,6,4,7,5,8,2] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => [1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1] => 0

[1,7,5,3,4,6,8,2] => [.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,1,1] => 0

[1,2,8,4,3,5,6,7] => [.,[.,[[[.,.],[.,[.,[.,.]]]],.]]] => [1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1] => 1

[1,7,4,2,3,5,6,8] => [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2] => 0

[1,8,7,4,3,2,5,6] => [.,[[[[[.,.],.],[.,[.,.]]],.],.]] => [1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,2,1] => 3

[1,6,3,8,2,4,7,5] => [.,[[[.,.],[.,[.,.]]],[[.,.],.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1] => 1

[1,7,5,4,2,6,3,8] => [.,[[[[.,[.,.]],.],[.,.]],[.,.]]] => [1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,2] => 1

[1,5,8,2,4,6,3,7] => [.,[[.,[[.,.],.]],[[.,[.,.]],.]]] => [1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1] => 2

[1,5,8,4,2,7,3,6] => [.,[[[.,[.,.]],.],[[[.,.],.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,2] => 3

[1,4,6,2,8,3,7,5] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2] => 1

[1,6,3,2,7,8,4,5] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]] => [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1] => 0

[1,7,4,5,3,8,6,2] => [.,[[[[.,.],.],[.,[.,.]]],[.,.]]] => [1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2,1] => 1

[1,8,3,2,4,5,6,7] => [.,[[[.,.],[.,[.,[.,[.,.]]]]],.]] => [1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1,1] => 1

[4,2,5,6,7,8,1,3] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1,1] => 0

[7,2,3,1,4,5,8,6] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1,1,1] => 0

[8,1,2,4,6,5,3,7] => [[.,[.,[[.,.],[[.,.],[.,.]]]]],.] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1,1] => 1

[8,1,2,5,4,6,3,7] => [[.,[.,[[[.,.],.],[.,[.,.]]]]],.] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,1] => 2

[8,1,2,6,4,5,3,7] => [[.,[.,[[[.,.],[.,.]],[.,.]]]],.] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,3,1,1] => 1

[8,1,2,5,6,4,3,7] => [[.,[.,[[[.,.],.],[.,[.,.]]]]],.] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,1] => 2

[8,1,2,6,5,4,3,7] => [[.,[.,[[[[.,.],.],.],[.,.]]]],.] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2,1] => 3

[1,7,5,4,2,8,3,6] => [.,[[[[.,[.,.]],.],[.,.]],[.,.]]] => [1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,2] => 1

[1,4,6,8,2,7,3,5] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2] => 1

[1,4,7,6,2,8,3,5] => [.,[[.,[.,.]],[[[.,.],.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2] => 1

[1,7,4,5,2,8,3,6] => [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2] => 0

[1,4,6,2,8,7,3,5] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2] => 1

[1,4,2,8,6,7,3,5] => [.,[[.,[.,.]],[[[.,.],[.,.]],.]]] => [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2] => 1

[1,4,7,2,6,8,3,5] => [.,[[.,[.,.]],[[[.,.],.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2] => 1

[1,2,3,6,8,5,7,4] => [.,[.,[.,[[[.,.],.],[[.,.],.]]]]] => [1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1] => 2

[1,4,2,7,6,8,3,5] => [.,[[.,[.,.]],[[[.,.],.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2] => 1

[1,4,2,6,8,7,3,5] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2] => 1

[1,7,4,3,2,5,8,6] => [.,[[[[.,.],.],[.,[.,.]]],[.,.]]] => [1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2,1] => 1

[1,8,7,3,4,2,5,6] => [.,[[[[.,.],[.,[.,[.,.]]]],.],.]] => [1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,1,1,1] => 2

[1,4,2,7,8,3,6,5] => [.,[[.,[.,.]],[[[.,.],.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2] => 1

[1,4,2,6,8,3,7,5] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2] => 1

[1,2,3,7,8,5,6,4] => [.,[.,[.,[[[.,.],[.,.]],[.,.]]]]] => [1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1] => 0

[1,2,3,7,5,8,6,4] => [.,[.,[.,[[[.,.],[.,.]],[.,.]]]]] => [1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1] => 0

[1,4,2,7,3,8,6,5] => [.,[[.,[.,.]],[[[.,.],.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2] => 1

[2,1,7,8,3,4,6,5] => [[.,.],[[.,[.,[[.,.],.]]],[.,.]]] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1,1,1] => 1

[1,2,3,8,7,5,6,4] => [.,[.,[.,[[[[.,.],[.,.]],.],.]]]] => [1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1] => 2

[10,1,2,3,4,5,6,7,8,9] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9] => 1

[10,9,1,2,3,4,5,6,7,8] => [[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [9,8] => 2

[11,1,2,3,4,5,6,7,8,9,10] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [10] => 1

[4,3,8,5,2,1,6,7] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [6,3,3,3,3,2,1] => 3

[4,6,5,1,7,2,3,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[2,3,1,8,5,4,7,6] => [[.,.],[.,[[[.,.],[[.,.],.]],.]]] => [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1,1,1] => 2

[2,4,1,5,8,3,7,6] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,1,1] => 2

[3,4,5,1,2,8,7,6] => [[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,2] => 2

[3,4,5,1,8,2,7,6] => [[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,2] => 2

[3,4,5,8,2,1,7,6] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,2,1] => 3

[3,4,5,2,8,1,7,6] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,2,1] => 3

[3,4,6,2,1,7,8,5] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2,1] => 1

[3,4,6,2,1,7,5,8] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2,1] => 1

[3,5,6,2,7,1,4,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => 1

[3,5,6,2,7,1,8,4] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => 1

[3,5,6,2,7,8,1,4] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => 1

[2,4,8,6,3,7,1,5] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1,1] => 1

[1,8,4,6,3,7,2,5] => [.,[[[[.,.],.],[[.,.],[.,.]]],.]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,2,1] => 2

[3,4,6,8,2,7,5,1] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2,1] => 2

[3,4,6,2,8,7,5,1] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2,1] => 2

[3,5,6,2,7,8,4,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => 1

[3,5,6,2,7,4,1,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => 1

[4,5,6,7,2,8,3,1] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1,1] => 0

[2,5,8,6,7,3,4,1] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1,1] => 1

[2,5,8,6,7,3,1,4] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1,1] => 1

[4,5,6,7,2,1,8,3] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1,1] => 0

[2,3,1,8,6,7,4,5] => [[.,.],[.,[[[.,[.,.]],[.,.]],.]]] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1,1,1] => 1

[1,8,3,2,6,7,5,4] => [.,[[[.,.],[[[.,.],.],[.,.]]],.]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,1,1] => 2

[2,5,1,6,7,8,4,3] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1,1] => 1

[2,5,1,6,7,4,8,3] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1,1] => 1

[2,5,1,6,7,4,3,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1,1] => 1

[3,5,6,1,7,4,2,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 0

[3,5,6,1,7,4,8,2] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 0

[3,4,6,1,8,7,5,2] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2] => 1

[3,4,6,8,1,7,5,2] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2] => 1

[2,4,8,6,1,7,5,3] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1,1] => 1

[3,5,6,8,7,1,4,2] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,2] => 1

[4,5,6,7,8,1,3,2] => [[.,[[.,.],.]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1] => 1

[4,5,6,7,1,3,8,2] => [[.,[[.,.],.]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1] => 1

[4,5,6,7,1,3,2,8] => [[.,[[.,.],.]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1] => 1

[4,5,6,7,3,1,8,2] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,2] => 1

[3,5,6,8,7,4,1,2] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,2] => 1

[1,8,5,6,7,4,3,2] => [.,[[[[[.,.],.],.],[.,[.,.]]],.]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,2,1] => 3

[4,2,5,6,1,7,3,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1,1] => 0

[4,3,5,6,7,1,8,2] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,2] => 1

[4,2,5,6,1,7,8,3] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1,1] => 0

[3,2,5,1,6,4,7,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => 1

[3,2,5,1,6,7,8,4] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => 1

[3,2,4,1,8,5,6,7] => [[[.,.],.],[.,[[.,[.,[.,.]]],.]]] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,2,1] => 2

[3,2,4,1,7,5,6,8] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2,1] => 1

[3,2,4,1,6,8,5,7] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2,1] => 2

[3,2,4,1,8,5,7,6] => [[[.,.],.],[.,[[.,[[.,.],.]],.]]] => [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,2,1] => 3

[3,2,5,1,6,7,4,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => 1

[3,2,4,1,5,8,6,7] => [[[.,.],.],[.,[.,[[.,[.,.]],.]]]] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,2,1] => 2

[2,5,4,6,1,7,3,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1,1] => 1

[2,5,4,6,8,1,7,3] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1,1] => 2

[2,4,1,7,5,8,6,3] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => 0

[2,4,1,7,5,3,8,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => 0

[2,4,1,7,3,8,6,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1,1] => 1

[4,8,3,7,2,1,5,6] => [[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,3,3,2,1] => 4

[4,8,3,2,7,1,5,6] => [[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,3,3,2,1] => 4

[3,2,1,4,7,5,8,6] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2,1] => 1

[4,8,3,2,1,5,6,7] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [6,3,3,3,3,2,1] => 3

[4,3,8,2,1,5,6,7] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [6,3,3,3,3,2,1] => 3

[1,9,8,7,6,5,4,3,2] => [.,[[[[[[[[.,.],.],.],.],.],.],.],.]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,1] => 7

[1,10,9,8,7,6,5,4,3,2] => [.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,2,1] => 8

[2,1,8,4,5,3,7,6] => [[.,.],[[[.,.],[.,[[.,.],.]]],.]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2,1,1] => 2

[8,1,7,3,4,2,6,5] => [[.,[[[.,.],[.,[[.,.],.]]],.]],.] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [7,5,2,1,1,1] => 3

[8,1,7,2,4,3,6,5] => [[.,[[.,[[.,.],[[.,.],.]]],.]],.] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [7,5,2,1,1] => 3

[8,1,3,2,7,4,6,5] => [[.,[[.,.],[[.,[[.,.],.]],.]]],.] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,1,1] => 3

[2,1,8,3,7,4,6,5] => [[.,.],[[.,[[.,[[.,.],.]],.]],.]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,1,1,1] => 3

[8,2,3,1,7,4,6,5] => [[[.,.],[.,[[.,[[.,.],.]],.]]],.] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,1,1,1] => 3

[8,2,3,1,5,4,7,6] => [[[.,.],[.,[[.,.],[[.,.],.]]]],.] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,1,1,1] => 2

[2,1,8,3,7,5,6,4] => [[.,.],[[.,[[[.,.],[.,.]],.]],.]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,1,1,1] => 2

[8,1,3,2,7,5,6,4] => [[.,[[.,.],[[[.,.],[.,.]],.]]],.] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [7,4,2,2,1,1] => 2

[8,1,7,2,6,4,5,3] => [[.,[[.,[[[.,.],[.,.]],.]],.]],.] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [7,5,3,1,1] => 3

[2,4,8,3,6,1,7,5] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1,1] => 1

[1,5,8,7,3,6,2,4] => [.,[[[.,.],[.,.]],[[[.,.],.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1,1] => 2

[1,7,2,8,4,6,5,3] => [.,[[.,[[.,.],[[.,.],.]]],[.,.]]] => [1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1] => 1

[2,3,6,8,4,5,7,1] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1,1] => 1

[1,3,7,8,4,6,5,2] => [.,[[.,.],[[.,[[.,.],.]],[.,.]]]] => [1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1,1] => 1

[1,5,7,8,2,4,6,3] => [.,[[.,[[.,.],.]],[[.,.],[.,.]]]] => [1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1] => 1

[1,2,7,8,5,4,6,3] => [.,[.,[[[[.,.],.],[.,.]],[.,.]]]] => [1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1] => 1

[2,8,3,5,4,1,6,7] => [[.,.],[[.,[[.,.],[.,[.,.]]]],.]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,1,1,1] => 1

[2,8,4,5,3,1,6,7] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,1,1] => 1

[3,4,2,1,8,5,6,7] => [[[.,.],.],[.,[[.,[.,[.,.]]],.]]] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,2,1] => 2

[1,7,5,8,3,4,6,2] => [.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,1,1] => 0

[1,6,8,5,4,3,2,7] => [.,[[[[[.,.],.],.],.],[[.,.],.]]] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3,2,1] => 4

[2,4,8,3,6,5,1,7] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1,1] => 1

[2,8,4,1,5,6,3,7] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,1,1] => 1

[1,7,3,8,5,4,6,2] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]] => [1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1] => 0

[2,7,3,8,4,6,5,1] => [[.,.],[[.,[.,[[.,.],.]]],[.,.]]] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1,1,1] => 1

[7,1,3,8,4,6,5,2] => [[.,[[.,.],[.,[[.,.],.]]]],[.,.]] => [1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [6,6,2,1,1,1] => 1

[1,4,3,2,8,5,6,7] => [.,[[[.,.],.],[[.,[.,[.,.]]],.]]] => [1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,1] => 2

[2,8,4,3,5,1,6,7] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,1,1] => 1

[2,8,3,4,5,1,6,7] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1,1,1] => 1

[3,2,1,4,8,5,6,7] => [[[.,.],.],[.,[[.,[.,[.,.]]],.]]] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,2,1] => 2

[1,2,8,4,5,3,7,6] => [.,[.,[[[.,.],[.,[[.,.],.]]],.]]] => [1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1] => 2

[1,4,2,8,5,3,6,7] => [.,[[.,[.,.]],[[.,[.,[.,.]]],.]]] => [1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2] => 1

[1,8,4,2,5,3,6,7] => [.,[[[.,[.,.]],[.,[.,[.,.]]]],.]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2] => 1

[1,5,2,8,4,3,6,7] => [.,[[.,[[.,.],.]],[[.,[.,.]],.]]] => [1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1] => 2

[1,2,8,5,4,3,6,7] => [.,[.,[[[[.,.],.],[.,[.,.]]],.]]] => [1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1] => 2

[1,2,5,4,3,8,6,7] => [.,[.,[[[.,.],.],[[.,[.,.]],.]]]] => [1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1] => 2

[1,2,4,8,5,3,7,6] => [.,[.,[[.,.],[[.,[[.,.],.]],.]]]] => [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1] => 2

[1,2,7,4,8,5,3,6] => [.,[.,[[[.,.],[.,[.,.]]],[.,.]]]] => [1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1] => 0

[1,5,2,7,8,4,3,6] => [.,[[.,[[.,.],.]],[[.,.],[.,.]]]] => [1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1] => 1

[1,2,8,5,7,4,3,6] => [.,[.,[[[[.,.],.],[[.,.],.]],.]]] => [1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1] => 3

[1,2,4,8,7,5,3,6] => [.,[.,[[.,.],[[[.,[.,.]],.],.]]]] => [1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1] => 2

[1,6,7,2,8,4,3,5] => [.,[[.,[[.,.],[.,.]]],[.,[.,.]]]] => [1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1] => 0

[7,1,2,8,5,3,4,6] => [[.,[.,[[.,[.,.]],[.,.]]]],[.,.]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2] => 0

[1,7,2,8,4,5,3,6] => [.,[[.,[[.,.],[.,[.,.]]]],[.,.]]] => [1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1] => 0

[1,4,2,7,8,5,3,6] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2] => 0

[1,2,7,3,5,8,4,6] => [.,[.,[[.,[[.,.],[.,.]]],[.,.]]]] => [1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1] => 0

[1,2,7,5,8,3,4,6] => [.,[.,[[[.,[.,.]],[.,.]],[.,.]]]] => [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2] => 0

[1,2,5,8,7,3,4,6] => [.,[.,[[.,[.,.]],[[[.,.],.],.]]]] => [1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2] => 2

[1,2,5,8,3,7,4,6] => [.,[.,[[.,[.,.]],[[[.,.],.],.]]]] => [1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2] => 2

[7,1,2,8,4,3,6,5] => [[.,[.,[[.,.],[[.,.],.]]]],[.,.]] => [1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [6,6,2,1,1] => 1

[1,2,8,4,7,5,3,6] => [.,[.,[[[.,.],[[.,[.,.]],.]],.]]] => [1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1,1] => 2

[1,2,8,7,4,5,3,6] => [.,[.,[[[[.,.],[.,[.,.]]],.],.]]] => [1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1,1] => 2

[8,1,6,2,7,4,3,5] => [[.,[[.,[[.,.],[.,.]]],[.,.]]],.] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [7,4,4,1,1] => 1

[7,1,2,8,6,4,3,5] => [[.,[.,[[[.,.],[.,.]],.]]],[.,.]] => [1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [6,6,3,1,1] => 1

[7,8,3,4,1,5,2,6] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,2,2] => 0

[9,2,1,3,4,5,6,7,8] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1,1,1,1,1,1] => 1

[9,2,3,1,4,5,6,7,8] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1,1,1,1,1,1] => 1

[3,4,2,5,6,7,8,9,1] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2,1] => 1

[5,8,7,4,3,6,2,1] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,4,3,2,1] => 5

[2,1,5,8,3,6,7,4] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1,1] => 1

[2,4,8,1,5,6,7,3] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,1,1] => 1

[3,4,8,2,5,6,7,1] => [[[.,.],.],[.,[[.,[.,[.,.]]],.]]] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,2,1] => 2

[3,4,1,8,5,6,7,2] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,2] => 1

[2,5,7,3,6,4,8,1] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[1,5,7,3,6,8,4,2] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1] => 0

[3,1,4,7,6,8,5,2] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,2] => 1

[3,8,2,1,7,6,5,4] => [[[.,.],.],[[[[[.,.],.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,2,1] => 5

[3,4,1,7,6,8,5,2] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,2] => 1

[1,4,2,7,8,6,5,3] => [.,[[.,[.,.]],[[[.,.],.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2] => 1

[1,5,7,2,8,6,4,3] => [.,[[.,[[.,.],.]],[[.,.],[.,.]]]] => [1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1] => 1

[1,5,7,8,2,6,4,3] => [.,[[.,[[.,.],.]],[[.,.],[.,.]]]] => [1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1] => 1

[1,4,8,7,2,6,5,3] => [.,[[.,[.,.]],[[[[.,.],.],.],.]]] => [1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,2] => 3

[3,2,8,1,7,6,5,4] => [[[.,.],.],[[[[[.,.],.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,2,1] => 5

[1,3,8,2,7,6,5,4] => [.,[[.,.],[[[[[.,.],.],.],.],.]]] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,1] => 4

[1,2,8,3,7,6,5,4] => [.,[.,[[.,[[[[.,.],.],.],.]],.]]] => [1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1] => 4

[1,8,2,3,7,6,5,4] => [.,[[.,[.,[[[[.,.],.],.],.]]],.]] => [1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1] => 4

[8,1,2,3,7,6,5,4] => [[.,[.,[.,[[[[.,.],.],.],.]]]],.] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1] => 4

[8,1,4,5,7,6,2,3] => [[.,[[.,[.,.]],[.,[[.,.],.]]]],.] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,2] => 2

[4,5,6,1,8,7,2,3] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3] => 1

[3,5,6,1,8,2,7,4] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,2] => 1

[2,5,6,1,8,3,7,4] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1,1] => 1

[2,4,6,1,3,8,7,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[3,4,6,1,2,8,7,5] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2] => 1

[8,1,3,5,7,2,6,4] => [[.,[[.,.],[[.,.],[[.,.],.]]]],.] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,1,1] => 2

[8,1,2,5,7,3,6,4] => [[.,[.,[[.,[.,.]],[[.,.],.]]]],.] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2] => 2

[2,3,6,1,4,8,7,5] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1,1] => 1

[8,1,2,4,3,7,6,5] => [[.,[.,[[.,.],[[[.,.],.],.]]]],.] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1,1] => 3

[8,1,3,4,2,7,6,5] => [[.,[[.,.],[.,[[[.,.],.],.]]]],.] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1,1,1] => 3

[8,1,6,7,2,3,5,4] => [[.,[[.,[.,[[.,.],.]]],[.,.]]],.] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [7,4,4,1] => 2

[2,7,1,3,4,8,6,5] => [[.,.],[[.,[.,[[.,.],.]]],[.,.]]] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1,1,1] => 1

[2,6,3,1,4,8,7,5] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1,1] => 1

[8,1,5,2,7,3,6,4] => [[.,[[.,[.,[.,.]]],[[.,.],.]]],.] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [7,4,3,3] => 2

[8,1,3,2,4,7,6,5] => [[.,[[.,.],[.,[[[.,.],.],.]]]],.] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1,1,1] => 3

[8,1,2,3,4,7,6,5] => [[.,[.,[.,[.,[[[.,.],.],.]]]]],.] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [7,2,1] => 3

[2,4,3,6,1,5,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,3,6,5,8,1,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,6,3,5,8,7,1] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,6,3,5,8,1,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,6,1,5,3,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,6,1,5,8,3,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,1,6,5,8,3,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,1,4,6,5,8,3,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,1,6,5,8,7,3] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,6,1,5,8,7,3] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,6,8,1,5,7,3] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,6,1,8,5,7,3] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,1,6,8,5,7,3] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,1,4,6,8,5,7,3] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,1,4,6,8,5,3,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,1,6,8,5,3,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,6,1,8,5,3,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,6,8,1,5,3,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,6,8,3,5,7,1] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,6,8,3,5,1,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,6,8,3,1,5,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,6,3,1,8,5,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,6,3,8,1,5,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,6,3,8,5,1,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,6,3,8,5,7,1] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,3,6,8,5,7,1] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,3,6,8,5,1,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,3,6,8,1,5,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,3,1,6,8,5,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,1,3,6,8,7,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,3,6,1,8,7,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,3,6,8,1,7,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,6,3,8,1,7,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,1,4,6,8,3,7,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,1,6,8,3,7,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,6,1,8,3,7,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,6,8,1,3,7,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,6,8,3,1,7,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[1,6,4,7,3,8,2,5] => [.,[[[[.,.],.],[.,.]],[.,[.,.]]]] => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2,1] => 1

[1,3,7,4,5,8,2,6] => [.,[[.,.],[[.,[.,[.,.]]],[.,.]]]] => [1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1,1] => 0

[1,7,6,3,4,8,2,5] => [.,[[[[.,.],[.,[.,.]]],.],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1,1,1] => 1

[1,2,7,4,8,3,5,6] => [.,[.,[[[.,.],[.,[.,.]]],[.,.]]]] => [1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1] => 0

[1,6,2,4,8,3,5,7] => [.,[[.,[[.,.],[.,.]]],[[.,.],.]]] => [1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1] => 1

[1,5,3,2,8,4,6,7] => [.,[[[.,.],[.,.]],[[.,[.,.]],.]]] => [1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1] => 1

[2,5,3,4,1,8,6,7] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1,1] => 1

[1,6,4,8,7,2,3,5] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,2] => 1

[2,7,8,3,6,1,4,5] => [[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1,1,1,1] => 1

[4,3,2,8,7,1,5,6] => [[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,3,3,2,1] => 4

[3,8,2,1,7,4,5,6] => [[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,2,2,1] => 3

[3,2,8,1,7,4,6,5] => [[[.,.],.],[[[.,[[.,.],.]],.],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,2,2,1] => 4

[3,4,6,8,7,5,1,2] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2] => 1

[1,4,6,2,7,8,5,3] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2] => 0

[1,2,7,5,4,8,6,3] => [.,[.,[[[[.,.],.],[.,.]],[.,.]]]] => [1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1] => 1

[1,6,2,5,4,8,7,3] => [.,[[.,[[[.,.],.],.]],[[.,.],.]]] => [1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,1] => 3

[7,1,2,5,8,3,6,4] => [[.,[.,[[.,[.,.]],[.,.]]]],[.,.]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2] => 0

[1,8,2,5,7,3,6,4] => [.,[[.,[[.,[.,.]],[[.,.],.]]],.]] => [1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2] => 2

[7,8,1,2,4,6,5,3] => [[.,[.,[[.,.],[[.,.],.]]]],[.,.]] => [1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [6,6,2,1,1] => 1

[2,3,8,5,4,1,6,7] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1,1,1] => 1

[1,5,8,6,4,3,2,7] => [.,[[[[.,.],.],.],[[.,[.,.]],.]]] => [1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,2,1] => 3

[3,4,6,1,5,8,2,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2] => 1

[1,8,7,6,4,3,2,5] => [.,[[[[[[.,.],.],[.,.]],.],.],.]] => [1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,2,1] => 4

[1,2,8,5,6,3,7,4] => [.,[.,[[[.,[.,.]],[.,[.,.]]],.]]] => [1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2] => 1

[6,1,2,5,7,3,8,4] => [[.,[.,[[.,[.,.]],.]]],[.,[.,.]]] => [1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [5,5,5,2] => 1

[4,2,1,5,6,3,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1,1] => 0

[1,3,6,8,5,7,2,4] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]] => [1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1] => 2

[2,4,6,3,7,1,8,5] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[1,3,6,4,8,7,2,5] => [.,[[.,.],[[.,[.,.]],[[.,.],.]]]] => [1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1] => 1

[1,2,4,5,8,3,7,6] => [.,[.,[[.,.],[.,[[[.,.],.],.]]]]] => [1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1] => 2

[2,8,3,5,4,1,7,6] => [[.,.],[[.,[[.,.],[[.,.],.]]],.]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,1,1,1] => 2

[1,5,7,8,4,3,2,6] => [.,[[[[.,.],.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2,1] => 2

[2,4,7,5,1,3,8,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => 0

[3,5,6,4,1,8,2,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,2] => 1

[1,6,5,8,4,3,2,7] => [.,[[[[[.,.],.],.],.],[[.,.],.]]] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3,2,1] => 4

[9,8,1,2,3,4,5,6,7] => [[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [8,7] => 2

[7,8,9,1,2,3,4,5,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,6,6] => 0

[6,7,8,9,1,2,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,5,5,5] => 0

[3,4,6,2,7,1,5,8] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2,1] => 1

[1,6,7,4,8,3,5,2] => [.,[[[[.,.],.],[.,.]],[.,[.,.]]]] => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2,1] => 1

[1,4,6,3,7,5,8,2] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1] => 1

[2,4,6,1,7,5,3,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[1,7,5,4,3,8,6,2] => [.,[[[[[.,.],.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,2,1] => 2

[1,4,6,3,5,8,7,2] => [.,[[[.,.],.],[[.,.],[[.,.],.]]]] => [1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1] => 2

[1,5,8,4,3,6,7,2] => [.,[[[[.,.],.],.],[[.,[.,.]],.]]] => [1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,2,1] => 3

[2,5,4,1,6,7,3,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1,1] => 1

[2,4,1,7,8,5,3,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => 0

[2,5,4,1,6,3,8,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1,1] => 2

[3,5,2,1,6,4,7,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => 1

[2,1,5,7,8,6,3,4] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[2,4,1,7,8,3,6,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1,1] => 1

[4,8,7,3,2,1,5,6] => [[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,3,3,2,1] => 4

[1,8,9,7,6,5,4,3,2] => [.,[[[[[[[.,.],.],.],.],.],.],[.,.]]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [6,6,5,4,3,2,1] => 5

[1,8,7,9,6,5,4,3,2] => [.,[[[[[[[.,.],.],.],.],.],.],[.,.]]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [6,6,5,4,3,2,1] => 5

[1,9,10,8,7,6,5,4,3,2] => [.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [7,7,6,5,4,3,2,1] => 6

[5,7,1,6,2,8,3,4] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4] => 0

[2,3,6,5,1,4,8,7] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1,1] => 2

[2,3,6,4,1,5,8,7] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1,1] => 1

[2,3,6,1,5,4,8,7] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1,1] => 2

[2,3,4,8,7,6,1,5] => [[.,.],[.,[.,[[[[.,.],.],.],.]]]] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1,1,1] => 3

[2,3,4,8,5,7,1,6] => [[.,.],[.,[.,[[.,[[.,.],.]],.]]]] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1,1,1] => 2

[2,1,4,5,8,7,3,6] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,1,1] => 2

[2,3,4,8,7,5,6,1] => [[.,.],[.,[.,[[[.,[.,.]],.],.]]]] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1,1,1] => 2

[2,3,4,8,7,5,1,6] => [[.,.],[.,[.,[[[.,[.,.]],.],.]]]] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1,1,1] => 2

[2,1,4,5,8,6,3,7] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,1,1] => 1

[2,3,4,8,5,6,1,7] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1,1] => 1

[2,3,4,8,7,1,6,5] => [[.,.],[.,[.,[[[[.,.],.],.],.]]]] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1,1,1] => 3

[2,3,4,8,1,7,6,5] => [[.,.],[.,[.,[[[[.,.],.],.],.]]]] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1,1,1] => 3

[2,3,4,8,1,6,7,5] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1,1,1] => 1

[2,3,4,8,5,1,7,6] => [[.,.],[.,[.,[[.,[[.,.],.]],.]]]] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1,1,1] => 2

[2,1,4,5,8,3,7,6] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,1,1] => 2

[2,3,4,8,5,1,6,7] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1,1] => 1

[2,3,4,8,1,6,5,7] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1,1,1] => 1

[2,3,4,8,1,5,7,6] => [[.,.],[.,[.,[[.,[[.,.],.]],.]]]] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1,1,1] => 2

[1,8,6,7,2,5,3,4] => [.,[[[.,[[.,[.,.]],.]],[.,.]],.]] => [1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2] => 2

[1,8,5,7,2,6,3,4] => [.,[[[.,[.,[.,.]]],[[.,.],.]],.]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,3] => 2

[1,8,2,7,5,6,3,4] => [.,[[.,[[[.,[.,.]],[.,.]],.]],.]] => [1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2] => 2

[1,8,2,7,4,6,3,5] => [.,[[.,[[[.,.],[[.,.],.]],.]],.]] => [1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,1] => 3

[1,8,4,7,2,6,3,5] => [.,[[[.,[.,.]],[[[.,.],.],.]],.]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,2] => 3

[1,8,4,7,5,6,2,3] => [.,[[[.,[.,.]],[[.,[.,.]],.]],.]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,2] => 2

[1,8,3,7,5,6,2,4] => [.,[[[.,.],[[[.,.],[.,.]],.]],.]] => [1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,1,1] => 2

[1,8,3,7,4,6,2,5] => [.,[[[.,.],[[.,[[.,.],.]],.]],.]] => [1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,1,1] => 3

[1,8,3,7,2,6,4,5] => [.,[[[.,.],[[[.,[.,.]],.],.]],.]] => [1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,1,1] => 3

[3,8,2,7,1,6,4,5] => [[[.,.],.],[[[[.,[.,.]],.],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,2,2,1] => 4

[3,8,2,7,4,6,1,5] => [[[.,.],.],[[[.,[[.,.],.]],.],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,2,2,1] => 4

[2,8,3,7,5,6,1,4] => [[.,.],[[.,[[[.,.],[.,.]],.]],.]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,1,1,1] => 2

[2,8,3,7,4,6,1,5] => [[.,.],[[.,[[.,[[.,.],.]],.]],.]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,1,1,1] => 3

[2,8,3,7,1,6,4,5] => [[.,.],[[.,[[[.,[.,.]],.],.]],.]] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,1,1,1] => 3

[1,6,7,4,2,8,5,3] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2] => 0

[1,6,7,3,8,5,2,4] => [.,[[[.,.],[[.,.],.]],[.,[.,.]]]] => [1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1] => 1

[7,3,1,8,4,2,5,6] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,2,2] => 0

[1,5,7,8,2,6,3,4] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3] => 0

[2,6,3,7,8,5,4,1] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1,1] => 1

[2,6,3,7,8,4,5,1] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1,1] => 0

[2,4,7,3,5,6,8,1] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => 0

[2,5,3,7,8,1,6,4] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[1,4,7,8,3,6,2,5] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1] => 2

[1,5,7,4,2,6,8,3] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2] => 1

[3,5,6,1,2,8,7,4] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,2] => 1

[3,4,5,8,2,7,1,6] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,2,1] => 3

[3,4,6,2,8,1,5,7] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2,1] => 2

[8,1,2,3,4,5,6,7,9] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,7] => 0

[7,8,1,2,3,4,5,6,9] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,6,6] => 0

[1,8,9,2,3,4,5,6,7] => [.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [6,6] => 0

[7,1,8,2,3,4,5,6,9] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,6,6] => 0

[1,8,2,9,3,4,5,6,7] => [.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [6,6] => 0

[1,7,9,2,3,4,5,6,8] => [.,[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]] => [1,1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0,0] => [6,5,5] => 1

[1,9,10,2,3,4,5,6,7,8] => [.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [7,7] => 0

[1,6,2,4,7,8,5,3] => [.,[[.,[[.,.],[.,.]]],[.,[.,.]]]] => [1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1] => 0

[1,4,7,2,5,8,6,3] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2] => 0

[7,3,8,4,5,6,1,2] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,2,2] => 0

[3,5,6,4,8,7,1,2] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,2] => 1

[1,8,5,2,7,3,6,4] => [.,[[[.,[.,[.,.]]],[[.,.],.]],.]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,3] => 2

[1,3,6,4,8,2,5,7] => [.,[[.,.],[[.,[.,.]],[[.,.],.]]]] => [1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1] => 1

[1,4,6,2,5,8,3,7] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2] => 1

[1,6,8,7,4,2,3,5] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,2] => 1

[6,1,7,8,2,4,3,5] => [[.,[.,[[.,.],[.,.]]]],[.,[.,.]]] => [1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [5,5,5,1,1] => 0

[1,2,8,3,6,5,7,4] => [.,[.,[[.,[[[.,.],.],[.,.]]],.]]] => [1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1] => 2

[1,6,3,8,5,7,2,4] => [.,[[[.,.],[[.,.],.]],[[.,.],.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,1,1] => 2

[1,6,4,3,7,2,8,5] => [.,[[[[.,.],.],[.,.]],[.,[.,.]]]] => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2,1] => 1

[2,6,3,4,8,7,1,5] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1,1] => 1

[7,1,3,4,5,2,8,6] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1,1] => 0

[1,8,3,5,4,2,7,6] => [.,[[[.,.],[[.,.],[[.,.],.]]],.]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,1,1] => 2

[1,4,7,5,3,8,2,6] => [.,[[[.,.],.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1] => 1

[2,4,6,7,3,1,8,5] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[1,7,5,8,2,6,4,3] => [.,[[[.,[[.,.],.]],[.,.]],[.,.]]] => [1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,1] => 1

[1,3,8,5,7,6,2,4] => [.,[[.,.],[[[.,.],[[.,.],.]],.]]] => [1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1,1] => 2

[8,1,2,5,6,3,7,4] => [[.,[.,[[.,[.,.]],[.,[.,.]]]]],.] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2] => 1

[1,8,2,5,7,6,3,4] => [.,[[.,[[.,[.,.]],[[.,.],.]]],.]] => [1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2] => 2

[5,1,8,6,2,7,3,4] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [6,4,4,4] => 1

[2,5,8,6,1,7,3,4] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1,1] => 1

[1,2,8,6,5,7,3,4] => [.,[.,[[[[.,[.,.]],.],[.,.]],.]]] => [1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2] => 2

[1,8,5,6,3,7,2,4] => [.,[[[[.,.],[.,.]],[.,[.,.]]],.]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,1,1] => 1

[1,7,6,5,4,2,8,3] => [.,[[[[[.,[.,.]],.],.],.],[.,.]]] => [1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3,2] => 3

[1,7,6,4,5,2,8,3] => [.,[[[[.,[.,.]],[.,.]],.],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,2] => 1

[1,8,3,6,5,7,2,4] => [.,[[[.,.],[[[.,.],.],[.,.]]],.]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,1,1] => 2

[8,1,3,5,7,6,2,4] => [[.,[[.,.],[[.,.],[[.,.],.]]]],.] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,1,1] => 2

[3,4,7,8,5,6,1,2] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2] => 0

[3,4,7,2,5,1,6,8] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2,1] => 1

[1,4,7,2,5,8,3,6] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2] => 0

[1,2,7,6,5,8,3,4] => [.,[.,[[[[.,[.,.]],.],.],[.,.]]]] => [1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2] => 2

[2,3,8,6,4,1,5,7] => [[.,.],[.,[[[.,[.,.]],[.,.]],.]]] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1,1,1] => 1

[7,8,1,2,5,6,3,4] => [[.,[.,[[.,[.,.]],[.,.]]]],[.,.]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2] => 0

[4,1,6,2,5,7,3,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[1,8,3,6,7,4,5,2] => [.,[[[.,.],[[.,[.,.]],[.,.]]],.]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1,1,1] => 1

[2,4,7,5,1,8,3,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => 0

[2,8,3,4,5,1,7,6] => [[.,.],[[.,[.,[.,[[.,.],.]]]],.]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1,1,1,1] => 2

[1,3,7,4,8,2,5,6] => [.,[[.,.],[[.,[.,[.,.]]],[.,.]]]] => [1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1,1] => 0

[2,4,7,3,6,1,8,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1,1] => 1

[2,4,7,1,6,5,3,8] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1,1] => 1

[1,2,7,8,5,4,3,6] => [.,[.,[[[[.,.],.],[.,.]],[.,.]]]] => [1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1] => 1

[2,8,1,4,5,6,3,7] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,1,1] => 1

[3,4,6,1,5,8,7,2] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2] => 1

[5,6,1,7,4,8,2,3] => [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,2] => 1

[2,5,6,1,7,4,8,3] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1,1] => 1

[1,6,4,7,5,8,2,3] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2] => 0

[1,3,7,4,6,8,2,5] => [.,[[.,.],[[.,[[.,.],.]],[.,.]]]] => [1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1,1] => 1

[1,7,6,5,4,8,2,3] => [.,[[[[[.,[.,.]],.],.],.],[.,.]]] => [1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3,2] => 3

[1,2,7,6,8,3,4,5] => [.,[.,[[[.,[.,[.,.]]],.],[.,.]]]] => [1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [4,4,3] => 1

[1,6,2,5,8,3,4,7] => [.,[[.,[[.,[.,.]],.]],[[.,.],.]]] => [1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2] => 2

[1,5,4,2,8,3,6,7] => [.,[[[.,[.,.]],.],[[.,[.,.]],.]]] => [1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,2] => 2

[1,7,6,8,5,4,2,3] => [.,[[[[[.,[.,.]],.],.],.],[.,.]]] => [1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3,2] => 3

[1,4,8,6,7,5,2,3] => [.,[[.,[.,.]],[[[.,.],[.,.]],.]]] => [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2] => 1

[2,4,8,6,7,3,5,1] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1,1] => 1

[3,4,8,5,6,7,2,1] => [[[.,.],.],[.,[[.,[.,[.,.]]],.]]] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,2,1] => 2

[5,4,3,8,6,7,2,1] => [[[[[.,.],.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,4,4,3,2,1] => 4

[1,3,8,7,5,6,2,4] => [.,[[.,.],[[[[.,.],[.,.]],.],.]]] => [1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,1,1] => 2

[5,8,6,7,4,3,2,1] => [[[[[.,.],.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,4,4,3,2,1] => 4

[4,8,7,5,6,3,2,1] => [[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,3,3,2,1] => 4

[2,1,4,3,8,6,5,7] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1,1] => 1

[2,4,1,3,8,6,5,7] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1,1] => 1

[2,4,8,1,3,6,5,7] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1,1] => 1

[2,4,1,8,3,6,5,7] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1,1] => 1

[2,1,4,8,3,6,5,7] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1,1] => 1

[2,1,4,8,6,3,5,7] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1,1] => 1

[2,4,8,1,6,3,5,7] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1,1] => 1

[2,4,8,6,1,3,5,7] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1,1] => 1

[2,1,7,3,8,5,6,4] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1,1] => 0

[7,1,8,2,6,4,5,3] => [[.,[.,[[[.,.],[.,.]],.]]],[.,.]] => [1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [6,6,3,1,1] => 1

[2,8,3,1,5,4,6,7] => [[.,.],[[.,[[.,.],[.,[.,.]]]],.]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,1,1,1] => 1

[2,5,3,4,7,1,8,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[2,4,8,3,5,7,6,1] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,1,1] => 2

[1,5,8,4,3,2,6,7] => [.,[[[[.,.],.],.],[[.,[.,.]],.]]] => [1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,2,1] => 3

[1,8,5,4,3,2,6,7] => [.,[[[[[.,.],.],.],[.,[.,.]]],.]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,2,1] => 3

[1,7,4,3,8,5,2,6] => [.,[[[[.,.],.],[.,[.,.]]],[.,.]]] => [1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2,1] => 1

[1,5,7,3,8,4,2,6] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1] => 0

[1,7,5,6,3,2,8,4] => [.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,1,1] => 0

[2,6,7,3,1,4,8,5] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1,1] => 0

[2,7,1,8,3,5,4,6] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1,1] => 0

[2,1,7,3,5,8,4,6] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1,1] => 0

[1,2,8,7,4,5,6,3] => [.,[.,[[[[.,.],[.,[.,.]]],.],.]]] => [1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1,1] => 2

[8,1,6,2,7,4,5,3] => [[.,[[.,[[.,.],[.,.]]],[.,.]]],.] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [7,4,4,1,1] => 1

[1,8,5,2,6,7,4,3] => [.,[[[.,[[.,.],.]],[.,[.,.]]],.]] => [1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,1] => 2

[1,7,8,5,2,6,4,3] => [.,[[[.,[[.,.],.]],[.,.]],[.,.]]] => [1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,1] => 1

[1,8,6,7,5,4,3,2] => [.,[[[[[[.,.],.],.],.],[.,.]],.]] => [1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3,2,1] => 4

[3,5,1,4,6,2,8,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,2] => 1

[2,1,5,7,3,6,8,4] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[2,4,7,1,6,5,8,3] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1,1] => 1

[3,4,6,2,7,8,5,1] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2,1] => 1

[3,5,6,4,7,1,8,2] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 0

[3,4,6,1,5,7,8,2] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2] => 0

[3,4,1,5,7,6,8,2] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2] => 0

[3,8,2,7,1,6,5,4] => [[[.,.],.],[[[[[.,.],.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,2,1] => 5

[3,8,2,7,6,1,5,4] => [[[.,.],.],[[[[[.,.],.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,2,1] => 5

[3,8,2,7,6,5,1,4] => [[[.,.],.],[[[[[.,.],.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,2,1] => 5

[3,8,2,7,6,5,4,1] => [[[.,.],.],[[[[[.,.],.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,2,1] => 5

[4,8,7,3,2,1,6,5] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,3,2,1] => 5

[4,8,7,3,2,6,1,5] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,3,2,1] => 5

[4,8,7,3,2,6,5,1] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,3,2,1] => 5

[4,8,7,3,6,2,5,1] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,3,2,1] => 5

[4,8,7,3,6,2,1,5] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,3,2,1] => 5

[4,8,7,3,6,5,2,1] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,3,2,1] => 5

[1,4,6,7,3,8,2,5] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1] => 1

[2,4,6,7,3,8,1,5] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[1,4,6,7,3,8,5,2] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1] => 1

[1,5,6,7,8,3,4,2] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => [1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1] => 0

[2,5,6,7,8,3,1,4] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1,1] => 0

[1,5,6,7,8,3,2,4] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => [1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1] => 0

[3,4,6,7,2,8,5,1] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2,1] => 1

[1,5,6,7,8,2,4,3] => [.,[[.,[[.,.],.]],[.,[.,[.,.]]]]] => [1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1] => 1

[1,5,6,7,8,4,2,3] => [.,[[[.,[.,.]],.],[.,[.,[.,.]]]]] => [1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2] => 1

[3,4,6,7,1,8,5,2] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2] => 0

[7,1,2,3,4,5,6,8,9] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,6,6] => 0

[1,4,3,6,2,5,7,8] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1] => 1

[1,4,3,7,2,5,6,8] => [.,[[[.,.],.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1] => 1

[1,4,3,7,6,8,2,5] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1] => 2

[1,4,3,7,5,8,2,6] => [.,[[[.,.],.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1] => 1

[1,4,3,7,2,6,5,8] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1] => 2

[1,5,3,7,4,8,2,6] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1] => 0

[1,3,2,6,5,8,4,7] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]] => [1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1] => 2

[1,5,4,8,2,6,3,7] => [.,[[[.,[.,.]],.],[[.,[.,.]],.]]] => [1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,2] => 2

[1,5,4,8,3,7,2,6] => [.,[[[[.,.],.],.],[[[.,.],.],.]]] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,2,1] => 4

[1,2,3,6,5,8,4,7] => [.,[.,[.,[[[.,.],.],[[.,.],.]]]]] => [1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1] => 2

[1,6,3,8,5,2,4,7] => [.,[[[.,.],[[.,.],.]],[[.,.],.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,1,1] => 2

[7,1,8,2,3,6,5,4] => [[.,[.,[.,[[[.,.],.],.]]]],[.,.]] => [1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [6,6,2,1] => 2

[1,5,2,3,8,4,7,6] => [.,[[.,[.,[.,.]]],[[[.,.],.],.]]] => [1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3] => 2

[1,2,5,3,8,4,7,6] => [.,[.,[[.,[.,.]],[[[.,.],.],.]]]] => [1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2] => 2

[1,2,4,8,3,7,6,5] => [.,[.,[[.,.],[[[[.,.],.],.],.]]]] => [1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1] => 3

[1,4,8,2,3,7,6,5] => [.,[[.,[.,.]],[[[[.,.],.],.],.]]] => [1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,2] => 3

[1,4,8,3,7,2,6,5] => [.,[[[.,.],.],[[[[.,.],.],.],.]]] => [1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,2,1] => 4

[1,5,4,8,2,7,6,3] => [.,[[[.,[.,.]],.],[[[.,.],.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,2] => 3

[1,4,2,5,8,7,6,3] => [.,[[.,[.,.]],[.,[[[.,.],.],.]]]] => [1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2] => 2

[1,3,4,8,7,2,6,5] => [.,[[.,.],[.,[[[[.,.],.],.],.]]]] => [1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1,1] => 3

[1,3,4,8,2,7,6,5] => [.,[[.,.],[.,[[[[.,.],.],.],.]]]] => [1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1,1] => 3

[2,3,7,5,4,1,8,6] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1,1] => 0

[1,7,6,5,3,8,4,2] => [.,[[[[[.,.],[.,.]],.],.],[.,.]]] => [1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3,1,1] => 2

[1,7,6,5,2,8,3,4] => [.,[[[[.,[.,[.,.]]],.],.],[.,.]]] => [1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3] => 2

[1,7,6,5,3,2,8,4] => [.,[[[[[.,.],[.,.]],.],.],[.,.]]] => [1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3,1,1] => 2

[5,1,6,2,4,7,8,3] => [[.,[.,[[.,.],.]]],[.,[.,[.,.]]]] => [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,1] => 1

[1,2,6,3,4,8,7,5] => [.,[.,[[.,[.,[.,.]]],[[.,.],.]]]] => [1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [4,3,3] => 1

[1,7,2,4,8,3,6,5] => [.,[[.,[[.,.],[[.,.],.]]],[.,.]]] => [1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1] => 1

[1,7,2,6,8,3,5,4] => [.,[[.,[[.,[[.,.],.]],.]],[.,.]]] => [1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1] => 2

[1,2,6,7,4,8,5,3] => [.,[.,[[[.,.],[.,.]],[.,[.,.]]]]] => [1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1] => 0

[1,7,6,2,4,8,3,5] => [.,[[[.,[[.,.],[.,.]]],.],[.,.]]] => [1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1,1] => 1

[2,7,3,6,4,8,1,5] => [[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1,1,1,1] => 1

[1,8,5,7,2,4,6,3] => [.,[[[.,[[.,.],.]],[[.,.],.]],.]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,3,1] => 3

[6,5,4,8,3,2,1,7] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,5,4,3,2,1] => 5

[4,3,8,7,6,2,1,5] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,3,2,1] => 5

[2,8,7,6,5,4,1,3] => [[.,.],[[[[[[.,.],.],.],.],.],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,1,1] => 5

[3,4,1,2,5,6,7,8,9] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2] => 0

[3,2,1,4,5,6,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2,1] => 1

[4,5,6,1,2,3,7,8,9] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3,3] => 0

[5,6,7,8,1,2,3,4,9] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,4,4,4,4] => 0

[6,1,2,3,7,5,8,4] => [[.,[.,[.,[[.,.],.]]]],[.,[.,.]]] => [1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,5,5,1] => 1

[7,1,2,3,8,6,5,4] => [[.,[.,[.,[[[.,.],.],.]]]],[.,.]] => [1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [6,6,2,1] => 2

[7,1,2,3,5,8,6,4] => [[.,[.,[.,[[.,.],[.,.]]]]],[.,.]] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1] => 0

[2,1,7,3,4,8,6,5] => [[.,.],[[.,[.,[[.,.],.]]],[.,.]]] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1,1,1] => 1

[8,1,2,3,5,7,6,4] => [[.,[.,[.,[[.,.],[[.,.],.]]]]],.] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,1] => 2

[8,1,2,3,6,7,5,4] => [[.,[.,[.,[[[.,.],.],[.,.]]]]],.] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1] => 2

[7,1,2,3,6,8,5,4] => [[.,[.,[.,[[[.,.],.],.]]]],[.,.]] => [1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [6,6,2,1] => 2

[7,1,2,3,8,5,6,4] => [[.,[.,[.,[[.,.],[.,.]]]]],[.,.]] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1] => 0

[8,1,2,3,7,5,6,4] => [[.,[.,[.,[[[.,.],[.,.]],.]]]],.] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,1] => 2

[8,1,2,3,6,5,7,4] => [[.,[.,[.,[[[.,.],.],[.,.]]]]],.] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1] => 2

[2,1,7,3,4,6,8,5] => [[.,.],[[.,[.,[[.,.],.]]],[.,.]]] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1,1,1] => 1

[7,1,2,3,5,6,8,4] => [[.,[.,[.,[[.,.],[.,.]]]]],[.,.]] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1] => 0

[6,1,2,3,8,7,4,5] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [6,5,5] => 1

[5,1,2,3,7,8,6,4] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4] => 0

[5,1,2,3,8,6,7,4] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [6,4,4,4] => 1

[6,1,2,3,5,8,7,4] => [[.,[.,[.,[[.,.],.]]]],[[.,.],.]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [6,5,5,1] => 2

[2,1,6,3,4,8,7,5] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1,1] => 1

[6,1,2,3,5,7,8,4] => [[.,[.,[.,[[.,.],.]]]],[.,[.,.]]] => [1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,5,5,1] => 1

[5,1,2,3,6,8,7,4] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [5,4,4,4] => 1

[7,8,1,2,6,3,5,4] => [[.,[.,[[.,[[.,.],.]],.]]],[.,.]] => [1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [6,6,3,1] => 2

[1,4,8,2,7,3,5,6] => [.,[[.,[.,.]],[[[.,[.,.]],.],.]]] => [1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2] => 2

[1,2,8,5,4,7,3,6] => [.,[.,[[[[.,.],.],[[.,.],.]],.]]] => [1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1] => 3

[1,3,8,5,4,2,7,6] => [.,[[.,.],[[[.,.],[[.,.],.]],.]]] => [1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1,1] => 2

[2,3,6,8,4,7,1,5] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1,1] => 1

[1,3,6,8,4,7,5,2] => [.,[[.,.],[[.,[.,.]],[[.,.],.]]]] => [1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1] => 1

[3,4,8,5,7,6,1,2] => [[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,2] => 2

[1,2,6,8,4,5,7,3] => [.,[.,[[[.,.],[.,.]],[[.,.],.]]]] => [1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1] => 1

[1,6,4,2,8,3,5,7] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,2] => 1

[1,6,3,8,5,4,2,7] => [.,[[[.,.],[[.,.],.]],[[.,.],.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,1,1] => 2

[7,1,2,3,6,5,4,8] => [[.,[.,[.,[[[.,.],.],.]]]],[.,.]] => [1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [6,6,2,1] => 2

[6,8,1,2,7,3,5,4] => [[.,[.,[.,[[.,.],.]]]],[[.,.],.]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [6,5,5,1] => 2

[1,6,2,3,8,5,4,7] => [.,[[.,[.,[[.,.],.]]],[[.,.],.]]] => [1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1] => 2

[1,5,8,2,7,6,3,4] => [.,[[.,[.,[.,.]]],[[[.,.],.],.]]] => [1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3] => 2

[1,2,5,3,8,7,4,6] => [.,[.,[[.,[.,.]],[[[.,.],.],.]]]] => [1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2] => 2

[1,5,8,4,7,2,6,3] => [.,[[[.,[.,.]],.],[[[.,.],.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,2] => 3

[1,3,2,5,8,7,4,6] => [.,[[.,.],[[.,.],[[[.,.],.],.]]]] => [1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1,1] => 2

[1,2,7,5,8,6,4,3] => [.,[.,[[[[.,.],.],[.,.]],[.,.]]]] => [1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1] => 1

[1,3,7,8,2,6,5,4] => [.,[[.,.],[[[[.,.],.],.],[.,.]]]] => [1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1,1] => 2

[2,3,7,8,1,6,5,4] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1,1,1] => 2

[8,1,2,6,7,3,5,4] => [[.,[.,[[.,[[.,.],.]],[.,.]]]],.] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [7,3,3,1] => 2

[8,1,2,6,7,5,3,4] => [[.,[.,[[[.,[.,.]],.],[.,.]]]],.] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2] => 2

[8,2,3,5,7,1,6,4] => [[[.,.],[.,[[.,.],[[.,.],.]]]],.] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,1,1,1] => 2

[8,7,1,2,4,6,3,5] => [[[.,[.,[[.,.],[[.,.],.]]]],.],.] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [7,6,2,1,1] => 3

[1,6,8,3,7,2,5,4] => [.,[[[.,.],[[.,.],.]],[[.,.],.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,1,1] => 2

[1,4,6,8,2,7,5,3] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2] => 1

[1,6,5,8,2,7,4,3] => [.,[[[.,[[.,.],.]],.],[[.,.],.]]] => [1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3,1] => 3

[1,8,4,5,7,2,6,3] => [.,[[[.,[.,.]],[.,[[.,.],.]]],.]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2] => 2

[1,6,8,3,7,5,2,4] => [.,[[[.,.],[[.,.],.]],[[.,.],.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,1,1] => 2

[2,8,4,5,7,1,6,3] => [[.,.],[[[.,.],[.,[[.,.],.]]],.]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2,1,1] => 2

[8,7,3,4,5,1,6,2] => [[[[.,[.,.]],[.,[.,[.,.]]]],.],.] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,2,2,2] => 2

[1,3,2,8,5,4,7,6] => [.,[[.,.],[[[.,.],[[.,.],.]],.]]] => [1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1,1] => 2

[8,1,4,5,2,3,7,6] => [[.,[[.,[.,.]],[.,[[.,.],.]]]],.] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,2] => 2

[5,4,6,1,7,8,2,3] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3] => 1

[8,1,5,6,7,2,3,4] => [[.,[[.,[.,[.,.]]],[.,[.,.]]]],.] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [7,3,3,3] => 1

[2,1,4,6,8,7,3,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[3,4,6,8,7,1,2,5] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2] => 1

[1,3,2,8,6,7,4,5] => [.,[[.,.],[[[.,[.,.]],[.,.]],.]]] => [1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1,1] => 1

[2,3,8,6,7,1,4,5] => [[.,.],[.,[[[.,[.,.]],[.,.]],.]]] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1,1,1] => 1

[8,1,3,2,6,7,4,5] => [[.,[[.,.],[[.,[.,.]],[.,.]]]],.] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,3,1,1,1] => 1

[2,3,8,7,1,6,5,4] => [[.,.],[.,[[[[[.,.],.],.],.],.]]] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,1,1] => 4

[3,4,7,8,6,1,5,2] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,2] => 1

[8,7,1,2,4,5,3,6] => [[[.,[.,[[.,.],[.,[.,.]]]]],.],.] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,1,1] => 2

[1,4,2,3,8,7,5,6] => [.,[[.,[.,.]],[[[.,[.,.]],.],.]]] => [1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2] => 2

[1,4,2,7,6,3,5,8] => [.,[[.,[.,.]],[[[.,.],.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2] => 1

[7,1,2,4,6,8,5,3] => [[.,[.,[[.,.],[[.,.],.]]]],[.,.]] => [1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [6,6,2,1,1] => 1

[7,1,2,6,8,5,3,4] => [[.,[.,[[[.,[.,.]],.],.]]],[.,.]] => [1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [6,6,3,2] => 2

[6,1,2,7,8,5,3,4] => [[.,[.,[[.,[.,.]],.]]],[.,[.,.]]] => [1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [5,5,5,2] => 1

[6,1,2,7,4,8,5,3] => [[.,[.,[[.,.],[.,.]]]],[.,[.,.]]] => [1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [5,5,5,1,1] => 0

[1,4,2,3,8,6,5,7] => [.,[[.,[.,.]],[[[.,.],[.,.]],.]]] => [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2] => 1

[1,4,2,3,8,5,7,6] => [.,[[.,[.,.]],[[.,[[.,.],.]],.]]] => [1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2] => 2

[8,1,2,6,7,4,5,3] => [[.,[.,[[[.,.],[.,.]],[.,.]]]],.] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,3,1,1] => 1

[6,1,2,8,7,3,5,4] => [[.,[.,[.,[[.,.],.]]]],[[.,.],.]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [6,5,5,1] => 2

[1,2,3,5,8,4,7,6] => [.,[.,[.,[[.,.],[[[.,.],.],.]]]]] => [1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1] => 2

[1,2,3,5,8,6,4,7] => [.,[.,[.,[[.,.],[[.,[.,.]],.]]]]] => [1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1] => 1

[7,1,2,8,3,6,5,4] => [[.,[.,[.,[[[.,.],.],.]]]],[.,.]] => [1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [6,6,2,1] => 2

[7,1,2,8,6,4,5,3] => [[.,[.,[[[.,.],[.,.]],.]]],[.,.]] => [1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [6,6,3,1,1] => 1

[8,1,2,7,4,6,5,3] => [[.,[.,[[[.,.],[[.,.],.]],.]]],.] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,1] => 3

[8,1,2,7,3,6,5,4] => [[.,[.,[[.,[[[.,.],.],.]],.]]],.] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1] => 4

[1,2,3,5,8,7,4,6] => [.,[.,[.,[[.,.],[[[.,.],.],.]]]]] => [1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1] => 2

[1,2,3,6,8,5,4,7] => [.,[.,[.,[[[.,.],.],[[.,.],.]]]]] => [1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1] => 2

[5,4,8,3,2,7,6,1] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,4,3,2,1] => 5

[4,8,5,3,2,7,6,1] => [[[[.,.],.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,3,3,2,1] => 4

[5,8,4,3,2,7,6,1] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,4,3,2,1] => 5

[6,8,5,7,4,3,2,1] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,5,4,3,2,1] => 5

[2,3,1,4,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1] => 0

[2,3,4,1,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1] => 0

[2,3,4,5,1,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1] => 0

[2,3,4,5,6,1,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1] => 0

[2,3,1,4,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1] => 0

[2,3,4,1,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1] => 0

[2,3,4,5,1,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1] => 0

[2,3,4,5,6,1,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1] => 0

[2,3,4,5,6,7,1,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1] => 0

[2,3,4,5,6,7,8,1,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1] => 0

[1,2,5,8,3,6,7,4] => [.,[.,[[.,[.,.]],[[.,[.,.]],.]]]] => [1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2] => 1

[1,6,5,8,2,4,7,3] => [.,[[[.,[[.,.],.]],.],[[.,.],.]]] => [1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3,1] => 3

[1,4,3,8,2,6,7,5] => [.,[[[.,.],.],[[[.,.],[.,.]],.]]] => [1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1] => 2

[5,4,8,3,2,1,6,7] => [[[[[.,.],.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,4,4,3,2,1] => 4

[1,8,4,3,5,2,7,6] => [.,[[[[.,.],.],[.,[[.,.],.]]],.]] => [1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2,1] => 3

[1,6,3,4,2,8,7,5] => [.,[[[.,.],[.,[.,.]]],[[.,.],.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1] => 1

[1,8,3,6,2,7,5,4] => [.,[[[.,.],[[[.,.],.],[.,.]]],.]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,1,1] => 2

[1,6,8,7,4,2,5,3] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,2] => 1

[1,7,6,2,8,4,5,3] => [.,[[[.,[[.,.],[.,.]]],.],[.,.]]] => [1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1,1] => 1

[1,5,3,2,7,4,8,6] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1] => 0

[2,1,7,3,8,5,4,6] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1,1] => 0

[1,6,2,3,7,8,5,4] => [.,[[.,[.,[[.,.],.]]],[.,[.,.]]]] => [1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1] => 1

[1,6,7,2,8,4,5,3] => [.,[[.,[[.,.],[.,.]]],[.,[.,.]]]] => [1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1] => 0

[5,1,2,7,8,3,6,4] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4] => 0

[2,4,1,7,8,6,3,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1,1] => 1

[7,1,8,2,4,5,6,3] => [[.,[.,[[.,.],[.,[.,.]]]]],[.,.]] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1] => 0

[8,1,2,6,4,3,7,5] => [[.,[.,[[[.,.],[.,.]],[.,.]]]],.] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,3,1,1] => 1

[1,2,7,5,4,3,8,6] => [.,[.,[[[[.,.],.],[.,.]],[.,.]]]] => [1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1] => 1

[1,7,2,4,3,8,6,5] => [.,[[.,[[.,.],[[.,.],.]]],[.,.]]] => [1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1] => 1

[1,7,2,8,3,6,5,4] => [.,[[.,[.,[[[.,.],.],.]]],[.,.]]] => [1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1] => 2

[1,8,7,6,5,2,4,3] => [.,[[[[[.,[[.,.],.]],.],.],.],.]] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1] => 5

[1,4,3,7,2,5,8,6] => [.,[[[.,.],.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1] => 1

[1,8,7,2,5,4,6,3] => [.,[[[.,[[[.,.],.],[.,.]]],.],.]] => [1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,1] => 3

[1,4,8,6,3,5,2,7] => [.,[[[.,.],.],[[[.,.],[.,.]],.]]] => [1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1] => 2

[1,3,5,6,8,4,2,7] => [.,[[.,.],[[.,.],[.,[[.,.],.]]]]] => [1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1,1] => 1

[3,1,4,6,8,7,2,5] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2] => 1

[1,6,3,8,7,2,5,4] => [.,[[[.,.],[[.,.],.]],[[.,.],.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,1,1] => 2

[1,6,2,4,8,7,5,3] => [.,[[.,[[.,.],[.,.]]],[[.,.],.]]] => [1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1] => 1

[1,3,7,2,6,8,4,5] => [.,[[.,.],[[[.,[.,.]],.],[.,.]]]] => [1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1,1] => 1

[3,8,7,2,1,4,6,5] => [[[.,.],.],[[[.,[[.,.],.]],.],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,2,2,1] => 4

[2,4,8,1,6,5,3,7] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1,1] => 1

[1,6,2,8,7,3,5,4] => [.,[[.,[.,[[.,.],.]]],[[.,.],.]]] => [1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1] => 2

[1,8,2,4,6,7,3,5] => [.,[[.,[[.,.],[[.,.],[.,.]]]],.]] => [1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1,1] => 1

[1,2,5,7,8,4,3,6] => [.,[.,[[[.,.],.],[[.,.],[.,.]]]]] => [1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1] => 1

[1,2,7,4,8,6,3,5] => [.,[.,[[[.,.],[[.,.],.]],[.,.]]]] => [1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1] => 1

[1,2,7,8,3,6,5,4] => [.,[.,[[.,[[[.,.],.],.]],[.,.]]]] => [1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1] => 2

[7,1,2,3,8,5,4,6] => [[.,[.,[.,[[.,.],[.,.]]]]],[.,.]] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1] => 0

[7,1,3,4,2,6,8,5] => [[.,[[.,.],[.,[[.,.],.]]]],[.,.]] => [1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [6,6,2,1,1,1] => 1

[3,4,7,2,5,8,1,6] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2,1] => 1

[2,8,3,1,5,6,4,7] => [[.,.],[[.,[[.,.],[.,[.,.]]]],.]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,1,1,1] => 1

[3,4,1,7,5,6,8,2] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2] => 0

[3,4,1,5,7,6,2,8] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2] => 0

[7,3,8,4,1,5,2,6] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,2,2] => 0

[1,6,4,7,2,5,3,8] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2] => 0

[1,6,4,8,2,5,3,7] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,2] => 1

[1,6,5,8,2,4,3,7] => [.,[[[.,[[.,.],.]],.],[[.,.],.]]] => [1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3,1] => 3

[1,6,8,2,4,3,7,5] => [.,[[.,[[.,.],[.,.]]],[[.,.],.]]] => [1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1] => 1

[1,6,2,4,3,7,8,5] => [.,[[.,[[.,.],[.,.]]],[.,[.,.]]]] => [1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1] => 0

[1,5,6,2,4,7,3,8] => [.,[[.,[[.,.],.]],[.,[.,[.,.]]]]] => [1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1] => 1

[1,5,6,2,4,7,8,3] => [.,[[.,[[.,.],.]],[.,[.,[.,.]]]]] => [1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1] => 1

[1,5,8,2,4,7,3,6] => [.,[[.,[[.,.],.]],[[[.,.],.],.]]] => [1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1] => 3

[1,5,7,2,4,8,3,6] => [.,[[.,[[.,.],.]],[[.,.],[.,.]]]] => [1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1] => 1

[1,6,5,7,2,4,3,8] => [.,[[[.,[[.,.],.]],.],[.,[.,.]]]] => [1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,1] => 2

[1,6,7,2,4,3,8,5] => [.,[[.,[[.,.],[.,.]]],[.,[.,.]]]] => [1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1] => 0

[1,5,6,7,2,4,8,3] => [.,[[.,[[.,.],.]],[.,[.,[.,.]]]]] => [1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1] => 1

[1,5,8,2,4,6,7,3] => [.,[[.,[[.,.],.]],[[.,[.,.]],.]]] => [1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1] => 2

[1,5,7,2,4,6,8,3] => [.,[[.,[[.,.],.]],[[.,.],[.,.]]]] => [1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1] => 1

[1,5,7,8,3,2,4,6] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1] => 0

[1,5,8,3,2,4,6,7] => [.,[[[.,.],[.,.]],[[.,[.,.]],.]]] => [1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1] => 1

[1,5,6,2,4,8,3,7] => [.,[[.,[[.,.],.]],[.,[[.,.],.]]]] => [1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1] => 2

[1,7,6,2,8,3,4,5] => [.,[[[.,[.,[.,[.,.]]]],.],[.,.]]] => [1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,5,4] => 1

[1,7,3,4,2,8,6,5] => [.,[[[.,.],[.,[[.,.],.]]],[.,.]]] => [1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1,1] => 1

[1,6,2,4,3,8,7,5] => [.,[[.,[[.,.],[.,.]]],[[.,.],.]]] => [1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1] => 1

[1,5,6,2,4,8,7,3] => [.,[[.,[[.,.],.]],[.,[[.,.],.]]]] => [1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1] => 2

[1,5,8,7,3,2,4,6] => [.,[[[.,.],[.,.]],[[[.,.],.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1,1] => 2

[1,4,2,3,5,8,7,6] => [.,[[.,[.,.]],[.,[[[.,.],.],.]]]] => [1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2] => 2

[1,5,2,3,4,8,7,6] => [.,[[.,[.,[.,.]]],[[[.,.],.],.]]] => [1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3] => 2

[1,6,5,2,3,8,7,4] => [.,[[[.,[.,[.,.]]],.],[[.,.],.]]] => [1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3] => 2

[1,7,4,2,8,6,5,3] => [.,[[[.,[.,.]],[[.,.],.]],[.,.]]] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,2] => 1

[1,6,7,5,2,3,8,4] => [.,[[[.,[.,[.,.]]],.],[.,[.,.]]]] => [1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3] => 1

[1,7,5,2,8,4,3,6] => [.,[[[.,[[.,.],.]],[.,.]],[.,.]]] => [1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,1] => 1

[1,7,5,6,2,8,3,4] => [.,[[[.,[.,[.,.]]],[.,.]],[.,.]]] => [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3] => 0

[1,5,7,6,2,4,8,3] => [.,[[.,[[.,.],.]],[[.,.],[.,.]]]] => [1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1] => 1

[1,5,8,3,2,4,7,6] => [.,[[[.,.],[.,.]],[[[.,.],.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1,1] => 2

[1,6,5,2,3,7,4,8] => [.,[[[.,[.,[.,.]]],.],[.,[.,.]]]] => [1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3] => 1

[1,6,5,2,3,7,8,4] => [.,[[[.,[.,[.,.]]],.],[.,[.,.]]]] => [1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3] => 1

[1,6,8,4,2,3,7,5] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,2] => 1

[1,7,4,6,2,8,3,5] => [.,[[[.,[.,.]],[[.,.],.]],[.,.]]] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,2] => 1

[1,7,3,5,2,8,4,6] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]] => [1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1] => 0

[1,6,8,5,2,3,7,4] => [.,[[[.,[.,[.,.]]],.],[[.,.],.]]] => [1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3] => 2

[1,6,4,2,3,7,8,5] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2] => 0

[1,6,4,2,3,7,5,8] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2] => 0

[1,5,8,6,2,4,7,3] => [.,[[.,[[.,.],.]],[[.,[.,.]],.]]] => [1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1] => 2

[1,5,7,3,2,4,8,6] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1] => 0

[1,7,3,4,2,8,5,6] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1,1] => 0

[1,7,4,2,8,5,3,6] => [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2] => 0

[1,6,7,4,2,3,8,5] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2] => 0

[1,6,4,2,3,8,5,7] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,2] => 1

[1,7,6,4,2,8,5,3] => [.,[[[[.,[.,.]],[.,.]],.],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,2] => 1

[1,7,5,2,8,6,4,3] => [.,[[[.,[[.,.],.]],[.,.]],[.,.]]] => [1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,1] => 1

[1,6,4,2,3,8,7,5] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,2] => 1

[1,6,7,4,3,5,8,2] => [.,[[[[.,.],.],[.,.]],[.,[.,.]]]] => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2,1] => 1

[3,5,4,1,6,7,8,2] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 0

[3,1,4,7,6,5,8,2] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,2] => 1

[1,7,6,4,3,5,8,2] => [.,[[[[[.,.],.],[.,.]],.],[.,.]]] => [1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,2,1] => 2

[1,3,6,4,2,8,5,7] => [.,[[.,.],[[.,[.,.]],[[.,.],.]]]] => [1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1] => 1

[1,8,6,4,2,7,5,3] => [.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2,2] => 1

[1,8,4,3,7,2,5,6] => [.,[[[[.,.],.],[[.,[.,.]],.]],.]] => [1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,2,1] => 3

[2,8,3,4,7,6,1,5] => [[.,.],[[.,[.,[[[.,.],.],.]]],.]] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,1,1,1] => 3

[2,4,3,7,8,6,1,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1,1] => 1

[1,4,7,3,8,2,5,6] => [.,[[[.,.],.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1] => 1

[2,5,3,4,8,6,1,7] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1,1] => 1

[7,1,3,4,2,8,5,6] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1,1] => 0

[8,2,3,4,7,6,1,5] => [[[.,.],[.,[.,[[[.,.],.],.]]]],.] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1,1,1,1] => 3

[1,7,8,4,2,6,5,3] => [.,[[[.,[.,.]],[[.,.],.]],[.,.]]] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,2] => 1

[2,4,3,8,5,6,1,7] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,1,1] => 1

[1,4,8,3,6,2,5,7] => [.,[[[.,.],.],[[[.,.],[.,.]],.]]] => [1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1] => 2

[1,5,4,7,6,8,2,3] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2] => 1

[1,7,4,6,5,8,2,3] => [.,[[[.,[.,.]],[[.,.],.]],[.,.]]] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,2] => 1

[1,6,2,7,5,8,3,4] => [.,[[.,[[.,[.,.]],.]],[.,[.,.]]]] => [1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2] => 1

[1,6,4,8,5,7,2,3] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,2] => 1

[1,8,4,6,5,7,2,3] => [.,[[[.,[.,.]],[[.,.],[.,.]]],.]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,2] => 1

[1,5,4,8,6,7,2,3] => [.,[[[.,[.,.]],.],[[.,[.,.]],.]]] => [1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,2] => 2

[1,8,2,6,5,7,3,4] => [.,[[.,[[[.,[.,.]],.],[.,.]]],.]] => [1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2] => 2

[1,7,2,8,5,6,3,4] => [.,[[.,[[.,[.,.]],[.,.]]],[.,.]]] => [1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2] => 0

[1,7,2,6,5,8,3,4] => [.,[[.,[[[.,[.,.]],.],.]],[.,.]]] => [1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2] => 2

[1,5,2,7,6,8,3,4] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3] => 0

[1,7,6,8,2,5,3,4] => [.,[[[.,[[.,[.,.]],.]],.],[.,.]]] => [1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2] => 2

[1,7,6,8,4,5,2,3] => [.,[[[[.,[.,.]],[.,.]],.],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,2] => 1

[1,3,2,7,6,8,4,5] => [.,[[.,.],[[[.,[.,.]],.],[.,.]]]] => [1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1,1] => 1

[1,7,6,8,2,4,3,5] => [.,[[[.,[[.,.],[.,.]]],.],[.,.]]] => [1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1,1] => 1

[1,8,6,7,2,4,3,5] => [.,[[[.,[[.,.],[.,.]]],[.,.]],.]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,4,1,1] => 1

[7,8,1,2,4,3,5,6] => [[.,[.,[[.,.],[.,[.,.]]]]],[.,.]] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1] => 0

[3,4,6,5,7,8,1,2] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2] => 0

[3,4,1,5,6,7,8,9,2] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2] => 0

[3,4,5,1,6,7,8,9,2] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2] => 0

[3,4,5,6,1,7,8,9,2] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2] => 0

[3,4,5,6,7,1,8,9,2] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2] => 0

[3,4,5,6,7,8,1,9,2] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2] => 0

[3,4,5,6,7,8,1,2,9] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2] => 0

[1,6,2,3,8,7,4,5] => [.,[[.,[.,[.,[.,.]]]],[[.,.],.]]] => [1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,4,4] => 1

[1,4,7,6,2,5,8,3] => [.,[[.,[.,.]],[[[.,.],.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2] => 1

[1,2,6,5,3,7,4,8] => [.,[.,[[[.,[.,.]],.],[.,[.,.]]]]] => [1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2] => 1

[1,2,6,5,3,7,8,4] => [.,[.,[[[.,[.,.]],.],[.,[.,.]]]]] => [1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2] => 1

[1,3,7,5,2,6,8,4] => [.,[[.,.],[[[.,.],[.,.]],[.,.]]]] => [1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1] => 0

[1,3,7,4,2,6,8,5] => [.,[[.,.],[[.,[[.,.],.]],[.,.]]]] => [1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1,1] => 1

[1,2,6,4,3,7,8,5] => [.,[.,[[[.,.],[.,.]],[.,[.,.]]]]] => [1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1] => 0

[1,2,6,4,3,7,5,8] => [.,[.,[[[.,.],[.,.]],[.,[.,.]]]]] => [1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1] => 0

[1,4,7,3,2,5,8,6] => [.,[[[.,.],.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1] => 1

[1,4,3,2,5,8,6,7] => [.,[[[.,.],.],[.,[[.,[.,.]],.]]]] => [1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,1] => 2

[1,5,3,2,4,8,6,7] => [.,[[[.,.],[.,.]],[[.,[.,.]],.]]] => [1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1] => 1

[1,7,5,3,2,8,6,4] => [.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,1,1] => 0

[1,5,3,2,4,8,7,6] => [.,[[[.,.],[.,.]],[[[.,.],.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1,1] => 2

[6,8,5,4,3,2,1,7] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,5,4,3,2,1] => 5

[1,8,2,4,3,7,6,5] => [.,[[.,[[.,.],[[[.,.],.],.]]],.]] => [1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,1] => 3

[1,6,3,4,8,7,5,2] => [.,[[[.,.],[.,[.,.]]],[[.,.],.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1] => 1

[1,4,5,8,3,7,6,2] => [.,[[[.,.],.],[.,[[[.,.],.],.]]]] => [1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,1] => 3

[1,8,5,2,3,7,6,4] => [.,[[[.,[.,[.,.]]],[[.,.],.]],.]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,3] => 2

[1,8,3,4,7,2,6,5] => [.,[[[.,.],[.,[[[.,.],.],.]]],.]] => [1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,1,1] => 3

[4,8,5,7,3,2,1,6] => [[[[.,.],.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,3,3,2,1] => 4

[7,1,8,2,5,4,3,6] => [[.,[.,[[[.,.],.],[.,.]]]],[.,.]] => [1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,1] => 1

[2,5,3,7,4,1,8,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[2,4,8,7,3,5,6,1] => [[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,1,1] => 2

[3,4,7,2,8,5,6,1] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2,1] => 1

[7,2,3,4,8,5,6,1] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1,1,1] => 0

[2,1,8,3,6,7,5,4] => [[.,.],[[.,[[[.,.],.],[.,.]]],.]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,1,1,1] => 2

[8,7,3,4,1,5,6,2] => [[[[.,[.,.]],[.,[.,[.,.]]]],.],.] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,2,2,2] => 2

[4,3,8,2,7,6,1,5] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,3,2,1] => 5

[2,8,3,7,1,5,6,4] => [[.,.],[[.,[[[.,.],[.,.]],.]],.]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,1,1,1] => 2

[8,1,2,7,3,5,6,4] => [[.,[.,[[.,[[.,.],[.,.]]],.]]],.] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,1] => 2

[8,1,6,2,4,5,3,7] => [[.,[[.,[[.,.],[.,.]]],[.,.]]],.] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [7,4,4,1,1] => 1

[5,8,1,6,2,3,4,7] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [6,4,4,4] => 1

[2,3,6,8,4,5,1,7] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1,1] => 1

[1,5,8,6,3,4,7,2] => [.,[[[.,.],[.,.]],[[.,[.,.]],.]]] => [1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1] => 1

[2,5,8,6,3,4,7,1] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1,1] => 1

[1,8,5,2,3,6,7,4] => [.,[[[.,[.,[.,.]]],[.,[.,.]]],.]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3] => 1

[1,8,3,2,5,6,7,4] => [.,[[[.,.],[[.,.],[.,[.,.]]]],.]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,1,1] => 1

[2,8,3,1,5,6,7,4] => [[.,.],[[.,[[.,.],[.,[.,.]]]],.]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,1,1,1] => 1

[4,8,3,2,5,6,7,1] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [6,3,3,3,3,2,1] => 3

[8,2,3,1,5,6,7,4] => [[[.,.],[.,[[.,.],[.,[.,.]]]]],.] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,1,1,1] => 1

[2,1,8,3,5,6,7,4] => [[.,.],[[.,[[.,.],[.,[.,.]]]],.]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,1,1,1] => 1

[1,4,8,2,3,6,7,5] => [.,[[.,[.,.]],[[[.,.],[.,.]],.]]] => [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2] => 1

[2,3,1,6,8,4,7,5] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1,1] => 1

[2,4,3,7,1,8,5,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => 0

[1,4,7,3,2,8,5,6] => [.,[[[.,.],.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1] => 1

[2,4,1,8,6,3,7,5] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1,1] => 1

[3,4,8,5,2,6,7,1] => [[[.,.],.],[.,[[.,[.,[.,.]]],.]]] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,2,1] => 2

[1,5,4,8,2,6,7,3] => [.,[[[.,[.,.]],.],[[.,[.,.]],.]]] => [1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,2] => 2

[2,8,4,5,1,6,7,3] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,1,1] => 1

[8,1,7,2,5,4,3,6] => [[.,[[.,[[[.,.],.],[.,.]]],.]],.] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [7,5,2,2,1] => 3

[8,1,7,2,5,4,6,3] => [[.,[[.,[[[.,.],.],[.,.]]],.]],.] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [7,5,2,2,1] => 3

[5,6,4,7,1,8,2,3] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3] => 1

[5,6,1,8,2,7,3,4] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [5,4,4,4] => 1

[4,5,1,8,6,7,2,3] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [5,3,3,3,3] => 1

[2,8,3,6,1,5,4,7] => [[.,.],[[.,[[[.,.],.],[.,.]]],.]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,1,1,1] => 2

[2,8,3,4,1,6,5,7] => [[.,.],[[.,[.,[[.,.],[.,.]]]],.]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1,1,1,1] => 1

[1,5,3,8,6,7,2,4] => [.,[[[.,.],[.,.]],[[.,[.,.]],.]]] => [1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1] => 1

[1,8,3,6,2,7,4,5] => [.,[[[.,.],[[.,[.,.]],[.,.]]],.]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1,1,1] => 1

[1,6,4,8,2,7,3,5] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,2] => 1

[2,7,3,6,4,5,1,8] => [[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1,1,1,1] => 1

[1,7,3,6,4,8,2,5] => [.,[[[.,.],[[.,[.,.]],.]],[.,.]]] => [1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1,1,1] => 1

[1,7,2,8,4,6,3,5] => [.,[[.,[[.,.],[[.,.],.]]],[.,.]]] => [1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1] => 1

[1,7,5,8,4,6,2,3] => [.,[[[[.,[.,.]],.],[.,.]],[.,.]]] => [1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,2] => 1

[1,7,5,8,2,6,3,4] => [.,[[[.,[.,[.,.]]],[.,.]],[.,.]]] => [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3] => 0

[1,7,5,6,3,8,2,4] => [.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,1,1] => 0

[3,4,2,7,5,6,1,8] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2,1] => 1

[3,4,1,7,5,8,2,6] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2] => 0

[2,3,1,7,5,8,4,6] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1,1] => 0

[2,3,1,8,4,7,5,6] => [[.,.],[.,[[.,[[.,[.,.]],.]],.]]] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1,1,1,1] => 2

[3,4,1,8,2,7,5,6] => [[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,2] => 2

[3,4,1,8,6,7,2,5] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,2] => 1

[3,4,2,5,1,8,6,7] => [[[.,.],.],[.,[.,[[.,[.,.]],.]]]] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,2,1] => 2

[2,5,7,8,6,3,4,1] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[2,1,4,7,6,3,8,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1,1] => 1

[4,2,5,1,6,7,8,3] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1,1] => 0

[2,4,8,5,7,1,3,6] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,1,1] => 2

[2,4,3,8,7,5,6,1] => [[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,1,1] => 2

[2,6,7,3,5,1,8,4] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1,1] => 1

[5,8,4,3,2,7,1,6] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,4,3,2,1] => 5

[2,8,3,1,6,4,5,7] => [[.,.],[[.,[[.,[.,.]],[.,.]]],.]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1,1,1,1] => 1

[8,2,1,3,4,7,5,6] => [[[.,.],[.,[.,[[.,[.,.]],.]]]],.] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,1,1,1,1] => 2

[1,4,8,2,6,3,5,7] => [.,[[.,[.,.]],[[[.,.],[.,.]],.]]] => [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2] => 1

[1,2,7,3,5,4,8,6] => [.,[.,[[.,[[.,.],[.,.]]],[.,.]]]] => [1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1] => 0

[1,2,3,8,4,5,7,6] => [.,[.,[.,[[.,[.,[[.,.],.]]],.]]]] => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [4,1] => 2

[1,2,8,3,4,5,7,6] => [.,[.,[[.,[.,[.,[[.,.],.]]]],.]]] => [1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [5,1] => 2

[1,3,8,2,6,4,5,7] => [.,[[.,.],[[[.,[.,.]],[.,.]],.]]] => [1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1,1] => 1

[1,5,7,2,3,6,4,8] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3] => 0

[1,7,2,3,5,4,8,6] => [.,[[.,[.,[[.,.],[.,.]]]],[.,.]]] => [1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1] => 0

[1,3,8,2,4,5,7,6] => [.,[[.,.],[[.,[.,[[.,.],.]]],.]]] => [1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1,1] => 2

[1,2,3,8,4,6,7,5] => [.,[.,[.,[[.,[[.,.],[.,.]]],.]]]] => [1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [4,1,1] => 1

[1,8,2,3,5,4,6,7] => [.,[[.,[.,[[.,.],[.,[.,.]]]]],.]] => [1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1] => 1

[1,7,8,2,3,6,4,5] => [.,[[.,[.,[[.,[.,.]],.]]],[.,.]]] => [1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [5,5,2] => 1

[1,6,7,8,2,3,5,4] => [.,[[.,[.,[[.,.],.]]],[.,[.,.]]]] => [1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1] => 1

[1,7,8,2,5,3,6,4] => [.,[[.,[[.,[.,.]],[.,.]]],[.,.]]] => [1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2] => 0

[1,7,8,2,4,5,3,6] => [.,[[.,[[.,.],[.,[.,.]]]],[.,.]]] => [1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1] => 0

[1,2,8,3,6,4,5,7] => [.,[.,[[.,[[.,[.,.]],[.,.]]],.]]] => [1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [5,2,2] => 1

[1,8,2,3,6,4,5,7] => [.,[[.,[.,[[.,[.,.]],[.,.]]]],.]] => [1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [6,2,2] => 1

[1,2,8,3,5,4,6,7] => [.,[.,[[.,[[.,.],[.,[.,.]]]],.]]] => [1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1] => 1

[1,2,7,8,3,6,4,5] => [.,[.,[[.,[[.,[.,.]],.]],[.,.]]]] => [1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [4,4,2] => 1

[1,5,2,7,8,3,6,4] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3] => 0

[1,3,2,8,4,6,7,5] => [.,[[.,.],[[.,[[.,.],[.,.]]],.]]] => [1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1,1] => 1

[1,8,2,3,4,6,7,5] => [.,[[.,[.,[.,[[.,.],[.,.]]]]],.]] => [1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [6,1,1] => 1

[1,7,8,2,4,3,6,5] => [.,[[.,[[.,.],[[.,.],.]]],[.,.]]] => [1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1] => 1

[4,5,8,6,7,1,2,3] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [5,3,3,3,3] => 1

[4,5,7,6,8,1,2,3] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [4,4,3,3,3] => 0

[4,6,7,5,8,1,2,3] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[4,6,5,7,8,1,2,3] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[2,4,6,3,7,5,1,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[2,5,3,1,6,4,8,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1,1] => 1

[2,5,3,7,6,4,1,8] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[2,6,3,7,5,4,1,8] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1,1] => 1

[1,7,5,2,3,8,4,6] => [.,[[[.,[.,[.,.]]],[.,.]],[.,.]]] => [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3] => 0

[2,1,3,7,5,4,8,6] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1,1] => 0

[2,3,1,8,6,5,4,7] => [[.,.],[.,[[[[.,.],.],[.,.]],.]]] => [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1,1,1] => 2

[2,5,3,1,8,6,4,7] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1,1] => 1

[1,5,2,8,3,4,7,6] => [.,[[.,[.,[.,.]]],[[[.,.],.],.]]] => [1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3] => 2

[1,2,6,3,8,7,4,5] => [.,[.,[[.,[.,[.,.]]],[[.,.],.]]]] => [1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [4,3,3] => 1

[1,2,8,3,6,4,7,5] => [.,[.,[[.,[[.,[.,.]],[.,.]]],.]]] => [1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [5,2,2] => 1

[1,2,7,6,3,4,8,5] => [.,[.,[[[.,[.,[.,.]]],.],[.,.]]]] => [1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [4,4,3] => 1

[2,1,3,8,7,5,4,6] => [[.,.],[.,[[[[.,.],[.,.]],.],.]]] => [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,1,1,1] => 2

[1,2,3,8,6,4,7,5] => [.,[.,[.,[[[.,[.,.]],[.,.]],.]]]] => [1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [4,2,2] => 1

[1,2,3,7,4,8,6,5] => [.,[.,[.,[[.,[[.,.],.]],[.,.]]]]] => [1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [3,3,1] => 1

[1,2,7,6,3,8,4,5] => [.,[.,[[[.,[.,[.,.]]],.],[.,.]]]] => [1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [4,4,3] => 1

[1,2,3,6,4,8,7,5] => [.,[.,[.,[[.,[.,.]],[[.,.],.]]]]] => [1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [3,2,2] => 1

[1,2,3,7,6,4,8,5] => [.,[.,[.,[[[.,[.,.]],.],[.,.]]]]] => [1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [3,3,2] => 1

[2,1,3,8,5,4,7,6] => [[.,.],[.,[[[.,.],[[.,.],.]],.]]] => [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1,1,1] => 2

[2,1,8,4,3,5,7,6] => [[.,.],[[[.,.],[.,[[.,.],.]]],.]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2,1,1] => 2

[1,8,7,4,2,3,5,6] => [.,[[[[.,[.,.]],[.,[.,.]]],.],.]] => [1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,2] => 2

[1,5,2,8,7,3,4,6] => [.,[[.,[.,[.,.]]],[[[.,.],.],.]]] => [1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3] => 2

[1,2,7,3,6,4,8,5] => [.,[.,[[.,[[.,[.,.]],.]],[.,.]]]] => [1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [4,4,2] => 1

[1,2,8,6,3,7,4,5] => [.,[.,[[[.,[.,[.,.]]],[.,.]],.]]] => [1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [5,3,3] => 1

[1,2,7,3,8,6,4,5] => [.,[.,[[.,[[.,[.,.]],.]],[.,.]]]] => [1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [4,4,2] => 1

[1,2,3,8,4,7,6,5] => [.,[.,[.,[[.,[[[.,.],.],.]],.]]]] => [1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [4,2,1] => 3

[1,2,7,3,4,8,6,5] => [.,[.,[[.,[.,[[.,.],.]]],[.,.]]]] => [1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [4,4,1] => 1

[1,2,6,3,8,4,7,5] => [.,[.,[[.,[.,[.,.]]],[[.,.],.]]]] => [1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [4,3,3] => 1

[1,5,2,3,8,7,4,6] => [.,[[.,[.,[.,.]]],[[[.,.],.],.]]] => [1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3] => 2

[1,8,4,2,7,3,5,6] => [.,[[[.,[.,.]],[[.,[.,.]],.]],.]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,2] => 2

[1,2,8,6,3,4,7,5] => [.,[.,[[[.,[.,[.,.]]],[.,.]],.]]] => [1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [5,3,3] => 1

[1,2,7,3,8,4,6,5] => [.,[.,[[.,[.,[[.,.],.]]],[.,.]]]] => [1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [4,4,1] => 1

[1,2,3,8,7,4,6,5] => [.,[.,[.,[[[.,[[.,.],.]],.],.]]]] => [1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [4,3,1] => 3

[1,2,3,8,7,6,4,5] => [.,[.,[.,[[[[.,[.,.]],.],.],.]]]] => [1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [4,3,2] => 3

[2,5,3,8,1,6,4,7] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1,1] => 1

[3,4,8,6,1,2,5,7] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,2] => 1

[2,4,8,1,5,7,6,3] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,1,1] => 2

[2,4,3,8,1,6,5,7] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1,1] => 1

[2,3,8,1,6,5,7,4] => [[.,.],[.,[[[[.,.],.],[.,.]],.]]] => [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1,1,1] => 2

[2,4,8,1,3,5,7,6] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,1,1] => 2

[3,4,8,6,1,5,7,2] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,2] => 1

[4,3,2,8,5,1,7,6] => [[[[.,.],.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,3,3,2,1] => 4

[3,4,2,8,5,6,1,7] => [[[.,.],.],[.,[[.,[.,[.,.]]],.]]] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,2,1] => 2

[4,3,8,5,2,6,7,1] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [6,3,3,3,3,2,1] => 3

[4,1,2,6,7,5,3,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[3,4,1,7,5,6,2,8] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2] => 0

[4,1,6,7,5,2,3,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[1,4,7,8,5,6,2,3] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2] => 0

[3,4,7,1,5,8,6,2] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2] => 0

[1,6,8,4,7,5,2,3] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,2] => 1

[1,3,8,6,2,7,5,4] => [.,[[.,.],[[[[.,.],.],[.,.]],.]]] => [1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1,1] => 2

[1,8,6,2,5,3,4,7] => [.,[[[.,[[.,[.,.]],.]],[.,.]],.]] => [1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2] => 2

[1,8,6,4,5,2,3,7] => [.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2,2] => 1

[3,4,1,7,5,2,6,8] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2] => 0

[2,5,4,3,6,8,1,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1,1] => 2

[1,2,7,3,6,5,8,4] => [.,[.,[[.,[[[.,.],.],.]],[.,.]]]] => [1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1] => 2

[2,8,7,6,3,4,1,5] => [[.,.],[[[[.,[.,[.,.]]],.],.],.]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,1,1,1] => 3

[3,8,4,5,6,1,2,7] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,2] => 1

[1,4,3,5,7,8,2,6] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]] => [1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1] => 1

[1,5,2,7,4,3,8,6] => [.,[[.,[[.,.],.]],[[.,.],[.,.]]]] => [1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1] => 1

[1,8,6,5,4,3,2,7] => [.,[[[[[[.,.],.],.],.],[.,.]],.]] => [1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3,2,1] => 4

[1,4,7,2,8,5,6,3] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2] => 0

[1,7,3,5,8,6,2,4] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]] => [1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1] => 0

[3,4,6,5,8,1,7,2] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2] => 1

[7,1,2,5,8,6,3,4] => [[.,[.,[[.,[.,.]],[.,.]]]],[.,.]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2] => 0

[1,7,2,5,8,6,3,4] => [.,[[.,[[.,[.,.]],[.,.]]],[.,.]]] => [1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2] => 0

[1,7,6,8,2,3,5,4] => [.,[[[.,[.,[[.,.],.]]],.],[.,.]]] => [1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1] => 2

[2,4,7,1,8,5,6,3] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => 0

[1,2,7,6,8,3,5,4] => [.,[.,[[[.,[[.,.],.]],.],[.,.]]]] => [1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1] => 2

[2,3,7,6,8,1,5,4] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1,1,1] => 2

[1,3,7,6,8,2,5,4] => [.,[[.,.],[[[[.,.],.],.],[.,.]]]] => [1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1,1] => 2

[1,7,4,2,6,8,5,3] => [.,[[[.,[.,.]],[[.,.],.]],[.,.]]] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,2] => 1

[7,1,8,2,5,4,6,3] => [[.,[.,[[[.,.],.],[.,.]]]],[.,.]] => [1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,1] => 1

[1,7,2,6,8,5,4,3] => [.,[[.,[[[[.,.],.],.],.]],[.,.]]] => [1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,1] => 3

[8,1,5,6,7,2,4,3] => [[.,[[.,[[.,.],.]],[.,[.,.]]]],.] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [7,3,3,3,1] => 2

[5,4,6,7,1,2,8,3] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3] => 1

[8,1,3,6,7,4,5,2] => [[.,[[.,.],[[.,[.,.]],[.,.]]]],.] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,3,1,1,1] => 1

[8,1,4,5,3,7,2,6] => [[.,[[[.,.],.],[.,[[.,.],.]]]],.] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,2,1] => 3

[8,1,7,2,4,5,6,3] => [[.,[[.,[[.,.],[.,[.,.]]]],.]],.] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,1,1] => 2

[7,3,1,4,5,6,2,8] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,2,2] => 0

[8,1,4,3,5,6,2,7] => [[.,[[[.,.],.],[.,[.,[.,.]]]]],.] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2,1] => 2

[5,6,1,4,2,3,7,8] => [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,2] => 1

[4,8,5,6,3,2,1,7] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [6,3,3,3,3,2,1] => 3

[5,4,8,7,3,2,1,6] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,4,3,2,1] => 5

[4,8,7,5,3,2,1,6] => [[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,3,3,2,1] => 4

[4,8,7,6,3,2,1,5] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,3,2,1] => 5

[4,3,8,7,2,5,1,6] => [[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,3,3,2,1] => 4

[4,3,8,2,7,5,6,1] => [[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,3,3,2,1] => 4

[1,4,3,8,2,6,5,7] => [.,[[[.,.],.],[[[.,.],[.,.]],.]]] => [1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1] => 2

[3,4,8,1,6,2,5,7] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,2] => 1

[2,4,8,3,6,1,5,7] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1,1] => 1

[1,3,2,4,8,6,5,7] => [.,[[.,.],[.,[[[.,.],[.,.]],.]]]] => [1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1,1] => 1

[3,1,2,4,8,6,5,7] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,2] => 1

[3,1,4,8,2,6,5,7] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,2] => 1

[2,1,3,4,8,6,5,7] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1,1,1] => 1

[1,2,3,4,8,6,5,7] => [.,[.,[.,[.,[[[.,.],[.,.]],.]]]]] => [1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [3,1,1] => 1

[2,8,4,5,7,3,6,1] => [[.,.],[[[.,.],[.,[[.,.],.]]],.]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2,1,1] => 2

[2,4,5,7,3,8,1,6] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1,1] => 0

[8,1,3,5,2,6,4,7] => [[.,[[.,.],[[.,.],[.,[.,.]]]]],.] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,1,1] => 1

[6,5,4,3,8,2,1,7] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,5,4,3,2,1] => 5

[5,8,4,3,7,2,6,1] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,4,3,2,1] => 5

[1,4,3,6,2,7,8,5] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1] => 1

[1,5,4,3,7,2,8,6] => [.,[[[[.,.],.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2,1] => 2

[1,3,8,6,4,7,5,2] => [.,[[.,.],[[[.,[.,.]],[.,.]],.]]] => [1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1,1] => 1

[1,5,7,3,2,6,8,4] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1] => 0

[1,6,7,3,2,5,8,4] => [.,[[[.,.],[[.,.],.]],[.,[.,.]]]] => [1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1] => 1

[1,6,4,7,2,3,8,5] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2] => 0

[8,1,3,7,4,2,6,5] => [[.,[[.,.],[[.,[[.,.],.]],.]]],.] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,1,1] => 3

[3,8,7,2,6,5,4,1] => [[[.,.],.],[[[[[.,.],.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,2,1] => 5

[1,2,7,8,5,6,4,3] => [.,[.,[[[[.,.],.],[.,.]],[.,.]]]] => [1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1] => 1

[5,8,4,3,2,1,6,7] => [[[[[.,.],.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,4,4,3,2,1] => 4

[3,8,7,6,2,1,4,5] => [[[.,.],.],[[[[.,[.,.]],.],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,2,2,1] => 4

[4,8,3,2,5,1,7,6] => [[[[.,.],.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,3,3,2,1] => 4

[2,8,7,6,5,1,3,4] => [[.,.],[[[[[.,[.,.]],.],.],.],.]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1,1,1] => 4

[4,8,3,2,1,5,7,6] => [[[[.,.],.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,3,3,2,1] => 4

[3,8,7,2,1,4,5,6] => [[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,2,2,1] => 3

[4,5,8,1,2,6,3,7] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [5,3,3,3,3] => 1

[1,4,5,7,2,6,3,8] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2] => 0

[1,7,3,5,6,2,4,8] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]] => [1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1] => 0

[8,1,3,5,7,2,4,6] => [[.,[[.,.],[[.,.],[[.,.],.]]]],.] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,1,1] => 2

[3,4,5,6,8,1,7,2] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,2] => 1

[8,2,3,5,6,7,1,4] => [[[.,.],[.,[[.,.],[.,[.,.]]]]],.] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,1,1,1] => 1

[1,7,2,3,5,4,6,8] => [.,[[.,[.,[[.,.],[.,.]]]],[.,.]]] => [1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1] => 0

[8,1,2,3,5,4,6,7] => [[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1] => 1

[2,7,8,1,3,5,4,6] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1,1] => 0

[2,7,8,3,5,6,1,4] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1,1] => 0

[2,4,5,7,8,1,6,3] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1,1] => 0

[2,3,6,7,8,1,5,4] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1,1] => 1

[1,3,6,7,2,5,4,8] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1] => 1

[7,1,8,2,5,3,6,4] => [[.,[.,[[.,[.,.]],[.,.]]]],[.,.]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2] => 0

[1,7,2,6,5,4,3,8] => [.,[[.,[[[[.,.],.],.],.]],[.,.]]] => [1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,1] => 3

[2,1,8,4,5,3,6,7] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,1,1] => 1

[2,1,4,8,5,7,3,6] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,1,1] => 2

[2,1,5,4,6,8,3,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1,1] => 2

[2,8,3,4,6,1,5,7] => [[.,.],[[.,[.,[[.,.],[.,.]]]],.]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1,1,1,1] => 1

[3,4,7,2,8,1,5,6] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2,1] => 1

[3,2,4,6,1,5,8,7] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2,1] => 2

[2,3,8,4,6,7,1,5] => [[.,.],[.,[[.,[[.,.],[.,.]]],.]]] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1,1,1] => 1

[2,4,3,5,8,7,1,6] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,1,1] => 2

[3,2,4,5,6,8,1,7] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,2,1] => 2

[1,5,7,8,4,6,2,3] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2] => 1

[1,3,5,7,8,6,2,4] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1] => 0

[3,5,1,6,8,2,7,4] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,2] => 1

[3,1,5,6,8,2,7,4] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,2] => 1

[2,3,5,6,8,1,7,4] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1,1,1] => 1

[2,5,1,6,8,3,7,4] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1,1] => 1

[5,1,2,6,8,3,7,4] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [5,4,4,4] => 1

[5,7,1,8,6,2,3,4] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4] => 0

[1,5,2,7,8,6,3,4] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3] => 0

[1,6,7,5,2,8,3,4] => [.,[[[.,[.,[.,.]]],.],[.,[.,.]]]] => [1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3] => 1

[1,2,6,7,5,8,3,4] => [.,[.,[[[.,[.,.]],.],[.,[.,.]]]]] => [1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2] => 1

[2,5,7,8,6,3,1,4] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[1,6,7,5,3,8,2,4] => [.,[[[[.,.],[.,.]],.],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,1,1] => 1

[1,6,7,5,4,2,8,3] => [.,[[[[.,[.,.]],.],.],[.,[.,.]]]] => [1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,2] => 2

[2,4,7,1,5,6,8,3] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => 0

[1,6,7,4,5,2,8,3] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2] => 0

[1,6,3,7,5,8,2,4] => [.,[[[.,.],[[.,.],.]],[.,[.,.]]]] => [1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1] => 1

[2,5,3,7,8,6,1,4] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[2,1,6,7,3,8,5,4] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1,1] => 1

[2,3,4,7,8,1,6,5] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1,1,1] => 1

[6,8,5,4,3,2,7,1] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,5,4,3,2,1] => 5

[6,8,5,4,3,7,2,1] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,5,4,3,2,1] => 5

[5,8,4,3,2,1,7,6] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,4,3,2,1] => 5

[2,4,5,7,3,8,6,1] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1,1] => 0

[2,5,6,1,8,4,3,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1,1] => 2

[4,5,6,8,1,3,2,7] => [[.,[[.,.],.]],[.,[.,[[.,.],.]]]] => [1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3,1] => 2

[1,4,5,6,8,3,2,7] => [.,[[[.,.],.],[.,[.,[[.,.],.]]]]] => [1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,1] => 2

[1,7,8,4,5,3,2,6] => [.,[[[[.,.],.],[.,[.,.]]],[.,.]]] => [1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2,1] => 1

[1,6,3,7,4,8,5,2] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]] => [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1] => 0

[2,5,6,3,7,8,4,1] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1,1] => 0

[2,5,6,3,1,7,8,4] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1,1] => 0

[1,3,7,8,6,4,2,5] => [.,[[.,.],[[[.,[.,.]],.],[.,.]]]] => [1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1,1] => 1

[2,5,1,7,3,8,6,4] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[5,1,6,7,8,2,4,3] => [[.,[.,[[.,.],.]]],[.,[.,[.,.]]]] => [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,1] => 1

[2,4,6,5,8,1,3,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[1,6,2,4,5,8,3,7] => [.,[[.,[[.,.],[.,.]]],[[.,.],.]]] => [1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1] => 1

[1,3,4,6,5,8,2,7] => [.,[[.,.],[.,[[.,.],[[.,.],.]]]]] => [1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1] => 1

[1,6,3,4,5,8,2,7] => [.,[[[.,.],[.,[.,.]]],[[.,.],.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1] => 1

[3,4,1,8,5,2,7,6] => [[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,2] => 2

[1,5,3,2,8,7,4,6] => [.,[[[.,.],[.,.]],[[[.,.],.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1,1] => 2

[1,7,6,4,5,8,3,2] => [.,[[[[[.,.],.],[.,.]],.],[.,.]]] => [1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,2,1] => 2

[3,4,2,5,8,6,7,1] => [[[.,.],.],[.,[.,[[.,[.,.]],.]]]] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,2,1] => 2

[4,1,3,5,6,8,7,2] => [[.,[[.,.],.]],[.,[.,[[.,.],.]]]] => [1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3,1] => 2

[2,4,8,6,7,1,3,5] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1,1] => 1

[2,3,5,8,6,7,1,4] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1,1,1] => 1

[1,2,8,3,5,6,7,4] => [.,[.,[[.,[[.,.],[.,[.,.]]]],.]]] => [1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1] => 1

[1,7,5,3,8,4,2,6] => [.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,1,1] => 0

[1,6,3,2,5,8,7,4] => [.,[[[.,.],[[.,.],.]],[[.,.],.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,1,1] => 2

[1,8,4,2,5,6,7,3] => [.,[[[.,[.,.]],[.,[.,[.,.]]]],.]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2] => 1

[3,8,4,1,5,6,7,2] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,2] => 1

[8,1,3,6,5,2,4,7] => [[.,[[.,.],[[[.,.],.],[.,.]]]],.] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2,1,1] => 2

[1,3,4,8,5,7,2,6] => [.,[[.,.],[.,[[.,[[.,.],.]],.]]]] => [1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1,1] => 2

[1,3,4,7,5,8,2,6] => [.,[[.,.],[.,[[.,[.,.]],[.,.]]]]] => [1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1] => 0

[1,3,5,2,4,8,7,6] => [.,[[.,.],[[.,.],[[[.,.],.],.]]]] => [1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1,1] => 2

[2,4,7,3,8,1,6,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1,1] => 1

[8,2,1,3,6,4,7,5] => [[[.,.],[.,[[.,[.,.]],[.,.]]]],.] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,3,1,1,1,1] => 1

[4,8,5,3,6,2,7,1] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [6,3,3,3,3,2,1] => 3

[1,5,8,7,4,6,2,3] => [.,[[[.,[.,.]],.],[[[.,.],.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,2] => 3

[1,7,2,4,6,5,8,3] => [.,[[.,[[.,.],[[.,.],.]]],[.,.]]] => [1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1] => 1

[4,1,5,2,6,8,7,3] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3] => 1

[3,4,5,1,6,8,7,2] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,2] => 1

[8,2,4,1,5,6,7,3] => [[[.,.],[[.,.],[.,[.,[.,.]]]]],.] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2,1,1] => 1

[1,7,8,3,5,4,6,2] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]] => [1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1] => 0

[3,4,5,1,8,6,7,2] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,2] => 1

[3,8,1,4,5,6,7,2] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,2] => 1

[3,4,5,7,8,2,6,1] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2,1] => 1

[3,4,6,2,8,5,1,7] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2,1] => 2

[3,4,6,8,1,5,2,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2] => 1

[3,4,8,2,1,5,6,7] => [[[.,.],.],[.,[[.,[.,[.,.]]],.]]] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,2,1] => 2

[3,5,6,8,4,1,2,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,2] => 1

[3,8,2,1,4,5,6,7] => [[[.,.],.],[[.,[.,[.,[.,.]]]],.]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,2,1] => 2

[4,1,5,6,7,8,3,2] => [[.,[[.,.],.]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1] => 1

[5,1,6,7,4,8,2,3] => [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,2] => 1

[6,1,2,3,7,8,5,4] => [[.,[.,[.,[[.,.],.]]]],[.,[.,.]]] => [1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,5,5,1] => 1

[6,1,2,3,8,5,4,7] => [[.,[.,[.,[[.,.],.]]]],[[.,.],.]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [6,5,5,1] => 2

[7,1,2,3,4,8,6,5] => [[.,[.,[.,[.,[[.,.],.]]]]],[.,.]] => [1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [6,6,1] => 1

[7,1,2,8,4,5,6,3] => [[.,[.,[[.,.],[.,[.,.]]]]],[.,.]] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1] => 0

[7,1,8,3,4,5,6,2] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1,1] => 0

[1,3,5,7,2,6,4,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1] => 0

[2,6,1,3,8,4,7,5] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1,1] => 1

[1,7,5,2,3,4,6,8] => [.,[[[.,[.,[.,.]]],[.,.]],[.,.]]] => [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3] => 0

[1,6,7,5,3,2,4,8] => [.,[[[[.,.],[.,.]],.],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,1,1] => 1

[1,7,3,6,5,2,4,8] => [.,[[[.,.],[[[.,.],.],.]],[.,.]]] => [1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,1,1] => 2

[8,1,3,7,2,6,4,5] => [[.,[[.,.],[[[.,[.,.]],.],.]]],.] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [7,4,3,1,1,1] => 3

[2,9,8,7,6,5,4,3,1] => [[.,.],[[[[[[[.,.],.],.],.],.],.],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,1,1] => 6

[4,8,5,6,7,3,2,1] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [6,3,3,3,3,2,1] => 3

[3,8,7,4,5,6,2,1] => [[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,2,2,1] => 3

[1,8,7,6,5,3,2,4] => [.,[[[[[[.,.],[.,.]],.],.],.],.]] => [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1,1] => 4

[2,8,7,6,3,4,5,1] => [[.,.],[[[[.,[.,[.,.]]],.],.],.]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,1,1,1] => 3

[2,9,8,7,6,5,3,4,1] => [[.,.],[[[[[[.,[.,.]],.],.],.],.],.]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,1,1,1] => 5

[1,8,7,6,5,2,3,4] => [.,[[[[[.,[.,[.,.]]],.],.],.],.]] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3] => 4

[2,10,9,8,7,6,5,4,3,1] => [[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,2,1,1] => 7

[3,4,1,2,8,6,7,5] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,2] => 1

[1,5,7,4,2,6,3,8] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2] => 1

[1,6,3,2,5,8,4,7] => [.,[[[.,.],[[.,.],.]],[[.,.],.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,1,1] => 2

[1,3,5,4,6,8,2,7] => [.,[[.,.],[[.,.],[.,[[.,.],.]]]]] => [1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1,1] => 1

[1,7,3,2,5,4,8,6] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]] => [1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1] => 0

[2,4,7,3,8,5,6,1] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => 0

[1,8,3,4,2,7,6,5] => [.,[[[.,.],[.,[[[.,.],.],.]]],.]] => [1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,1,1] => 3

[2,8,3,4,7,1,5,6] => [[.,.],[[.,[.,[[.,[.,.]],.]]],.]] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1,1,1,1] => 2

[1,8,6,4,5,2,7,3] => [.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2,2] => 1

[1,8,5,3,6,2,7,4] => [.,[[[[.,.],[.,.]],[.,[.,.]]],.]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,1,1] => 1

[3,4,7,8,2,5,6,1] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2,1] => 1

[1,8,2,4,5,6,7,3] => [.,[[.,[[.,.],[.,[.,[.,.]]]]],.]] => [1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1] => 1

[3,1,4,6,5,7,8,2] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2] => 0

[1,4,7,3,5,6,8,2] => [.,[[[.,.],.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1] => 1

[1,3,2,7,5,8,6,4] => [.,[[.,.],[[[.,.],[.,.]],[.,.]]]] => [1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1] => 0

[1,4,2,5,8,3,7,6] => [.,[[.,[.,.]],[.,[[[.,.],.],.]]]] => [1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2] => 2

[1,4,2,7,8,5,6,3] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2] => 0

[1,5,2,4,8,7,6,3] => [.,[[.,[[.,.],.]],[[[.,.],.],.]]] => [1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1] => 3

[1,2,6,4,8,7,5,3] => [.,[.,[[[.,.],[.,.]],[[.,.],.]]]] => [1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1] => 1

[1,2,7,4,8,6,5,3] => [.,[.,[[[.,.],[[.,.],.]],[.,.]]]] => [1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1] => 1

[1,3,2,7,5,8,4,6] => [.,[[.,.],[[[.,.],[.,.]],[.,.]]]] => [1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1] => 0

[2,3,1,7,5,4,8,6] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1,1] => 0

[1,3,2,8,5,7,4,6] => [.,[[.,.],[[[.,.],[[.,.],.]],.]]] => [1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1,1] => 2

[1,4,2,5,8,7,3,6] => [.,[[.,[.,.]],[.,[[[.,.],.],.]]]] => [1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2] => 2

[1,5,2,4,8,7,3,6] => [.,[[.,[[.,.],.]],[[[.,.],.],.]]] => [1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1] => 3

[1,2,6,4,8,7,3,5] => [.,[.,[[[.,.],[.,.]],[[.,.],.]]]] => [1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1] => 1

[1,2,7,8,5,6,3,4] => [.,[.,[[[.,[.,.]],[.,.]],[.,.]]]] => [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2] => 0

[1,2,6,8,5,7,3,4] => [.,[.,[[[.,[.,.]],.],[[.,.],.]]]] => [1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2] => 2

[1,5,6,8,2,7,3,4] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3] => 1

[1,3,8,2,6,7,4,5] => [.,[[.,.],[[[.,[.,.]],[.,.]],.]]] => [1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1,1] => 1

[1,4,7,2,8,6,3,5] => [.,[[.,[.,.]],[[[.,.],.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2] => 1

[1,6,7,8,2,5,3,4] => [.,[[.,[[.,[.,.]],.]],[.,[.,.]]]] => [1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2] => 1

[1,2,6,8,3,7,5,4] => [.,[.,[[.,[[.,.],.]],[[.,.],.]]]] => [1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1] => 2

[1,5,7,8,2,3,6,4] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3] => 0

[1,5,2,7,8,4,6,3] => [.,[[.,[[.,.],.]],[[.,.],[.,.]]]] => [1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1] => 1

[1,4,7,2,8,3,6,5] => [.,[[.,[.,.]],[[[.,.],.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2] => 1

[1,3,6,2,4,8,7,5] => [.,[[.,.],[[.,[.,.]],[[.,.],.]]]] => [1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1] => 1

[1,6,7,3,4,8,5,2] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]] => [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1] => 0

[1,5,3,7,4,8,6,2] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1] => 0

[2,8,4,1,5,3,7,6] => [[.,.],[[[.,.],[.,[[.,.],.]]],.]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2,1,1] => 2

[3,8,4,1,5,7,2,6] => [[.,[.,.]],[[.,[.,[[.,.],.]]],.]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2,2] => 2

[1,3,6,4,2,8,7,5] => [.,[[.,.],[[.,[.,.]],[[.,.],.]]]] => [1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1] => 1

[1,3,7,4,2,8,6,5] => [.,[[.,.],[[.,[[.,.],.]],[.,.]]]] => [1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1,1] => 1

[1,3,8,4,2,7,6,5] => [.,[[.,.],[[.,[[[.,.],.],.]],.]]] => [1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,1,1] => 3

[1,2,8,4,7,3,6,5] => [.,[.,[[[.,.],[[[.,.],.],.]],.]]] => [1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,1] => 3

[1,2,7,4,8,3,6,5] => [.,[.,[[[.,.],[[.,.],.]],[.,.]]]] => [1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1] => 1

[1,2,6,4,8,3,7,5] => [.,[.,[[[.,.],[.,.]],[[.,.],.]]]] => [1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1] => 1

[1,5,2,4,8,3,7,6] => [.,[[.,[[.,.],.]],[[[.,.],.],.]]] => [1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1] => 3

[1,8,4,5,7,2,3,6] => [.,[[[.,[.,.]],[.,[[.,.],.]]],.]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2] => 2

[1,8,3,5,2,7,4,6] => [.,[[[.,.],[[.,.],[[.,.],.]]],.]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,1,1] => 2

[2,8,3,5,1,4,7,6] => [[.,.],[[.,[[.,.],[[.,.],.]]],.]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,1,1,1] => 2

[2,3,8,6,1,4,7,5] => [[.,.],[.,[[[.,[.,.]],[.,.]],.]]] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1,1,1] => 1

[1,3,8,6,2,7,4,5] => [.,[[.,.],[[[.,[.,.]],[.,.]],.]]] => [1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1,1] => 1

[1,4,8,6,7,2,3,5] => [.,[[.,[.,.]],[[[.,.],[.,.]],.]]] => [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2] => 1

[1,5,6,8,7,2,3,4] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3] => 1

[1,2,6,8,5,3,7,4] => [.,[.,[[[.,[.,.]],.],[[.,.],.]]]] => [1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2] => 2

[1,2,7,8,5,3,6,4] => [.,[.,[[[.,[.,.]],[.,.]],[.,.]]]] => [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2] => 0

[1,2,5,8,7,3,6,4] => [.,[.,[[.,[.,.]],[[[.,.],.],.]]]] => [1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2] => 2

[1,2,6,8,7,3,5,4] => [.,[.,[[.,[[.,.],.]],[[.,.],.]]]] => [1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1] => 2

[1,2,7,8,6,3,5,4] => [.,[.,[[[.,[[.,.],.]],.],[.,.]]]] => [1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1] => 2

[1,6,7,8,5,2,3,4] => [.,[[[.,[.,[.,.]]],.],[.,[.,.]]]] => [1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3] => 1

[1,5,7,8,6,2,3,4] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3] => 0

[1,4,7,6,8,2,3,5] => [.,[[.,[.,.]],[[[.,.],.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2] => 1

[1,3,7,6,2,8,4,5] => [.,[[.,.],[[[.,[.,.]],.],[.,.]]]] => [1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1,1] => 1

[2,3,8,7,4,1,6,5] => [[.,.],[.,[[[.,[[.,.],.]],.],.]]] => [1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,1,1,1] => 3

[1,2,8,4,7,6,3,5] => [.,[.,[[[.,.],[[[.,.],.],.]],.]]] => [1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,1] => 3

[1,2,5,8,7,6,3,4] => [.,[.,[[.,[.,.]],[[[.,.],.],.]]]] => [1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2] => 2

[1,2,6,8,7,5,3,4] => [.,[.,[[[.,[.,.]],.],[[.,.],.]]]] => [1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2] => 2

[1,2,7,8,6,5,3,4] => [.,[.,[[[[.,[.,.]],.],.],[.,.]]]] => [1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2] => 2

[2,3,7,6,4,5,8,1] => [[.,.],[.,[[[.,[.,.]],.],[.,.]]]] => [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1,1,1] => 1

[1,2,3,8,5,4,7,6] => [.,[.,[.,[[[.,.],[[.,.],.]],.]]]] => [1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1] => 2

[2,1,5,3,8,6,4,7] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1,1] => 1

[1,2,3,8,5,6,4,7] => [.,[.,[.,[[[.,.],[.,[.,.]]],.]]]] => [1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1] => 1

[1,2,3,8,6,4,5,7] => [.,[.,[.,[[[.,[.,.]],[.,.]],.]]]] => [1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [4,2,2] => 1

[1,2,3,8,6,5,4,7] => [.,[.,[.,[[[[.,.],.],[.,.]],.]]]] => [1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1] => 2

[1,2,3,8,5,4,6,7] => [.,[.,[.,[[[.,.],[.,[.,.]]],.]]]] => [1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1] => 1

[5,1,6,2,8,7,3,4] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [5,4,4,4] => 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] => [4,4,3,1,1,1,1] => 1

[2,1,3,7,8,5,6,4] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1,1] => 0

[2,1,3,6,8,5,7,4] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1,1] => 2

[1,2,3,8,6,7,4,5] => [.,[.,[.,[[[.,[.,.]],[.,.]],.]]]] => [1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [4,2,2] => 1

[1,2,3,8,7,5,4,6] => [.,[.,[.,[[[[.,.],[.,.]],.],.]]]] => [1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1] => 2

[1,2,3,8,7,4,5,6] => [.,[.,[.,[[[.,[.,[.,.]]],.],.]]]] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [4,3] => 2

[1,2,3,8,5,7,4,6] => [.,[.,[.,[[[.,.],[[.,.],.]],.]]]] => [1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1] => 2

[2,1,3,6,8,7,4,5] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1,1] => 1

[1,2,3,9,4,5,6,7,8] => [.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]] => [1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [5] => 1

[1,2,9,3,4,5,6,7,8] => [.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [6] => 1

[1,2,3,4,5,10,6,7,8,9] => [.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]] => [1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [4] => 1

[1,8,3,4,2,5,6,7] => [.,[[[.,.],[.,[.,[.,[.,.]]]]],.]] => [1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1,1] => 1

[1,8,4,3,2,5,6,7] => [.,[[[[.,.],.],[.,[.,[.,.]]]],.]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,1] => 2

[2,5,3,7,6,8,1,4] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[2,6,3,7,4,8,1,5] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1,1] => 0

[2,6,3,7,1,5,4,8] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1,1] => 1

[4,8,3,5,7,2,6,1] => [[[[.,.],.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,3,3,2,1] => 4

[4,8,3,5,6,7,2,1] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [6,3,3,3,3,2,1] => 3

[4,8,3,7,2,5,6,1] => [[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,3,3,2,1] => 4

[3,5,6,7,2,8,4,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => 1

[3,4,5,6,7,8,9,2,1] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2,1] => 1

[1,6,2,5,3,4,8,7] => [.,[[.,[[.,[.,.]],.]],[[.,.],.]]] => [1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2] => 2

[1,3,8,2,4,6,5,7] => [.,[[.,.],[[.,[[.,.],[.,.]]],.]]] => [1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1,1] => 1

[1,7,2,3,6,4,8,5] => [.,[[.,[.,[[.,[.,.]],.]]],[.,.]]] => [1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [5,5,2] => 1

[1,6,8,2,5,3,7,4] => [.,[[.,[[.,[.,.]],.]],[[.,.],.]]] => [1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2] => 2

[1,8,2,5,3,4,7,6] => [.,[[.,[[.,[.,.]],[[.,.],.]]],.]] => [1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2] => 2

[1,8,2,3,6,4,7,5] => [.,[[.,[.,[[.,[.,.]],[.,.]]]],.]] => [1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [6,2,2] => 1

[1,3,5,2,8,4,7,6] => [.,[[.,.],[[.,.],[[[.,.],.],.]]]] => [1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1,1] => 2

[1,2,7,3,5,4,6,8] => [.,[.,[[.,[[.,.],[.,.]]],[.,.]]]] => [1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1] => 0

[1,8,2,7,3,4,6,5] => [.,[[.,[[.,[.,[[.,.],.]]],.]],.]] => [1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [6,4,1] => 3

[1,5,8,2,3,7,4,6] => [.,[[.,[.,[.,.]]],[[[.,.],.],.]]] => [1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3] => 2

[1,6,8,2,3,5,4,7] => [.,[[.,[.,[[.,.],.]]],[[.,.],.]]] => [1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1] => 2

[8,1,4,7,5,2,3,6] => [[.,[[.,[.,.]],[[.,[.,.]],.]]],.] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,2,2] => 2

[6,1,2,3,8,7,5,4] => [[.,[.,[.,[[.,.],.]]]],[[.,.],.]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [6,5,5,1] => 2

[1,3,6,8,7,4,2,5] => [.,[[.,.],[[.,[.,.]],[[.,.],.]]]] => [1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1] => 1

[1,2,8,5,7,3,4,6] => [.,[.,[[[.,[.,.]],[[.,.],.]],.]]] => [1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2] => 2

[1,7,8,4,6,2,5,3] => [.,[[[.,[.,.]],[[.,.],.]],[.,.]]] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,2] => 1

[2,7,3,1,5,8,4,6] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1,1] => 0

[1,5,2,8,7,4,6,3] => [.,[[.,[[.,.],.]],[[[.,.],.],.]]] => [1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1] => 3

[1,6,7,4,5,3,8,2] => [.,[[[[.,.],.],[.,.]],[.,[.,.]]]] => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2,1] => 1

[1,4,7,2,8,5,3,6] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2] => 0

[1,2,4,8,6,5,3,7] => [.,[.,[[.,.],[[[.,.],[.,.]],.]]]] => [1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1] => 1

[1,7,3,2,4,8,5,6] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1,1] => 0

[1,3,6,5,2,8,4,7] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]] => [1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1] => 2

[4,3,8,7,5,2,6,1] => [[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,3,3,2,1] => 4

[2,5,6,3,4,8,7,1] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1,1] => 1

[2,5,3,6,8,7,4,1] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1,1] => 1

[4,8,7,3,5,2,6,1] => [[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,3,3,2,1] => 4

[3,8,7,2,6,4,5,1] => [[[.,.],.],[[[[.,[.,.]],.],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,2,2,1] => 4

[1,8,5,3,6,2,4,7] => [.,[[[[.,.],[.,.]],[.,[.,.]]],.]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,1,1] => 1

[1,5,3,4,8,6,2,7] => [.,[[[.,.],[.,.]],[[.,[.,.]],.]]] => [1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1] => 1

[1,6,7,4,8,2,3,5] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2] => 0

[8,2,1,3,5,6,7,4] => [[[.,.],[.,[[.,.],[.,[.,.]]]]],.] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,1,1,1] => 1

[2,8,3,6,7,5,4,1] => [[.,.],[[.,[[[.,.],.],[.,.]]],.]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,1,1,1] => 2

[1,5,8,4,7,2,3,6] => [.,[[[.,[.,.]],.],[[[.,.],.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,2] => 3

[2,1,8,4,5,7,3,6] => [[.,.],[[[.,.],[.,[[.,.],.]]],.]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2,1,1] => 2

[1,3,4,8,6,5,2,7] => [.,[[.,.],[.,[[[.,.],[.,.]],.]]]] => [1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1,1] => 1

[2,6,3,8,4,7,5,1] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1,1] => 1

[2,8,3,6,4,5,7,1] => [[.,.],[[.,[[.,[.,.]],[.,.]]],.]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1,1,1,1] => 1

[2,1,5,6,8,3,7,4] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1,1] => 1

[1,6,8,3,2,7,4,5] => [.,[[[.,.],[.,[.,.]]],[[.,.],.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1] => 1

[5,4,8,3,6,2,7,1] => [[[[[.,.],.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,4,4,3,2,1] => 4

[1,5,6,4,8,2,7,3] => [.,[[[.,[.,.]],.],[.,[[.,.],.]]]] => [1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2] => 2

[3,1,5,6,4,8,7,2] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,2] => 1

[3,5,1,6,4,7,8,2] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 0

[1,2,6,4,3,8,5,7] => [.,[.,[[[.,.],[.,.]],[[.,.],.]]]] => [1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1] => 1

[1,2,6,3,5,8,7,4] => [.,[.,[[.,[[.,.],.]],[[.,.],.]]]] => [1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1] => 2

[2,3,5,1,8,4,7,6] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1,1,1] => 2

[2,3,6,1,8,5,4,7] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1,1] => 2

[1,2,7,6,4,8,5,3] => [.,[.,[[[[.,.],[.,.]],.],[.,.]]]] => [1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1] => 1

[1,2,7,3,6,8,5,4] => [.,[.,[[.,[[[.,.],.],.]],[.,.]]]] => [1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1] => 2

[2,3,6,1,8,5,7,4] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1,1] => 2

[1,2,5,8,4,7,3,6] => [.,[.,[[[.,.],.],[[[.,.],.],.]]]] => [1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1] => 3

[1,3,6,8,5,2,7,4] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]] => [1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1] => 2

[1,2,6,8,5,4,3,7] => [.,[.,[[[[.,.],.],.],[[.,.],.]]]] => [1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1] => 3

[1,3,5,8,2,4,7,6] => [.,[[.,.],[[.,.],[[[.,.],.],.]]]] => [1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1,1] => 2

[1,4,6,8,3,2,5,7] => [.,[[[.,.],.],[[.,.],[[.,.],.]]]] => [1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1] => 2

[4,6,1,7,5,8,2,3] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[1,3,7,5,6,8,2,4] => [.,[[.,.],[[[.,.],[.,.]],[.,.]]]] => [1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1] => 0

[1,2,6,7,3,8,5,4] => [.,[.,[[.,[[.,.],.]],[.,[.,.]]]]] => [1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1] => 1

[1,2,5,7,3,8,6,4] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => [1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2] => 0

[2,3,6,5,8,7,1,4] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1,1] => 2

[1,2,7,5,6,8,4,3] => [.,[.,[[[[.,.],.],[.,.]],[.,.]]]] => [1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1] => 1

[2,4,7,6,8,3,5,1] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1,1] => 1

[1,4,6,8,3,5,7,2] => [.,[[[.,.],.],[[.,.],[[.,.],.]]]] => [1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1] => 2

[1,3,5,8,2,7,4,6] => [.,[[.,.],[[.,.],[[[.,.],.],.]]]] => [1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1,1] => 2

[1,2,5,8,4,7,6,3] => [.,[.,[[[.,.],.],[[[.,.],.],.]]]] => [1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1] => 3

[1,2,5,8,7,4,3,6] => [.,[.,[[[.,.],.],[[[.,.],.],.]]]] => [1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1] => 3

[1,3,5,8,7,2,4,6] => [.,[[.,.],[[.,.],[[[.,.],.],.]]]] => [1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1,1] => 2

[2,6,3,4,7,1,5,8] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1,1] => 0

[2,7,3,4,5,8,1,6] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1,1,1] => 0

[2,5,7,3,6,8,1,4] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[8,2,1,7,3,4,5,6] => [[[.,.],[[.,[.,[.,[.,.]]]],.]],.] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,1,1,1,1] => 2

[7,1,6,2,3,4,5,8] => [[.,[[.,[.,[.,[.,.]]]],.]],[.,.]] => [1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [6,6,4] => 1

[8,2,7,3,4,5,6,1] => [[[.,.],[[.,[.,[.,[.,.]]]],.]],.] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,1,1,1,1] => 2

[8,1,6,2,3,4,5,7] => [[.,[[.,[.,[.,[.,.]]]],[.,.]]],.] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [7,4,4] => 1

[8,1,7,3,4,5,6,2] => [[.,[[[.,.],[.,[.,[.,.]]]],.]],.] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,1,1,1] => 2

[8,1,5,7,2,3,6,4] => [[.,[[.,[.,[.,.]]],[[.,.],.]]],.] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [7,4,3,3] => 2

[1,7,5,8,2,3,6,4] => [.,[[[.,[.,[.,.]]],[.,.]],[.,.]]] => [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3] => 0

[7,2,1,8,3,4,5,6] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1,1,1] => 0

[7,2,8,3,4,5,6,1] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1,1,1] => 0

[1,7,8,3,4,5,6,2] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1,1] => 0

[1,4,5,8,3,6,7,2] => [.,[[[.,.],.],[.,[[.,[.,.]],.]]]] => [1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,1] => 2

[2,5,7,1,8,3,6,4] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[1,6,2,8,4,5,7,3] => [.,[[.,[[.,.],[.,.]]],[[.,.],.]]] => [1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1] => 1

[3,2,8,7,1,4,6,5] => [[[.,.],.],[[[.,[[.,.],.]],.],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,2,2,1] => 4

[1,8,3,7,2,4,5,6] => [.,[[[.,.],[[.,[.,[.,.]]],.]],.]] => [1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,1,1,1] => 2

[1,7,6,2,3,4,5,8] => [.,[[[.,[.,[.,[.,.]]]],.],[.,.]]] => [1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,5,4] => 1

[1,8,6,2,3,4,5,7] => [.,[[[.,[.,[.,[.,.]]]],[.,.]],.]] => [1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [6,4,4] => 1

[2,8,7,3,4,5,6,1] => [[.,.],[[[.,[.,[.,[.,.]]]],.],.]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,1,1,1,1] => 2

[3,8,7,2,4,5,6,1] => [[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,2,2,1] => 3

[1,5,8,7,2,3,6,4] => [.,[[.,[.,[.,.]]],[[[.,.],.],.]]] => [1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3] => 2

[3,4,7,2,5,1,8,6] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2,1] => 1

[1,2,8,3,7,5,4,6] => [.,[.,[[.,[[[.,.],[.,.]],.]],.]]] => [1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1] => 2

[1,6,3,8,7,4,2,5] => [.,[[[.,.],[.,[.,.]]],[[.,.],.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1] => 1

[1,2,3,4,5,10,9,8,7,6] => [.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]] => [1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1] => 4

[3,1,2,4,5,6,7,8,9] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2] => 0

[3,4,1,6,5,8,7,2] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2] => 1

[3,1,4,6,2,8,7,5] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2] => 1

[1,4,6,5,2,8,7,3] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2] => 1

[3,4,5,6,1,8,7,2] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,2] => 1

[3,4,5,8,7,2,1,6] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,2,1] => 3

[1,4,7,2,6,3,5,8] => [.,[[.,[.,.]],[[[.,.],.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2] => 1

[1,4,8,6,3,7,2,5] => [.,[[[.,.],.],[[[.,.],[.,.]],.]]] => [1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1] => 2

[1,4,8,3,7,6,5,2] => [.,[[[.,.],.],[[[[.,.],.],.],.]]] => [1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,2,1] => 4

[1,8,2,7,6,5,4,3] => [.,[[.,[[[[[.,.],.],.],.],.]],.]] => [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,1] => 5

[8,1,3,6,5,7,4,2] => [[.,[[.,.],[[[.,.],.],[.,.]]]],.] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2,1,1] => 2

[1,7,8,5,4,3,6,2] => [.,[[[[[.,.],.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,2,1] => 2

[1,8,4,5,3,2,6,7] => [.,[[[[.,.],.],[.,[.,[.,.]]]],.]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,1] => 2

[3,4,1,8,5,7,6,2] => [[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,2] => 2

[1,6,4,5,7,2,3,8] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2] => 0

[1,8,6,5,7,3,4,2] => [.,[[[[[.,.],[.,.]],.],[.,.]],.]] => [1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3,1,1] => 2

[1,7,5,3,6,8,4,2] => [.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,1,1] => 0

[1,2,5,8,6,7,3,4] => [.,[.,[[.,[.,.]],[[.,[.,.]],.]]]] => [1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2] => 1

[1,5,3,6,8,7,4,2] => [.,[[[.,.],[.,.]],[.,[[.,.],.]]]] => [1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1] => 1

[3,5,4,6,1,8,2,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,2] => 1

[1,4,5,6,8,7,2,3] => [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => [1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2] => 1

[1,4,6,3,7,2,8,5] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1] => 1

[1,7,3,6,5,2,8,4] => [.,[[[.,.],[[[.,.],.],.]],[.,.]]] => [1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,1,1] => 2

[1,3,4,7,6,2,8,5] => [.,[[.,.],[.,[[[.,.],.],[.,.]]]]] => [1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1,1] => 1

[2,8,3,6,1,7,5,4] => [[.,.],[[.,[[[.,.],.],[.,.]]],.]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,1,1,1] => 2

[8,1,3,6,2,7,5,4] => [[.,[[.,.],[[[.,.],.],[.,.]]]],.] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2,1,1] => 2

[1,2,4,7,3,8,6,5] => [.,[.,[[.,.],[[[.,.],.],[.,.]]]]] => [1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1] => 1

[1,8,7,2,6,5,4,3] => [.,[[[.,[[[[.,.],.],.],.]],.],.]] => [1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,1] => 5

[2,8,7,1,6,5,4,3] => [[.,.],[[[[[[.,.],.],.],.],.],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,1,1] => 5

[3,4,8,6,5,1,7,2] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,2] => 1

[1,4,8,6,2,7,5,3] => [.,[[.,[.,.]],[[[.,.],[.,.]],.]]] => [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2] => 1

[3,4,6,5,1,2,8,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2] => 1

[1,4,6,2,3,8,7,5] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2] => 1

[1,3,2,7,4,8,6,5] => [.,[[.,.],[[.,[[.,.],.]],[.,.]]]] => [1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1,1] => 1

[2,3,1,7,6,4,8,5] => [[.,.],[.,[[[.,[.,.]],.],[.,.]]]] => [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1,1,1] => 1

[5,6,7,1,2,8,4,3] => [[.,[.,[[.,.],.]]],[.,[.,[.,.]]]] => [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,1] => 1

[1,7,2,3,8,6,5,4] => [.,[[.,[.,[[[.,.],.],.]]],[.,.]]] => [1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1] => 2

[2,1,3,7,4,8,6,5] => [[.,.],[.,[[.,[[.,.],.]],[.,.]]]] => [1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1,1,1] => 1

[2,6,3,4,7,5,1,8] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1,1] => 0

[1,7,6,8,3,2,4,5] => [.,[[[[.,.],[.,[.,.]]],.],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1,1,1] => 1

[1,2,7,3,4,6,5,8] => [.,[.,[[.,[.,[[.,.],.]]],[.,.]]]] => [1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [4,4,1] => 1

[1,7,8,4,3,5,6,2] => [.,[[[[.,.],.],[.,[.,.]]],[.,.]]] => [1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2,1] => 1

[1,6,2,8,3,5,7,4] => [.,[[.,[.,[[.,.],.]]],[[.,.],.]]] => [1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1] => 2

[2,6,1,7,3,5,4,8] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1,1] => 1

[1,8,3,7,6,2,4,5] => [.,[[[.,.],[[[.,[.,.]],.],.]],.]] => [1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,1,1] => 3

[2,6,8,7,3,4,1,5] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1,1] => 1

[1,8,6,5,3,2,4,7] => [.,[[[[[.,.],[.,.]],.],[.,.]],.]] => [1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3,1,1] => 2

[3,8,7,4,6,2,5,1] => [[[.,.],.],[[[.,[[.,.],.]],.],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,2,2,1] => 4

[1,5,7,8,4,3,6,2] => [.,[[[[.,.],.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2,1] => 2

[3,4,5,8,6,7,1,2] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,2] => 1

[2,1,7,3,8,4,6,5] => [[.,.],[[.,[.,[[.,.],.]]],[.,.]]] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1,1,1] => 1

[7,1,3,2,8,4,6,5] => [[.,[[.,.],[.,[[.,.],.]]]],[.,.]] => [1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [6,6,2,1,1,1] => 1

[7,1,8,2,4,3,6,5] => [[.,[.,[[.,.],[[.,.],.]]]],[.,.]] => [1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [6,6,2,1,1] => 1

[8,1,7,2,5,3,6,4] => [[.,[[.,[[.,[.,.]],[.,.]]],.]],.] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [7,5,2,2] => 2

[5,1,7,2,8,3,6,4] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4] => 0

[8,1,6,2,4,3,7,5] => [[.,[[.,[[.,.],[.,.]]],[.,.]]],.] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [7,4,4,1,1] => 1

[8,1,6,2,5,3,7,4] => [[.,[[.,[[.,[.,.]],.]],[.,.]]],.] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [7,4,4,2] => 2

[8,1,6,2,7,3,5,4] => [[.,[[.,[.,[[.,.],.]]],[.,.]]],.] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [7,4,4,1] => 2

[6,1,8,2,7,3,5,4] => [[.,[.,[.,[[.,.],.]]]],[[.,.],.]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [6,5,5,1] => 2

[6,1,7,2,8,3,5,4] => [[.,[.,[.,[[.,.],.]]]],[.,[.,.]]] => [1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,5,5,1] => 1

[6,1,7,2,5,3,8,4] => [[.,[.,[[.,[.,.]],.]]],[.,[.,.]]] => [1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [5,5,5,2] => 1

[6,1,7,2,4,3,8,5] => [[.,[.,[[.,.],[.,.]]]],[.,[.,.]]] => [1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [5,5,5,1,1] => 0

[7,1,6,2,8,3,5,4] => [[.,[[.,[.,[[.,.],.]]],.]],[.,.]] => [1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [6,6,4,1] => 2

[7,1,8,2,6,3,5,4] => [[.,[.,[[.,[[.,.],.]],.]]],[.,.]] => [1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [6,6,3,1] => 2

[1,8,2,7,5,4,6,3] => [.,[[.,[[[[.,.],.],[.,.]],.]],.]] => [1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,1] => 3

[1,8,2,7,4,3,5,6] => [.,[[.,[[[.,.],[.,[.,.]]],.]],.]] => [1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,1,1] => 2

[1,8,6,4,7,2,3,5] => [.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2,2] => 1

[1,8,4,2,6,3,5,7] => [.,[[[.,[.,.]],[[.,.],[.,.]]],.]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,2] => 1

[1,8,5,4,3,6,2,7] => [.,[[[[[.,.],.],.],[.,[.,.]]],.]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,2,1] => 3

[1,8,4,2,5,3,7,6] => [.,[[[.,[.,.]],[.,[[.,.],.]]],.]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2] => 2

[1,8,5,4,2,6,7,3] => [.,[[[[.,[.,.]],.],[.,[.,.]]],.]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,2] => 2

[6,5,4,3,8,2,7,1] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,5,4,3,2,1] => 5

[2,1,7,8,3,6,4,5] => [[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1,1,1,1] => 1

[7,8,1,3,2,4,6,5] => [[.,[[.,.],[.,[[.,.],.]]]],[.,.]] => [1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [6,6,2,1,1,1] => 1

[2,5,3,6,1,8,7,4] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1,1] => 1

[2,6,7,3,1,8,4,5] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1,1] => 0

[2,6,7,1,3,5,4,8] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1,1] => 1

[5,1,2,7,3,6,4,8] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4] => 0

[3,5,4,6,8,7,1,2] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,2] => 1

[1,5,4,6,8,2,3,7] => [.,[[[.,[.,.]],.],[.,[[.,.],.]]]] => [1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2] => 2

[1,6,7,3,2,4,8,5] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]] => [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1] => 0

[1,5,3,6,2,7,8,4] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => [1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1] => 0

[4,1,5,7,6,2,3,8] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [4,4,3,3,3] => 0

[4,5,1,8,6,2,3,7] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [5,3,3,3,3] => 1

[7,8,1,3,2,4,5,6] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1,1] => 0

[2,5,3,6,1,4,7,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1,1] => 0

[2,6,7,3,1,4,5,8] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1,1] => 0

[4,6,7,1,5,2,3,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[3,2,5,6,1,4,7,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => 1

[3,5,2,6,1,4,7,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => 1

[5,1,4,6,7,2,3,8] => [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,2] => 1

[3,5,4,6,7,8,1,2] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 0

[1,5,4,6,7,2,3,8] => [.,[[[.,[.,.]],.],[.,[.,[.,.]]]]] => [1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2] => 1

[1,6,7,3,2,4,5,8] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]] => [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1] => 0

[1,5,3,6,2,4,7,8] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => [1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1] => 0

[2,5,4,6,7,1,3,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1,1] => 1

[4,2,5,6,7,1,3,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1,1] => 0

[4,5,2,6,7,1,3,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1,1] => 0

[5,4,1,6,7,2,3,8] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3] => 1

[1,3,6,7,5,2,8,4] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1] => 1

[7,3,4,1,5,6,2,8] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,2,2] => 0

[7,3,4,1,5,2,6,8] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,2,2] => 0

[1,3,6,7,2,5,8,4] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1] => 1

[1,7,4,6,2,8,5,3] => [.,[[[.,[.,.]],[[.,.],.]],[.,.]]] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,2] => 1

[1,3,4,5,8,7,2,6] => [.,[[.,.],[.,[.,[[[.,.],.],.]]]]] => [1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1] => 2

[2,4,5,1,6,8,7,3] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,1,1] => 1

[3,1,2,5,6,8,7,4] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,2] => 1

[3,1,4,6,5,8,2,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2] => 1

[2,3,4,5,8,6,1,7] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1,1] => 1

[2,3,4,5,8,1,7,6] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1,1] => 2

[3,1,4,6,5,8,7,2] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2] => 1

[5,6,1,4,7,2,8,3] => [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,2] => 1

[3,1,4,6,7,8,5,2] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2] => 0

[1,4,5,2,6,8,7,3] => [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => [1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2] => 1

[5,6,1,2,7,4,8,3] => [[.,[.,[[.,.],.]]],[.,[.,[.,.]]]] => [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,1] => 1

[2,3,6,7,1,5,8,4] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1,1] => 1

[2,3,6,7,5,1,8,4] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1,1] => 1

[7,3,4,5,8,6,1,2] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,2,2] => 0

[7,3,4,5,8,1,6,2] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,2,2] => 0

[7,3,4,5,8,1,2,6] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,2,2] => 0

[1,3,4,5,8,6,2,7] => [.,[[.,.],[.,[.,[[.,[.,.]],.]]]]] => [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1] => 1

[1,3,4,5,8,2,7,6] => [.,[[.,.],[.,[.,[[[.,.],.],.]]]]] => [1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1] => 2

[2,1,7,3,5,8,6,4] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1,1] => 0

[2,7,3,1,5,4,6,8] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1,1] => 0

[2,6,3,1,4,8,5,7] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1,1] => 1

[2,7,3,1,4,8,5,6] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1,1,1] => 0

[2,1,7,3,6,8,4,5] => [[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1,1,1,1] => 1

[2,7,3,1,5,6,8,4] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1,1] => 0

[2,4,7,5,1,6,8,3] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => 0

[2,1,6,8,3,7,4,5] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1,1] => 1

[2,1,8,3,5,7,4,6] => [[.,.],[[.,[[.,.],[[.,.],.]]],.]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,1,1,1] => 2

[2,1,7,3,6,4,5,8] => [[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1,1,1,1] => 1

[2,7,3,1,5,6,4,8] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1,1] => 0

[2,4,7,5,1,6,3,8] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => 0

[2,4,7,1,8,5,3,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => 0

[2,4,8,5,1,6,3,7] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,1,1] => 1

[2,7,1,8,3,5,6,4] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1,1] => 0

[2,1,8,3,6,4,5,7] => [[.,.],[[.,[[.,[.,.]],[.,.]]],.]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1,1,1,1] => 1

[2,1,8,3,7,4,5,6] => [[.,.],[[.,[[.,[.,[.,.]]],.]],.]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,1,1,1,1] => 2

[2,1,8,3,6,7,4,5] => [[.,.],[[.,[[.,[.,.]],[.,.]]],.]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1,1,1,1] => 1

[2,4,8,5,1,6,7,3] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,1,1] => 1

[3,2,1,8,4,5,6,7] => [[[.,.],.],[[.,[.,[.,[.,.]]]],.]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,2,1] => 2

[1,6,8,3,7,2,4,5] => [.,[[[.,.],[.,[.,.]]],[[.,.],.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1] => 1

[1,2,6,8,4,7,3,5] => [.,[.,[[[.,.],[.,.]],[[.,.],.]]]] => [1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1] => 1

[1,2,4,8,3,6,7,5] => [.,[.,[[.,.],[[[.,.],[.,.]],.]]]] => [1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1] => 1

[1,2,8,4,3,5,7,6] => [.,[.,[[[.,.],[.,[[.,.],.]]],.]]] => [1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1] => 2

[1,2,5,3,7,6,4,8] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => [1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2] => 0

[1,2,6,3,8,5,4,7] => [.,[.,[[.,[[.,.],.]],[[.,.],.]]]] => [1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1] => 2

[1,2,8,5,3,6,4,7] => [.,[.,[[[.,[.,.]],[.,[.,.]]],.]]] => [1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2] => 1

[1,2,7,3,8,5,4,6] => [.,[.,[[.,[[.,.],[.,.]]],[.,.]]]] => [1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1] => 0

[1,6,2,8,4,3,5,7] => [.,[[.,[[.,.],[.,.]]],[[.,.],.]]] => [1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1] => 1

[1,6,4,2,7,3,5,8] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2] => 0

[1,8,6,3,2,4,5,7] => [.,[[[[.,.],[.,[.,.]]],[.,.]],.]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,4,1,1,1] => 1

[1,7,3,2,8,4,5,6] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1,1] => 0

[1,8,7,2,4,5,6,3] => [.,[[[.,[[.,.],[.,[.,.]]]],.],.]] => [1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,1,1] => 2

[1,8,7,3,5,6,2,4] => [.,[[[[.,.],[[.,.],[.,.]]],.],.]] => [1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,1,1] => 2

[1,3,2,8,7,4,5,6] => [.,[[.,.],[[[.,[.,[.,.]]],.],.]]] => [1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1,1,1] => 2

[1,8,3,2,6,4,5,7] => [.,[[[.,.],[[.,[.,.]],[.,.]]],.]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1,1,1] => 1

[1,7,6,3,2,4,5,8] => [.,[[[[.,.],[.,[.,.]]],.],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1,1,1] => 1

[1,2,8,4,3,7,5,6] => [.,[.,[[[.,.],[[.,[.,.]],.]],.]]] => [1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1,1] => 2

[1,2,5,3,8,6,4,7] => [.,[.,[[.,[.,.]],[[.,[.,.]],.]]]] => [1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2] => 1

[1,2,7,5,3,6,4,8] => [.,[.,[[[.,[.,.]],[.,.]],[.,.]]]] => [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2] => 0

[1,2,6,3,7,5,4,8] => [.,[.,[[.,[[.,.],.]],[.,[.,.]]]]] => [1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1] => 1

[1,2,3,7,5,4,8,6] => [.,[.,[.,[[[.,.],[.,.]],[.,.]]]]] => [1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1] => 0

[1,8,2,7,6,4,5,3] => [.,[[.,[[[[.,.],[.,.]],.],.]],.]] => [1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,1] => 3

[2,9,8,7,6,5,4,1,3] => [[.,.],[[[[[[[.,.],.],.],.],.],.],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,1,1] => 6

[2,8,7,6,5,1,4,3] => [[.,.],[[[[[[.,.],.],.],.],.],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,1,1] => 5

[1,8,4,3,6,5,2,7] => [.,[[[[.,.],.],[[.,.],[.,.]]],.]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,2,1] => 2

[1,8,4,6,5,3,2,7] => [.,[[[[.,.],.],[[.,.],[.,.]]],.]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,2,1] => 2

[1,8,6,3,4,5,2,7] => [.,[[[[.,.],[.,[.,.]]],[.,.]],.]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,4,1,1,1] => 1

[1,8,6,7,4,2,5,3] => [.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2,2] => 1

[3,4,7,1,5,2,8,6] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2] => 0

[1,8,2,7,4,3,6,5] => [.,[[.,[[[.,.],[[.,.],.]],.]],.]] => [1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,1] => 3

[2,4,8,1,6,3,7,5] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1,1] => 1

[2,4,5,3,8,6,1,7] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,1,1] => 1

[1,8,4,5,2,6,7,3] => [.,[[[.,[.,.]],[.,[.,[.,.]]]],.]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2] => 1

[2,4,1,6,7,8,5,3] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[1,8,4,3,6,2,7,5] => [.,[[[[.,.],.],[[.,.],[.,.]]],.]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,2,1] => 2

[2,5,7,3,6,8,4,1] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[3,4,7,8,1,2,6,5] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,2] => 1

[2,3,6,8,5,1,4,7] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1,1] => 2

[1,8,5,2,4,6,3,7] => [.,[[[.,[[.,.],.]],[.,[.,.]]],.]] => [1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,1] => 2

[1,8,4,2,3,5,7,6] => [.,[[[.,[.,.]],[.,[[.,.],.]]],.]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2] => 2

[2,5,6,8,3,4,1,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1,1] => 1

[2,5,6,8,4,3,1,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1,1] => 2

[2,5,7,8,3,1,4,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[2,4,7,3,8,1,5,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => 0

[5,4,6,3,8,2,1,7] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [5,4,4,4,3,2,1] => 4

[2,5,7,8,3,1,6,4] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[2,6,7,8,1,3,5,4] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1,1] => 1

[4,6,7,8,1,5,2,3] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[4,6,7,8,1,2,5,3] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[2,7,1,3,5,4,8,6] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1,1] => 0

[2,3,6,4,7,1,5,8] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1,1] => 0

[1,3,4,8,2,7,5,6] => [.,[[.,.],[.,[[[.,[.,.]],.],.]]]] => [1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1,1] => 2

[3,1,4,8,2,6,7,5] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,2] => 1

[3,4,6,8,5,1,7,2] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2] => 1

[1,8,2,3,5,7,4,6] => [.,[[.,[.,[[.,.],[[.,.],.]]]],.]] => [1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1] => 2

[2,7,3,6,1,4,5,8] => [[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1,1,1,1] => 1

[4,5,6,2,7,1,3,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1,1] => 0

[1,6,2,7,4,8,3,5] => [.,[[.,[[.,.],[.,.]]],[.,[.,.]]]] => [1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1] => 0

[8,2,4,5,1,6,7,3] => [[[.,.],[[.,.],[.,[.,[.,.]]]]],.] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2,1,1] => 1

[3,8,4,5,6,1,7,2] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,2] => 1

[7,2,3,4,8,1,5,6] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1,1,1] => 0

[7,2,3,8,4,1,5,6] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1,1,1] => 0

[7,6,5,1,2,3,8,4] => [[[[.,[.,[.,[.,.]]]],.],.],[.,.]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [6,6,5,4] => 2

[3,5,6,4,1,2,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 0

[3,5,6,4,1,2,8,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,2] => 1

[7,2,3,4,5,1,8,6] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1,1,1] => 0

[3,5,6,4,1,8,7,2] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,2] => 1

[7,6,5,1,2,8,3,4] => [[[[.,[.,[.,[.,.]]]],.],.],[.,.]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [6,6,5,4] => 2

[7,6,5,1,8,2,3,4] => [[[[.,[.,[.,[.,.]]]],.],.],[.,.]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [6,6,5,4] => 2

[2,5,6,4,1,7,8,3] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1,1] => 1

[2,5,6,4,1,7,3,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1,1] => 1

[2,4,5,6,1,8,7,3] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,1,1] => 1

[2,8,3,4,7,5,1,6] => [[.,.],[[.,[.,[[.,[.,.]],.]]],.]] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1,1,1,1] => 2

[2,3,5,8,6,7,4,1] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1,1,1] => 1

[8,1,3,2,5,6,7,4] => [[.,[[.,.],[[.,.],[.,[.,.]]]]],.] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,1,1] => 1

[3,2,8,7,4,5,1,6] => [[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,2,2,1] => 3

[2,1,4,8,7,5,3,6] => [[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,1,1] => 2

[2,1,5,8,3,6,4,7] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1,1] => 1

[3,8,1,4,5,6,2,7] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,2] => 1

[3,4,7,5,6,2,1,8] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2,1] => 1

[1,6,8,5,2,7,4,3] => [.,[[[.,[[.,.],.]],.],[[.,.],.]]] => [1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3,1] => 3

[1,8,2,5,6,4,3,7] => [.,[[.,[[[.,.],.],[.,[.,.]]]],.]] => [1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,1] => 2

[1,5,2,4,6,7,8,3] => [.,[[.,[[.,.],.]],[.,[.,[.,.]]]]] => [1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1] => 1

[4,1,5,3,6,7,8,2] => [[.,[[.,.],.]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1] => 1

[4,5,3,1,6,7,8,2] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,2] => 1

[3,5,2,1,6,7,8,4] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => 1

[1,5,3,2,6,7,8,4] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => [1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1] => 0

[3,2,5,6,1,7,8,4] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => 1

[3,2,8,7,6,1,4,5] => [[[.,.],.],[[[[.,[.,.]],.],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,2,2,1] => 4

[1,7,4,6,2,3,8,5] => [.,[[[.,[.,.]],[[.,.],.]],[.,.]]] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,2] => 1

[1,7,4,2,3,6,8,5] => [.,[[[.,[.,.]],[[.,.],.]],[.,.]]] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,2] => 1

[1,8,2,5,3,7,6,4] => [.,[[.,[[.,[.,.]],[[.,.],.]]],.]] => [1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2] => 2

[3,5,1,4,6,7,8,2] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 0

[8,1,3,5,4,7,2,6] => [[.,[[.,.],[[.,.],[[.,.],.]]]],.] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,1,1] => 2

[2,8,1,7,6,5,4,3] => [[.,.],[[[[[[.,.],.],.],.],.],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,1,1] => 5

[3,4,6,8,5,7,1,2] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2] => 1

[8,1,3,4,5,2,6,7] => [[.,[[.,.],[.,[.,[.,[.,.]]]]]],.] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1,1,1] => 1

[1,6,8,4,2,5,3,7] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,2] => 1

[1,4,8,5,2,6,7,3] => [.,[[.,[.,.]],[[.,[.,[.,.]]],.]]] => [1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2] => 1

[4,1,5,3,6,8,2,7] => [[.,[[.,.],.]],[.,[.,[[.,.],.]]]] => [1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3,1] => 2

[1,5,3,2,8,6,4,7] => [.,[[[.,.],[.,.]],[[.,[.,.]],.]]] => [1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1] => 1

[1,7,3,6,2,8,5,4] => [.,[[[.,.],[[[.,.],.],.]],[.,.]]] => [1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,1,1] => 2

[8,1,3,2,4,5,6,7] => [[.,[[.,.],[.,[.,[.,[.,.]]]]]],.] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1,1,1] => 1

[3,5,1,4,6,7,2,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 0

[8,1,4,3,5,6,7,2] => [[.,[[[.,.],.],[.,[.,[.,.]]]]],.] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2,1] => 2

[2,6,3,4,7,5,8,1] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1,1] => 0

[3,4,1,6,5,8,2,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2] => 1

[7,3,1,4,8,5,6,2] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,2,2] => 0

[4,1,6,2,7,8,5,3] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[2,1,3,4,8,7,5,6] => [[.,.],[.,[.,[[[.,[.,.]],.],.]]]] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1,1,1] => 2

[4,5,6,7,8,9,1,2,3] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3,3] => 0

[5,6,7,8,9,1,2,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,4,4,4,4] => 0

[2,8,7,6,1,5,4,3] => [[.,.],[[[[[[.,.],.],.],.],.],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,1,1] => 5

[3,8,7,2,1,6,5,4] => [[[.,.],.],[[[[[.,.],.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,2,1] => 5

[8,1,4,2,3,6,5,7] => [[.,[[.,[.,.]],[[.,.],[.,.]]]],.] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2,2] => 1

[8,2,3,6,1,4,5,7] => [[[.,.],[.,[[.,[.,.]],[.,.]]]],.] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,3,1,1,1,1] => 1

[8,2,3,6,4,1,5,7] => [[[.,.],[.,[[.,[.,.]],[.,.]]]],.] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,3,1,1,1,1] => 1

[2,6,3,8,4,1,5,7] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1,1] => 1

[2,6,3,8,1,4,5,7] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1,1] => 1

[2,8,3,6,1,4,5,7] => [[.,.],[[.,[[.,[.,.]],[.,.]]],.]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1,1,1,1] => 1

[2,8,3,6,4,1,5,7] => [[.,.],[[.,[[.,[.,.]],[.,.]]],.]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1,1,1,1] => 1

[8,2,1,3,6,4,5,7] => [[[.,.],[.,[[.,[.,.]],[.,.]]]],.] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,3,1,1,1,1] => 1

[1,6,4,2,7,5,8,3] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2] => 0

[1,4,7,2,5,6,8,3] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2] => 0

[1,6,5,4,2,7,8,3] => [.,[[[[.,[.,.]],.],.],[.,[.,.]]]] => [1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,2] => 2

[4,2,5,3,6,1,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1,1] => 0

[1,6,5,2,4,8,7,3] => [.,[[[.,[[.,.],.]],.],[[.,.],.]]] => [1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3,1] => 3

[1,4,6,2,8,5,7,3] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2] => 1

[3,4,8,5,2,1,6,7] => [[[.,.],.],[.,[[.,[.,[.,.]]],.]]] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,2,1] => 2

[1,2,8,5,7,3,6,4] => [.,[.,[[[.,[.,.]],[[.,.],.]],.]]] => [1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2] => 2

[1,3,6,8,7,5,2,4] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]] => [1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1] => 2

[1,8,2,5,4,7,6,3] => [.,[[.,[[[.,.],.],[[.,.],.]]],.]] => [1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,1] => 3

[7,1,2,4,5,8,6,3] => [[.,[.,[[.,.],[.,[.,.]]]]],[.,.]] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1] => 0

[1,2,7,3,5,8,6,4] => [.,[.,[[.,[[.,.],[.,.]]],[.,.]]]] => [1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1] => 0

[1,6,3,7,8,5,2,4] => [.,[[[.,.],[[.,.],.]],[.,[.,.]]]] => [1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1] => 1

[1,8,6,7,5,3,4,2] => [.,[[[[[.,.],[.,.]],.],[.,.]],.]] => [1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3,1,1] => 2

[1,5,8,7,2,6,4,3] => [.,[[.,[[.,.],.]],[[[.,.],.],.]]] => [1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1] => 3

[2,4,1,3,8,5,7,6] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,1,1] => 2

[2,4,1,3,5,8,7,6] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,1,1] => 2

[1,8,4,6,3,5,7,2] => [.,[[[[.,.],.],[[.,.],[.,.]]],.]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,2,1] => 2

[1,4,6,3,8,5,7,2] => [.,[[[.,.],.],[[.,.],[[.,.],.]]]] => [1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1] => 2

[2,4,1,8,3,5,7,6] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,1,1] => 2

[1,4,3,6,8,5,7,2] => [.,[[[.,.],.],[[.,.],[[.,.],.]]]] => [1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1] => 2

[2,1,8,3,6,5,7,4] => [[.,.],[[.,[[[.,.],.],[.,.]]],.]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,1,1,1] => 2

[2,8,1,4,3,5,7,6] => [[.,.],[[[.,.],[.,[[.,.],.]]],.]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2,1,1] => 2

[1,4,8,3,6,5,7,2] => [.,[[[.,.],.],[[[.,.],[.,.]],.]]] => [1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1] => 2

[1,4,8,6,3,5,7,2] => [.,[[[.,.],.],[[[.,.],[.,.]],.]]] => [1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1] => 2

[2,8,4,1,3,5,7,6] => [[.,.],[[[.,.],[.,[[.,.],.]]],.]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2,1,1] => 2

[1,8,6,4,3,5,7,2] => [.,[[[[[.,.],.],[.,.]],[.,.]],.]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2,2,1] => 2

[7,3,8,1,4,2,5,6] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,2,2] => 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] => [4,4,3,2,2,2] => 1

[3,4,1,2,6,8,7,5] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2] => 1

[3,4,1,2,8,5,7,6] => [[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,2] => 2

[3,4,1,2,5,8,7,6] => [[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,2] => 2

[7,3,8,1,4,5,2,6] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,2,2] => 0

[7,3,8,1,4,5,6,2] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,2,2] => 0

[6,5,8,4,3,2,1,7] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,5,4,3,2,1] => 5

[5,8,7,4,3,2,1,6] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,4,3,2,1] => 5

[1,6,2,5,8,4,3,7] => [.,[[.,[[[.,.],.],.]],[[.,.],.]]] => [1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,1] => 3

[2,8,3,5,1,7,4,6] => [[.,.],[[.,[[.,.],[[.,.],.]]],.]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,1,1,1] => 2

[2,8,3,4,1,7,5,6] => [[.,.],[[.,[.,[[.,[.,.]],.]]],.]] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1,1,1,1] => 2

[2,4,8,3,1,5,7,6] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,1,1] => 2

[2,3,8,4,1,6,7,5] => [[.,.],[.,[[.,[[.,.],[.,.]]],.]]] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1,1,1] => 1

[2,3,8,5,1,6,7,4] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1,1,1] => 1

[3,4,8,7,1,5,6,2] => [[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,2] => 2

[2,4,8,6,1,5,7,3] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1,1] => 1

[2,3,5,4,1,8,6,7] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1,1,1] => 1

[2,3,6,4,8,1,5,7] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1,1] => 1

[1,8,4,6,3,5,2,7] => [.,[[[[.,.],.],[[.,.],[.,.]]],.]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,2,1] => 2

[2,3,6,8,1,5,4,7] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1,1] => 2

[2,5,6,1,4,7,8,3] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1,1] => 1

[2,5,6,1,4,7,3,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1,1] => 1

[1,8,7,6,3,2,4,5] => [.,[[[[[.,.],[.,[.,.]]],.],.],.]] => [1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,1,1] => 3

[2,3,4,7,6,1,5,8] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1,1,1] => 1

[1,8,4,5,2,7,3,6] => [.,[[[.,[.,.]],[.,[[.,.],.]]],.]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2] => 2

[1,8,4,5,2,7,6,3] => [.,[[[.,[.,.]],[.,[[.,.],.]]],.]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2] => 2

[3,4,1,5,6,8,7,2] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,2] => 1

[2,3,1,8,6,4,7,5] => [[.,.],[.,[[[.,[.,.]],[.,.]],.]]] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1,1,1] => 1

[1,8,4,3,6,2,5,7] => [.,[[[[.,.],.],[[.,.],[.,.]]],.]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,2,1] => 2

[2,3,1,8,6,4,5,7] => [[.,.],[.,[[[.,[.,.]],[.,.]],.]]] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1,1,1] => 1

[1,8,4,5,2,6,3,7] => [.,[[[.,[.,.]],[.,[.,[.,.]]]],.]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2] => 1

[2,3,4,6,5,8,1,7] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1,1] => 1

[2,3,4,7,5,1,8,6] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1,1] => 0

[2,3,4,7,5,1,6,8] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1,1] => 0

[2,3,4,7,1,6,5,8] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1,1,1] => 1

[2,3,4,7,1,6,8,5] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1,1,1] => 1

[2,3,4,6,1,8,7,5] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1,1] => 1

[1,8,4,5,2,3,6,7] => [.,[[[.,[.,.]],[.,[.,[.,.]]]],.]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2] => 1

[1,5,7,4,6,3,2,8] => [.,[[[[.,.],.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2,1] => 2

[8,1,3,5,4,6,2,7] => [[.,[[.,.],[[.,.],[.,[.,.]]]]],.] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,1,1] => 1

[8,1,6,2,4,3,5,7] => [[.,[[.,[[.,.],[.,.]]],[.,.]]],.] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [7,4,4,1,1] => 1

[8,7,1,2,4,3,5,6] => [[[.,[.,[[.,.],[.,[.,.]]]]],.],.] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,1,1] => 2

[1,7,6,2,4,3,5,8] => [.,[[[.,[[.,.],[.,.]]],.],[.,.]]] => [1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1,1] => 1

[1,7,6,3,4,5,2,8] => [.,[[[[.,.],[.,[.,.]]],.],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1,1,1] => 1

[1,7,2,5,4,3,6,8] => [.,[[.,[[[.,.],.],[.,.]]],[.,.]]] => [1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1] => 1

[8,7,1,3,4,5,2,6] => [[[.,[[.,.],[.,[.,[.,.]]]]],.],.] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,1,1,1] => 2

[8,1,2,5,4,3,6,7] => [[.,[.,[[[.,.],.],[.,[.,.]]]]],.] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,1] => 2

[5,1,8,6,2,3,4,7] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [6,4,4,4] => 1

[8,2,3,6,1,4,7,5] => [[[.,.],[.,[[.,[.,.]],[.,.]]]],.] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,3,1,1,1,1] => 1

[1,8,2,6,3,4,7,5] => [.,[[.,[[.,[.,[.,.]]],[.,.]]],.]] => [1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [6,3,3] => 1

[8,1,3,6,4,7,2,5] => [[.,[[.,.],[[.,[.,.]],[.,.]]]],.] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,3,1,1,1] => 1

[8,2,1,3,5,7,4,6] => [[[.,.],[.,[[.,.],[[.,.],.]]]],.] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,1,1,1] => 2

[1,3,7,2,5,8,4,6] => [.,[[.,.],[[[.,.],[.,.]],[.,.]]]] => [1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1] => 0

[1,7,2,3,5,8,4,6] => [.,[[.,[.,[[.,.],[.,.]]]],[.,.]]] => [1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1] => 0

[8,1,2,3,5,7,4,6] => [[.,[.,[.,[[.,.],[[.,.],.]]]]],.] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,1] => 2

[7,1,2,3,5,8,4,6] => [[.,[.,[.,[[.,.],[.,.]]]]],[.,.]] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1] => 0

[2,6,3,7,1,4,8,5] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1,1] => 0

[2,6,3,8,1,4,7,5] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1,1] => 1

[2,3,1,8,5,4,6,7] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1,1,1] => 1

[3,4,7,6,1,8,5,2] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,2] => 1

[3,5,2,6,7,1,8,4] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => 1

[6,1,2,8,3,4,7,5] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [6,5,5] => 1

[2,8,3,6,4,7,1,5] => [[.,.],[[.,[[.,[.,.]],[.,.]]],.]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1,1,1,1] => 1

[1,2,8,3,5,7,4,6] => [.,[.,[[.,[[.,.],[[.,.],.]]],.]]] => [1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1] => 2

[1,8,3,2,5,7,4,6] => [.,[[[.,.],[[.,.],[[.,.],.]]],.]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,1,1] => 2

[2,8,1,7,6,5,3,4] => [[.,.],[[[[[.,[.,.]],.],.],.],.]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1,1,1] => 4

[2,4,3,8,1,6,7,5] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1,1] => 1

[2,4,3,7,1,6,8,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1,1] => 1

[5,1,6,4,2,3,7,8] => [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,2] => 1

[3,2,4,7,8,1,5,6] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2,1] => 1

[5,1,6,7,4,2,3,8] => [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,2] => 1

[2,5,3,7,1,6,4,8] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[2,4,3,7,1,6,5,8] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1,1] => 1

[2,4,7,1,5,8,6,3] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => 0

[2,4,6,7,1,5,8,3] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[3,2,4,6,1,5,7,8] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2,1] => 1

[4,5,1,3,6,8,2,7] => [[.,[[.,.],.]],[.,[.,[[.,.],.]]]] => [1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3,1] => 2

[2,3,8,1,5,7,4,6] => [[.,.],[.,[[[.,.],[[.,.],.]],.]]] => [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1,1,1] => 2

[7,1,6,2,8,3,4,5] => [[.,[[.,[.,[.,[.,.]]]],.]],[.,.]] => [1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [6,6,4] => 1

[8,3,1,4,5,6,7,2] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2,2] => 1

[7,1,2,5,8,3,4,6] => [[.,[.,[[.,[.,.]],[.,.]]]],[.,.]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2] => 0

[3,1,4,5,2,8,7,6] => [[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,2] => 2

[1,6,4,5,2,8,7,3] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,2] => 1

[1,7,4,2,6,3,5,8] => [.,[[[.,[.,.]],[[.,.],.]],[.,.]]] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,2] => 1

[1,8,3,5,6,7,2,4] => [.,[[[.,.],[[.,.],[.,[.,.]]]],.]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,1,1] => 1

[4,1,3,5,6,7,2,8] => [[.,[[.,.],.]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1] => 1

[1,5,8,4,6,7,3,2] => [.,[[[[.,.],.],.],[[.,[.,.]],.]]] => [1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,2,1] => 3

[1,4,8,3,6,7,5,2] => [.,[[[.,.],.],[[[.,.],[.,.]],.]]] => [1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1] => 2

[4,3,8,2,1,7,5,6] => [[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,3,3,2,1] => 4

[1,8,2,5,6,7,4,3] => [.,[[.,[[[.,.],.],[.,[.,.]]]],.]] => [1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,1] => 2

[8,1,3,5,6,7,4,2] => [[.,[[.,.],[[.,.],[.,[.,.]]]]],.] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,1,1] => 1

[1,6,4,5,8,2,3,7] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,2] => 1

[1,7,6,5,8,3,4,2] => [.,[[[[[.,.],[.,.]],.],.],[.,.]]] => [1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3,1,1] => 2

[1,8,5,3,6,7,4,2] => [.,[[[[.,.],[.,.]],[.,[.,.]]],.]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,1,1] => 1

[1,2,8,5,6,7,3,4] => [.,[.,[[[.,[.,.]],[.,[.,.]]],.]]] => [1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2] => 1

[4,2,1,5,6,7,3,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1,1] => 0

[1,5,3,8,6,7,4,2] => [.,[[[.,.],[.,.]],[[.,[.,.]],.]]] => [1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1] => 1

[1,4,5,8,6,7,3,2] => [.,[[[.,.],.],[.,[[.,[.,.]],.]]]] => [1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,1] => 2

[1,4,8,5,6,7,2,3] => [.,[[.,[.,.]],[[.,[.,[.,.]]],.]]] => [1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2] => 1

[3,4,8,5,6,7,1,2] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,2] => 1

[2,6,3,1,4,5,8,7] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1,1] => 1

[8,10,1,2,3,4,5,6,7,9] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,1,0,0] => [8,7,7] => 1

[3,5,6,1,4,8,7,2] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,2] => 1

[3,5,6,2,4,1,7,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => 1

[2,5,6,1,4,8,3,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1,1] => 2

[1,8,4,6,7,5,3,2] => [.,[[[[.,.],.],[[.,.],[.,.]]],.]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,2,1] => 2

[8,1,4,5,6,7,3,2] => [[.,[[[.,.],.],[.,[.,[.,.]]]]],.] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2,1] => 2

[5,6,7,1,4,2,3,8] => [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,2] => 1

[1,8,4,6,2,5,3,7] => [.,[[[.,[.,.]],[[.,.],[.,.]]],.]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,2] => 1

[2,3,5,8,6,1,7,4] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1,1,1] => 1

[1,8,7,2,3,6,5,4] => [.,[[[.,[.,[[[.,.],.],.]]],.],.]] => [1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1] => 4

[1,7,8,2,6,4,3,5] => [.,[[.,[[[.,.],[.,.]],.]],[.,.]]] => [1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1,1] => 1

[1,7,3,8,2,6,4,5] => [.,[[[.,.],[[.,[.,.]],.]],[.,.]]] => [1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1,1,1] => 1

[1,2,7,3,6,4,5,8] => [.,[.,[[.,[[.,[.,.]],.]],[.,.]]]] => [1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [4,4,2] => 1

[1,6,2,8,4,3,7,5] => [.,[[.,[[.,.],[.,.]]],[[.,.],.]]] => [1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1] => 1

[1,3,8,7,2,4,6,5] => [.,[[.,.],[[[.,[[.,.],.]],.],.]]] => [1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,1,1] => 3

[1,8,3,7,2,5,4,6] => [.,[[[.,.],[[[.,.],[.,.]],.]],.]] => [1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,1,1] => 2

[2,1,3,8,4,6,7,5] => [[.,.],[.,[[.,[[.,.],[.,.]]],.]]] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1,1,1] => 1

[1,2,3,4,8,5,7,6] => [.,[.,[.,[.,[[.,[[.,.],.]],.]]]]] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [3,1] => 2

[2,4,8,7,5,6,3,1] => [[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,1,1] => 2

[2,5,7,3,4,8,6,1] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[2,4,6,3,5,7,1,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[1,4,6,3,7,2,5,8] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1] => 1

[8,2,3,4,5,1,7,6] => [[[.,.],[.,[.,[.,[[.,.],.]]]]],.] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,1,1,1,1] => 2

[1,8,3,4,2,7,5,6] => [.,[[[.,.],[.,[[.,[.,.]],.]]],.]] => [1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1,1,1] => 2

[2,8,3,4,1,6,7,5] => [[.,.],[[.,[.,[[.,.],[.,.]]]],.]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1,1,1,1] => 1

[2,1,4,7,5,3,6,8] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => 0

[8,1,3,6,2,4,7,5] => [[.,[[.,.],[[.,[.,.]],[.,.]]]],.] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,3,1,1,1] => 1

[2,1,8,3,7,5,4,6] => [[.,.],[[.,[[[.,.],[.,.]],.]],.]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,1,1,1] => 2

[7,1,8,2,5,6,3,4] => [[.,[.,[[.,[.,.]],[.,.]]]],[.,.]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2] => 0

[1,3,8,2,5,7,4,6] => [.,[[.,.],[[[.,.],[[.,.],.]],.]]] => [1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1,1] => 2

[3,4,8,5,6,1,7,2] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,2] => 1

[1,4,8,6,2,7,3,5] => [.,[[.,[.,.]],[[[.,.],[.,.]],.]]] => [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2] => 1

[3,5,6,8,4,1,7,2] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,2] => 1

[8,2,3,1,4,5,7,6] => [[[.,.],[.,[.,[.,[[.,.],.]]]]],.] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,1,1,1,1] => 2

[4,5,6,1,3,2,7,8] => [[.,[[.,.],.]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1] => 1

[4,5,7,1,2,6,3,8] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [4,4,3,3,3] => 0

[2,7,1,3,5,6,4,8] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1,1] => 0

[2,8,1,3,4,6,7,5] => [[.,.],[[.,[.,[[.,.],[.,.]]]],.]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1,1,1,1] => 1

[7,8,1,2,5,3,6,4] => [[.,[.,[[.,[.,.]],[.,.]]]],[.,.]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2] => 0

[3,8,4,1,2,5,7,6] => [[.,[.,.]],[[.,[.,[[.,.],.]]],.]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2,2] => 2

[1,2,6,7,5,3,8,4] => [.,[.,[[[.,[.,.]],.],[.,[.,.]]]]] => [1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2] => 1

[1,7,5,3,2,8,4,6] => [.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,1,1] => 0

[1,6,7,5,3,8,4,2] => [.,[[[[.,.],[.,.]],.],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,1,1] => 1

[1,6,5,7,2,3,8,4] => [.,[[[.,[.,[.,.]]],.],[.,[.,.]]]] => [1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3] => 1

[1,3,8,2,6,5,7,4] => [.,[[.,.],[[[[.,.],.],[.,.]],.]]] => [1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1,1] => 2

[1,2,5,7,6,3,4,8] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => [1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2] => 0

[1,3,4,8,2,5,7,6] => [.,[[.,.],[.,[[.,[[.,.],.]],.]]]] => [1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1,1] => 2

[1,5,7,6,2,3,4,8] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3] => 0

[1,5,3,8,2,6,4,7] => [.,[[[.,.],[.,.]],[[.,[.,.]],.]]] => [1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1] => 1

[1,4,8,3,2,5,7,6] => [.,[[[.,.],.],[[.,[[.,.],.]],.]]] => [1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,1] => 3

[1,4,8,3,5,7,6,2] => [.,[[[.,.],.],[[.,[[.,.],.]],.]]] => [1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,1] => 3

[1,2,4,8,3,5,7,6] => [.,[.,[[.,.],[[.,[[.,.],.]],.]]]] => [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1] => 2

[1,3,8,4,2,6,7,5] => [.,[[.,.],[[.,[[.,.],[.,.]]],.]]] => [1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1,1] => 1

[1,4,8,2,3,5,7,6] => [.,[[.,[.,.]],[[.,[[.,.],.]],.]]] => [1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2] => 2

[1,7,5,2,8,4,6,3] => [.,[[[.,[[.,.],.]],[.,.]],[.,.]]] => [1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,1] => 1

[3,4,7,1,8,6,2,5] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,2] => 1

[3,4,6,8,2,1,5,7] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2,1] => 2

[1,5,6,8,3,4,2,7] => [.,[[[.,.],[.,.]],[.,[[.,.],.]]]] => [1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1] => 1

[4,5,1,6,8,3,2,7] => [[.,[[.,.],.]],[.,[.,[[.,.],.]]]] => [1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3,1] => 2

[1,4,5,7,3,8,6,2] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]] => [1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1] => 1

[1,5,3,6,7,8,4,2] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => [1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1] => 0

[3,2,5,6,7,8,1,4] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => 1

[7,1,8,3,4,2,5,6] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1,1] => 0

[1,7,4,8,5,2,6,3] => [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2] => 0

[1,3,7,8,5,2,6,4] => [.,[[.,.],[[[.,.],[.,.]],[.,.]]]] => [1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1] => 0

[2,5,7,8,1,6,3,4] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[1,6,4,7,8,2,5,3] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2] => 0

[2,5,6,1,7,8,4,3] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1,1] => 1

[5,6,1,2,7,8,4,3] => [[.,[.,[[.,.],.]]],[.,[.,[.,.]]]] => [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,1] => 1

[1,6,7,4,8,5,3,2] => [.,[[[[.,.],.],[.,.]],[.,[.,.]]]] => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2,1] => 1

[1,8,2,4,6,3,5,7] => [.,[[.,[[.,.],[[.,.],[.,.]]]],.]] => [1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1,1] => 1

[1,5,7,4,3,6,2,8] => [.,[[[[.,.],.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2,1] => 2

[1,8,4,5,3,6,2,7] => [.,[[[[.,.],.],[.,[.,[.,.]]]],.]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,1] => 2

[1,8,2,4,6,3,7,5] => [.,[[.,[[.,.],[[.,.],[.,.]]]],.]] => [1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1,1] => 1

[1,8,2,5,4,6,7,3] => [.,[[.,[[[.,.],.],[.,[.,.]]]],.]] => [1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,1] => 2

[1,4,7,5,2,6,8,3] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2] => 0

[1,5,7,4,2,8,6,3] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2] => 1

[1,3,7,2,8,6,4,5] => [.,[[.,.],[[[.,[.,.]],.],[.,.]]]] => [1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1,1] => 1

[1,4,3,7,8,6,2,5] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1] => 2

[1,5,3,6,8,2,7,4] => [.,[[[.,.],[.,.]],[.,[[.,.],.]]]] => [1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1] => 1

[7,9,1,2,3,4,5,6,8] => [[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [7,6,6] => 1

[2,3,6,4,7,8,5,1] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1,1] => 0

[1,6,3,5,2,4,8,7] => [.,[[[.,.],[[.,.],.]],[[.,.],.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,1,1] => 2

[2,4,8,1,5,3,7,6] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,1,1] => 2

[3,4,8,1,6,2,7,5] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,2] => 1

[1,8,4,6,7,3,5,2] => [.,[[[[.,.],.],[[.,.],[.,.]]],.]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,2,1] => 2

[8,1,2,4,6,7,3,5] => [[.,[.,[[.,.],[[.,.],[.,.]]]]],.] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1,1] => 1

[3,1,8,2,4,5,7,6] => [[.,[.,.]],[[.,[.,[[.,.],.]]],.]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2,2] => 2

[8,1,3,7,6,2,4,5] => [[.,[[.,.],[[[.,[.,.]],.],.]]],.] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [7,4,3,1,1,1] => 3

[2,3,6,8,7,1,4,5] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1,1] => 1

[4,3,2,8,5,7,1,6] => [[[[.,.],.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,3,3,2,1] => 4

[3,2,4,7,5,8,6,1] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2,1] => 1

[2,4,3,5,1,8,6,7] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,1,1] => 1

[2,5,6,8,7,3,4,1] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1,1] => 1

[3,4,5,1,8,7,2,6] => [[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,2] => 2

[2,4,6,8,3,7,5,1] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[3,4,5,2,8,7,1,6] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,2,1] => 3

[3,2,4,5,8,7,1,6] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,2,1] => 3

[8,1,2,3,4,6,5,7] => [[.,[.,[.,[.,[[.,.],[.,.]]]]]],.] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [7,1,1] => 1

[1,5,6,7,3,4,8,2] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => [1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1] => 0

[8,1,3,7,6,4,2,5] => [[.,[[.,.],[[[.,[.,.]],.],.]]],.] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [7,4,3,1,1,1] => 3

[3,4,2,8,5,1,7,6] => [[[.,.],.],[.,[[.,[[.,.],.]],.]]] => [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,2,1] => 3

[3,4,1,8,2,6,7,5] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,2] => 1

[2,5,7,6,3,1,8,4] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[2,5,7,3,8,4,6,1] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[1,3,7,5,8,6,4,2] => [.,[[.,.],[[[.,.],[.,.]],[.,.]]]] => [1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1] => 0

[1,8,3,2,4,7,5,6] => [.,[[[.,.],[.,[[.,[.,.]],.]]],.]] => [1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1,1,1] => 2

[3,2,4,7,8,5,6,1] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2,1] => 1

[8,2,1,3,4,5,7,6] => [[[.,.],[.,[.,[.,[[.,.],.]]]]],.] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,1,1,1,1] => 2

[5,4,8,7,3,2,6,1] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,4,3,2,1] => 5

[1,5,4,8,3,7,6,2] => [.,[[[[.,.],.],.],[[[.,.],.],.]]] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,2,1] => 4

[6,5,4,8,3,2,7,1] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,5,4,3,2,1] => 5

[7,3,1,4,8,2,5,6] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,2,2] => 0

[4,5,1,2,7,6,8,3] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [4,4,3,3,3] => 0

[1,3,8,4,5,7,2,6] => [.,[[.,.],[[.,[.,[[.,.],.]]],.]]] => [1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1,1] => 2

[1,3,7,4,2,8,5,6] => [.,[[.,.],[[.,[.,[.,.]]],[.,.]]]] => [1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1,1] => 0

[2,8,1,3,6,5,4,7] => [[.,.],[[.,[[[.,.],.],[.,.]]],.]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,1,1,1] => 2

[3,4,2,6,8,7,1,5] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2,1] => 2

[2,7,8,3,4,5,1,6] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1,1,1] => 0

[1,7,2,3,5,6,8,4] => [.,[[.,[.,[[.,.],[.,.]]]],[.,.]]] => [1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1] => 0

[3,4,6,2,8,5,7,1] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2,1] => 2

[3,4,6,1,8,5,2,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2] => 1

[4,1,6,7,5,8,2,3] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[3,8,2,4,5,6,7,1] => [[[.,.],.],[[.,[.,[.,[.,.]]]],.]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,2,1] => 2

[2,8,7,3,4,5,1,6] => [[.,.],[[[.,[.,[.,[.,.]]]],.],.]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,1,1,1,1] => 2

[4,5,7,1,2,6,8,3] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [4,4,3,3,3] => 0

[1,8,6,5,4,2,3,7] => [.,[[[[[.,[.,.]],.],.],[.,.]],.]] => [1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3,2] => 3

[1,8,7,2,3,5,4,6] => [.,[[[.,[.,[[.,.],[.,.]]]],.],.]] => [1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,1] => 2

[1,8,7,2,5,3,4,6] => [.,[[[.,[[.,[.,.]],[.,.]]],.],.]] => [1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2] => 2

[7,1,2,8,3,5,6,4] => [[.,[.,[.,[[.,.],[.,.]]]]],[.,.]] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1] => 0

[6,1,7,8,2,5,3,4] => [[.,[.,[[.,[.,.]],.]]],[.,[.,.]]] => [1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [5,5,5,2] => 1

[5,6,8,4,7,3,2,1] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [5,4,4,4,3,2,1] => 4

[7,1,8,3,4,2,6,5] => [[.,[[.,.],[.,[[.,.],.]]]],[.,.]] => [1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [6,6,2,1,1,1] => 1

[3,1,4,8,2,5,7,6] => [[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,2] => 2

[8,1,7,2,4,5,3,6] => [[.,[[.,[[.,.],[.,[.,.]]]],.]],.] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,1,1] => 2

[8,1,3,6,2,5,4,7] => [[.,[[.,.],[[[.,.],.],[.,.]]]],.] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2,1,1] => 2

[8,1,3,5,4,2,6,7] => [[.,[[.,.],[[.,.],[.,[.,.]]]]],.] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,1,1] => 1

[8,1,5,6,2,3,7,4] => [[.,[[.,[.,[.,.]]],[.,[.,.]]]],.] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [7,3,3,3] => 1

[8,1,4,5,3,2,6,7] => [[.,[[[.,.],.],[.,[.,[.,.]]]]],.] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2,1] => 2

[8,1,4,3,5,2,6,7] => [[.,[[[.,.],.],[.,[.,[.,.]]]]],.] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2,1] => 2

[2,6,3,1,5,4,7,8] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1,1] => 1

[7,3,1,4,5,2,6,8] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,2,2] => 0

[2,3,6,1,5,4,7,8] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1,1] => 1

[3,5,2,4,1,6,7,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => 1

[6,7,1,2,8,3,5,4] => [[.,[.,[.,[[.,.],.]]]],[.,[.,.]]] => [1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,5,5,1] => 1

[2,4,6,1,5,3,7,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[5,7,1,6,2,3,8,4] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4] => 0

[4,2,5,3,1,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1,1] => 0

[3,4,6,1,5,2,7,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2] => 0

[3,4,6,1,7,8,5,2] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2] => 0

[3,4,8,6,7,1,5,2] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,2] => 1

[8,1,7,2,5,6,3,4] => [[.,[[.,[[.,[.,.]],[.,.]]],.]],.] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [7,5,2,2] => 2

[7,1,2,8,5,6,3,4] => [[.,[.,[[.,[.,.]],[.,.]]]],[.,.]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2] => 0

[3,4,8,1,2,6,7,5] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,2] => 1

[3,4,6,5,1,8,2,7] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2] => 1

[2,4,7,6,5,8,1,3] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1,1] => 1

[8,1,3,5,7,4,6,2] => [[.,[[.,.],[[.,.],[[.,.],.]]]],.] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,1,1] => 2

[8,1,3,7,5,2,6,4] => [[.,[[.,.],[[[.,.],[.,.]],.]]],.] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [7,4,2,2,1,1] => 2

[3,4,8,7,5,1,6,2] => [[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,2] => 2

[2,1,4,8,7,5,6,3] => [[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,1,1] => 2

[2,4,8,1,6,7,3,5] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1,1] => 1

[5,1,8,2,6,7,3,4] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [6,4,4,4] => 1

[8,2,3,4,6,7,1,5] => [[[.,.],[.,[.,[[.,.],[.,.]]]]],.] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1,1,1,1] => 1

[5,4,8,3,2,6,1,7] => [[[[[.,.],.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,4,4,3,2,1] => 4

[1,5,3,2,8,4,7,6] => [.,[[[.,.],[.,.]],[[[.,.],.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1,1] => 2

[6,1,2,7,3,8,5,4] => [[.,[.,[.,[[.,.],.]]]],[.,[.,.]]] => [1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,5,5,1] => 1

[1,8,4,2,7,6,5,3] => [.,[[[.,[.,.]],[[[.,.],.],.]],.]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,2] => 3

[1,8,3,7,2,6,5,4] => [.,[[[.,.],[[[[.,.],.],.],.]],.]] => [1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,1,1] => 4

[1,5,4,8,3,2,7,6] => [.,[[[[.,.],.],.],[[[.,.],.],.]]] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,2,1] => 4

[1,2,6,3,8,5,7,4] => [.,[.,[[.,[[.,.],.]],[[.,.],.]]]] => [1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1] => 2

[1,5,2,6,8,4,7,3] => [.,[[.,[[.,.],.]],[.,[[.,.],.]]]] => [1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1] => 2

[1,3,8,7,6,2,5,4] => [.,[[.,.],[[[[[.,.],.],.],.],.]]] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,1] => 4

[1,6,4,5,2,3,7,8] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2] => 0

[1,7,4,5,2,3,6,8] => [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2] => 0

[1,7,3,5,2,4,6,8] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]] => [1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1] => 0

[1,6,3,5,2,4,7,8] => [.,[[[.,.],[[.,.],.]],[.,[.,.]]]] => [1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1] => 1

[1,6,3,4,2,5,7,8] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]] => [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1] => 0

[1,7,3,4,2,5,6,8] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1,1] => 0

[1,8,6,7,3,4,2,5] => [.,[[[[.,.],[.,[.,.]]],[.,.]],.]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,4,1,1,1] => 1

[1,7,3,4,2,6,5,8] => [.,[[[.,.],[.,[[.,.],.]]],[.,.]]] => [1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1,1] => 1

[1,5,2,8,4,7,3,6] => [.,[[.,[[.,.],.]],[[[.,.],.],.]]] => [1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1] => 3

[1,4,2,8,5,7,3,6] => [.,[[.,[.,.]],[[.,[[.,.],.]],.]]] => [1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2] => 2

[1,7,3,5,2,6,4,8] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]] => [1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1] => 0

[1,8,4,7,3,5,2,6] => [.,[[[[.,.],.],[[.,[.,.]],.]],.]] => [1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,2,1] => 3

[1,7,3,6,2,5,4,8] => [.,[[[.,.],[[[.,.],.],.]],[.,.]]] => [1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,1,1] => 2

[1,7,3,6,2,4,5,8] => [.,[[[.,.],[[.,[.,.]],.]],[.,.]]] => [1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1,1,1] => 1

[1,7,4,6,2,3,5,8] => [.,[[[.,[.,.]],[[.,.],.]],[.,.]]] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,2] => 1

[1,8,5,6,2,3,4,7] => [.,[[[.,[.,[.,.]]],[.,[.,.]]],.]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3] => 1

[1,8,5,6,2,4,3,7] => [.,[[[.,[[.,.],.]],[.,[.,.]]],.]] => [1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,1] => 2

[1,3,2,8,5,6,4,7] => [.,[[.,.],[[[.,.],[.,[.,.]]],.]]] => [1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1,1] => 1

[1,4,2,8,5,6,3,7] => [.,[[.,[.,.]],[[.,[.,[.,.]]],.]]] => [1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2] => 1

[1,5,2,8,4,6,3,7] => [.,[[.,[[.,.],.]],[[.,[.,.]],.]]] => [1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1] => 2

[1,6,2,8,4,5,3,7] => [.,[[.,[[.,.],[.,.]]],[[.,.],.]]] => [1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1] => 1

[8,1,2,4,5,3,6,7] => [[.,[.,[[.,.],[.,[.,[.,.]]]]]],.] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1,1] => 1

[1,6,4,7,2,8,3,5] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2] => 0

[1,4,7,3,5,8,2,6] => [.,[[[.,.],.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1] => 1

[1,7,5,3,4,8,2,6] => [.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,1,1] => 0

[1,7,6,4,8,2,3,5] => [.,[[[[.,[.,.]],[.,.]],.],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,2] => 1

[1,8,5,7,2,3,4,6] => [.,[[[.,[.,[.,.]]],[[.,.],.]],.]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,3] => 2

[1,6,5,8,2,3,4,7] => [.,[[[.,[.,[.,.]]],.],[[.,.],.]]] => [1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3] => 2

[1,5,7,4,8,2,3,6] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2] => 1

[1,7,2,8,6,3,4,5] => [.,[[.,[[.,[.,[.,.]]],.]],[.,.]]] => [1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [5,5,3] => 1

[1,4,8,7,2,3,5,6] => [.,[[.,[.,.]],[[[.,[.,.]],.],.]]] => [1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2] => 2

[1,5,8,7,2,3,4,6] => [.,[[.,[.,[.,.]]],[[[.,.],.],.]]] => [1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3] => 2

[6,1,8,2,7,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [6,5,5] => 1

[1,8,7,6,4,5,3,2] => [.,[[[[[[.,.],.],[.,.]],.],.],.]] => [1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,2,1] => 4

[2,4,1,7,5,8,3,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => 0

[3,4,7,1,6,8,2,5] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,2] => 1

[3,4,7,1,6,8,5,2] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,2] => 1

[2,4,1,7,5,3,6,8] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => 0

[3,4,1,7,8,6,2,5] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,2] => 1

[4,8,3,2,5,6,1,7] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [6,3,3,3,3,2,1] => 3

[3,4,7,1,6,2,5,8] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,2] => 1

[3,4,7,1,6,2,8,5] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,2] => 1

[2,4,7,3,6,1,5,8] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1,1] => 1

[6,5,8,4,3,2,7,1] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,5,4,3,2,1] => 5

[5,4,8,3,7,2,6,1] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,4,3,2,1] => 5

[6,5,8,4,7,3,2,1] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,5,4,3,2,1] => 5

[5,4,6,3,8,2,7,1] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [5,4,4,4,3,2,1] => 4

[3,2,1,8,7,6,4,5] => [[[.,.],.],[[[[.,[.,.]],.],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,2,2,1] => 4

[3,2,1,8,7,4,6,5] => [[[.,.],.],[[[.,[[.,.],.]],.],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,2,2,1] => 4

[4,3,8,5,7,6,2,1] => [[[[.,.],.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,3,3,2,1] => 4

[2,5,6,3,8,4,1,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1,1] => 1

[1,5,3,7,4,2,8,6] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1] => 0

[1,6,7,3,4,2,8,5] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]] => [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1] => 0

[1,7,6,3,4,2,8,5] => [.,[[[[.,.],[.,[.,.]]],.],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1,1,1] => 1

[1,2,7,4,3,6,8,5] => [.,[.,[[[.,.],[[.,.],.]],[.,.]]]] => [1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1] => 1

[1,7,8,2,4,5,6,3] => [.,[[.,[[.,.],[.,[.,.]]]],[.,.]]] => [1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1] => 0

[1,6,8,3,2,5,7,4] => [.,[[[.,.],[[.,.],.]],[[.,.],.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,1,1] => 2

[1,5,3,8,2,6,7,4] => [.,[[[.,.],[.,.]],[[.,[.,.]],.]]] => [1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1] => 1

[1,5,3,2,4,7,8,6] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1] => 0

[6,7,1,2,4,5,8,3] => [[.,[.,[[.,.],[.,.]]]],[.,[.,.]]] => [1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [5,5,5,1,1] => 0

[1,8,2,3,5,6,7,4] => [.,[[.,[.,[[.,.],[.,[.,.]]]]],.]] => [1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1] => 1

[8,7,1,2,4,5,6,3] => [[[.,[.,[[.,.],[.,[.,.]]]]],.],.] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,1,1] => 2

[7,8,1,2,4,5,6,3] => [[.,[.,[[.,.],[.,[.,.]]]]],[.,.]] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1] => 0

[1,4,7,6,3,2,5,8] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1] => 2

[4,8,3,2,7,6,1,5] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,3,2,1] => 5

[4,3,8,2,7,1,6,5] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,3,2,1] => 5

[4,3,2,8,1,7,6,5] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,3,2,1] => 5

[2,3,6,7,4,1,8,5] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1,1] => 0

[2,6,3,4,7,8,1,5] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1,1] => 0

[1,3,6,4,7,2,5,8] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => [1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1] => 0

[2,6,7,3,8,4,1,5] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1,1] => 0

[3,4,6,7,8,5,1,2] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2] => 0

[1,2,6,4,7,5,8,3] => [.,[.,[[[.,.],[.,.]],[.,[.,.]]]]] => [1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1] => 0

[1,6,2,5,4,7,8,3] => [.,[[.,[[[.,.],.],.]],[.,[.,.]]]] => [1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1] => 2

[1,8,2,5,6,3,7,4] => [.,[[.,[[.,[.,.]],[.,[.,.]]]],.]] => [1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2] => 1

[1,2,6,4,8,5,7,3] => [.,[.,[[[.,.],[.,.]],[[.,.],.]]]] => [1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1] => 1

[7,8,3,1,4,2,5,6] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,2,2] => 0

[7,1,2,5,4,8,6,3] => [[.,[.,[[[.,.],.],[.,.]]]],[.,.]] => [1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,1] => 1

[1,2,7,5,8,3,6,4] => [.,[.,[[[.,[.,.]],[.,.]],[.,.]]]] => [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2] => 0

[1,3,6,7,8,5,2,4] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1] => 1

[1,2,6,4,7,8,5,3] => [.,[.,[[[.,.],[.,.]],[.,[.,.]]]]] => [1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1] => 0

[1,3,5,7,4,6,8,2] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1] => 0

[1,3,5,4,7,2,6,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1] => 0

[1,3,5,4,7,8,2,6] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1] => 0

[1,3,5,4,7,2,8,6] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1] => 0

[1,3,5,7,4,8,2,6] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1] => 0

[1,3,5,7,4,8,6,2] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1] => 0

[1,3,5,7,8,4,2,6] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1] => 0

[1,6,3,2,7,4,8,5] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]] => [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1] => 0

[3,5,1,6,2,8,7,4] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,2] => 1

[1,3,7,2,5,4,8,6] => [.,[[.,.],[[[.,.],[.,.]],[.,.]]]] => [1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1] => 0

[1,3,7,5,2,4,8,6] => [.,[[.,.],[[[.,.],[.,.]],[.,.]]]] => [1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1] => 0

[2,5,3,7,4,8,1,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[1,5,7,4,8,3,2,6] => [.,[[[[.,.],.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2,1] => 2

[1,5,7,2,4,8,6,3] => [.,[[.,[[.,.],.]],[[.,.],[.,.]]]] => [1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1] => 1

[1,4,7,3,8,6,2,5] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1] => 2

[2,4,7,8,3,1,5,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => 0

[3,2,4,8,1,5,6,7] => [[[.,.],.],[.,[[.,[.,[.,.]]],.]]] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,2,1] => 2

[3,2,4,6,8,1,5,7] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2,1] => 2

[2,4,8,7,3,1,5,6] => [[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,1,1] => 2

[8,2,3,7,4,1,6,5] => [[[.,.],[.,[[.,[[.,.],.]],.]]],.] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,1,1,1] => 3

[2,3,7,8,4,1,6,5] => [[.,.],[.,[[.,[[.,.],.]],[.,.]]]] => [1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1,1,1] => 1

[2,3,7,4,1,6,8,5] => [[.,.],[.,[[.,[[.,.],.]],[.,.]]]] => [1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1,1,1] => 1

[2,4,7,3,1,5,8,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => 0

[1,4,6,5,8,3,7,2] => [.,[[[.,.],.],[[.,.],[[.,.],.]]]] => [1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1] => 2

[1,4,6,8,5,7,3,2] => [.,[[[.,.],.],[[.,.],[[.,.],.]]]] => [1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1] => 2

[1,4,6,8,5,3,7,2] => [.,[[[.,.],.],[[.,.],[[.,.],.]]]] => [1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1] => 2

[1,4,6,3,8,7,5,2] => [.,[[[.,.],.],[[.,.],[[.,.],.]]]] => [1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1] => 2

[2,4,8,7,1,5,3,6] => [[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,1,1] => 2

[2,4,8,7,3,5,1,6] => [[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,1,1] => 2

[2,3,4,7,8,5,6,1] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1,1] => 0

[2,3,7,1,4,8,6,5] => [[.,.],[.,[[.,[[.,.],.]],[.,.]]]] => [1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1,1,1] => 1

[2,6,1,3,7,8,5,4] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1,1] => 1

[1,5,3,2,6,4,7,8] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => [1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1] => 0

[1,5,3,2,6,7,4,8] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => [1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1] => 0

[1,7,3,2,8,5,4,6] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]] => [1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1] => 0

[1,3,2,7,5,4,8,6] => [.,[[.,.],[[[.,.],[.,.]],[.,.]]]] => [1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1] => 0

[1,6,2,8,5,3,4,7] => [.,[[.,[[.,[.,.]],.]],[[.,.],.]]] => [1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2] => 2

[1,5,2,6,8,4,3,7] => [.,[[.,[[.,.],.]],[.,[[.,.],.]]]] => [1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1] => 2

[1,5,7,2,8,4,3,6] => [.,[[.,[[.,.],.]],[[.,.],[.,.]]]] => [1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1] => 1

[1,5,8,2,7,4,3,6] => [.,[[.,[[.,.],.]],[[[.,.],.],.]]] => [1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1] => 3

[1,7,2,3,4,8,6,5] => [.,[[.,[.,[.,[[.,.],.]]]],[.,.]]] => [1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [5,5,1] => 1

[2,3,1,8,4,5,7,6] => [[.,.],[.,[[.,[.,[[.,.],.]]],.]]] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1,1,1] => 2

[7,1,2,3,4,6,8,5] => [[.,[.,[.,[.,[[.,.],.]]]]],[.,.]] => [1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [6,6,1] => 1

[6,1,2,3,4,8,7,5] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [6,5,5] => 1

[1,8,2,3,4,7,6,5] => [.,[[.,[.,[.,[[[.,.],.],.]]]],.]] => [1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [6,2,1] => 3

[8,1,2,3,4,6,7,5] => [[.,[.,[.,[.,[[.,.],[.,.]]]]]],.] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [7,1,1] => 1

[2,8,1,3,5,4,7,6] => [[.,.],[[.,[[.,.],[[.,.],.]]],.]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,1,1,1] => 2

[1,7,8,3,5,4,2,6] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]] => [1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1] => 0

[2,4,7,8,1,5,3,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => 0

[1,8,7,3,5,4,2,6] => [.,[[[[.,.],[[.,.],[.,.]]],.],.]] => [1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,1,1] => 2

[1,7,2,3,4,6,8,5] => [.,[[.,[.,[.,[[.,.],.]]]],[.,.]]] => [1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [5,5,1] => 1

[1,6,2,3,4,8,7,5] => [.,[[.,[.,[.,[.,.]]]],[[.,.],.]]] => [1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,4,4] => 1

[3,8,7,6,2,4,1,5] => [[[.,.],.],[[[[.,[.,.]],.],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,2,2,1] => 4

[1,8,7,6,4,2,3,5] => [.,[[[[[.,[.,.]],[.,.]],.],.],.]] => [1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,2] => 3

[2,8,7,6,3,1,4,5] => [[.,.],[[[[.,[.,[.,.]]],.],.],.]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,1,1,1] => 3

[1,8,7,6,2,4,3,5] => [.,[[[[.,[[.,.],[.,.]]],.],.],.]] => [1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,1] => 3

[1,8,7,6,3,4,2,5] => [.,[[[[[.,.],[.,[.,.]]],.],.],.]] => [1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,1,1] => 3

[2,8,1,4,5,6,7,3] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,1,1] => 1

[2,3,7,1,6,8,5,4] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1,1,1] => 2

[1,3,7,2,6,8,5,4] => [.,[[.,.],[[[[.,.],.],.],[.,.]]]] => [1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1,1] => 2

[1,2,7,5,6,3,8,4] => [.,[.,[[[.,[.,.]],[.,.]],[.,.]]]] => [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2] => 0

[3,8,7,6,2,1,5,4] => [[[.,.],.],[[[[[.,.],.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,2,1] => 5

[2,3,7,5,6,8,1,4] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1,1] => 0

[3,8,7,6,4,2,1,5] => [[[.,.],.],[[[[.,[.,.]],.],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,2,2,1] => 4

[3,4,6,1,5,7,2,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2] => 0

[2,4,1,5,8,6,3,7] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,1,1] => 1

[1,3,6,5,7,8,2,4] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1] => 1

[2,3,1,6,8,5,7,4] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1,1] => 2

[1,5,8,3,4,6,7,2] => [.,[[[.,.],[.,.]],[[.,[.,.]],.]]] => [1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1] => 1

[2,3,8,1,6,5,4,7] => [[.,.],[.,[[[[.,.],.],[.,.]],.]]] => [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1,1,1] => 2

[8,1,4,7,2,5,3,6] => [[.,[[.,[.,.]],[[.,[.,.]],.]]],.] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,2,2] => 2

[6,1,2,7,5,3,8,4] => [[.,[.,[[.,[.,.]],.]]],[.,[.,.]]] => [1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [5,5,5,2] => 1

[1,4,5,7,2,6,8,3] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2] => 0

[2,3,8,7,6,5,1,4] => [[.,.],[.,[[[[[.,.],.],.],.],.]]] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,1,1] => 4

[1,2,8,7,3,6,5,4] => [.,[.,[[[.,[[[.,.],.],.]],.],.]]] => [1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1] => 4

[1,5,8,7,3,2,6,4] => [.,[[[.,.],[.,.]],[[[.,.],.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1,1] => 2

[1,5,8,3,7,2,6,4] => [.,[[[.,.],[.,.]],[[[.,.],.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1,1] => 2

[1,6,8,4,2,7,5,3] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,2] => 1

[1,5,8,4,2,7,6,3] => [.,[[[.,[.,.]],.],[[[.,.],.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,2] => 3

[1,5,8,2,3,7,6,4] => [.,[[.,[.,[.,.]]],[[[.,.],.],.]]] => [1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3] => 2

[5,6,8,4,3,2,1,7] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [5,4,4,4,3,2,1] => 4

[1,6,2,8,7,5,4,3] => [.,[[.,[[[.,.],.],.]],[[.,.],.]]] => [1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,1] => 3

[1,6,4,8,7,2,5,3] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,2] => 1

[1,6,4,8,2,7,5,3] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,2] => 1

[1,4,5,8,2,7,6,3] => [.,[[.,[.,.]],[.,[[[.,.],.],.]]]] => [1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2] => 2

[2,4,5,8,3,7,1,6] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,1,1] => 2

[1,4,5,8,3,2,7,6] => [.,[[[.,.],.],[.,[[[.,.],.],.]]]] => [1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,1] => 3

[2,3,5,4,8,7,1,6] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1,1,1] => 2

[1,6,3,4,8,2,7,5] => [.,[[[.,.],[.,[.,.]]],[[.,.],.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1] => 1

[1,3,5,4,8,2,7,6] => [.,[[.,.],[[.,.],[[[.,.],.],.]]]] => [1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1,1] => 2

[7,1,2,4,3,8,6,5] => [[.,[.,[[.,.],[[.,.],.]]]],[.,.]] => [1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [6,6,2,1,1] => 1

[3,4,2,6,7,8,1,5] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2,1] => 1

[3,1,4,2,6,8,7,5] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2] => 1

[2,6,7,3,5,4,1,8] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1,1] => 1

[2,7,8,3,5,4,1,6] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1,1] => 0

[2,1,6,3,7,5,4,8] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1,1] => 1

[2,7,1,3,6,8,4,5] => [[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1,1,1,1] => 1

[4,6,1,2,7,5,3,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[2,10,9,8,7,6,5,4,1,3] => [[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,2,1,1] => 7

[3,2,8,7,6,5,1,4] => [[[.,.],.],[[[[[.,.],.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,2,1] => 5

[4,8,5,7,6,3,2,1] => [[[[.,.],.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,3,3,2,1] => 4

[5,8,1,6,7,2,3,4] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [6,4,4,4] => 1

[5,7,6,1,8,2,3,4] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4] => 0

[5,6,8,1,7,2,3,4] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [5,4,4,4] => 1

[2,4,5,7,3,6,8,1] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1,1] => 0

[2,4,5,3,6,8,1,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,1,1] => 1

[3,5,6,4,1,7,8,2] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 0

[3,1,5,6,7,4,8,2] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 0

[1,6,7,3,4,5,8,2] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]] => [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1] => 0

[3,5,2,6,1,7,8,4] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => 1

[3,5,2,6,7,4,8,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => 1

[7,1,3,4,6,8,2,5] => [[.,[[.,.],[.,[[.,.],.]]]],[.,.]] => [1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [6,6,2,1,1,1] => 1

[4,6,7,1,2,5,8,3] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[1,5,4,6,2,7,8,3] => [.,[[[.,[.,.]],.],[.,[.,[.,.]]]]] => [1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2] => 1

[5,6,4,1,2,7,8,3] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3] => 1

[5,6,7,4,1,2,8,3] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3] => 1

[1,7,8,5,6,3,4,2] => [.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,1,1] => 0

[1,7,5,8,6,3,4,2] => [.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,1,1] => 0

[1,5,7,8,6,3,4,2] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1] => 0

[1,5,7,8,3,6,4,2] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1] => 0

[1,3,7,8,5,6,4,2] => [.,[[.,.],[[[.,.],[.,.]],[.,.]]]] => [1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1] => 0

[1,7,5,3,8,6,4,2] => [.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,1,1] => 0

[1,7,5,8,3,6,4,2] => [.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,1,1] => 0

[1,7,8,5,3,6,4,2] => [.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,1,1] => 0

[1,7,8,3,5,6,4,2] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]] => [1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1] => 0

[1,7,3,8,5,6,4,2] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]] => [1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1] => 0

[1,7,3,5,8,6,4,2] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]] => [1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1] => 0

[1,5,3,7,8,6,4,2] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1] => 0

[2,5,7,3,8,4,1,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[8,7,1,2,5,3,4,6] => [[[.,[.,[[.,[.,.]],[.,.]]]],.],.] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [7,6,2,2] => 2

[7,1,3,4,6,8,5,2] => [[.,[[.,.],[.,[[.,.],.]]]],[.,.]] => [1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [6,6,2,1,1,1] => 1

[2,8,3,6,7,5,1,4] => [[.,.],[[.,[[[.,.],.],[.,.]]],.]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,1,1,1] => 2

[3,2,4,5,8,1,7,6] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,2,1] => 3

[2,5,7,8,3,6,1,4] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[2,4,6,7,3,5,8,1] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[3,4,8,2,5,7,6,1] => [[[.,.],.],[.,[[.,[[.,.],.]],.]]] => [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,2,1] => 3

[2,6,3,7,5,1,8,4] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1,1] => 1

[2,4,5,8,7,6,1,3] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,1,1] => 2

[3,1,5,6,2,8,7,4] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,2] => 1

[1,2,4,6,3,8,7,5] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => [1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1] => 1

[3,4,5,1,8,7,6,2] => [[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,2] => 2

[1,4,5,2,8,7,6,3] => [.,[[.,[.,.]],[.,[[[.,.],.],.]]]] => [1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2] => 2

[1,6,4,2,8,7,5,3] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,2] => 1

[1,5,3,6,2,8,7,4] => [.,[[[.,.],[.,.]],[.,[[.,.],.]]]] => [1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1] => 1

[1,5,8,3,2,7,6,4] => [.,[[[.,.],[.,.]],[[[.,.],.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1,1] => 2

[1,3,8,2,4,7,6,5] => [.,[[.,.],[[.,[[[.,.],.],.]],.]]] => [1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,1,1] => 3

[1,5,2,3,8,7,6,4] => [.,[[.,[.,[.,.]]],[[[.,.],.],.]]] => [1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3] => 2

[1,6,3,7,5,8,4,2] => [.,[[[.,.],[[.,.],.]],[.,[.,.]]]] => [1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1] => 1

[1,3,7,4,5,8,6,2] => [.,[[.,.],[[.,[.,[.,.]]],[.,.]]]] => [1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1,1] => 0

[1,6,5,2,8,3,7,4] => [.,[[[.,[.,[.,.]]],.],[[.,.],.]]] => [1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3] => 2

[1,8,2,7,3,6,5,4] => [.,[[.,[[.,[[[.,.],.],.]],.]],.]] => [1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1] => 4

[2,1,3,8,4,7,5,6] => [[.,.],[.,[[.,[[.,[.,.]],.]],.]]] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1,1,1,1] => 2

[8,1,2,7,4,3,6,5] => [[.,[.,[[[.,.],[[.,.],.]],.]]],.] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,1] => 3

[8,2,3,1,4,6,5,7] => [[[.,.],[.,[.,[[.,.],[.,.]]]]],.] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1,1,1,1] => 1

[2,4,8,3,1,5,6,7] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,1,1] => 1

[3,4,2,7,1,5,6,8] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2,1] => 1

[1,3,7,2,8,4,6,5] => [.,[[.,.],[[.,[[.,.],.]],[.,.]]]] => [1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1,1] => 1

[1,4,2,5,8,6,7,3] => [.,[[.,[.,.]],[.,[[.,[.,.]],.]]]] => [1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2] => 1

[1,7,5,8,6,4,3,2] => [.,[[[[[.,.],.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,2,1] => 2

[1,3,8,7,4,6,5,2] => [.,[[.,.],[[[.,[[.,.],.]],.],.]]] => [1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,1,1] => 3

[1,2,8,7,6,3,5,4] => [.,[.,[[[[.,[[.,.],.]],.],.],.]]] => [1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1] => 4

[2,3,1,8,7,4,5,6] => [[.,.],[.,[[[.,[.,[.,.]]],.],.]]] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1,1,1,1] => 2

[2,4,1,8,5,7,3,6] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,1,1] => 2

[8,1,2,3,4,5,9,6,7] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,7] => 0

[8,1,2,3,4,9,5,6,7] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,7] => 0

[8,1,2,9,3,4,5,6,7] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,7] => 0

[8,1,9,2,3,4,5,6,7] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,7] => 0

[8,2,3,4,6,1,5,7] => [[[.,.],[.,[.,[[.,.],[.,.]]]]],.] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1,1,1,1] => 1

[8,2,3,4,7,5,1,6] => [[[.,.],[.,[.,[[.,[.,.]],.]]]],.] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,1,1,1,1] => 2

[8,2,3,4,7,1,6,5] => [[[.,.],[.,[.,[[[.,.],.],.]]]],.] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1,1,1,1] => 3

[4,8,3,7,5,2,1,6] => [[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,3,3,2,1] => 4

[8,2,3,4,1,7,5,6] => [[[.,.],[.,[.,[[.,[.,.]],.]]]],.] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,1,1,1,1] => 2

[7,2,3,4,1,5,8,6] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1,1,1] => 0

[1,2,3,4,8,7,5,6] => [.,[.,[.,[.,[[[.,[.,.]],.],.]]]]] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [3,2] => 2

[1,2,8,5,3,4,6,7] => [.,[.,[[[.,[.,.]],[.,[.,.]]],.]]] => [1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2] => 1

[1,8,4,2,3,5,6,7] => [.,[[[.,[.,.]],[.,[.,[.,.]]]],.]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2] => 1

[1,6,4,8,5,2,7,3] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,2] => 1

[2,3,8,5,7,1,6,4] => [[.,.],[.,[[[.,.],[[.,.],.]],.]]] => [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1,1,1] => 2

[2,3,8,6,7,5,1,4] => [[.,.],[.,[[[[.,.],.],[.,.]],.]]] => [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1,1,1] => 2

[1,3,8,6,7,5,2,4] => [.,[[.,.],[[[[.,.],.],[.,.]],.]]] => [1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1,1] => 2

[5,7,1,8,2,6,3,4] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4] => 0

[7,1,8,2,4,6,5,3] => [[.,[.,[[.,.],[[.,.],.]]]],[.,.]] => [1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [6,6,2,1,1] => 1

[1,6,2,8,4,7,5,3] => [.,[[.,[[.,.],[.,.]]],[[.,.],.]]] => [1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1] => 1

[1,3,8,5,7,2,6,4] => [.,[[.,.],[[[.,.],[[.,.],.]],.]]] => [1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1,1] => 2

[1,8,3,7,2,5,6,4] => [.,[[[.,.],[[[.,.],[.,.]],.]],.]] => [1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,1,1] => 2

[5,7,1,8,2,3,6,4] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4] => 0

[7,1,8,2,3,5,6,4] => [[.,[.,[.,[[.,.],[.,.]]]]],[.,.]] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1] => 0

[2,8,3,6,7,1,5,4] => [[.,.],[[.,[[[.,.],.],[.,.]]],.]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,1,1,1] => 2

[1,8,7,2,3,6,4,5] => [.,[[[.,[.,[[.,[.,.]],.]]],.],.]] => [1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [6,5,2] => 3

[1,8,7,2,6,3,4,5] => [.,[[[.,[[.,[.,[.,.]]],.]],.],.]] => [1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [6,5,3] => 3

[1,8,7,3,6,2,4,5] => [.,[[[[.,.],[[.,[.,.]],.]],.],.]] => [1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1,1,1] => 3

[1,8,2,7,6,3,4,5] => [.,[[.,[[[.,[.,[.,.]]],.],.]],.]] => [1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [6,4,3] => 3

[1,5,2,8,6,7,4,3] => [.,[[.,[[.,.],.]],[[.,[.,.]],.]]] => [1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1] => 2

[1,2,8,6,7,5,3,4] => [.,[.,[[[[.,[.,.]],.],[.,.]],.]]] => [1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2] => 2

[1,8,3,6,7,5,2,4] => [.,[[[.,.],[[[.,.],.],[.,.]]],.]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,1,1] => 2

[8,1,3,7,5,6,2,4] => [[.,[[.,.],[[[.,.],[.,.]],.]]],.] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [7,4,2,2,1,1] => 2

[8,1,4,2,6,7,5,3] => [[.,[[.,[.,.]],[[.,.],[.,.]]]],.] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2,2] => 1

[1,2,8,6,7,3,5,4] => [.,[.,[[[.,[[.,.],.]],[.,.]],.]]] => [1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1] => 2

[8,1,2,7,3,6,4,5] => [[.,[.,[[.,[[.,[.,.]],.]],.]]],.] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [7,4,2] => 3

[8,1,7,2,6,3,4,5] => [[.,[[.,[[.,[.,[.,.]]],.]],.]],.] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [7,5,3] => 3

[8,1,7,2,3,6,4,5] => [[.,[[.,[.,[[.,[.,.]],.]]],.]],.] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [7,5,2] => 3

[8,1,3,7,2,5,6,4] => [[.,[[.,.],[[[.,.],[.,.]],.]]],.] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [7,4,2,2,1,1] => 2

[1,8,3,6,7,2,5,4] => [.,[[[.,.],[[[.,.],.],[.,.]]],.]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,1,1] => 2

[1,7,8,2,3,6,5,4] => [.,[[.,[.,[[[.,.],.],.]]],[.,.]]] => [1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1] => 2

[8,7,1,2,3,6,4,5] => [[[.,[.,[.,[[.,[.,.]],.]]]],.],.] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [7,6,2] => 3

[1,7,4,8,6,2,3,5] => [.,[[[.,[.,.]],[[.,.],.]],[.,.]]] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,2] => 1

[4,2,5,6,7,1,8,3] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1,1] => 0

[8,1,3,6,7,2,4,5] => [[.,[[.,.],[[.,[.,.]],[.,.]]]],.] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,3,1,1,1] => 1

[8,1,4,2,7,5,3,6] => [[.,[[.,[.,.]],[[.,[.,.]],.]]],.] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,2,2] => 2

[1,7,5,2,8,6,3,4] => [.,[[[.,[.,[.,.]]],[.,.]],[.,.]]] => [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3] => 0

[1,5,8,4,2,6,3,7] => [.,[[[.,[.,.]],.],[[.,[.,.]],.]]] => [1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,2] => 2

[1,4,2,6,5,7,3,8] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2] => 0

[5,6,1,4,2,7,3,8] => [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,2] => 1

[2,4,1,6,5,7,3,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[1,5,2,6,4,7,3,8] => [.,[[.,[[.,.],.]],[.,[.,[.,.]]]]] => [1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1] => 1

[2,5,1,6,4,7,3,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1,1] => 1

[4,5,2,6,1,7,3,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1,1] => 0

[4,5,1,6,3,7,2,8] => [[.,[[.,.],.]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1] => 1

[4,5,3,6,1,7,2,8] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,2] => 1

[1,4,3,6,2,7,5,8] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1] => 1

[3,4,1,6,5,7,2,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2] => 0

[3,5,4,6,1,7,2,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 0

[3,5,1,6,4,7,2,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 0

[1,5,3,6,4,7,2,8] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => [1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1] => 0

[1,5,3,6,2,7,4,8] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => [1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1] => 0

[3,5,2,6,1,7,4,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => 1

[3,5,2,6,4,7,1,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => 1

[3,4,2,6,1,7,5,8] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2,1] => 1

[2,4,3,6,1,7,5,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[2,5,3,6,4,7,1,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1,1] => 0

[2,5,3,6,1,7,4,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1,1] => 0

[1,5,7,2,8,3,6,4] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3] => 0

[2,5,7,3,1,8,4,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[2,1,5,6,8,4,3,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1,1] => 2

[1,3,7,2,8,5,4,6] => [.,[[.,.],[[[.,.],[.,.]],[.,.]]]] => [1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1] => 0

[1,5,4,3,6,8,2,7] => [.,[[[[.,.],.],.],[.,[[.,.],.]]]] => [1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1] => 3

[1,6,4,5,7,8,3,2] => [.,[[[[.,.],.],[.,.]],[.,[.,.]]]] => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2,1] => 1

[2,1,5,6,8,4,7,3] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1,1] => 2

[2,1,5,6,8,7,3,4] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1,1] => 1

[1,5,7,8,4,2,6,3] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2] => 1

[3,4,6,8,5,7,2,1] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2,1] => 2

[2,5,6,8,1,7,4,3] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1,1] => 2

[4,5,6,1,8,7,3,2] => [[.,[[.,.],.]],[.,[.,[[.,.],.]]]] => [1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3,1] => 2

[2,4,7,1,3,6,5,8] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1,1] => 1

[2,6,1,3,7,5,4,8] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1,1] => 1

[5,1,6,2,7,4,3,8] => [[.,[.,[[.,.],.]]],[.,[.,[.,.]]]] => [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,1] => 1

[5,4,1,6,2,7,3,8] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3] => 1

[5,1,6,4,2,7,3,8] => [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,2] => 1

[3,4,2,6,7,1,5,8] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2,1] => 1

[3,5,6,2,4,7,1,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => 1

[1,7,8,2,5,4,3,6] => [.,[[.,[[[.,.],.],[.,.]]],[.,.]]] => [1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1] => 1

[2,5,6,4,7,1,3,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1,1] => 1

[1,4,5,3,7,8,2,6] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]] => [1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1] => 1

[1,4,8,2,7,6,3,5] => [.,[[.,[.,.]],[[[[.,.],.],.],.]]] => [1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,2] => 3

[1,4,6,7,3,5,8,2] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1] => 1

[2,3,1,8,4,7,6,5] => [[.,.],[.,[[.,[[[.,.],.],.]],.]]] => [1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,1,1,1] => 3

[1,6,3,8,2,7,5,4] => [.,[[[.,.],[[.,.],.]],[[.,.],.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,1,1] => 2

[1,7,5,3,8,2,6,4] => [.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,1,1] => 0

[1,7,6,4,3,8,2,5] => [.,[[[[[.,.],.],[.,.]],.],[.,.]]] => [1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,2,1] => 2

[1,6,8,2,5,7,4,3] => [.,[[.,[[[.,.],.],.]],[[.,.],.]]] => [1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,1] => 3

[1,5,8,2,7,4,6,3] => [.,[[.,[[.,.],.]],[[[.,.],.],.]]] => [1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1] => 3

[5,6,4,8,3,7,2,1] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [5,4,4,4,3,2,1] => 4

[2,4,3,8,6,7,1,5] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1,1] => 1

[1,8,2,7,4,5,3,6] => [.,[[.,[[[.,.],[.,[.,.]]],.]],.]] => [1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,1,1] => 2

[2,3,1,8,5,6,4,7] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1,1,1] => 1

[1,8,5,6,3,4,2,7] => [.,[[[[.,.],[.,.]],[.,[.,.]]],.]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,1,1] => 1

[1,8,5,6,4,7,2,3] => [.,[[[[.,[.,.]],.],[.,[.,.]]],.]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,2] => 2

[3,4,2,6,5,8,1,7] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2,1] => 2

[1,8,3,5,4,7,2,6] => [.,[[[.,.],[[.,.],[[.,.],.]]],.]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,1,1] => 2

[3,4,2,7,1,8,5,6] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2,1] => 1

[2,4,3,8,1,7,5,6] => [[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,1,1] => 2

[2,6,3,8,1,7,4,5] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1,1] => 1

[2,7,1,8,3,6,4,5] => [[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1,1,1,1] => 1

[3,4,7,5,8,6,2,1] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2,1] => 1

[1,5,8,2,7,3,6,4] => [.,[[.,[.,[.,.]]],[[[.,.],.],.]]] => [1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3] => 2

[1,7,4,8,6,2,5,3] => [.,[[[.,[.,.]],[[.,.],.]],[.,.]]] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,2] => 1

[6,1,2,7,4,5,8,3] => [[.,[.,[[.,.],[.,.]]]],[.,[.,.]]] => [1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [5,5,5,1,1] => 0

[2,5,8,3,4,1,6,7] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1,1] => 1

[2,6,7,3,8,5,4,1] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1,1] => 1

[1,6,8,4,7,2,3,5] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,2] => 1

[1,4,5,7,8,2,6,3] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2] => 0

[3,4,5,7,8,6,1,2] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2] => 0

[3,4,5,7,6,8,1,2] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2] => 0

[3,4,5,6,8,7,1,2] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,2] => 1

[1,4,5,8,7,2,3,6] => [.,[[.,[.,.]],[.,[[[.,.],.],.]]]] => [1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2] => 2

[1,2,5,8,3,6,4,7] => [.,[.,[[.,[.,.]],[[.,[.,.]],.]]]] => [1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2] => 1

[1,4,5,8,6,2,3,7] => [.,[[.,[.,.]],[.,[[.,[.,.]],.]]]] => [1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2] => 1

[1,6,7,4,8,2,5,3] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2] => 0

[1,4,5,6,8,2,7,3] => [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => [1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2] => 1

[1,4,5,8,6,2,7,3] => [.,[[.,[.,.]],[.,[[.,[.,.]],.]]]] => [1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2] => 1

[1,2,5,8,3,4,7,6] => [.,[.,[[.,[.,.]],[[[.,.],.],.]]]] => [1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2] => 2

[1,6,7,2,3,5,8,4] => [.,[[.,[.,[[.,.],.]]],[.,[.,.]]]] => [1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1] => 1

[7,8,1,2,3,5,4,6] => [[.,[.,[.,[[.,.],[.,.]]]]],[.,.]] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1] => 0

[1,6,7,2,3,5,4,8] => [.,[[.,[.,[[.,.],.]]],[.,[.,.]]]] => [1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1] => 1

[1,4,5,7,6,2,3,8] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2] => 0

[1,2,5,7,3,6,4,8] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => [1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2] => 0

[1,2,5,7,3,6,8,4] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => [1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2] => 0

[1,6,8,2,3,5,7,4] => [.,[[.,[.,[[.,.],.]]],[[.,.],.]]] => [1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1] => 2

[1,6,8,4,5,2,3,7] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,2] => 1

[1,6,8,4,5,2,7,3] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,2] => 1

[1,6,8,2,3,4,7,5] => [.,[[.,[.,[.,[.,.]]]],[[.,.],.]]] => [1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,4,4] => 1

[1,6,8,2,3,7,4,5] => [.,[[.,[.,[.,[.,.]]]],[[.,.],.]]] => [1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,4,4] => 1

[1,4,5,7,6,2,8,3] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2] => 0

[7,8,1,2,3,4,6,5] => [[.,[.,[.,[.,[[.,.],.]]]]],[.,.]] => [1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [6,6,1] => 1

[7,8,1,2,3,6,4,5] => [[.,[.,[.,[[.,[.,.]],.]]]],[.,.]] => [1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [6,6,2] => 1

[1,6,7,2,3,8,5,4] => [.,[[.,[.,[[.,.],.]]],[.,[.,.]]]] => [1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1] => 1

[1,2,5,6,3,8,7,4] => [.,[.,[[.,[.,.]],[.,[[.,.],.]]]]] => [1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2] => 1

[1,7,8,4,3,5,2,6] => [.,[[[[.,.],.],[.,[.,.]]],[.,.]]] => [1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2,1] => 1

[1,6,7,8,4,3,2,5] => [.,[[[[.,.],.],[.,.]],[.,[.,.]]]] => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2,1] => 1

[1,2,7,8,6,3,4,5] => [.,[.,[[[.,[.,[.,.]]],.],[.,.]]]] => [1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [4,4,3] => 1

[1,7,2,8,4,5,6,3] => [.,[[.,[[.,.],[.,[.,.]]]],[.,.]]] => [1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1] => 0

[6,7,1,2,8,5,3,4] => [[.,[.,[[.,[.,.]],.]]],[.,[.,.]]] => [1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [5,5,5,2] => 1

[1,6,7,8,4,2,5,3] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2] => 0

[6,1,2,4,7,3,8,5] => [[.,[.,[[.,.],[.,.]]]],[.,[.,.]]] => [1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [5,5,5,1,1] => 0

[1,7,5,3,6,4,8,2] => [.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,1,1] => 0

[5,1,2,6,7,4,8,3] => [[.,[.,[[.,.],.]]],[.,[.,[.,.]]]] => [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,1] => 1

[1,6,5,7,8,3,4,2] => [.,[[[[.,.],[.,.]],.],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,1,1] => 1

[6,1,2,3,7,5,4,8] => [[.,[.,[.,[[.,.],.]]]],[.,[.,.]]] => [1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,5,5,1] => 1

[1,5,7,3,4,8,6,2] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1] => 0

[1,5,8,3,4,7,6,2] => [.,[[[.,.],[.,.]],[[[.,.],.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1,1] => 2

[7,1,2,3,5,6,4,8] => [[.,[.,[.,[[.,.],[.,.]]]]],[.,.]] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1] => 0

[8,1,2,3,5,6,4,7] => [[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1] => 1

[8,1,2,3,5,4,7,6] => [[.,[.,[.,[[.,.],[[.,.],.]]]]],.] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,1] => 2

[3,8,1,2,4,5,7,6] => [[.,[.,.]],[[.,[.,[[.,.],.]]],.]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2,2] => 2

[1,6,4,3,7,5,8,2] => [.,[[[[.,.],.],[.,.]],[.,[.,.]]]] => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2,1] => 1

[1,5,7,3,4,6,8,2] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1] => 0

[7,1,2,3,5,4,8,6] => [[.,[.,[.,[[.,.],[.,.]]]]],[.,.]] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1] => 0

[6,1,2,3,5,8,4,7] => [[.,[.,[.,[[.,.],.]]]],[[.,.],.]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [6,5,5,1] => 2

[6,1,2,3,5,7,4,8] => [[.,[.,[.,[[.,.],.]]]],[.,[.,.]]] => [1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,5,5,1] => 1

[5,1,2,3,7,6,4,8] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4] => 0

[5,1,2,3,8,6,4,7] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [6,4,4,4] => 1

[1,5,6,3,4,7,8,2] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => [1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1] => 0

[8,2,3,7,4,5,1,6] => [[[.,.],[.,[[.,[.,[.,.]]],.]]],.] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,1,1,1,1] => 2

[7,2,3,4,5,8,6,1] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1,1,1] => 0

[8,2,3,4,5,7,1,6] => [[[.,.],[.,[.,[.,[[.,.],.]]]]],.] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,1,1,1,1] => 2

[8,2,3,5,7,1,4,6] => [[[.,.],[.,[[.,.],[[.,.],.]]]],.] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,1,1,1] => 2

[7,2,3,4,8,5,1,6] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1,1,1] => 0

[1,8,3,2,4,5,7,6] => [.,[[[.,.],[.,[.,[[.,.],.]]]],.]] => [1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1,1,1] => 2

[1,5,3,8,7,6,4,2] => [.,[[[.,.],[.,.]],[[[.,.],.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1,1] => 2

[1,2,8,7,5,6,3,4] => [.,[.,[[[[.,[.,.]],[.,.]],.],.]]] => [1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2] => 2

[1,4,8,6,5,7,2,3] => [.,[[.,[.,.]],[[[.,.],[.,.]],.]]] => [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2] => 1

[1,7,8,5,4,6,3,2] => [.,[[[[[.,.],.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,2,1] => 2

[1,5,8,4,6,3,7,2] => [.,[[[[.,.],.],.],[[.,[.,.]],.]]] => [1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,2,1] => 3

[5,8,4,3,6,2,1,7] => [[[[[.,.],.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,4,4,3,2,1] => 4

[1,8,3,6,5,2,7,4] => [.,[[[.,.],[[[.,.],.],[.,.]]],.]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,1,1] => 2

[1,8,2,4,7,6,5,3] => [.,[[.,[[.,.],[[[.,.],.],.]]],.]] => [1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,1] => 3

[4,3,8,2,5,1,6,7] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [6,3,3,3,3,2,1] => 3

[8,1,3,4,5,7,6,2] => [[.,[[.,.],[.,[.,[[.,.],.]]]]],.] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,1,1,1] => 2

[1,8,2,5,6,3,4,7] => [.,[[.,[[.,[.,.]],[.,[.,.]]]],.]] => [1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2] => 1

[1,3,7,5,6,2,4,8] => [.,[[.,.],[[[.,.],[.,.]],[.,.]]]] => [1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1] => 0

[1,6,7,4,3,5,2,8] => [.,[[[[.,.],.],[.,.]],[.,[.,.]]]] => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2,1] => 1

[1,8,5,2,3,7,4,6] => [.,[[[.,[.,[.,.]]],[[.,.],.]],.]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,3] => 2

[1,8,2,5,3,6,7,4] => [.,[[.,[[.,[.,.]],[.,[.,.]]]],.]] => [1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2] => 1

[1,6,7,4,3,2,8,5] => [.,[[[[.,.],.],[.,.]],[.,[.,.]]]] => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2,1] => 1

[1,5,2,6,4,7,8,3] => [.,[[.,[[.,.],.]],[.,[.,[.,.]]]]] => [1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1] => 1

[1,5,4,6,2,3,7,8] => [.,[[[.,[.,.]],.],[.,[.,[.,.]]]]] => [1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2] => 1

[6,1,2,8,3,7,4,5] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [6,5,5] => 1

[1,5,4,2,6,7,3,8] => [.,[[[.,[.,.]],.],[.,[.,[.,.]]]]] => [1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2] => 1

[1,6,2,7,5,8,4,3] => [.,[[.,[[[.,.],.],.]],[.,[.,.]]]] => [1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1] => 2

[1,3,2,7,8,5,6,4] => [.,[[.,.],[[[.,.],[.,.]],[.,.]]]] => [1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1] => 0

[1,6,2,4,8,7,3,5] => [.,[[.,[[.,.],[.,.]]],[[.,.],.]]] => [1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1] => 1

[1,5,4,2,6,3,8,7] => [.,[[[.,[.,.]],.],[.,[[.,.],.]]]] => [1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2] => 2

[2,1,9,8,7,6,5,4,3] => [[.,.],[[[[[[[.,.],.],.],.],.],.],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,1,1] => 6

[1,2,9,8,7,6,5,4,3] => [.,[.,[[[[[[[.,.],.],.],.],.],.],.]]] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,1] => 6

[1,3,2,9,8,7,6,5,4] => [.,[[.,.],[[[[[[.,.],.],.],.],.],.]]] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,1,1] => 5

[1,2,3,9,8,7,6,5,4] => [.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]] => [1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,1] => 5

[1,2,4,3,9,8,7,6,5] => [.,[.,[[.,.],[[[[[.,.],.],.],.],.]]]] => [1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,1,1] => 4

[1,2,3,4,9,8,7,6,5] => [.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]] => [1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1] => 4

[1,2,3,5,4,9,8,7,6] => [.,[.,[.,[[.,.],[[[[.,.],.],.],.]]]]] => [1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1,1] => 3

[1,2,3,4,5,9,8,7,6] => [.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]] => [1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1] => 3

[1,2,3,4,6,5,9,8,7] => [.,[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]] => [1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1] => 2

[1,2,3,4,5,7,6,9,8] => [.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]] => [1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1] => 1

[1,2,10,9,8,7,6,5,4,3] => [.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,3,2,1] => 7

[1,2,3,10,9,8,7,6,5,4] => [.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]] => [1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,2,1] => 6

[1,2,3,4,10,9,8,7,6,5] => [.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]] => [1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2,1] => 5

[1,2,3,4,5,6,10,9,8,7] => [.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]] => [1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1] => 3

[1,2,3,4,5,6,7,10,9,8] => [.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]] => [1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [2,1] => 2

[1,7,8,4,5,6,2,3] => [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2] => 0

[1,5,8,4,2,6,7,3] => [.,[[[.,[.,.]],.],[[.,[.,.]],.]]] => [1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,2] => 2

[1,6,3,8,5,2,7,4] => [.,[[[.,.],[[.,.],.]],[[.,.],.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,1,1] => 2

[1,7,3,4,8,6,2,5] => [.,[[[.,.],[.,[[.,.],.]]],[.,.]]] => [1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1,1] => 1

[7,1,9,2,3,4,5,6,8] => [[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [7,6,6] => 1

[8,1,10,2,3,4,5,6,7,9] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,1,0,0] => [8,7,7] => 1

[2,4,8,5,3,7,1,6] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,1,1] => 2

[2,4,1,8,5,3,7,6] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,1,1] => 2

[2,4,8,6,3,1,7,5] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1,1] => 1

[3,4,6,8,2,1,7,5] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2,1] => 2

[3,4,1,5,8,2,7,6] => [[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,2] => 2

[8,1,4,5,3,2,7,6] => [[.,[[[.,.],.],[.,[[.,.],.]]]],.] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,2,1] => 3

[3,4,1,5,2,8,7,6] => [[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,2] => 2

[3,4,6,2,1,8,7,5] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2,1] => 2

[3,5,6,2,1,7,8,4] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => 1

[3,4,6,2,7,8,1,5] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2,1] => 1

[3,5,6,2,1,7,4,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => 1

[3,4,1,6,8,7,2,5] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2] => 1

[3,5,6,1,8,7,2,4] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,2] => 1

[2,1,3,8,6,7,4,5] => [[.,.],[.,[[[.,[.,.]],[.,.]],.]]] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1,1,1] => 1

[8,1,3,2,6,7,5,4] => [[.,[[.,.],[[[.,.],.],[.,.]]]],.] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2,1,1] => 2

[2,3,8,6,7,1,5,4] => [[.,.],[.,[[[[.,.],.],[.,.]],.]]] => [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1,1,1] => 2

[2,4,1,8,6,7,5,3] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1,1] => 1

[3,5,6,1,8,7,4,2] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,2] => 1

[3,4,1,6,8,7,5,2] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2] => 1

[3,4,6,8,7,1,5,2] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2] => 1

[8,1,4,6,2,7,5,3] => [[.,[[.,[.,.]],[[.,.],[.,.]]]],.] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2,2] => 1

[3,5,1,6,7,8,4,2] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 0

[4,5,6,1,7,8,3,2] => [[.,[[.,.],.]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1] => 1

[4,5,6,1,7,3,8,2] => [[.,[[.,.],.]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1] => 1

[3,5,1,6,7,4,8,2] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 0

[3,5,1,6,7,4,2,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 0

[4,5,6,1,7,3,2,8] => [[.,[[.,.],.]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1] => 1

[1,6,4,8,7,5,2,3] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,2] => 1

[1,8,6,2,4,7,3,5] => [.,[[[.,[[.,.],[.,.]]],[.,.]],.]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,4,1,1] => 1

[8,1,6,2,4,7,3,5] => [[.,[[.,[[.,.],[.,.]]],[.,.]]],.] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [7,4,4,1,1] => 1

[1,8,6,3,4,7,2,5] => [.,[[[[.,.],[.,[.,.]]],[.,.]],.]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,4,1,1,1] => 1

[1,7,2,5,4,8,3,6] => [.,[[.,[[[.,.],.],[.,.]]],[.,.]]] => [1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1] => 1

[7,1,2,5,4,8,3,6] => [[.,[.,[[[.,.],.],[.,.]]]],[.,.]] => [1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,1] => 1

[1,2,7,5,4,8,3,6] => [.,[.,[[[[.,.],.],[.,.]],[.,.]]]] => [1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1] => 1

[2,3,7,5,4,8,1,6] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1,1] => 0

[1,3,7,5,4,8,2,6] => [.,[[.,.],[[[.,.],[.,.]],[.,.]]]] => [1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1] => 0

[1,5,8,4,7,3,2,6] => [.,[[[[.,.],.],.],[[[.,.],.],.]]] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,2,1] => 4

[1,7,3,5,4,8,2,6] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]] => [1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1] => 0

[1,4,3,2,7,8,5,6] => [.,[[[.,.],.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1] => 1

[2,4,3,1,7,8,5,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => 0

[2,7,3,5,4,8,1,6] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1,1] => 0

[3,2,1,4,7,8,5,6] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2,1] => 1

[2,5,8,6,3,1,4,7] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1,1] => 1

[2,3,5,8,1,4,7,6] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1,1,1] => 2

[2,3,6,8,1,5,7,4] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1,1] => 2

[2,5,7,6,3,1,4,8] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[2,8,7,6,3,1,5,4] => [[.,.],[[[[.,[[.,.],.]],.],.],.]] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,1,1,1] => 4

[2,4,8,1,6,5,7,3] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1,1] => 1

[2,3,6,8,1,4,7,5] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1,1] => 1

[2,3,6,1,8,4,7,5] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1,1] => 1

[2,4,8,1,3,7,5,6] => [[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,1,1] => 2

[3,4,8,7,1,2,5,6] => [[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,2] => 2

[1,8,4,2,3,6,7,5] => [.,[[[.,[.,.]],[[.,.],[.,.]]],.]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,2] => 1

[2,5,8,3,4,6,7,1] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1,1] => 1

[2,6,8,3,4,7,1,5] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1,1] => 1

[2,6,3,1,8,4,5,7] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1,1] => 1

[2,4,3,7,8,1,5,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => 0

[2,6,3,1,8,7,4,5] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1,1] => 1

[3,5,6,4,7,8,1,2] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 0

[4,3,8,7,2,1,5,6] => [[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,3,3,2,1] => 4

[1,8,6,3,7,4,2,5] => [.,[[[[.,.],[.,[.,.]]],[.,.]],.]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,4,1,1,1] => 1

[1,8,6,5,7,2,3,4] => [.,[[[[.,[.,[.,.]]],.],[.,.]],.]] => [1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3] => 2

[8,1,3,7,4,2,5,6] => [[.,[[.,.],[[.,[.,[.,.]]],.]]],.] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,1,1,1] => 2

[4,3,8,7,5,2,1,6] => [[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,3,3,2,1] => 4

[3,4,7,5,6,1,8,2] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2] => 0

[2,4,7,5,6,3,8,1] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => 0

[3,5,6,7,1,4,8,2] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 0

[5,8,4,3,2,6,7,1] => [[[[[.,.],.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,4,4,3,2,1] => 4

[1,8,5,6,2,4,7,3] => [.,[[[.,[[.,.],.]],[.,[.,.]]],.]] => [1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,1] => 2

[8,1,5,6,2,4,7,3] => [[.,[[.,[[.,.],.]],[.,[.,.]]]],.] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [7,3,3,3,1] => 2

[1,4,5,2,8,6,7,3] => [.,[[.,[.,.]],[.,[[.,[.,.]],.]]]] => [1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2] => 1

[2,3,1,7,8,6,4,5] => [[.,.],[.,[[[.,[.,.]],.],[.,.]]]] => [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1,1,1] => 1

[4,5,6,1,2,8,7,3] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3] => 1

[1,5,4,2,7,8,3,6] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2] => 1

[5,6,8,4,3,2,7,1] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [5,4,4,4,3,2,1] => 4

[2,5,8,3,1,6,7,4] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1,1] => 1

[1,5,8,3,2,6,7,4] => [.,[[[.,.],[.,.]],[[.,[.,.]],.]]] => [1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1] => 1

[1,3,8,6,2,4,7,5] => [.,[[.,.],[[[.,[.,.]],[.,.]],.]]] => [1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1,1] => 1

[2,4,5,8,3,6,1,7] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,1,1] => 1

[2,4,6,5,1,7,8,3] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[1,4,7,5,6,8,2,3] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2] => 0

[1,4,7,6,5,8,2,3] => [.,[[.,[.,.]],[[[.,.],.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2] => 1

[5,6,1,7,4,2,8,3] => [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,2] => 1

[2,7,8,3,4,6,1,5] => [[.,.],[[.,[.,[[.,.],.]]],[.,.]]] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1,1,1] => 1

[2,7,3,1,8,6,4,5] => [[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1,1,1,1] => 1

[2,8,4,3,1,5,7,6] => [[.,.],[[[.,.],[.,[[.,.],.]]],.]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2,1,1] => 2

[3,4,6,7,5,8,1,2] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2] => 0

[3,4,5,7,6,1,8,2] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2] => 0

[2,5,1,3,6,8,7,4] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1,1] => 1

[1,4,5,8,2,3,7,6] => [.,[[.,[.,.]],[.,[[[.,.],.],.]]]] => [1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2] => 2

[1,2,6,4,5,8,3,7] => [.,[.,[[[.,.],[.,.]],[[.,.],.]]]] => [1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1] => 1

[1,5,2,4,6,8,3,7] => [.,[[.,[[.,.],.]],[.,[[.,.],.]]]] => [1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1] => 2

[1,3,7,5,8,2,4,6] => [.,[[.,.],[[[.,.],[.,.]],[.,.]]]] => [1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1] => 0

[2,4,1,3,8,6,7,5] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1,1] => 1

[1,7,3,5,8,2,6,4] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]] => [1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1] => 0

[1,8,4,2,6,7,3,5] => [.,[[[.,[.,.]],[[.,.],[.,.]]],.]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,2] => 1

[5,1,7,2,3,6,8,4] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4] => 0

[2,6,1,7,3,5,8,4] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1,1] => 1

[7,1,2,5,3,6,8,4] => [[.,[.,[[.,[.,.]],[.,.]]]],[.,.]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2] => 0

[8,1,3,2,4,6,7,5] => [[.,[[.,.],[.,[[.,.],[.,.]]]]],.] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1,1,1] => 1

[1,8,3,4,7,2,5,6] => [.,[[[.,.],[.,[[.,[.,.]],.]]],.]] => [1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1,1,1] => 2

[1,3,7,4,8,2,6,5] => [.,[[.,.],[[.,[[.,.],.]],[.,.]]]] => [1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1,1] => 1

[1,4,6,8,2,3,7,5] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2] => 1

[2,6,8,1,7,3,4,5] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1,1] => 1

[1,8,3,2,7,5,6,4] => [.,[[[.,.],[[[.,.],[.,.]],.]],.]] => [1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,1,1] => 2

[2,6,7,3,8,1,5,4] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1,1] => 1

[3,8,7,2,4,1,5,6] => [[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,2,2,1] => 3

[7,1,6,2,3,8,5,4] => [[.,[[.,[.,[[.,.],.]]],.]],[.,.]] => [1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [6,6,4,1] => 2

[2,4,1,7,6,8,5,3] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1,1] => 1

[3,4,1,7,8,5,6,2] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2] => 0

[1,7,2,4,5,8,3,6] => [.,[[.,[[.,.],[.,[.,.]]]],[.,.]]] => [1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1] => 0

[1,7,4,5,8,3,2,6] => [.,[[[[.,.],.],[.,[.,.]]],[.,.]]] => [1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2,1] => 1

[1,2,6,4,7,8,3,5] => [.,[.,[[[.,.],[.,.]],[.,[.,.]]]]] => [1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1] => 0

[1,3,6,4,7,2,8,5] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => [1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1] => 0

[1,6,7,3,8,2,5,4] => [.,[[[.,.],[[.,.],.]],[.,[.,.]]]] => [1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1] => 1

[2,3,8,7,1,6,4,5] => [[.,.],[.,[[[[.,[.,.]],.],.],.]]] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,1,1,1] => 3

[7,3,8,4,1,2,5,6] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,2,2] => 0

[2,4,8,7,5,6,1,3] => [[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,1,1] => 2

[2,3,7,8,5,6,1,4] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1,1] => 0

[2,4,7,8,1,6,3,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1,1] => 1

[2,8,3,4,1,5,7,6] => [[.,.],[[.,[.,[.,[[.,.],.]]]],.]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1,1,1,1] => 2

[2,5,3,1,8,6,7,4] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1,1] => 1

[2,5,1,3,8,6,7,4] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1,1] => 1

[4,5,1,2,8,6,7,3] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [5,3,3,3,3] => 1

[7,3,4,8,5,6,1,2] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,2,2] => 0

[1,7,2,4,8,6,3,5] => [.,[[.,[[.,.],[[.,.],.]]],[.,.]]] => [1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1] => 1

[2,8,3,1,6,5,4,7] => [[.,.],[[.,[[[.,.],.],[.,.]]],.]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,1,1,1] => 2

[2,5,8,3,6,7,4,1] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1,1] => 1

[1,5,8,3,7,4,2,6] => [.,[[[.,.],[.,.]],[[[.,.],.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1,1] => 2

[6,1,8,2,3,5,4,7] => [[.,[.,[.,[[.,.],.]]]],[[.,.],.]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [6,5,5,1] => 2

[7,1,2,4,8,5,6,3] => [[.,[.,[[.,.],[.,[.,.]]]]],[.,.]] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1] => 0

[7,1,3,2,4,8,6,5] => [[.,[[.,.],[.,[[.,.],.]]]],[.,.]] => [1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [6,6,2,1,1,1] => 1

[7,2,1,3,4,5,8,6] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1,1,1] => 0

[2,8,3,6,4,7,5,1] => [[.,.],[[.,[[.,[.,.]],[.,.]]],.]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1,1,1,1] => 1

[1,8,3,5,6,2,4,7] => [.,[[[.,.],[[.,.],[.,[.,.]]]],.]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,1,1] => 1

[1,4,8,5,6,2,3,7] => [.,[[.,[.,.]],[[.,[.,[.,.]]],.]]] => [1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2] => 1

[1,2,8,5,3,7,4,6] => [.,[.,[[[.,[.,.]],[[.,.],.]],.]]] => [1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2] => 2

[1,8,2,5,4,7,3,6] => [.,[[.,[[[.,.],.],[[.,.],.]]],.]] => [1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,1] => 3

[1,7,4,2,5,3,8,6] => [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2] => 0

[7,1,3,2,8,4,5,6] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1,1] => 0

[2,8,3,1,4,5,6,7] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1,1,1] => 1

[5,6,1,7,8,2,4,3] => [[.,[.,[[.,.],.]]],[.,[.,[.,.]]]] => [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,1] => 1

[5,6,1,7,2,4,8,3] => [[.,[.,[[.,.],.]]],[.,[.,[.,.]]]] => [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,1] => 1

[5,6,1,7,8,4,2,3] => [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,2] => 1

[1,4,8,6,3,2,5,7] => [.,[[[.,.],.],[[[.,.],[.,.]],.]]] => [1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1] => 2

[1,4,2,3,6,8,7,5] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2] => 1

[8,1,6,7,2,5,3,4] => [[.,[[.,[[.,[.,.]],.]],[.,.]]],.] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [7,4,4,2] => 2

[1,2,7,5,6,8,3,4] => [.,[.,[[[.,[.,.]],[.,.]],[.,.]]]] => [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2] => 0

[1,8,6,5,3,7,2,4] => [.,[[[[[.,.],[.,.]],.],[.,.]],.]] => [1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3,1,1] => 2

[1,6,3,5,7,2,8,4] => [.,[[[.,.],[[.,.],.]],[.,[.,.]]]] => [1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1] => 1

[1,5,4,6,7,8,2,3] => [.,[[[.,[.,.]],.],[.,[.,[.,.]]]]] => [1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2] => 1

[1,7,8,3,5,6,2,4] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]] => [1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1] => 0

[1,3,7,5,8,2,6,4] => [.,[[.,.],[[[.,.],[.,.]],[.,.]]]] => [1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1] => 0

[2,6,8,3,7,1,4,5] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1,1] => 1

[4,5,8,1,6,2,3,7] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [5,3,3,3,3] => 1

[2,4,3,8,1,5,6,7] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,1,1] => 1

[3,1,8,4,2,5,6,7] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,2] => 1

[3,8,4,2,1,5,6,7] => [[[.,.],.],[[.,[.,[.,[.,.]]]],.]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,2,1] => 2

[2,3,8,4,1,5,6,7] => [[.,.],[.,[[.,[.,[.,[.,.]]]],.]]] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1,1,1] => 1

[3,4,2,8,1,5,6,7] => [[[.,.],.],[.,[[.,[.,[.,.]]],.]]] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,2,1] => 2

[2,1,4,8,5,3,6,7] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,1,1] => 1

[3,2,8,4,1,5,6,7] => [[[.,.],.],[[.,[.,[.,[.,.]]]],.]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,2,1] => 2

[2,8,4,3,1,5,6,7] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,1,1] => 1

[5,6,4,3,2,8,1,7] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [5,4,4,4,3,2,1] => 4

[3,4,8,1,2,5,7,6] => [[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,2] => 2

[3,4,8,2,1,5,7,6] => [[[.,.],.],[.,[[.,[[.,.],.]],.]]] => [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,2,1] => 3

[3,4,8,1,5,7,6,2] => [[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,2] => 2

[1,5,6,3,4,8,2,7] => [.,[[[.,.],[.,.]],[.,[[.,.],.]]]] => [1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1] => 1

[1,4,3,6,5,8,2,7] => [.,[[[.,.],.],[[.,.],[[.,.],.]]]] => [1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1] => 2

[8,1,3,4,7,2,6,5] => [[.,[[.,.],[.,[[[.,.],.],.]]]],.] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1,1,1] => 3

[2,8,3,4,7,5,6,1] => [[.,.],[[.,[.,[[.,[.,.]],.]]],.]] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1,1,1,1] => 2

[1,8,3,4,7,6,2,5] => [.,[[[.,.],[.,[[[.,.],.],.]]],.]] => [1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,1,1] => 3

[2,1,3,8,4,6,5,7] => [[.,.],[.,[[.,[[.,.],[.,.]]],.]]] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1,1,1] => 1

[1,3,2,8,5,4,6,7] => [.,[[.,.],[[[.,.],[.,[.,.]]],.]]] => [1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1,1] => 1

[1,5,6,8,7,4,2,3] => [.,[[[.,[.,.]],.],[.,[[.,.],.]]]] => [1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2] => 2

[1,4,8,5,7,6,2,3] => [.,[[.,[.,.]],[[.,[[.,.],.]],.]]] => [1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2] => 2

[2,4,8,5,7,3,6,1] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,1,1] => 2

[7,8,1,2,6,3,4,5] => [[.,[.,[[.,[.,[.,.]]],.]]],[.,.]] => [1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [6,6,3] => 1

[3,4,8,5,1,6,7,2] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,2] => 1

[1,4,8,2,6,3,7,5] => [.,[[.,[.,.]],[[[.,.],[.,.]],.]]] => [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2] => 1

[1,2,7,8,5,3,4,6] => [.,[.,[[[.,[.,.]],[.,.]],[.,.]]]] => [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2] => 0

[1,7,5,6,8,4,3,2] => [.,[[[[[.,.],.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,2,1] => 2

[3,1,8,4,5,6,7,2] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,2] => 1

[2,1,4,8,6,5,3,7] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1,1] => 1

[2,4,1,8,6,5,3,7] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1,1] => 1

[2,3,7,8,5,1,4,6] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1,1] => 0

[2,7,3,8,5,1,4,6] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1,1] => 0

[1,4,2,8,7,5,3,6] => [.,[[.,[.,.]],[[[.,[.,.]],.],.]]] => [1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2] => 2

[1,2,6,8,4,5,3,7] => [.,[.,[[[.,.],[.,.]],[[.,.],.]]]] => [1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1] => 1

[7,1,2,8,4,5,3,6] => [[.,[.,[[.,.],[.,[.,.]]]]],[.,.]] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1] => 0

[1,8,7,5,3,2,4,6] => [.,[[[[[.,.],[.,.]],[.,.]],.],.]] => [1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3,1,1] => 2

[1,8,7,4,2,5,3,6] => [.,[[[[.,[.,.]],[.,[.,.]]],.],.]] => [1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,2] => 2

[1,5,3,8,7,4,2,6] => [.,[[[.,.],[.,.]],[[[.,.],.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1,1] => 2

[2,3,1,8,7,5,4,6] => [[.,.],[.,[[[[.,.],[.,.]],.],.]]] => [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,1,1,1] => 2

[1,8,6,3,2,4,7,5] => [.,[[[[.,.],[.,[.,.]]],[.,.]],.]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,4,1,1,1] => 1

[4,3,2,8,7,6,1,5] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,3,2,1] => 5

[2,4,5,1,3,8,7,6] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,1,1] => 2

[1,7,5,8,6,3,2,4] => [.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,1,1] => 0

[1,7,4,2,5,8,6,3] => [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2] => 0

[1,8,5,2,7,4,6,3] => [.,[[[.,[[.,.],.]],[[.,.],.]],.]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,3,1] => 3

[2,3,1,7,5,8,6,4] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1,1] => 0

[1,8,7,5,6,2,3,4] => [.,[[[[.,[.,[.,.]]],[.,.]],.],.]] => [1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3] => 2

[1,8,3,2,7,6,4,5] => [.,[[[.,.],[[[.,[.,.]],.],.]],.]] => [1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,1,1] => 3

[3,4,7,8,1,6,2,5] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,2] => 1

[1,8,5,7,6,2,3,4] => [.,[[[.,[.,[.,.]]],[[.,.],.]],.]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,3] => 2

[1,8,6,7,5,2,3,4] => [.,[[[[.,[.,[.,.]]],.],[.,.]],.]] => [1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3] => 2

[8,1,4,2,3,6,7,5] => [[.,[[.,[.,.]],[[.,.],[.,.]]]],.] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2,2] => 1

[1,7,4,6,8,2,5,3] => [.,[[[.,[.,.]],[[.,.],.]],[.,.]]] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,2] => 1

[7,3,1,4,5,2,8,6] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,2,2] => 0

[8,1,2,4,6,7,5,3] => [[.,[.,[[.,.],[[.,.],[.,.]]]]],.] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1,1] => 1

[8,1,3,6,7,5,4,2] => [[.,[[.,.],[[[.,.],.],[.,.]]]],.] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2,1,1] => 2

[3,5,1,6,8,4,7,2] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,2] => 1

[5,8,4,7,3,2,6,1] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,4,3,2,1] => 5

[2,6,8,3,7,4,1,5] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1,1] => 1

[8,1,6,2,7,5,3,4] => [[.,[[.,[[.,[.,.]],.]],[.,.]]],.] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [7,4,4,2] => 2

[5,1,7,2,3,8,6,4] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4] => 0

[8,2,3,5,1,7,6,4] => [[[.,.],[.,[[.,.],[[.,.],.]]]],.] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,1,1,1] => 2

[7,1,3,8,4,2,6,5] => [[.,[[.,.],[.,[[.,.],.]]]],[.,.]] => [1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [6,6,2,1,1,1] => 1

[4,1,5,2,7,6,3,8] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [4,4,3,3,3] => 0

[2,5,1,3,7,6,4,8] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[1,8,5,3,6,4,2,7] => [.,[[[[.,.],[.,.]],[.,[.,.]]],.]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,1,1] => 1

[5,4,8,3,2,1,7,6] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,4,3,2,1] => 5

[6,1,2,7,8,3,5,4] => [[.,[.,[.,[[.,.],.]]]],[.,[.,.]]] => [1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,5,5,1] => 1

[3,8,7,2,1,6,4,5] => [[[.,.],.],[[[[.,[.,.]],.],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,2,2,1] => 4

[2,8,7,1,6,3,5,4] => [[.,.],[[[[.,[[.,.],.]],.],.],.]] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,1,1,1] => 4

[5,8,6,4,3,2,1,7] => [[[[[.,.],.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,4,4,3,2,1] => 4

[1,3,7,5,4,2,8,6] => [.,[[.,.],[[[.,.],[.,.]],[.,.]]]] => [1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1] => 0

[3,4,7,5,8,6,1,2] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2] => 0

[2,4,7,1,5,3,8,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => 0

[2,3,6,7,4,8,1,5] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1,1] => 0

[1,3,6,7,4,8,5,2] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => [1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1] => 0

[1,7,4,2,6,3,8,5] => [.,[[[.,[.,.]],[[.,.],.]],[.,.]]] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,2] => 1

[9,1,2,3,4,5,6,8,7] => [[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1] => 2

[10,1,2,3,4,5,6,7,9,8] => [[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1] => 2

[2,3,4,7,5,8,1,6] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1,1] => 0

[1,3,7,4,8,6,2,5] => [.,[[.,.],[[.,[[.,.],.]],[.,.]]]] => [1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1,1] => 1

[1,5,6,8,4,7,3,2] => [.,[[[[.,.],.],.],[.,[[.,.],.]]]] => [1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1] => 3

[3,4,1,7,5,8,6,2] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2] => 0

[1,8,7,2,3,5,6,4] => [.,[[[.,[.,[[.,.],[.,.]]]],.],.]] => [1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,1] => 2

[2,8,3,1,6,7,5,4] => [[.,.],[[.,[[[.,.],.],[.,.]]],.]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,1,1,1] => 2

[8,2,3,1,5,7,6,4] => [[[.,.],[.,[[.,.],[[.,.],.]]]],.] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,1,1,1] => 2

[2,3,7,4,1,8,5,6] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1,1,1] => 0

[8,1,4,7,2,5,6,3] => [[.,[[.,[.,.]],[[.,[.,.]],.]]],.] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,2,2] => 2

[2,3,6,5,8,1,4,7] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1,1] => 2

[2,3,5,8,6,1,4,7] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1,1,1] => 1

[1,2,3,7,4,6,8,5] => [.,[.,[.,[[.,[[.,.],.]],[.,.]]]]] => [1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [3,3,1] => 1

[1,2,7,5,3,8,4,6] => [.,[.,[[[.,[.,.]],[.,.]],[.,.]]]] => [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2] => 0

[1,2,3,7,6,8,4,5] => [.,[.,[.,[[[.,[.,.]],.],[.,.]]]]] => [1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [3,3,2] => 1

[1,2,3,6,8,7,4,5] => [.,[.,[.,[[.,[.,.]],[[.,.],.]]]]] => [1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [3,2,2] => 1

[1,2,3,7,8,4,6,5] => [.,[.,[.,[[.,[[.,.],.]],[.,.]]]]] => [1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [3,3,1] => 1

[1,2,3,6,8,4,7,5] => [.,[.,[.,[[.,[.,.]],[[.,.],.]]]]] => [1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [3,2,2] => 1

[1,2,3,7,8,6,4,5] => [.,[.,[.,[[[.,[.,.]],.],[.,.]]]]] => [1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [3,3,2] => 1

[2,6,8,3,7,4,5,1] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1,1] => 1

[1,8,4,3,7,5,6,2] => [.,[[[[.,.],.],[[.,[.,.]],.]],.]] => [1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,2,1] => 3

[1,8,5,6,4,7,3,2] => [.,[[[[[.,.],.],.],[.,[.,.]]],.]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,2,1] => 3

[2,3,8,7,5,4,6,1] => [[.,.],[.,[[[[.,.],[.,.]],.],.]]] => [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,1,1,1] => 2

[1,8,2,7,4,5,6,3] => [.,[[.,[[[.,.],[.,[.,.]]],.]],.]] => [1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,1,1] => 2

[3,4,6,8,7,2,5,1] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2,1] => 2

[1,8,3,5,7,4,6,2] => [.,[[[.,.],[[.,.],[[.,.],.]]],.]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,1,1] => 2

[5,1,2,8,6,3,4,7] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [6,4,4,4] => 1

[7,1,8,6,2,3,5,4] => [[.,[[.,[.,[[.,.],.]]],.]],[.,.]] => [1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [6,6,4,1] => 2

[7,8,1,2,6,5,3,4] => [[.,[.,[[[.,[.,.]],.],.]]],[.,.]] => [1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [6,6,3,2] => 2

[1,4,8,2,7,5,3,6] => [.,[[.,[.,.]],[[[.,[.,.]],.],.]]] => [1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2] => 2

[1,2,8,7,5,4,3,6] => [.,[.,[[[[[.,.],.],[.,.]],.],.]]] => [1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,1] => 3

[3,4,8,7,5,6,1,2] => [[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,2] => 2

[2,3,8,7,4,1,5,6] => [[.,.],[.,[[[.,[.,[.,.]]],.],.]]] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1,1,1,1] => 2

[2,7,3,8,6,4,1,5] => [[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1,1,1,1] => 1

[1,8,3,7,6,4,5,2] => [.,[[[.,.],[[[.,[.,.]],.],.]],.]] => [1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,1,1] => 3

[1,2,8,7,6,5,3,4] => [.,[.,[[[[[.,[.,.]],.],.],.],.]]] => [1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2] => 4

[3,1,2,4,6,8,7,5] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2] => 1

[3,1,8,4,5,7,6,2] => [[.,[.,.]],[[.,[.,[[.,.],.]]],.]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2,2] => 2

[1,3,4,8,7,5,2,6] => [.,[[.,.],[.,[[[.,[.,.]],.],.]]]] => [1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1,1] => 2

[3,1,4,7,8,5,2,6] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2] => 0

[1,7,8,4,2,3,6,5] => [.,[[[.,[.,.]],[[.,.],.]],[.,.]]] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,2] => 1

[2,4,3,7,5,8,1,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => 0

[1,4,7,3,6,2,8,5] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1] => 2

[1,8,3,4,2,6,7,5] => [.,[[[.,.],[.,[[.,.],[.,.]]]],.]] => [1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1,1,1] => 1

[8,2,3,5,4,7,1,6] => [[[.,.],[.,[[.,.],[[.,.],.]]]],.] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,1,1,1] => 2

[1,8,6,4,2,3,7,5] => [.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2,2] => 1

[3,8,4,5,6,2,1,7] => [[[.,.],.],[[.,[.,[.,[.,.]]]],.]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,2,1] => 2

[2,4,3,5,7,8,1,6] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1,1] => 0

[1,8,4,2,6,5,3,7] => [.,[[[.,[.,.]],[[.,.],[.,.]]],.]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,2] => 1

[3,2,4,8,1,5,7,6] => [[[.,.],.],[.,[[.,[[.,.],.]],.]]] => [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,2,1] => 3

[2,4,8,3,1,7,5,6] => [[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,1,1] => 2

[4,8,3,2,1,7,6,5] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,3,2,1] => 5

[2,4,3,8,7,1,5,6] => [[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,1,1] => 2

[3,4,1,8,6,2,7,5] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,2] => 1

[3,8,7,4,2,1,5,6] => [[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,2,2,1] => 3

[3,4,8,1,5,2,7,6] => [[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,2] => 2

[8,1,2,4,3,5,6,7] => [[.,[.,[[.,.],[.,[.,[.,.]]]]]],.] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1,1] => 1

[5,8,7,4,6,3,2,1] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,4,3,2,1] => 5

[4,8,7,6,3,5,2,1] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,3,2,1] => 5

[3,8,7,6,5,2,4,1] => [[[.,.],.],[[[[[.,.],.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,2,1] => 5

[5,8,4,7,6,3,2,1] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,4,3,2,1] => 5

[6,8,5,4,7,3,2,1] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,5,4,3,2,1] => 5

[3,8,7,6,2,5,4,1] => [[[.,.],.],[[[[[.,.],.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,2,1] => 5

[4,8,7,6,3,2,5,1] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,3,2,1] => 5

[3,8,7,6,5,2,1,4] => [[[.,.],.],[[[[[.,.],.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,2,1] => 5

[3,1,4,5,6,7,8,2,9] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2] => 0

[3,2,8,7,6,1,5,4] => [[[.,.],.],[[[[[.,.],.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,2,1] => 5

[1,6,8,3,4,5,7,2] => [.,[[[.,.],[.,[.,.]]],[[.,.],.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1] => 1

[8,2,7,3,4,1,5,6] => [[[.,.],[[.,[.,[.,[.,.]]]],.]],.] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,1,1,1,1] => 2

[1,5,2,7,8,6,4,3] => [.,[[.,[[.,.],.]],[[.,.],[.,.]]]] => [1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1] => 1

[1,4,2,8,6,5,7,3] => [.,[[.,[.,.]],[[[.,.],[.,.]],.]]] => [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2] => 1

[3,5,1,6,8,7,2,4] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,2] => 1

[8,1,4,5,2,6,7,3] => [[.,[[.,[.,.]],[.,[.,[.,.]]]]],.] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2] => 1

[4,2,1,5,6,7,8,3] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1,1] => 0

[3,4,6,5,1,7,8,2] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2] => 0

[1,5,3,2,4,7,6,8] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1] => 0

[1,5,3,2,7,4,6,8] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1] => 0

[1,7,3,2,5,4,6,8] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]] => [1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1] => 0

[1,5,3,7,2,4,6,8] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1] => 0

[1,3,2,7,5,4,6,8] => [.,[[.,.],[[[.,.],[.,.]],[.,.]]]] => [1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1] => 0

[1,3,7,2,5,4,6,8] => [.,[[.,.],[[[.,.],[.,.]],[.,.]]]] => [1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1] => 0

[1,3,7,5,2,4,6,8] => [.,[[.,.],[[[.,.],[.,.]],[.,.]]]] => [1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1] => 0

[1,7,5,3,2,4,6,8] => [.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,1,1] => 0

[1,2,3,4,5,7,9,6,8] => [.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]] => [1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1] => 1

[2,9,8,7,1,6,5,4,3] => [[.,.],[[[[[[[.,.],.],.],.],.],.],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,1,1] => 6

[2,10,9,8,7,1,6,5,4,3] => [[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,2,1,1] => 7

[2,10,1,9,8,7,6,5,4,3] => [[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,2,1,1] => 7

[1,7,2,3,6,8,5,4] => [.,[[.,[.,[[[.,.],.],.]]],[.,.]]] => [1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1] => 2

[1,7,5,4,8,2,6,3] => [.,[[[[.,[.,.]],.],[.,.]],[.,.]]] => [1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,2] => 1

[1,7,5,4,8,6,3,2] => [.,[[[[[.,.],.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,2,1] => 2

[3,5,6,4,8,1,2,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,2] => 1

[1,5,6,4,8,7,2,3] => [.,[[[.,[.,.]],.],[.,[[.,.],.]]]] => [1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2] => 2

[7,1,3,4,5,8,2,6] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1,1] => 0

[1,6,4,2,8,5,3,7] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,2] => 1

[1,5,6,4,8,3,7,2] => [.,[[[[.,.],.],.],[.,[[.,.],.]]]] => [1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1] => 3

[2,5,6,4,8,3,1,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1,1] => 2

[3,5,6,1,4,7,8,2] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 0

[7,1,3,2,4,8,5,6] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1,1] => 0

[3,4,6,8,7,2,1,5] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2,1] => 2

[3,5,6,8,1,7,2,4] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,2] => 1

[5,1,4,2,3,6,7,8] => [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,2] => 1

[2,1,4,8,6,3,7,5] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1,1] => 1

[1,6,7,5,3,4,8,2] => [.,[[[[.,.],[.,.]],.],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,1,1] => 1

[1,6,7,5,8,2,3,4] => [.,[[[.,[.,[.,.]]],.],[.,[.,.]]]] => [1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3] => 1

[2,4,7,3,5,8,6,1] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => 0

[2,5,3,7,1,8,4,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[4,5,1,3,6,2,8,7] => [[.,[[.,.],.]],[.,[.,[[.,.],.]]]] => [1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3,1] => 2

[3,4,7,6,8,1,2,5] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,2] => 1

[3,4,6,2,5,8,7,1] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2,1] => 2

[1,8,2,3,6,5,7,4] => [.,[[.,[.,[[[.,.],.],[.,.]]]],.]] => [1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1] => 2

[1,3,7,2,6,5,8,4] => [.,[[.,.],[[[[.,.],.],.],[.,.]]]] => [1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1,1] => 2

[1,3,6,4,2,5,8,7] => [.,[[.,.],[[.,[.,.]],[[.,.],.]]]] => [1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1] => 1

[1,5,4,7,3,6,8,2] => [.,[[[[.,.],.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2,1] => 2

[7,2,8,3,4,1,5,6] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1,1,1] => 0

[1,5,3,7,6,8,4,2] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1] => 0

[1,6,3,7,8,2,4,5] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]] => [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1] => 0

[1,4,3,7,8,5,2,6] => [.,[[[.,.],.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1] => 1

[3,2,4,7,8,5,1,6] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2,1] => 1

[1,5,4,3,7,8,2,6] => [.,[[[[.,.],.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2,1] => 2

[1,8,2,7,6,4,3,5] => [.,[[.,[[[[.,.],[.,.]],.],.]],.]] => [1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,1] => 3

[1,8,2,7,5,3,6,4] => [.,[[.,[[[.,[.,.]],[.,.]],.]],.]] => [1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2] => 2

[1,3,7,6,5,8,2,4] => [.,[[.,.],[[[[.,.],.],.],[.,.]]]] => [1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1,1] => 2

[1,8,2,5,7,6,4,3] => [.,[[.,[[[.,.],.],[[.,.],.]]],.]] => [1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,1] => 3

[1,8,2,6,4,7,5,3] => [.,[[.,[[[.,.],[.,.]],[.,.]]],.]] => [1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1,1] => 1

[1,6,4,7,5,3,8,2] => [.,[[[[.,.],.],[.,.]],[.,[.,.]]]] => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2,1] => 1

[1,4,7,3,5,2,6,8] => [.,[[[.,.],.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1] => 1

[2,4,5,8,1,6,7,3] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,1,1] => 1

[2,7,3,8,1,5,6,4] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1,1] => 0

[1,6,8,5,2,4,3,7] => [.,[[[.,[[.,.],.]],.],[[.,.],.]]] => [1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3,1] => 3

[7,8,1,2,4,3,6,5] => [[.,[.,[[.,.],[[.,.],.]]]],[.,.]] => [1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [6,6,2,1,1] => 1

[8,1,4,3,5,7,6,2] => [[.,[[[.,.],.],[.,[[.,.],.]]]],.] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,2,1] => 3

[1,4,8,7,3,5,6,2] => [.,[[[.,.],.],[[[.,[.,.]],.],.]]] => [1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,1] => 3

[1,8,7,6,5,3,4,2] => [.,[[[[[[.,.],[.,.]],.],.],.],.]] => [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1,1] => 4

[2,4,7,8,1,6,5,3] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1,1] => 1

[4,6,7,1,2,8,5,3] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[1,7,8,5,4,3,2,6] => [.,[[[[[.,.],.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,2,1] => 2

[1,2,6,7,8,4,3,5] => [.,[.,[[[.,.],[.,.]],[.,[.,.]]]]] => [1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1] => 0

[1,3,6,7,4,2,8,5] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => [1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1] => 0

[1,7,8,2,6,4,5,3] => [.,[[.,[[[.,.],[.,.]],.]],[.,.]]] => [1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1,1] => 1

[1,8,2,3,6,5,4,7] => [.,[[.,[.,[[[.,.],.],[.,.]]]],.]] => [1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1] => 2

[1,8,5,4,6,2,3,7] => [.,[[[[.,[.,.]],.],[.,[.,.]]],.]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,2] => 2

[1,8,5,4,6,3,2,7] => [.,[[[[[.,.],.],.],[.,[.,.]]],.]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,2,1] => 3

[3,5,4,1,6,2,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 0

[1,5,8,4,7,3,6,2] => [.,[[[[.,.],.],.],[[[.,.],.],.]]] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,2,1] => 4

[1,6,4,3,7,8,5,2] => [.,[[[[.,.],.],[.,.]],[.,[.,.]]]] => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2,1] => 1

[7,1,3,4,8,6,5,2] => [[.,[[.,.],[.,[[.,.],.]]]],[.,.]] => [1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [6,6,2,1,1,1] => 1

[1,6,4,2,7,8,3,5] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2] => 0

[1,2,4,3,8,5,7,6] => [.,[.,[[.,.],[[.,[[.,.],.]],.]]]] => [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1] => 2

[1,5,8,4,7,6,2,3] => [.,[[[.,[.,.]],.],[[[.,.],.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,2] => 3

[1,2,6,8,3,7,4,5] => [.,[.,[[.,[.,[.,.]]],[[.,.],.]]]] => [1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [4,3,3] => 1

[4,8,3,2,5,7,6,1] => [[[[.,.],.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,3,3,2,1] => 4

[1,8,3,5,2,6,7,4] => [.,[[[.,.],[[.,.],[.,[.,.]]]],.]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,1,1] => 1

[8,1,3,4,2,6,5,7] => [[.,[[.,.],[.,[[.,.],[.,.]]]]],.] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1,1,1] => 1

[8,1,3,2,5,6,4,7] => [[.,[[.,.],[[.,.],[.,[.,.]]]]],.] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,1,1] => 1

[8,1,2,4,5,3,7,6] => [[.,[.,[[.,.],[.,[[.,.],.]]]]],.] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,1,1] => 2

[2,4,6,7,8,1,5,3] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[2,4,6,8,1,7,5,3] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,7,8,3,5,6,1] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => 0

[2,5,6,4,7,1,8,3] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1,1] => 1

[1,2,6,5,8,7,3,4] => [.,[.,[[[.,[.,.]],.],[[.,.],.]]]] => [1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2] => 2

[1,5,2,8,4,6,7,3] => [.,[[.,[[.,.],.]],[[.,[.,.]],.]]] => [1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1] => 2

[1,5,2,7,4,6,8,3] => [.,[[.,[[.,.],.]],[[.,.],[.,.]]]] => [1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1] => 1

[5,1,2,7,3,6,8,4] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4] => 0

[5,1,2,8,3,6,7,4] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [6,4,4,4] => 1

[7,1,2,8,3,6,4,5] => [[.,[.,[.,[[.,[.,.]],.]]]],[.,.]] => [1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [6,6,2] => 1

[6,1,8,2,3,5,7,4] => [[.,[.,[.,[[.,.],.]]]],[[.,.],.]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [6,5,5,1] => 2

[6,1,7,2,3,5,8,4] => [[.,[.,[.,[[.,.],.]]]],[.,[.,.]]] => [1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,5,5,1] => 1

[1,6,8,2,4,5,7,3] => [.,[[.,[[.,.],[.,.]]],[[.,.],.]]] => [1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1] => 1

[4,3,8,7,5,6,2,1] => [[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,3,3,2,1] => 4

[1,8,2,7,4,6,5,3] => [.,[[.,[[[.,.],[[.,.],.]],.]],.]] => [1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,1] => 3

[7,1,6,2,3,5,8,4] => [[.,[[.,[.,[[.,.],.]]],.]],[.,.]] => [1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [6,6,4,1] => 2

[8,1,6,2,3,5,7,4] => [[.,[[.,[.,[[.,.],.]]],[.,.]]],.] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [7,4,4,1] => 2

[8,1,7,2,3,5,6,4] => [[.,[[.,[.,[[.,.],[.,.]]]],.]],.] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,1] => 2

[1,8,7,2,4,5,3,6] => [.,[[[.,[[.,.],[.,[.,.]]]],.],.]] => [1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,1,1] => 2

[8,7,1,2,3,4,6,5] => [[[.,[.,[.,[.,[[.,.],.]]]]],.],.] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [7,6,1] => 3

[8,6,1,2,3,4,7,5] => [[[.,[.,[.,[.,[.,.]]]]],[.,.]],.] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [7,5,5] => 1

[8,1,6,2,3,5,4,7] => [[.,[[.,[.,[[.,.],.]]],[.,.]]],.] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [7,4,4,1] => 2

[1,7,6,2,4,5,3,8] => [.,[[[.,[[.,.],[.,.]]],.],[.,.]]] => [1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1,1] => 1

[1,8,3,5,7,2,6,4] => [.,[[[.,.],[[.,.],[[.,.],.]]],.]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,1,1] => 2

[2,3,4,6,8,5,7,1] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1,1] => 1

[2,3,5,7,4,8,6,1] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1,1] => 0

[2,4,6,3,7,8,5,1] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[2,5,7,1,8,6,3,4] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[2,4,1,8,5,6,3,7] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,1,1] => 1

[1,6,2,7,8,5,3,4] => [.,[[.,[[.,[.,.]],.]],[.,[.,.]]]] => [1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2] => 1

[3,5,2,6,7,8,4,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => 1

[4,5,1,6,7,3,8,2] => [[.,[[.,.],.]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1] => 1

[6,7,1,2,3,5,8,4] => [[.,[.,[.,[[.,.],.]]]],[.,[.,.]]] => [1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,5,5,1] => 1

[3,1,4,8,5,6,2,7] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,2] => 1

[6,7,8,1,2,3,4,5,9] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,5,5,5] => 0

[5,6,7,1,8,2,3,4,9] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,4,4,4,4] => 0

[8,1,3,5,7,6,4,2] => [[.,[[.,.],[[.,.],[[.,.],.]]]],.] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,1,1] => 2

[8,1,7,3,4,6,2,5] => [[.,[[[.,.],[.,[[.,.],.]]],.]],.] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [7,5,2,1,1,1] => 3

[2,8,3,7,4,6,5,1] => [[.,.],[[.,[[.,[[.,.],.]],.]],.]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,1,1,1] => 3

[8,1,7,2,6,4,3,5] => [[.,[[.,[[[.,.],[.,.]],.]],.]],.] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [7,5,3,1,1] => 3

[8,2,3,7,4,6,1,5] => [[[.,.],[.,[[.,[[.,.],.]],.]]],.] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,1,1,1] => 3

[2,4,8,5,7,6,3,1] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,1,1] => 2

[8,1,7,2,4,6,5,3] => [[.,[[.,[[.,.],[[.,.],.]]],.]],.] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [7,5,2,1,1] => 3

[1,5,4,8,2,3,7,6] => [.,[[[.,[.,.]],.],[[[.,.],.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,2] => 3

[1,7,8,2,3,5,6,4] => [.,[[.,[.,[[.,.],[.,.]]]],[.,.]]] => [1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1] => 0

[1,7,6,3,2,8,4,5] => [.,[[[[.,.],[.,[.,.]]],.],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1,1,1] => 1

[1,7,6,2,5,8,4,3] => [.,[[[.,[[[.,.],.],.]],.],[.,.]]] => [1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,1] => 3

[1,7,6,5,8,4,2,3] => [.,[[[[[.,[.,.]],.],.],.],[.,.]]] => [1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3,2] => 3

[7,1,2,6,3,5,4,8] => [[.,[.,[[.,[[.,.],.]],.]]],[.,.]] => [1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [6,6,3,1] => 2

[1,5,8,6,4,2,3,7] => [.,[[[.,[.,.]],.],[[.,[.,.]],.]]] => [1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,2] => 2

[2,4,6,1,5,7,3,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[1,6,2,3,5,8,7,4] => [.,[[.,[.,[[.,.],.]]],[[.,.],.]]] => [1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1] => 2

[3,4,6,5,1,2,7,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2] => 0

[4,3,8,2,5,7,1,6] => [[[[.,.],.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,3,3,2,1] => 4

[4,5,1,6,2,8,7,3] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3] => 1

[9,2,3,4,5,6,7,8,1] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1,1,1,1,1,1] => 1

[1,2,4,6,8,5,7,3] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => [1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1] => 1

[3,2,4,5,1,8,6,7] => [[[.,.],.],[.,[.,[[.,[.,.]],.]]]] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,2,1] => 2

[1,4,5,3,8,2,6,7] => [.,[[[.,.],.],[.,[[.,[.,.]],.]]]] => [1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,1] => 2

[1,5,4,8,2,3,6,7] => [.,[[[.,[.,.]],.],[[.,[.,.]],.]]] => [1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,2] => 2

[1,5,6,8,3,7,2,4] => [.,[[[.,.],[.,.]],[.,[[.,.],.]]]] => [1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1] => 1

[7,1,2,5,8,4,6,3] => [[.,[.,[[[.,.],.],[.,.]]]],[.,.]] => [1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,1] => 1

[1,6,2,7,4,8,5,3] => [.,[[.,[[.,.],[.,.]]],[.,[.,.]]]] => [1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1] => 0

[5,1,6,8,7,2,3,4] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [5,4,4,4] => 1

[1,5,7,6,8,2,3,4] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3] => 0

[1,6,8,3,2,5,4,7] => [.,[[[.,.],[[.,.],.]],[[.,.],.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,1,1] => 2

[1,5,4,7,6,2,8,3] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2] => 1

[2,3,7,6,5,1,8,4] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1,1,1] => 2

[3,1,2,4,8,5,7,6] => [[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,2] => 2

[1,7,2,5,3,8,6,4] => [.,[[.,[[.,[.,.]],[.,.]]],[.,.]]] => [1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2] => 0

[2,4,8,3,7,1,5,6] => [[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,1,1] => 2

[3,8,7,2,4,6,1,5] => [[[.,.],.],[[[.,[[.,.],.]],.],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,2,2,1] => 4

[8,2,3,7,1,4,5,6] => [[[.,.],[.,[[.,[.,[.,.]]],.]]],.] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,1,1,1,1] => 2

[2,8,3,7,1,4,5,6] => [[.,.],[[.,[[.,[.,[.,.]]],.]],.]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,1,1,1,1] => 2

[3,4,5,1,7,6,8,2] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2] => 0

[1,7,3,4,5,2,8,6] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1,1] => 0

[1,7,2,5,4,3,8,6] => [.,[[.,[[[.,.],.],[.,.]]],[.,.]]] => [1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1] => 1

[2,6,7,3,4,8,1,5] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1,1] => 0

[1,5,8,7,4,3,6,2] => [.,[[[[.,.],.],.],[[[.,.],.],.]]] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,2,1] => 4

[1,7,2,4,6,8,3,5] => [.,[[.,[[.,.],[[.,.],.]]],[.,.]]] => [1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1] => 1

[1,8,6,2,7,3,5,4] => [.,[[[.,[.,[[.,.],.]]],[.,.]],.]] => [1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [6,4,4,1] => 2

[1,7,8,6,2,3,5,4] => [.,[[[.,[.,[[.,.],.]]],.],[.,.]]] => [1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1] => 2

[2,1,8,3,5,7,6,4] => [[.,.],[[.,[[.,.],[[.,.],.]]],.]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,1,1,1] => 2

[2,8,1,3,6,7,5,4] => [[.,.],[[.,[[[.,.],.],[.,.]]],.]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,1,1,1] => 2

[3,2,4,5,6,7,8,1,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2,1] => 1

[2,5,6,3,1,4,8,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1,1] => 1

[2,4,7,8,5,3,1,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => 0

[2,1,4,7,8,5,3,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => 0

[6,1,2,7,5,8,3,4] => [[.,[.,[[.,[.,.]],.]]],[.,[.,.]]] => [1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [5,5,5,2] => 1

[2,7,3,1,4,6,8,5] => [[.,.],[[.,[.,[[.,.],.]]],[.,.]]] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1,1,1] => 1

[2,8,3,1,6,5,7,4] => [[.,.],[[.,[[[.,.],.],[.,.]]],.]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,1,1,1] => 2

[2,8,4,1,5,7,6,3] => [[.,.],[[[.,.],[.,[[.,.],.]]],.]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2,1,1] => 2

[1,8,4,2,5,7,6,3] => [.,[[[.,[.,.]],[.,[[.,.],.]]],.]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2] => 2

[1,8,5,2,4,7,6,3] => [.,[[[.,[[.,.],.]],[[.,.],.]],.]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,3,1] => 3

[1,4,6,2,8,7,5,3] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2] => 1

[2,4,6,1,8,7,5,3] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,8,4,5,1,7,6,3] => [[.,.],[[[.,.],[.,[[.,.],.]]],.]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2,1,1] => 2

[1,8,2,4,5,7,6,3] => [.,[[.,[[.,.],[.,[[.,.],.]]]],.]] => [1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1,1] => 2

[1,2,8,3,5,7,6,4] => [.,[.,[[.,[[.,.],[[.,.],.]]],.]]] => [1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1] => 2

[1,3,8,2,5,7,6,4] => [.,[[.,.],[[[.,.],[[.,.],.]],.]]] => [1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1,1] => 2

[2,3,8,1,5,7,6,4] => [[.,.],[.,[[[.,.],[[.,.],.]],.]]] => [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1,1,1] => 2

[1,6,2,8,7,5,3,4] => [.,[[.,[[.,[.,.]],.]],[[.,.],.]]] => [1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2] => 2

[1,6,3,8,7,5,2,4] => [.,[[[.,.],[[.,.],.]],[[.,.],.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,1,1] => 2

[2,8,1,4,5,7,6,3] => [[.,.],[[[.,.],[.,[[.,.],.]]],.]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2,1,1] => 2

[2,3,6,8,7,5,1,4] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1,1] => 2

[3,8,4,5,1,6,2,7] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,2] => 1

[1,5,8,4,6,2,3,7] => [.,[[[.,[.,.]],.],[[.,[.,.]],.]]] => [1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,2] => 2

[1,6,5,8,7,2,3,4] => [.,[[[.,[.,[.,.]]],.],[[.,.],.]]] => [1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3] => 2

[5,1,2,7,6,8,3,4] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4] => 0

[6,1,7,2,5,8,3,4] => [[.,[.,[[.,[.,.]],.]]],[.,[.,.]]] => [1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [5,5,5,2] => 1

[1,7,6,5,8,2,3,4] => [.,[[[[.,[.,[.,.]]],.],.],[.,.]]] => [1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3] => 2

[1,6,8,5,7,2,3,4] => [.,[[[.,[.,[.,.]]],.],[[.,.],.]]] => [1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3] => 2

[1,6,3,8,7,2,4,5] => [.,[[[.,.],[.,[.,.]]],[[.,.],.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1] => 1

[1,7,3,2,4,6,8,5] => [.,[[[.,.],[.,[[.,.],.]]],[.,.]]] => [1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1,1] => 1

[5,1,2,6,8,7,3,4] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [5,4,4,4] => 1

[1,8,6,2,5,7,3,4] => [.,[[[.,[[.,[.,.]],.]],[.,.]],.]] => [1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2] => 2

[5,7,8,1,2,6,3,4] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4] => 0

[8,1,5,7,6,2,3,4] => [[.,[[.,[.,[.,.]]],[[.,.],.]]],.] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [7,4,3,3] => 2

[1,5,8,7,6,2,3,4] => [.,[[.,[.,[.,.]]],[[[.,.],.],.]]] => [1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3] => 2

[7,8,1,3,4,5,2,6] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1,1] => 0

[1,7,4,8,2,5,3,6] => [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2] => 0

[7,1,8,2,4,6,3,5] => [[.,[.,[[.,.],[[.,.],.]]]],[.,.]] => [1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [6,6,2,1,1] => 1

[1,5,4,8,6,3,7,2] => [.,[[[[.,.],.],.],[[.,[.,.]],.]]] => [1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,2,1] => 3

[3,8,4,5,2,6,7,1] => [[[.,.],.],[[.,[.,[.,[.,.]]]],.]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,2,1] => 2

[2,5,1,3,7,8,6,4] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[2,4,7,5,3,6,1,8] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => 0

[2,5,7,3,4,1,6,8] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[2,3,5,8,6,4,7,1] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1,1,1] => 1

[2,4,7,3,8,6,5,1] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1,1] => 1

[3,4,2,7,5,8,6,1] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2,1] => 1

[2,3,6,1,8,7,5,4] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1,1] => 2

[4,1,5,6,8,3,7,2] => [[.,[[.,.],.]],[.,[.,[[.,.],.]]]] => [1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3,1] => 2

[8,1,2,3,4,5,6,7,10,9] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,1,0,0] => [8,7,7] => 1

[1,7,2,3,4,5,6,9,8] => [.,[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]] => [1,1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0,0] => [6,5,5] => 1

[1,3,8,5,2,7,4,6] => [.,[[.,.],[[[.,.],[[.,.],.]],.]]] => [1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1,1] => 2

[1,3,8,6,7,2,4,5] => [.,[[.,.],[[[.,[.,.]],[.,.]],.]]] => [1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1,1] => 1

[2,8,3,7,6,1,4,5] => [[.,.],[[.,[[[.,[.,.]],.],.]],.]] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,1,1,1] => 3

[1,3,8,7,6,2,4,5] => [.,[[.,.],[[[[.,[.,.]],.],.],.]]] => [1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,1,1] => 3

[4,5,6,8,1,2,7,3] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3] => 1

[1,4,6,8,7,2,3,5] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2] => 1

[1,6,5,7,8,2,3,4] => [.,[[[.,[.,[.,.]]],.],[.,[.,.]]]] => [1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3] => 1

[8,1,2,7,4,5,3,6] => [[.,[.,[[[.,.],[.,[.,.]]],.]]],.] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,1,1] => 2

[8,1,3,7,5,6,4,2] => [[.,[[.,.],[[[.,.],[.,.]],.]]],.] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [7,4,2,2,1,1] => 2

[1,2,5,3,8,6,7,4] => [.,[.,[[.,[.,.]],[[.,[.,.]],.]]]] => [1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2] => 1

[4,1,6,5,7,8,2,3] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[1,3,8,2,5,6,7,4] => [.,[[.,.],[[[.,.],[.,[.,.]]],.]]] => [1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1,1] => 1

[1,8,6,7,2,5,4,3] => [.,[[[.,[[[.,.],.],.]],[.,.]],.]] => [1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2,1] => 3

[1,6,7,3,8,5,4,2] => [.,[[[.,.],[[.,.],.]],[.,[.,.]]]] => [1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1] => 1

[4,5,6,2,7,3,8,1] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1,1] => 0

[4,5,6,3,7,1,8,2] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,2] => 1

[3,8,4,1,5,2,6,7] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,2] => 1

[2,5,4,6,1,3,7,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1,1] => 1

[2,5,6,4,1,3,7,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1,1] => 1

[7,1,2,5,4,6,3,8] => [[.,[.,[[[.,.],.],[.,.]]]],[.,.]] => [1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,1] => 1

[2,4,1,6,5,3,7,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[3,1,4,6,5,2,7,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2] => 0

[4,3,8,5,7,2,6,1] => [[[[.,.],.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,3,3,2,1] => 4

[7,2,3,1,8,4,5,6] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1,1,1] => 0

[2,1,4,8,3,7,5,6] => [[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,1,1] => 2

[1,2,7,8,4,3,6,5] => [.,[.,[[[.,.],[[.,.],.]],[.,.]]]] => [1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1] => 1

[3,5,4,6,7,1,8,2] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 0

[1,4,2,6,5,8,7,3] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2] => 1

[1,3,2,6,4,8,7,5] => [.,[[.,.],[[.,[.,.]],[[.,.],.]]]] => [1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1] => 1

[1,4,2,5,3,8,7,6] => [.,[[.,[.,.]],[.,[[[.,.],.],.]]]] => [1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2] => 2

[1,5,2,6,4,8,7,3] => [.,[[.,[[.,.],.]],[.,[[.,.],.]]]] => [1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1] => 2

[1,6,2,5,3,8,7,4] => [.,[[.,[[.,[.,.]],.]],[[.,.],.]]] => [1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2] => 2

[1,7,3,5,4,8,6,2] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]] => [1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1] => 0

[1,8,2,6,3,7,5,4] => [.,[[.,[[.,[[.,.],.]],[.,.]]],.]] => [1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1] => 2

[1,8,3,6,4,7,5,2] => [.,[[[.,.],[[.,[.,.]],[.,.]]],.]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1,1,1] => 1

[1,7,2,6,4,8,5,3] => [.,[[.,[[[.,.],[.,.]],.]],[.,.]]] => [1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1,1] => 1

[1,7,2,6,3,8,5,4] => [.,[[.,[[.,[[.,.],.]],.]],[.,.]]] => [1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1] => 2

[1,5,2,7,4,8,6,3] => [.,[[.,[[.,.],.]],[[.,.],[.,.]]]] => [1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1] => 1

[1,4,2,8,5,7,6,3] => [.,[[.,[.,.]],[[.,[[.,.],.]],.]]] => [1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2] => 2

[1,5,3,8,4,7,6,2] => [.,[[[.,.],[.,.]],[[[.,.],.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1,1] => 2

[4,8,7,3,5,2,1,6] => [[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,3,3,2,1] => 4

[2,3,8,7,4,6,1,5] => [[.,.],[.,[[[.,[[.,.],.]],.],.]]] => [1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,1,1,1] => 3

[2,3,8,7,5,6,1,4] => [[.,.],[.,[[[[.,.],[.,.]],.],.]]] => [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,1,1,1] => 2

[2,4,8,6,5,1,7,3] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1,1] => 1

[1,6,8,3,7,4,2,5] => [.,[[[.,.],[.,[.,.]]],[[.,.],.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1] => 1

[1,7,5,8,2,4,3,6] => [.,[[[.,[[.,.],.]],[.,.]],[.,.]]] => [1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,1] => 1

[1,5,6,3,8,2,4,7] => [.,[[[.,.],[.,.]],[.,[[.,.],.]]]] => [1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1] => 1

[1,5,8,7,2,4,6,3] => [.,[[.,[[.,.],.]],[[[.,.],.],.]]] => [1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1] => 3

[1,4,8,7,3,6,5,2] => [.,[[[.,.],.],[[[[.,.],.],.],.]]] => [1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,2,1] => 4

[1,7,8,3,2,6,5,4] => [.,[[[.,.],[[[.,.],.],.]],[.,.]]] => [1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,1,1] => 2

[1,7,5,4,8,3,2,6] => [.,[[[[[.,.],.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,2,1] => 2

[1,7,4,5,6,8,2,3] => [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2] => 0

[1,6,4,2,3,5,7,8] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2] => 0

[1,8,7,2,3,4,5,6] => [.,[[[.,[.,[.,[.,[.,.]]]]],.],.]] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5] => 2

[1,5,8,6,2,3,4,7] => [.,[[.,[.,[.,.]]],[[.,[.,.]],.]]] => [1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3] => 1

[1,6,5,7,2,3,4,8] => [.,[[[.,[.,[.,.]]],.],[.,[.,.]]]] => [1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3] => 1

[1,7,5,6,2,3,4,8] => [.,[[[.,[.,[.,.]]],[.,.]],[.,.]]] => [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3] => 0

[1,3,2,7,6,4,5,8] => [.,[[.,.],[[[.,[.,.]],.],[.,.]]]] => [1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1,1] => 1

[1,2,3,7,6,4,5,8] => [.,[.,[.,[[[.,[.,.]],.],[.,.]]]]] => [1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [3,3,2] => 1

[1,5,4,2,3,7,6,8] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2] => 1

[1,5,4,2,3,8,6,7] => [.,[[[.,[.,.]],.],[[.,[.,.]],.]]] => [1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,2] => 2

[1,3,2,8,6,4,5,7] => [.,[[.,.],[[[.,[.,.]],[.,.]],.]]] => [1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1,1] => 1

[1,7,5,8,2,3,4,6] => [.,[[[.,[.,[.,.]]],[.,.]],[.,.]]] => [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3] => 0

[1,8,7,5,2,3,4,6] => [.,[[[[.,[.,[.,.]]],[.,.]],.],.]] => [1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3] => 2

[2,1,5,8,6,3,7,4] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1,1] => 1

[2,5,3,8,6,1,7,4] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1,1] => 1

[2,4,6,8,5,3,7,1] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[3,8,4,1,5,7,6,2] => [[.,[.,.]],[[.,[.,[[.,.],.]]],.]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2,2] => 2

[2,8,3,5,6,7,1,4] => [[.,.],[[.,[[.,.],[.,[.,.]]]],.]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,1,1,1] => 1

[2,3,7,4,6,1,8,5] => [[.,.],[.,[[.,[[.,.],.]],[.,.]]]] => [1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1,1,1] => 1

[2,4,6,3,5,7,8,1] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[2,3,6,1,5,7,8,4] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1,1] => 1

[4,6,1,2,5,7,8,3] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[2,4,1,6,5,7,8,3] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[1,2,8,6,4,5,7,3] => [.,[.,[[[[.,.],[.,.]],[.,.]],.]]] => [1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1] => 1

[1,8,5,3,4,6,7,2] => [.,[[[[.,.],[.,.]],[.,[.,.]]],.]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,1,1] => 1

[7,1,6,2,3,8,4,5] => [[.,[[.,[.,[.,[.,.]]]],.]],[.,.]] => [1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [6,6,4] => 1

[1,8,2,3,4,5,6,7,9] => [.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [6,6] => 0

[1,4,5,8,6,3,2,7] => [.,[[[.,.],.],[.,[[.,[.,.]],.]]]] => [1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,1] => 2

[4,5,2,6,7,3,1,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1,1] => 0

[4,3,5,1,6,7,8,2] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,2] => 1

[5,7,6,1,2,3,8,4] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4] => 0

[1,8,7,6,5,4,3,2,9] => [.,[[[[[[[.,.],.],.],.],.],.],[.,.]]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [6,6,5,4,3,2,1] => 5

[1,9,8,7,6,5,4,3,2,10] => [.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [7,7,6,5,4,3,2,1] => 6

[1,8,4,3,2,6,7,5] => [.,[[[[.,.],.],[[.,.],[.,.]]],.]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,2,1] => 2

[5,4,3,8,2,1,7,6] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,4,3,2,1] => 5

[1,8,6,7,3,2,4,5] => [.,[[[[.,.],[.,[.,.]]],[.,.]],.]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,4,1,1,1] => 1

[1,8,4,3,2,7,5,6] => [.,[[[[.,.],.],[[.,[.,.]],.]],.]] => [1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,2,1] => 3

[5,4,3,8,2,1,6,7] => [[[[[.,.],.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,4,4,3,2,1] => 4

[1,8,4,3,2,5,7,6] => [.,[[[[.,.],.],[.,[[.,.],.]]],.]] => [1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2,1] => 3

[5,4,3,8,2,6,7,1] => [[[[[.,.],.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,4,4,3,2,1] => 4

[4,5,6,7,8,1,2,9,3] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3,3] => 0

[4,5,6,7,1,2,8,9,3] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3,3] => 0

[4,5,6,1,2,7,8,9,3] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3,3] => 0

[4,5,1,2,6,7,8,9,3] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3,3] => 0

[7,2,3,4,5,8,1,6] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1,1,1] => 0

[8,1,5,2,3,7,6,4] => [[.,[[.,[.,[.,.]]],[[.,.],.]]],.] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [7,4,3,3] => 2

[1,5,4,8,6,3,2,7] => [.,[[[[.,.],.],.],[[.,[.,.]],.]]] => [1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,2,1] => 3

[1,8,7,5,3,6,4,2] => [.,[[[[[.,.],[.,.]],[.,.]],.],.]] => [1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3,1,1] => 2

[1,7,4,2,6,5,3,8] => [.,[[[.,[.,.]],[[.,.],.]],[.,.]]] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,2] => 1

[1,5,8,3,6,7,4,2] => [.,[[[.,.],[.,.]],[[.,[.,.]],.]]] => [1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1] => 1

[1,8,2,5,6,7,3,4] => [.,[[.,[[.,[.,.]],[.,[.,.]]]],.]] => [1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2] => 1

[8,1,4,2,6,5,3,7] => [[.,[[.,[.,.]],[[.,.],[.,.]]]],.] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2,2] => 1

[7,8,1,2,3,4,5,9,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,6,6] => 0

[7,1,8,2,9,3,4,5,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,6,6] => 0

[6,1,7,2,8,3,9,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,5,5,5] => 0

[5,1,6,2,7,3,8,4,9] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,4,4,4,4] => 0

[7,1,8,2,3,9,4,5,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,6,6] => 0

[6,1,7,2,8,3,4,9,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,5,5,5] => 0

[2,3,5,7,4,6,8,1] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1,1] => 0

[2,4,7,8,5,3,6,1] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => 0

[2,4,7,5,8,3,6,1] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => 0

[1,8,5,7,2,4,3,6] => [.,[[[.,[[.,.],.]],[[.,.],.]],.]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,3,1] => 3

[1,8,5,4,2,3,6,7] => [.,[[[[.,[.,.]],.],[.,[.,.]]],.]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,2] => 2

[1,3,6,8,5,4,2,7] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]] => [1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1] => 2

[1,6,3,8,2,7,4,5] => [.,[[[.,.],[.,[.,.]]],[[.,.],.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1] => 1

[1,4,2,7,5,8,3,6] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2] => 0

[1,8,2,3,6,7,5,4] => [.,[[.,[.,[[[.,.],.],[.,.]]]],.]] => [1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1] => 2

[1,3,6,8,2,7,5,4] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]] => [1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1] => 2

[1,6,5,4,3,8,2,7] => [.,[[[[[.,.],.],.],.],[[.,.],.]]] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3,2,1] => 4

[1,8,3,4,5,6,2,7] => [.,[[[.,.],[.,[.,[.,[.,.]]]]],.]] => [1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1,1] => 1

[1,8,3,6,2,4,5,7] => [.,[[[.,.],[[.,[.,.]],[.,.]]],.]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1,1,1] => 1

[1,4,5,8,3,6,2,7] => [.,[[[.,.],.],[.,[[.,[.,.]],.]]]] => [1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,1] => 2

[1,2,7,8,4,5,3,6] => [.,[.,[[[.,.],[.,[.,.]]],[.,.]]]] => [1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1] => 0

[1,4,7,3,2,6,8,5] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1] => 2

[1,5,7,3,6,2,8,4] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1] => 0

[1,2,5,4,8,3,7,6] => [.,[.,[[[.,.],.],[[[.,.],.],.]]]] => [1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1] => 3

[1,4,3,5,8,2,7,6] => [.,[[[.,.],.],[.,[[[.,.],.],.]]]] => [1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,1] => 3

[1,4,3,6,8,7,2,5] => [.,[[[.,.],.],[[.,.],[[.,.],.]]]] => [1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1] => 2

[1,5,3,7,6,8,2,4] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1] => 0

[1,6,4,5,7,8,2,3] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2] => 0

[3,2,4,6,8,7,1,5] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2,1] => 2

[6,5,4,8,3,7,2,1] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,5,4,3,2,1] => 5

[4,3,8,7,2,6,5,1] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,3,2,1] => 5

[2,4,5,8,7,3,1,6] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,1,1] => 2

[2,4,5,8,6,7,1,3] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,1,1] => 1

[4,1,5,8,6,7,2,3] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [5,3,3,3,3] => 1

[3,4,5,8,6,7,2,1] => [[[.,.],.],[.,[.,[[.,[.,.]],.]]]] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,2,1] => 2

[3,4,5,8,7,1,2,6] => [[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,2] => 2

[3,8,4,5,6,7,2,1] => [[[.,.],.],[[.,[.,[.,[.,.]]]],.]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,2,1] => 2

[5,1,4,6,7,2,8,3] => [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,2] => 1

[1,6,2,5,4,8,3,7] => [.,[[.,[[[.,.],.],.]],[[.,.],.]]] => [1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,1] => 3

[1,6,7,4,3,8,5,2] => [.,[[[[.,.],.],[.,.]],[.,[.,.]]]] => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2,1] => 1

[2,5,7,3,1,4,8,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[1,2,6,7,4,3,8,5] => [.,[.,[[[.,.],[.,.]],[.,[.,.]]]]] => [1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1] => 0

[8,2,3,4,7,1,5,6] => [[[.,.],[.,[.,[[.,[.,.]],.]]]],.] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,1,1,1,1] => 2

[2,4,5,8,3,1,6,7] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,1,1] => 1

[2,4,3,8,5,1,6,7] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,1,1] => 1

[1,5,6,7,3,8,2,4] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => [1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1] => 0

[1,6,5,4,8,3,2,7] => [.,[[[[[.,.],.],.],.],[[.,.],.]]] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3,2,1] => 4

[1,7,3,5,8,4,6,2] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]] => [1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1] => 0

[3,8,7,2,4,6,5,1] => [[[.,.],.],[[[.,[[.,.],.]],.],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,2,2,1] => 4

[1,3,7,6,4,8,5,2] => [.,[[.,.],[[[.,[.,.]],.],[.,.]]]] => [1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1,1] => 1

[1,8,6,3,4,2,5,7] => [.,[[[[.,.],[.,[.,.]]],[.,.]],.]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,4,1,1,1] => 1

[1,4,7,8,5,2,3,6] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2] => 0

[8,1,2,7,5,4,3,6] => [[.,[.,[[[[.,.],.],[.,.]],.]]],.] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [7,4,2,2,1] => 3

[1,8,7,5,3,2,6,4] => [.,[[[[[.,.],[.,.]],[.,.]],.],.]] => [1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3,1,1] => 2

[3,4,6,8,1,5,7,2] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2] => 1

[1,7,5,2,6,4,8,3] => [.,[[[.,[[.,.],.]],[.,.]],[.,.]]] => [1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,1] => 1

[1,2,5,7,8,4,6,3] => [.,[.,[[[.,.],.],[[.,.],[.,.]]]]] => [1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1] => 1

[1,7,2,8,4,3,5,6] => [.,[[.,[[.,.],[.,[.,.]]]],[.,.]]] => [1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1] => 0

[1,6,3,5,7,8,2,4] => [.,[[[.,.],[[.,.],.]],[.,[.,.]]]] => [1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1] => 1

[1,5,3,4,7,8,2,6] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1] => 0

[5,4,1,6,7,8,2,3] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3] => 1

[5,1,4,6,7,8,2,3] => [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,2] => 1

[8,1,4,6,5,2,7,3] => [[.,[[.,[.,.]],[[.,.],[.,.]]]],.] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2,2] => 1

[1,2,4,7,6,3,8,5] => [.,[.,[[.,.],[[[.,.],.],[.,.]]]]] => [1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1] => 1

[1,2,8,7,4,3,6,5] => [.,[.,[[[[.,.],[[.,.],.]],.],.]]] => [1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,1] => 3

[1,3,6,4,7,8,2,5] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => [1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1] => 0

[1,6,4,3,7,8,2,5] => [.,[[[[.,.],.],[.,.]],[.,[.,.]]]] => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2,1] => 1

[1,5,6,3,7,8,2,4] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => [1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1] => 0

[6,7,1,2,3,4,8,9,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,5,5,5] => 0

[1,5,2,4,3,8,7,6] => [.,[[.,[[.,.],.]],[[[.,.],.],.]]] => [1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1] => 3

[1,6,3,8,4,5,7,2] => [.,[[[.,.],[.,[.,.]]],[[.,.],.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1] => 1

[2,3,8,4,7,5,6,1] => [[.,.],[.,[[.,[[.,[.,.]],.]],.]]] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1,1,1,1] => 2

[2,4,7,8,6,1,5,3] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1,1] => 1

[2,4,8,5,1,7,3,6] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,1,1] => 2

[2,8,3,5,1,6,4,7] => [[.,.],[[.,[[.,.],[.,[.,.]]]],.]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,1,1,1] => 1

[1,4,6,2,7,5,3,8] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2] => 0

[8,2,1,4,5,6,7,3] => [[[.,.],[[.,.],[.,[.,[.,.]]]]],.] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2,1,1] => 1

[1,4,8,5,2,6,3,7] => [.,[[.,[.,.]],[[.,[.,[.,.]]],.]]] => [1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2] => 1

[1,2,8,4,3,6,7,5] => [.,[.,[[[.,.],[[.,.],[.,.]]],.]]] => [1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1] => 1

[1,2,7,5,3,4,6,8] => [.,[.,[[[.,[.,.]],[.,.]],[.,.]]]] => [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2] => 0

[1,7,3,2,6,8,4,5] => [.,[[[.,.],[[.,[.,.]],.]],[.,.]]] => [1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1,1,1] => 1

[1,8,4,2,7,6,3,5] => [.,[[[.,[.,.]],[[[.,.],.],.]],.]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,2] => 3

[3,4,6,2,1,8,5,7] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2,1] => 2

[5,6,4,8,3,2,1,7] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [5,4,4,4,3,2,1] => 4

[4,5,1,6,7,8,3,2] => [[.,[[.,.],.]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1] => 1

[6,7,1,2,4,8,5,3] => [[.,[.,[[.,.],[.,.]]]],[.,[.,.]]] => [1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [5,5,5,1,1] => 0

[1,6,3,4,7,8,5,2] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]] => [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1] => 0

[2,3,6,4,7,5,8,1] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1,1] => 0

[7,8,1,3,4,5,6,2] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1,1] => 0

[1,8,2,6,7,3,4,5] => [.,[[.,[[.,[.,[.,.]]],[.,.]]],.]] => [1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [6,3,3] => 1

[7,1,2,6,3,8,5,4] => [[.,[.,[[.,[[.,.],.]],.]]],[.,.]] => [1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [6,6,3,1] => 2

[8,1,2,6,3,7,5,4] => [[.,[.,[[.,[[.,.],.]],[.,.]]]],.] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [7,3,3,1] => 2

[8,1,2,7,6,3,5,4] => [[.,[.,[[[.,[[.,.],.]],.],.]]],.] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [7,4,3,1] => 4

[6,1,2,7,4,3,8,5] => [[.,[.,[[.,.],[.,.]]]],[.,[.,.]]] => [1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [5,5,5,1,1] => 0

[5,1,2,6,3,8,7,4] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [5,4,4,4] => 1

[5,1,2,7,3,8,6,4] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4] => 0

[6,1,2,7,3,5,8,4] => [[.,[.,[.,[[.,.],.]]]],[.,[.,.]]] => [1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,5,5,1] => 1

[4,2,1,5,3,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1,1] => 0

[4,1,5,2,6,3,7,8,9] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3,3] => 0

[3,1,4,2,5,6,7,8,9] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2] => 0

[1,5,8,4,7,6,3,2] => [.,[[[[.,.],.],.],[[[.,.],.],.]]] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,2,1] => 4

[3,4,8,1,7,5,6,2] => [[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,2] => 2

[8,1,2,4,5,6,7,3] => [[.,[.,[[.,.],[.,[.,[.,.]]]]]],.] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1,1] => 1

[1,8,3,6,7,2,4,5] => [.,[[[.,.],[[.,[.,.]],[.,.]]],.]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1,1,1] => 1

[1,2,8,3,7,4,6,5] => [.,[.,[[.,[[.,[[.,.],.]],.]],.]]] => [1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [5,3,1] => 3

[1,9,2,3,4,5,6,7,8,10] => [.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [7,7] => 0

[4,2,5,6,7,8,3,1] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1,1] => 0

[4,1,3,5,6,7,8,2] => [[.,[[.,.],.]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1] => 1

[4,5,8,6,1,2,7,3] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [5,3,3,3,3] => 1

[1,6,5,2,3,4,8,7] => [.,[[[.,[.,[.,.]]],.],[[.,.],.]]] => [1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3] => 2

[1,2,3,4,5,6,8,7,9] => [.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]] => [1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,1] => 0

[9,2,3,4,5,6,7,1,8] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1,1,1,1,1,1] => 1

[1,3,5,8,6,4,7,2] => [.,[[.,.],[[.,.],[[.,[.,.]],.]]]] => [1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1,1] => 1

[1,3,5,8,6,7,2,4] => [.,[[.,.],[[.,.],[[.,[.,.]],.]]]] => [1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1,1] => 1

[1,2,7,5,3,4,8,6] => [.,[.,[[[.,[.,.]],[.,.]],[.,.]]]] => [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2] => 0

[1,7,8,2,5,3,4,6] => [.,[[.,[[.,[.,.]],[.,.]]],[.,.]]] => [1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2] => 0

[1,2,8,7,3,4,6,5] => [.,[.,[[[.,[.,[[.,.],.]]],.],.]]] => [1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [5,4,1] => 3

[1,2,6,8,5,3,4,7] => [.,[.,[[[.,[.,.]],.],[[.,.],.]]]] => [1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2] => 2

[1,5,8,6,2,4,3,7] => [.,[[.,[[.,.],.]],[[.,[.,.]],.]]] => [1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1] => 2

[1,2,5,3,6,8,7,4] => [.,[.,[[.,[.,.]],[.,[[.,.],.]]]]] => [1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2] => 1

[1,7,2,3,5,8,6,4] => [.,[[.,[.,[[.,.],[.,.]]]],[.,.]]] => [1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1] => 0

[2,8,3,7,5,1,6,4] => [[.,.],[[.,[[[.,.],[.,.]],.]],.]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,1,1,1] => 2

[1,8,2,3,7,5,6,4] => [.,[[.,[.,[[[.,.],[.,.]],.]]],.]] => [1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1] => 2

[1,6,7,8,2,4,3,5] => [.,[[.,[[.,.],[.,.]]],[.,[.,.]]]] => [1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1] => 0

[1,8,5,6,4,3,2,7] => [.,[[[[[.,.],.],.],[.,[.,.]]],.]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,2,1] => 3

[2,8,3,5,6,4,1,7] => [[.,.],[[.,[[.,.],[.,[.,.]]]],.]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,1,1,1] => 1

[4,1,5,7,6,8,2,3] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [4,4,3,3,3] => 0

[1,5,2,7,4,3,6,8] => [.,[[.,[[.,.],.]],[[.,.],[.,.]]]] => [1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1] => 1

[2,7,3,5,1,6,8,4] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1,1] => 0

[1,3,6,5,2,7,4,8] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1] => 1

[1,2,6,5,3,4,7,8] => [.,[.,[[[.,[.,.]],.],[.,[.,.]]]]] => [1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2] => 1

[1,7,2,5,6,8,3,4] => [.,[[.,[[.,[.,.]],[.,.]]],[.,.]]] => [1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2] => 0

[1,7,2,4,8,3,5,6] => [.,[[.,[[.,.],[.,[.,.]]]],[.,.]]] => [1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1] => 0

[1,6,2,4,5,3,7,8] => [.,[[.,[[.,.],[.,.]]],[.,[.,.]]]] => [1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1] => 0

[1,3,2,8,4,5,7,6] => [.,[[.,.],[[.,[.,[[.,.],.]]],.]]] => [1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1,1] => 2

[1,6,8,2,4,3,5,7] => [.,[[.,[[.,.],[.,.]]],[[.,.],.]]] => [1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1] => 1

[1,6,7,2,5,3,4,8] => [.,[[.,[[.,[.,.]],.]],[.,[.,.]]]] => [1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2] => 1

[1,2,8,3,6,7,4,5] => [.,[.,[[.,[[.,[.,.]],[.,.]]],.]]] => [1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [5,2,2] => 1

[1,7,2,5,3,4,8,6] => [.,[[.,[[.,[.,.]],[.,.]]],[.,.]]] => [1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2] => 0

[1,7,5,6,2,3,8,4] => [.,[[[.,[.,[.,.]]],[.,.]],[.,.]]] => [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3] => 0

[1,7,4,3,8,2,5,6] => [.,[[[[.,.],.],[.,[.,.]]],[.,.]]] => [1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2,1] => 1

[1,2,5,4,8,3,6,7] => [.,[.,[[[.,.],.],[[.,[.,.]],.]]]] => [1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1] => 2

[7,1,3,8,2,4,5,6] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1,1] => 0

[8,1,3,7,2,4,5,6] => [[.,[[.,.],[[.,[.,[.,.]]],.]]],.] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,1,1,1] => 2

[1,6,4,7,8,2,3,5] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2] => 0

[1,3,7,8,5,6,2,4] => [.,[[.,.],[[[.,.],[.,.]],[.,.]]]] => [1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1] => 0

[1,3,8,7,4,2,6,5] => [.,[[.,.],[[[.,[[.,.],.]],.],.]]] => [1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,1,1] => 3

[3,8,4,5,1,6,7,2] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,2] => 1

[8,1,4,5,7,6,3,2] => [[.,[[[.,.],.],[.,[[.,.],.]]]],.] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,2,1] => 3

[2,4,1,8,5,7,6,3] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,1,1] => 2

[1,8,4,2,3,7,6,5] => [.,[[[.,[.,.]],[[[.,.],.],.]],.]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,2] => 3

[2,8,3,7,4,1,6,5] => [[.,.],[[.,[[.,[[.,.],.]],.]],.]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,1,1,1] => 3

[2,3,1,8,7,6,4,5] => [[.,.],[.,[[[[.,[.,.]],.],.],.]]] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,1,1,1] => 3

[1,3,4,8,7,2,5,6] => [.,[[.,.],[.,[[[.,[.,.]],.],.]]]] => [1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1,1] => 2

[8,1,3,4,6,7,2,5] => [[.,[[.,.],[.,[[.,.],[.,.]]]]],.] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1,1,1] => 1

[1,8,4,7,6,5,2,3] => [.,[[[.,[.,.]],[[[.,.],.],.]],.]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,2] => 3

[2,3,4,7,6,8,1,5] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1,1,1] => 1

[4,5,2,6,7,1,8,3] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1,1] => 0

[4,8,5,3,7,2,1,6] => [[[[.,.],.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,3,3,2,1] => 4

[7,8,3,4,1,5,6,2] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,2,2] => 0

[3,5,6,8,1,4,2,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,2] => 1

[5,1,2,4,6,7,8,3] => [[.,[.,[[.,.],.]]],[.,[.,[.,.]]]] => [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,1] => 1

[5,8,4,6,3,2,7,1] => [[[[[.,.],.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,4,4,3,2,1] => 4

[5,4,3,8,6,2,7,1] => [[[[[.,.],.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,4,4,3,2,1] => 4

[1,3,2,4,5,6,7,8,9] => [.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 0

[2,4,6,3,8,7,5,1] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,3,6,8,7,1,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,6,3,8,7,1,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,6,5,8,7,1,3] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,6,8,5,7,3,1] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,6,8,5,7,1,3] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,6,8,3,7,1,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,6,8,1,7,3,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,6,5,8,3,7,1] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,6,5,8,1,7,3] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,6,8,5,1,7,3] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,6,8,7,3,5,1] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,6,8,7,1,5,3] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,6,8,7,1,3,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,6,8,5,1,3,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,6,5,1,8,3,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,6,5,3,8,1,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,6,5,8,3,1,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,6,8,5,3,1,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,6,8,7,3,1,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[2,4,6,8,7,5,1,3] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 1

[1,8,6,5,3,2,7,4] => [.,[[[[[.,.],[.,.]],.],[.,.]],.]] => [1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3,1,1] => 2

[1,6,3,5,8,2,4,7] => [.,[[[.,.],[[.,.],.]],[[.,.],.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,1,1] => 2

[6,1,2,7,8,4,5,3] => [[.,[.,[[.,.],[.,.]]]],[.,[.,.]]] => [1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [5,5,5,1,1] => 0

[4,3,8,2,7,6,5,1] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,3,2,1] => 5

[3,8,7,6,2,5,1,4] => [[[.,.],.],[[[[[.,.],.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,2,1] => 5

[4,8,3,7,2,1,6,5] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,3,2,1] => 5

[4,8,3,7,6,2,5,1] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,3,2,1] => 5

[1,6,4,2,5,3,7,8] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2] => 0

[1,8,6,2,7,3,4,5] => [.,[[[.,[.,[.,[.,.]]]],[.,.]],.]] => [1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [6,4,4] => 1

[1,6,3,2,4,5,7,8] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]] => [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1] => 0

[1,5,2,6,4,3,7,8] => [.,[[.,[[.,.],.]],[.,[.,[.,.]]]]] => [1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1] => 1

[1,5,2,4,6,3,7,8] => [.,[[.,[[.,.],.]],[.,[.,[.,.]]]]] => [1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1] => 1

[1,8,6,2,3,7,4,5] => [.,[[[.,[.,[.,[.,.]]]],[.,.]],.]] => [1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [6,4,4] => 1

[1,5,2,8,6,3,4,7] => [.,[[.,[.,[.,.]]],[[.,[.,.]],.]]] => [1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3] => 1

[1,3,6,8,2,7,4,5] => [.,[[.,.],[[.,[.,.]],[[.,.],.]]]] => [1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1] => 1

[1,4,3,8,2,5,6,7] => [.,[[[.,.],.],[[.,[.,[.,.]]],.]]] => [1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,1] => 2

[1,7,2,3,8,5,4,6] => [.,[[.,[.,[[.,.],[.,.]]]],[.,.]]] => [1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1] => 0

[1,3,8,4,2,5,6,7] => [.,[[.,.],[[.,[.,[.,[.,.]]]],.]]] => [1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1,1] => 1

[1,6,2,8,5,4,3,7] => [.,[[.,[[[.,.],.],.]],[[.,.],.]]] => [1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,1] => 3

[1,7,2,3,8,6,4,5] => [.,[[.,[.,[[.,[.,.]],.]]],[.,.]]] => [1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [5,5,2] => 1

[1,5,3,8,2,7,4,6] => [.,[[[.,.],[.,.]],[[[.,.],.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1,1] => 2

[1,4,8,2,5,6,3,7] => [.,[[.,[.,.]],[[.,[.,[.,.]]],.]]] => [1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2] => 1

[1,5,7,3,2,8,4,6] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1] => 0

[1,2,7,3,6,8,4,5] => [.,[.,[[.,[[.,[.,.]],.]],[.,.]]]] => [1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [4,4,2] => 1

[1,7,2,3,6,8,4,5] => [.,[[.,[.,[[.,[.,.]],.]]],[.,.]]] => [1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [5,5,2] => 1

[1,4,8,3,2,5,6,7] => [.,[[[.,.],.],[[.,[.,[.,.]]],.]]] => [1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,1] => 2

[1,7,2,5,8,3,4,6] => [.,[[.,[[.,[.,.]],[.,.]]],[.,.]]] => [1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2] => 0

[2,9,3,4,5,6,7,8,1] => [[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1,1,1,1,1,1] => 1

[2,5,6,3,4,7,1,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1,1] => 0

[1,3,7,5,6,8,4,2] => [.,[[.,.],[[[.,.],[.,.]],[.,.]]]] => [1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1] => 0

[1,3,6,7,4,5,8,2] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => [1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1] => 0

[1,5,6,3,4,2,7,8] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => [1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1] => 0

[1,5,3,6,4,2,7,8] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => [1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1] => 0

[1,5,3,7,4,6,2,8] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1] => 0

[1,5,7,3,6,4,8,2] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1] => 0

[2,3,6,4,1,8,7,5] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1,1] => 1

[2,3,1,7,8,5,6,4] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1,1] => 0

[3,8,2,1,7,6,4,5] => [[[.,.],.],[[[[.,[.,.]],.],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,2,2,1] => 4

[1,5,4,7,3,6,2,8] => [.,[[[[.,.],.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2,1] => 2

[1,7,3,6,8,4,5,2] => [.,[[[.,.],[[.,[.,.]],.]],[.,.]]] => [1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1,1,1] => 1

[1,2,6,4,7,5,3,8] => [.,[.,[[[.,.],[.,.]],[.,[.,.]]]]] => [1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1] => 0

[1,6,5,7,3,8,4,2] => [.,[[[[.,.],[.,.]],.],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,1,1] => 1

[1,5,6,8,4,2,7,3] => [.,[[[.,[.,.]],.],[.,[[.,.],.]]]] => [1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2] => 2

[2,4,7,8,6,1,3,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1,1] => 1

[4,1,5,6,3,2,7,8] => [[.,[[.,.],.]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1] => 1

[1,7,5,6,4,3,2,8] => [.,[[[[[.,.],.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,2,1] => 2

[2,3,6,5,7,8,1,4] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1,1] => 1

[7,3,8,4,1,5,6,2] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,2,2] => 0

[4,3,5,6,1,7,8,2] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,2] => 1

[3,5,2,6,4,7,8,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => 1

[3,1,5,6,4,7,8,2] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 0

[3,1,4,6,7,5,8,2] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2] => 0

[3,4,1,7,2,6,8,5] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,2] => 1

[2,4,7,5,8,1,3,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => 0

[7,1,3,8,4,5,6,2] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1,1] => 0

[2,6,7,1,3,5,8,4] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1,1] => 1

[2,3,4,6,8,7,1,5] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1,1] => 1

[5,6,4,7,1,2,8,3] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3] => 1

[4,5,1,7,6,8,2,3] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [4,4,3,3,3] => 0

[3,4,1,7,8,5,2,6] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2] => 0

[2,3,7,8,5,4,1,6] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1,1] => 0

[4,5,8,1,2,6,7,3] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [5,3,3,3,3] => 1

[1,3,4,8,6,2,7,5] => [.,[[.,.],[.,[[[.,.],[.,.]],.]]]] => [1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1,1] => 1

[2,7,3,4,1,5,6,8] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1,1,1] => 0

[3,5,2,4,6,7,8,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => 1

[1,4,8,5,6,2,7,3] => [.,[[.,[.,.]],[[.,[.,[.,.]]],.]]] => [1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2] => 1

[1,3,8,5,2,6,7,4] => [.,[[.,.],[[[.,.],[.,[.,.]]],.]]] => [1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1,1] => 1

[1,6,4,3,2,7,8,5] => [.,[[[[.,.],.],[.,.]],[.,[.,.]]]] => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2,1] => 1

[1,7,5,2,3,6,8,4] => [.,[[[.,[.,[.,.]]],[.,.]],[.,.]]] => [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3] => 0

[8,1,2,5,3,6,7,4] => [[.,[.,[[.,[.,.]],[.,[.,.]]]]],.] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2] => 1

[2,4,7,8,5,1,3,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => 0

[2,5,3,8,4,1,6,7] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1,1] => 1

[2,4,8,3,5,7,1,6] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,1,1] => 2

[8,1,7,2,4,3,5,6] => [[.,[[.,[[.,.],[.,[.,.]]]],.]],.] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,1,1] => 2

[1,3,8,2,4,7,5,6] => [.,[[.,.],[[.,[[.,[.,.]],.]],.]]] => [1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1,1,1] => 2

[1,3,7,2,4,6,5,8] => [.,[[.,.],[[.,[[.,.],.]],[.,.]]]] => [1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1,1] => 1

[1,7,3,2,4,6,5,8] => [.,[[[.,.],[.,[[.,.],.]]],[.,.]]] => [1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1,1] => 1

[1,8,3,7,4,2,5,6] => [.,[[[.,.],[[.,[.,[.,.]]],.]],.]] => [1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,1,1,1] => 2

[8,7,3,1,4,2,5,6] => [[[[.,[.,.]],[.,[.,[.,.]]]],.],.] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,2,2,2] => 2

[2,8,4,3,5,7,1,6] => [[.,.],[[[.,.],[.,[[.,.],.]]],.]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2,1,1] => 2

[3,2,8,7,4,1,5,6] => [[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,2,2,1] => 3

[4,1,6,5,2,7,8,3] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[5,4,1,6,7,2,8,3] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3] => 1

[1,8,3,6,7,4,2,5] => [.,[[[.,.],[[.,[.,.]],[.,.]]],.]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1,1,1] => 1

[1,6,3,5,2,7,8,4] => [.,[[[.,.],[[.,.],.]],[.,[.,.]]]] => [1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1] => 1

[1,5,7,3,2,6,4,8] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1] => 0

[8,1,6,7,2,4,3,5] => [[.,[[.,[[.,.],[.,.]]],[.,.]]],.] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [7,4,4,1,1] => 1

[1,6,7,3,5,4,8,2] => [.,[[[.,.],[[.,.],.]],[.,[.,.]]]] => [1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1] => 1

[1,7,3,5,6,8,4,2] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]] => [1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1] => 0

[1,7,8,3,6,4,5,2] => [.,[[[.,.],[[.,[.,.]],.]],[.,.]]] => [1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1,1,1] => 1

[1,8,7,6,4,5,2,3] => [.,[[[[[.,[.,.]],[.,.]],.],.],.]] => [1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,2] => 3

[1,4,6,2,5,3,7,8] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2] => 0

[1,6,3,2,5,4,7,8] => [.,[[[.,.],[[.,.],.]],[.,[.,.]]]] => [1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1] => 1

[1,6,8,2,5,4,7,3] => [.,[[.,[[[.,.],.],.]],[[.,.],.]]] => [1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,1] => 3

[1,5,4,2,6,3,7,8] => [.,[[[.,[.,.]],.],[.,[.,[.,.]]]]] => [1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2] => 1

[1,2,6,4,3,5,7,8] => [.,[.,[[[.,.],[.,.]],[.,[.,.]]]]] => [1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1] => 0

[1,6,8,2,7,5,4,3] => [.,[[.,[[[.,.],.],.]],[[.,.],.]]] => [1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,1] => 3

[1,5,4,7,2,6,8,3] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2] => 1

[1,3,7,6,2,8,5,4] => [.,[[.,.],[[[[.,.],.],.],[.,.]]]] => [1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1,1] => 2

[1,7,6,2,8,4,3,5] => [.,[[[.,[[.,.],[.,.]]],.],[.,.]]] => [1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1,1] => 1

[1,5,2,8,4,3,7,6] => [.,[[.,[[.,.],.]],[[[.,.],.],.]]] => [1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1] => 3

[1,2,8,4,3,6,5,7] => [.,[.,[[[.,.],[[.,.],[.,.]]],.]]] => [1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1] => 1

[1,2,8,5,6,3,4,7] => [.,[.,[[[.,[.,.]],[.,[.,.]]],.]]] => [1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2] => 1

[1,7,3,5,2,8,6,4] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]] => [1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1] => 0

[1,6,7,2,5,8,4,3] => [.,[[.,[[[.,.],.],.]],[.,[.,.]]]] => [1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1] => 2

[1,5,8,3,2,7,4,6] => [.,[[[.,.],[.,.]],[[[.,.],.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1,1] => 2

[1,4,5,8,2,6,3,7] => [.,[[.,[.,.]],[.,[[.,[.,.]],.]]]] => [1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2] => 1

[1,7,6,4,8,2,5,3] => [.,[[[[.,[.,.]],[.,.]],.],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,2] => 1

[1,4,8,6,5,2,7,3] => [.,[[.,[.,.]],[[[.,.],[.,.]],.]]] => [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2] => 1

[1,3,8,2,6,5,4,7] => [.,[[.,.],[[[[.,.],.],[.,.]],.]]] => [1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1,1] => 2

[1,7,6,3,8,2,4,5] => [.,[[[[.,.],[.,[.,.]]],.],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1,1,1] => 1

[1,5,2,7,6,4,8,3] => [.,[[.,[[.,.],.]],[[.,.],[.,.]]]] => [1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1] => 1

[1,2,4,3,8,7,5,6] => [.,[.,[[.,.],[[[.,[.,.]],.],.]]]] => [1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1] => 2

[1,4,3,8,7,2,5,6] => [.,[[[.,.],.],[[[.,[.,.]],.],.]]] => [1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,1] => 3

[1,3,8,6,2,4,5,7] => [.,[[.,.],[[[.,[.,.]],[.,.]],.]]] => [1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1,1] => 1

[1,3,8,5,4,2,6,7] => [.,[[.,.],[[[.,.],[.,[.,.]]],.]]] => [1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1,1] => 1

[1,7,2,4,8,6,5,3] => [.,[[.,[[.,.],[[.,.],.]]],[.,.]]] => [1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1] => 1

[1,3,2,8,7,5,4,6] => [.,[[.,.],[[[[.,.],[.,.]],.],.]]] => [1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,1,1] => 2

[1,2,8,6,5,4,3,7] => [.,[.,[[[[[.,.],.],.],[.,.]],.]]] => [1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1] => 3

[8,1,3,4,6,5,2,7] => [[.,[[.,.],[.,[[.,.],[.,.]]]]],.] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1,1,1] => 1

[1,8,6,4,3,2,7,5] => [.,[[[[[.,.],.],[.,.]],[.,.]],.]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2,2,1] => 2

[1,8,7,6,4,2,5,3] => [.,[[[[[.,[.,.]],[.,.]],.],.],.]] => [1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,2] => 3

[1,4,8,6,7,5,3,2] => [.,[[[.,.],.],[[[.,.],[.,.]],.]]] => [1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1] => 2

[1,7,3,6,8,5,4,2] => [.,[[[.,.],[[[.,.],.],.]],[.,.]]] => [1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,1,1] => 2

[1,8,3,6,7,5,4,2] => [.,[[[.,.],[[[.,.],.],[.,.]]],.]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,1,1] => 2

[1,6,2,7,4,5,3,8] => [.,[[.,[[.,.],[.,.]]],[.,[.,.]]]] => [1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1] => 0

[1,8,2,6,4,3,5,7] => [.,[[.,[[[.,.],[.,.]],[.,.]]],.]] => [1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1,1] => 1

[1,7,2,6,4,3,5,8] => [.,[[.,[[[.,.],[.,.]],.]],[.,.]]] => [1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1,1] => 1

[1,7,2,5,4,6,3,8] => [.,[[.,[[[.,.],.],[.,.]]],[.,.]]] => [1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1] => 1

[8,2,3,6,7,1,4,5] => [[[.,.],[.,[[.,[.,.]],[.,.]]]],.] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,3,1,1,1,1] => 1

[2,4,8,7,5,3,1,6] => [[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,1,1] => 2

[2,8,7,3,4,6,5,1] => [[.,.],[[[.,[.,[[.,.],.]]],.],.]] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,1,1,1] => 3

[2,8,7,1,6,5,3,4] => [[.,.],[[[[[.,[.,.]],.],.],.],.]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1,1,1] => 4

[8,7,1,2,4,3,6,5] => [[[.,[.,[[.,.],[[.,.],.]]]],.],.] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [7,6,2,1,1] => 3

[2,1,8,7,3,4,6,5] => [[.,.],[[[.,[.,[[.,.],.]]],.],.]] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,1,1,1] => 3

[2,8,7,3,4,1,6,5] => [[.,.],[[[.,[.,[[.,.],.]]],.],.]] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,1,1,1] => 3

[2,8,7,3,1,4,6,5] => [[.,.],[[[.,[.,[[.,.],.]]],.],.]] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,1,1,1] => 3

[2,4,3,1,8,7,5,6] => [[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,1,1] => 2

[8,7,1,2,4,6,5,3] => [[[.,[.,[[.,.],[[.,.],.]]]],.],.] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [7,6,2,1,1] => 3

[7,1,2,3,5,4,6,8] => [[.,[.,[.,[[.,.],[.,.]]]]],[.,.]] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1] => 0

[1,9,2,3,4,5,6,8,7] => [.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [7,1] => 2

[7,1,2,6,4,5,3,8] => [[.,[.,[[[.,.],[.,.]],.]]],[.,.]] => [1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [6,6,3,1,1] => 1

[7,1,2,4,3,5,6,8] => [[.,[.,[[.,.],[.,[.,.]]]]],[.,.]] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1] => 0

[1,9,2,3,4,5,8,7,6] => [.,[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1] => 3

[8,1,3,5,2,4,6,7] => [[.,[[.,.],[[.,.],[.,[.,.]]]]],.] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,1,1] => 1

[1,8,3,5,7,2,4,6] => [.,[[[.,.],[[.,.],[[.,.],.]]],.]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,1,1] => 2

[1,3,4,5,6,7,8,2,9] => [.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 0

[1,5,7,3,6,8,2,4] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1] => 0

[1,3,4,7,6,8,2,5] => [.,[[.,.],[.,[[[.,.],.],[.,.]]]]] => [1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1,1] => 1

[8,1,3,6,7,4,2,5] => [[.,[[.,.],[[.,[.,.]],[.,.]]]],.] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,3,1,1,1] => 1

[1,2,4,7,8,5,3,6] => [.,[.,[[.,.],[[.,[.,.]],[.,.]]]]] => [1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1] => 0

[3,1,4,7,6,8,2,5] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,2] => 1

[2,8,3,6,7,4,1,5] => [[.,.],[[.,[[.,[.,.]],[.,.]]],.]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1,1,1,1] => 1

[1,8,2,7,5,4,3,6] => [.,[[.,[[[[.,.],.],[.,.]],.]],.]] => [1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,1] => 3

[6,7,1,2,8,4,3,5] => [[.,[.,[[.,.],[.,.]]]],[.,[.,.]]] => [1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [5,5,5,1,1] => 0

[2,1,3,8,6,5,4,7] => [[.,.],[.,[[[[.,.],.],[.,.]],.]]] => [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1,1,1] => 2

[1,3,2,8,6,5,4,7] => [.,[[.,.],[[[[.,.],.],[.,.]],.]]] => [1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1,1] => 2

[3,4,1,7,6,8,2,5] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,2] => 1

[4,5,7,6,1,8,2,3] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [4,4,3,3,3] => 0

[1,5,7,8,6,3,2,4] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1] => 0

[1,4,8,6,7,3,2,5] => [.,[[[.,.],.],[[[.,.],[.,.]],.]]] => [1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1] => 2

[2,4,8,6,7,3,1,5] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1,1] => 1

[2,3,8,7,5,4,1,6] => [[.,.],[.,[[[[.,.],[.,.]],.],.]]] => [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,1,1,1] => 2

[1,3,8,7,5,4,2,6] => [.,[[.,.],[[[[.,.],[.,.]],.],.]]] => [1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,1,1] => 2

[1,3,9,8,7,6,5,4,2] => [.,[[.,.],[[[[[[.,.],.],.],.],.],.]]] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,1,1] => 5

[1,5,8,4,3,7,6,2] => [.,[[[[.,.],.],.],[[[.,.],.],.]]] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,2,1] => 4

[8,1,7,2,5,6,4,3] => [[.,[[.,[[[.,.],.],[.,.]]],.]],.] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [7,5,2,2,1] => 3

[8,1,3,5,2,7,6,4] => [[.,[[.,.],[[.,.],[[.,.],.]]]],.] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,1,1] => 2

[2,4,1,6,7,5,8,3] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[8,1,4,5,6,3,7,2] => [[.,[[[.,.],.],[.,[.,[.,.]]]]],.] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2,1] => 2

[8,1,4,5,6,2,7,3] => [[.,[[.,[.,.]],[.,[.,[.,.]]]]],.] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2] => 1

[2,4,5,1,7,6,3,8] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1,1] => 0

[3,4,5,6,2,8,1,7] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,2,1] => 2

[2,6,3,1,4,7,5,8] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1,1] => 0

[2,3,5,1,4,8,7,6] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1,1,1] => 2

[2,7,1,3,8,4,6,5] => [[.,.],[[.,[.,[[.,.],.]]],[.,.]]] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1,1,1] => 1

[3,4,7,6,1,2,8,5] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,2] => 1

[8,7,3,1,4,5,6,2] => [[[[.,[.,.]],[.,[.,[.,.]]]],.],.] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,2,2,2] => 2

[1,6,3,8,4,2,5,7] => [.,[[[.,.],[.,[.,.]]],[[.,.],.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1] => 1

[1,8,3,4,5,2,6,7] => [.,[[[.,.],[.,[.,[.,[.,.]]]]],.]] => [1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1,1] => 1

[1,8,6,4,2,5,3,7] => [.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2,2] => 1

[1,2,7,4,3,5,6,8] => [.,[.,[[[.,.],[.,[.,.]]],[.,.]]]] => [1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1] => 0

[1,7,8,6,2,4,3,5] => [.,[[[.,[[.,.],[.,.]]],.],[.,.]]] => [1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1,1] => 1

[7,1,2,5,3,4,6,8] => [[.,[.,[[.,[.,.]],[.,.]]]],[.,.]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2] => 0

[1,6,7,3,2,8,4,5] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]] => [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1] => 0

[1,8,6,3,2,7,4,5] => [.,[[[[.,.],[.,[.,.]]],[.,.]],.]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,4,1,1,1] => 1

[1,4,6,2,8,5,3,7] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2] => 1

[1,5,6,2,8,4,3,7] => [.,[[.,[[.,.],.]],[.,[[.,.],.]]]] => [1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1] => 2

[1,2,4,7,3,6,5,8] => [.,[.,[[.,.],[[[.,.],.],[.,.]]]]] => [1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1] => 1

[1,2,5,7,4,6,8,3] => [.,[.,[[[.,.],.],[[.,.],[.,.]]]]] => [1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1] => 1

[1,2,4,7,6,8,3,5] => [.,[.,[[.,.],[[[.,.],.],[.,.]]]]] => [1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1] => 1

[2,3,7,1,8,6,4,5] => [[.,.],[.,[[[.,[.,.]],.],[.,.]]]] => [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1,1,1] => 1

[1,7,8,6,5,4,2,3] => [.,[[[[[.,[.,.]],.],.],.],[.,.]]] => [1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3,2] => 3

[1,8,7,3,2,5,6,4] => [.,[[[[.,.],[[.,.],[.,.]]],.],.]] => [1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,1,1] => 2

[5,7,1,2,3,8,6,4] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4] => 0

[1,8,6,4,2,5,7,3] => [.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2,2] => 1

[3,5,2,1,4,6,7,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => 1

[1,3,8,7,5,4,6,2] => [.,[[.,.],[[[[.,.],[.,.]],.],.]]] => [1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,1,1] => 2

[1,2,3,4,5,7,9,8,6] => [.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]] => [1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1] => 1

[1,2,3,4,6,9,8,7,5] => [.,[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]] => [1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1] => 2

[1,2,3,5,9,8,7,6,4] => [.,[.,[.,[[.,.],[[[[.,.],.],.],.]]]]] => [1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1,1] => 3

[1,2,4,9,8,7,6,5,3] => [.,[.,[[.,.],[[[[[.,.],.],.],.],.]]]] => [1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,1,1] => 4

[7,1,3,4,5,6,8,2] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1,1] => 0

[1,8,3,5,6,2,7,4] => [.,[[[.,.],[[.,.],[.,[.,.]]]],.]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,1,1] => 1

[1,7,8,5,2,6,3,4] => [.,[[[.,[.,[.,.]]],[.,.]],[.,.]]] => [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3] => 0

[1,5,7,3,8,6,2,4] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1] => 0

[4,3,2,8,7,1,6,5] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,3,2,1] => 5

[3,8,7,2,6,5,1,4] => [[[.,.],.],[[[[[.,.],.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,2,1] => 5

[1,6,7,4,2,5,8,3] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2] => 0

[1,6,7,5,8,3,2,4] => [.,[[[[.,.],[.,.]],.],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,1,1] => 1

[6,1,7,2,8,4,3,5] => [[.,[.,[[.,.],[.,.]]]],[.,[.,.]]] => [1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [5,5,5,1,1] => 0

[2,7,8,3,1,5,4,6] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1,1] => 0

[2,4,6,7,8,5,1,3] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[2,4,6,7,8,3,1,5] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[5,6,1,2,8,3,7,4] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [5,4,4,4] => 1

[1,5,7,8,4,2,3,6] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2] => 1

[1,3,6,4,2,5,7,8] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => [1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1] => 0

[1,4,5,7,8,3,6,2] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]] => [1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1] => 1

[1,5,7,8,3,6,2,4] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1] => 0

[1,5,7,8,2,4,3,6] => [.,[[.,[[.,.],.]],[[.,.],[.,.]]]] => [1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1] => 1

[1,8,4,6,3,2,7,5] => [.,[[[[.,.],.],[[.,.],[.,.]]],.]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,2,1] => 2

[3,5,6,1,4,2,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 0

[1,6,3,8,4,2,7,5] => [.,[[[.,.],[.,[.,.]]],[[.,.],.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1] => 1

[7,1,3,2,4,6,8,5] => [[.,[[.,.],[.,[[.,.],.]]]],[.,.]] => [1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [6,6,2,1,1,1] => 1

[2,5,7,1,6,3,4,8] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[2,5,6,3,4,8,1,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1,1] => 1

[7,2,1,3,4,8,5,6] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1,1,1] => 0

[2,4,5,7,1,8,6,3] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1,1] => 0

[8,1,6,2,3,4,7,5] => [[.,[[.,[.,[.,[.,.]]]],[.,.]]],.] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [7,4,4] => 1

[1,8,3,4,5,2,7,6] => [.,[[[.,.],[.,[.,[[.,.],.]]]],.]] => [1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1,1,1] => 2

[1,8,3,6,4,7,2,5] => [.,[[[.,.],[[.,[.,.]],[.,.]]],.]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1,1,1] => 1

[1,4,7,2,5,6,3,8] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2] => 0

[3,4,8,2,5,1,7,6] => [[[.,.],.],[.,[[.,[[.,.],.]],.]]] => [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,2,1] => 3

[1,7,2,5,8,4,3,6] => [.,[[.,[[[.,.],.],[.,.]]],[.,.]]] => [1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1] => 1

[1,4,6,7,8,3,5,2] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1] => 1

[4,1,5,3,6,8,7,2] => [[.,[[.,.],.]],[.,[.,[[.,.],.]]]] => [1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3,1] => 2

[1,6,8,3,5,2,7,4] => [.,[[[.,.],[[.,.],.]],[[.,.],.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,1,1] => 2

[2,4,7,8,5,6,1,3] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => 0

[1,5,6,8,7,3,2,4] => [.,[[[.,.],[.,.]],[.,[[.,.],.]]]] => [1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1] => 1

[1,4,8,3,6,5,2,7] => [.,[[[.,.],.],[[[.,.],[.,.]],.]]] => [1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1] => 2

[1,3,8,6,4,7,2,5] => [.,[[.,.],[[[.,[.,.]],[.,.]],.]]] => [1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1,1] => 1

[1,2,8,6,4,3,7,5] => [.,[.,[[[[.,.],[.,.]],[.,.]],.]]] => [1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1] => 1

[8,1,4,5,7,3,2,6] => [[.,[[[.,.],.],[.,[[.,.],.]]]],.] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,2,1] => 3

[1,8,4,7,6,2,3,5] => [.,[[[.,[.,.]],[[[.,.],.],.]],.]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,2] => 3

[7,2,3,8,4,5,6,1] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1,1,1] => 0

[5,8,4,3,7,2,1,6] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,4,3,2,1] => 5

[6,1,2,8,7,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [6,5,5] => 1

[4,5,1,7,6,2,8,3] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [4,4,3,3,3] => 0

[3,4,8,1,5,2,6,7] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,2] => 1

[1,5,8,6,2,7,4,3] => [.,[[.,[[.,.],.]],[[.,[.,.]],.]]] => [1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1] => 2

[3,4,6,7,8,2,1,5] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2,1] => 1

[1,2,6,7,8,5,3,4] => [.,[.,[[[.,[.,.]],.],[.,[.,.]]]]] => [1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2] => 1

[1,6,7,4,8,3,2,5] => [.,[[[[.,.],.],[.,.]],[.,[.,.]]]] => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2,1] => 1

[1,4,6,7,8,3,2,5] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1] => 1

[6,1,8,7,2,3,5,4] => [[.,[.,[.,[[.,.],.]]]],[[.,.],.]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [6,5,5,1] => 2

[8,6,1,2,7,3,4,5] => [[[.,[.,[.,[.,[.,.]]]]],[.,.]],.] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [7,5,5] => 1

[4,3,8,2,5,7,6,1] => [[[[.,.],.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,3,3,2,1] => 4

[3,8,1,4,5,7,2,6] => [[.,[.,.]],[[.,[.,[[.,.],.]]],.]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2,2] => 2

[3,8,1,4,2,5,7,6] => [[.,[.,.]],[[.,[.,[[.,.],.]]],.]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2,2] => 2

[2,7,1,3,5,6,8,4] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1,1] => 0

[2,3,6,1,5,8,7,4] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1,1] => 2

[3,4,7,1,5,6,8,2] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2] => 0

[2,4,8,5,3,6,7,1] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,1,1] => 1

[2,4,5,3,8,6,7,1] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,1,1] => 1

[4,8,5,3,2,6,7,1] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [6,3,3,3,3,2,1] => 3

[7,1,2,8,5,6,4,3] => [[.,[.,[[[.,.],.],[.,.]]]],[.,.]] => [1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,1] => 1

[2,3,5,8,4,6,7,1] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1,1,1] => 1

[3,4,5,8,2,6,7,1] => [[[.,.],.],[.,[.,[[.,[.,.]],.]]]] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,2,1] => 2

[5,4,8,3,2,6,7,1] => [[[[[.,.],.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,4,4,3,2,1] => 4

[3,4,5,2,7,1,6,8] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2,1] => 1

[1,5,7,6,3,2,8,4] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1] => 0

[3,4,5,2,1,8,6,7] => [[[.,.],.],[.,[.,[[.,[.,.]],.]]]] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,2,1] => 2

[1,5,4,6,3,8,2,7] => [.,[[[[.,.],.],.],[.,[[.,.],.]]]] => [1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1] => 3

[1,8,6,4,7,3,2,5] => [.,[[[[[.,.],.],[.,.]],[.,.]],.]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2,2,1] => 2

[1,5,7,6,2,8,4,3] => [.,[[.,[[.,.],.]],[[.,.],[.,.]]]] => [1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1] => 1

[1,6,5,2,7,8,4,3] => [.,[[[.,[[.,.],.]],.],[.,[.,.]]]] => [1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,1] => 2

[3,4,6,5,7,1,2,8] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2] => 0

[2,3,6,7,8,5,1,4] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1,1] => 1

[1,7,8,4,6,2,3,5] => [.,[[[.,[.,.]],[[.,.],.]],[.,.]]] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,2] => 1

[7,1,3,4,6,2,8,5] => [[.,[[.,.],[.,[[.,.],.]]]],[.,.]] => [1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [6,6,2,1,1,1] => 1

[1,4,7,5,8,6,3,2] => [.,[[[.,.],.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1] => 1

[1,4,8,7,5,2,6,3] => [.,[[.,[.,.]],[[[.,[.,.]],.],.]]] => [1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2] => 2

[1,5,6,4,2,3,7,8] => [.,[[[.,[.,.]],.],[.,[.,[.,.]]]]] => [1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2] => 1

[1,8,7,3,2,5,4,6] => [.,[[[[.,.],[[.,.],[.,.]]],.],.]] => [1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,1,1] => 2

[1,2,5,4,8,7,3,6] => [.,[.,[[[.,.],.],[[[.,.],.],.]]]] => [1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1] => 3

[1,2,4,8,6,3,5,7] => [.,[.,[[.,.],[[[.,.],[.,.]],.]]]] => [1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1] => 1

[1,5,2,4,7,3,8,6] => [.,[[.,[[.,.],.]],[[.,.],[.,.]]]] => [1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1] => 1

[1,2,7,6,8,4,3,5] => [.,[.,[[[[.,.],[.,.]],.],[.,.]]]] => [1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1] => 1

[1,6,3,2,5,7,8,4] => [.,[[[.,.],[[.,.],.]],[.,[.,.]]]] => [1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1] => 1

[1,7,3,4,2,6,8,5] => [.,[[[.,.],[.,[[.,.],.]]],[.,.]]] => [1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1,1] => 1

[1,6,3,5,8,4,2,7] => [.,[[[.,.],[[.,.],.]],[[.,.],.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,1,1] => 2

[1,5,6,3,2,8,4,7] => [.,[[[.,.],[.,.]],[.,[[.,.],.]]]] => [1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1] => 1

[1,2,5,8,4,6,3,7] => [.,[.,[[[.,.],.],[[.,[.,.]],.]]]] => [1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1] => 2

[1,5,3,2,7,8,4,6] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1] => 0

[1,7,6,4,3,8,5,2] => [.,[[[[[.,.],.],[.,.]],.],[.,.]]] => [1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,2,1] => 2

[1,4,7,3,6,8,5,2] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1] => 2

[1,6,3,5,7,8,4,2] => [.,[[[.,.],[[.,.],.]],[.,[.,.]]]] => [1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1] => 1

[1,5,6,3,2,7,8,4] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => [1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1] => 0

[1,2,7,6,8,4,5,3] => [.,[.,[[[[.,.],[.,.]],.],[.,.]]]] => [1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1] => 1

[1,8,4,7,5,3,2,6] => [.,[[[[.,.],.],[[.,[.,.]],.]],.]] => [1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,2,1] => 3

[1,2,6,8,4,3,7,5] => [.,[.,[[[.,.],[.,.]],[[.,.],.]]]] => [1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1] => 1

[1,5,3,7,8,4,6,2] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1] => 0

[1,5,7,3,8,2,6,4] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1] => 0

[1,3,7,5,8,6,2,4] => [.,[[.,.],[[[.,.],[.,.]],[.,.]]]] => [1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1] => 0

[2,4,7,3,5,6,1,8] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => 0

[3,4,5,8,1,6,7,2] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,2] => 1

[2,3,8,1,5,6,4,7] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1,1,1] => 1

[1,5,3,8,2,4,6,7] => [.,[[[.,.],[.,.]],[[.,[.,.]],.]]] => [1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1] => 1

[3,5,4,6,1,7,8,2] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 0

[3,5,6,4,1,7,2,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 0

[2,5,6,1,7,4,3,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1,1] => 1

[2,7,8,3,1,4,5,6] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1,1,1] => 0

[1,5,3,2,8,6,7,4] => [.,[[[.,.],[.,.]],[[.,[.,.]],.]]] => [1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1] => 1

[1,8,5,3,2,6,7,4] => [.,[[[[.,.],[.,.]],[.,[.,.]]],.]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,1,1] => 1

[1,5,6,7,3,2,8,4] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => [1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1] => 0

[1,7,5,2,3,4,8,6] => [.,[[[.,[.,[.,.]]],[.,.]],[.,.]]] => [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3] => 0

[1,7,5,2,4,8,6,3] => [.,[[[.,[[.,.],.]],[.,.]],[.,.]]] => [1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,1] => 1

[1,6,7,8,3,2,4,5] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]] => [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1] => 0

[1,4,8,6,2,3,5,7] => [.,[[.,[.,.]],[[[.,.],[.,.]],.]]] => [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2] => 1

[1,8,4,5,6,7,2,3] => [.,[[[.,[.,.]],[.,[.,[.,.]]]],.]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2] => 1

[1,2,8,6,3,5,7,4] => [.,[.,[[[.,[[.,.],.]],[.,.]],.]]] => [1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1] => 2

[1,2,7,8,4,3,5,6] => [.,[.,[[[.,.],[.,[.,.]]],[.,.]]]] => [1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1] => 0

[1,8,6,7,4,2,3,5] => [.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2,2] => 1

[1,6,7,8,4,2,3,5] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2] => 0

[1,6,7,8,3,4,2,5] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]] => [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1] => 0

[1,7,4,2,3,8,5,6] => [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2] => 0

[1,7,8,4,2,3,5,6] => [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2] => 0

[1,7,3,5,6,2,8,4] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]] => [1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1] => 0

[1,7,8,3,4,2,5,6] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1,1] => 0

[1,2,3,7,8,5,4,6] => [.,[.,[.,[[[.,.],[.,.]],[.,.]]]]] => [1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1] => 0

[1,2,7,4,6,3,8,5] => [.,[.,[[[.,.],[[.,.],.]],[.,.]]]] => [1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1] => 1

[1,7,8,4,5,2,3,6] => [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2] => 0

[1,7,8,3,4,5,2,6] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1,1] => 0

[1,2,8,4,5,6,3,7] => [.,[.,[[[.,.],[.,[.,[.,.]]]],.]]] => [1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1] => 1

[1,8,4,5,6,2,3,7] => [.,[[[.,[.,.]],[.,[.,[.,.]]]],.]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2] => 1

[4,8,7,3,2,5,1,6] => [[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,3,3,2,1] => 4

[1,8,7,6,4,3,5,2] => [.,[[[[[[.,.],.],[.,.]],.],.],.]] => [1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,2,1] => 4

[2,3,7,5,6,8,4,1] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1,1] => 0

[3,2,4,7,5,8,1,6] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2,1] => 1

[2,3,7,5,4,8,6,1] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1,1] => 0

[2,1,3,4,8,5,7,6] => [[.,.],[.,[.,[[.,[[.,.],.]],.]]]] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1,1,1] => 2

[1,2,3,4,5,9,6,8,7] => [.,[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]] => [1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [3,1] => 2

[7,1,2,3,4,8,5,9,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,6,6] => 0

[1,7,2,3,4,5,9,8,6] => [.,[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]] => [1,1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0,0] => [6,5,5] => 1

[6,1,2,3,7,4,8,9,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,5,5,5] => 0

[5,7,1,2,6,8,3,4] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4] => 0

[1,5,2,3,6,8,7,4] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3] => 1

[1,2,3,4,5,6,7,8,11,10,9] => [.,[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]] => [1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1] => 2

[2,1,3,8,5,7,4,6] => [[.,.],[.,[[[.,.],[[.,.],.]],.]]] => [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1,1,1] => 2

[7,3,1,2,8,4,5,6] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,2,2] => 0

[2,1,4,7,6,3,5,8] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1,1] => 1

[4,5,1,3,6,7,8,2] => [[.,[[.,.],.]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1] => 1

[1,5,8,2,4,7,6,3] => [.,[[.,[[.,.],.]],[[[.,.],.],.]]] => [1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1] => 3

[1,6,8,2,7,4,5,3] => [.,[[.,[[.,.],[.,.]]],[[.,.],.]]] => [1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1] => 1

[2,4,8,6,5,7,3,1] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1,1] => 1

[1,4,7,2,6,8,5,3] => [.,[[.,[.,.]],[[[.,.],.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2] => 1

[2,3,7,6,5,1,4,8] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1,1,1] => 2

[2,3,8,4,1,6,5,7] => [[.,.],[.,[[.,[[.,.],[.,.]]],.]]] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1,1,1] => 1

[2,4,8,7,5,1,3,6] => [[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,1,1] => 2

[1,5,3,2,8,7,6,4] => [.,[[[.,.],[.,.]],[[[.,.],.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1,1] => 2

[3,4,7,5,8,1,2,6] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2] => 0

[2,7,8,3,4,1,5,6] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1,1,1] => 0

[2,4,3,7,1,8,6,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1,1] => 1

[2,3,7,6,5,8,1,4] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1,1,1] => 2

[1,3,6,4,7,5,2,8] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => [1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1] => 0

[1,4,7,3,6,5,2,8] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1] => 2

[1,4,8,3,7,5,2,6] => [.,[[[.,.],.],[[[.,[.,.]],.],.]]] => [1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,1] => 3

[7,3,1,4,8,5,2,6] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,2,2] => 0

[1,3,7,4,8,5,2,6] => [.,[[.,.],[[.,[.,[.,.]]],[.,.]]]] => [1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1,1] => 0

[1,3,6,4,8,5,2,7] => [.,[[.,.],[[.,[.,.]],[[.,.],.]]]] => [1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1] => 1

[1,3,5,4,8,6,2,7] => [.,[[.,.],[[.,.],[[.,[.,.]],.]]]] => [1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1,1] => 1

[1,5,2,4,7,6,3,8] => [.,[[.,[[.,.],.]],[[.,.],[.,.]]]] => [1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1] => 1

[1,5,2,4,8,6,3,7] => [.,[[.,[[.,.],.]],[[.,[.,.]],.]]] => [1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1] => 2

[1,5,2,8,7,4,3,6] => [.,[[.,[[.,.],.]],[[[.,.],.],.]]] => [1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1] => 3

[1,4,2,7,3,6,8,5] => [.,[[.,[.,.]],[[[.,.],.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2] => 1

[1,7,6,3,2,4,8,5] => [.,[[[[.,.],[.,[.,.]]],.],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1,1,1] => 1

[1,6,3,2,4,7,8,5] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]] => [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1] => 0

[1,2,3,7,5,8,4,6] => [.,[.,[.,[[[.,.],[.,.]],[.,.]]]]] => [1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1] => 0

[1,3,7,6,2,4,5,8] => [.,[[.,.],[[[.,[.,.]],.],[.,.]]]] => [1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1,1] => 1

[2,7,3,8,4,5,6,1] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1,1,1] => 0

[2,3,6,8,4,1,7,5] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1,1] => 1

[1,7,2,8,6,3,5,4] => [.,[[.,[[.,[[.,.],.]],.]],[.,.]]] => [1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1] => 2

[3,2,4,6,7,8,1,5] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2,1] => 1

[1,8,5,6,2,7,4,3] => [.,[[[.,[[.,.],.]],[.,[.,.]]],.]] => [1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,1] => 2

[4,3,8,2,1,5,7,6] => [[[[.,.],.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,3,3,2,1] => 4

[1,5,8,2,6,4,7,3] => [.,[[.,[[.,.],.]],[[.,[.,.]],.]]] => [1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1] => 2

[1,5,7,4,6,8,3,2] => [.,[[[[.,.],.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2,1] => 2

[1,4,7,5,6,8,3,2] => [.,[[[.,.],.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1] => 1

[8,1,2,6,4,5,7,3] => [[.,[.,[[[.,.],[.,.]],[.,.]]]],.] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,3,1,1] => 1

[1,7,3,4,5,8,2,6] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1,1] => 0

[1,2,7,4,5,8,3,6] => [.,[.,[[[.,.],[.,[.,.]]],[.,.]]]] => [1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1] => 0

[1,5,8,7,4,6,3,2] => [.,[[[[.,.],.],.],[[[.,.],.],.]]] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,2,1] => 4

[1,6,4,5,7,3,8,2] => [.,[[[[.,.],.],[.,.]],[.,[.,.]]]] => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2,1] => 1

[1,5,4,7,8,6,2,3] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2] => 1

[1,5,7,8,6,2,4,3] => [.,[[.,[[.,.],.]],[[.,.],[.,.]]]] => [1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1] => 1

[4,1,5,6,7,8,9,2,3] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3,3] => 0

[7,1,8,2,5,6,4,3] => [[.,[.,[[[.,.],.],[.,.]]]],[.,.]] => [1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,1] => 1

[1,5,3,8,4,6,2,7] => [.,[[[.,.],[.,.]],[[.,[.,.]],.]]] => [1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1] => 1

[1,7,6,4,8,5,3,2] => [.,[[[[[.,.],.],[.,.]],.],[.,.]]] => [1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,2,1] => 2

[8,2,3,5,1,4,6,7] => [[[.,.],[.,[[.,.],[.,[.,.]]]]],.] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,1,1,1] => 1

[1,7,8,5,3,4,6,2] => [.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,1,1] => 0

[1,5,8,3,6,4,7,2] => [.,[[[.,.],[.,.]],[[.,[.,.]],.]]] => [1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1] => 1

[1,8,2,6,5,3,7,4] => [.,[[.,[[[.,[.,.]],.],[.,.]]],.]] => [1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2] => 2

[8,1,4,2,3,5,7,6] => [[.,[[.,[.,.]],[.,[[.,.],.]]]],.] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,2] => 2

[8,1,2,4,6,5,7,3] => [[.,[.,[[.,.],[[.,.],[.,.]]]]],.] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1,1] => 1

[5,8,4,3,6,2,7,1] => [[[[[.,.],.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,4,4,3,2,1] => 4

[1,7,2,6,3,4,8,5] => [.,[[.,[[.,[.,[.,.]]],.]],[.,.]]] => [1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [5,5,3] => 1

[7,1,2,6,3,4,5,8] => [[.,[.,[[.,[.,[.,.]]],.]]],[.,.]] => [1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [6,6,3] => 1

[1,3,8,4,7,2,6,5] => [.,[[.,.],[[.,[[[.,.],.],.]],.]]] => [1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,1,1] => 3

[1,5,3,2,6,8,4,7] => [.,[[[.,.],[.,.]],[.,[[.,.],.]]]] => [1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1] => 1

[1,3,6,8,7,2,5,4] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]] => [1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1] => 2

[2,6,3,7,1,4,5,8] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1,1] => 0

[1,7,6,5,3,2,4,8] => [.,[[[[[.,.],[.,.]],.],.],[.,.]]] => [1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3,1,1] => 2

[1,7,2,8,5,4,3,6] => [.,[[.,[[[.,.],.],[.,.]]],[.,.]]] => [1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1] => 1

[5,4,8,3,6,2,1,7] => [[[[[.,.],.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,4,4,3,2,1] => 4

[8,2,7,3,4,5,1,6] => [[[.,.],[[.,[.,[.,[.,.]]]],.]],.] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,1,1,1,1] => 2

[8,1,5,2,4,6,3,7] => [[.,[[.,[[.,.],.]],[.,[.,.]]]],.] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [7,3,3,3,1] => 2

[2,6,8,7,3,4,5,1] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1,1] => 1

[1,7,8,5,6,4,2,3] => [.,[[[[.,[.,.]],.],[.,.]],[.,.]]] => [1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,2] => 1

[8,1,3,2,4,6,5,7] => [[.,[[.,.],[.,[[.,.],[.,.]]]]],.] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1,1,1] => 1

[1,5,3,6,8,7,2,4] => [.,[[[.,.],[.,.]],[.,[[.,.],.]]]] => [1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1] => 1

[1,2,7,6,4,5,8,3] => [.,[.,[[[[.,.],[.,.]],.],[.,.]]]] => [1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1] => 1

[4,5,6,2,7,3,1,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1,1] => 0

[3,5,1,4,6,8,2,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,2] => 1

[5,4,8,3,7,2,1,6] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,4,3,2,1] => 5

[5,4,8,3,2,7,1,6] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,4,3,2,1] => 5

[3,4,5,6,7,8,2,9,1] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2,1] => 1

[1,4,8,6,3,2,7,5] => [.,[[[.,.],.],[[[.,.],[.,.]],.]]] => [1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1] => 2

[1,3,5,8,4,7,2,6] => [.,[[.,.],[[.,.],[[[.,.],.],.]]]] => [1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1,1] => 2

[2,3,8,7,5,1,6,4] => [[.,.],[.,[[[[.,.],[.,.]],.],.]]] => [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,1,1,1] => 2

[4,1,3,5,6,2,8,7] => [[.,[[.,.],.]],[.,[.,[[.,.],.]]]] => [1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3,1] => 2

[8,2,3,5,6,1,4,7] => [[[.,.],[.,[[.,.],[.,[.,.]]]]],.] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,1,1,1] => 1

[8,2,3,4,6,1,7,5] => [[[.,.],[.,[.,[[.,.],[.,.]]]]],.] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1,1,1,1] => 1

[1,7,4,3,5,2,8,6] => [.,[[[[.,.],.],[.,[.,.]]],[.,.]]] => [1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2,1] => 1

[3,8,2,7,6,4,1,5] => [[[.,.],.],[[[[.,[.,.]],.],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,2,2,1] => 4

[1,5,2,8,7,6,4,3] => [.,[[.,[[.,.],.]],[[[.,.],.],.]]] => [1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1] => 3

[8,3,4,5,1,6,7,2] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2,2] => 1

[1,3,7,8,5,4,6,2] => [.,[[.,.],[[[.,.],[.,.]],[.,.]]]] => [1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1] => 0

[1,3,2,7,8,5,4,6] => [.,[[.,.],[[[.,.],[.,.]],[.,.]]]] => [1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1] => 0

[1,5,7,6,8,3,4,2] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1] => 0

[1,4,8,2,3,6,5,7] => [.,[[.,[.,.]],[[[.,.],[.,.]],.]]] => [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2] => 1

[1,4,6,7,3,5,2,8] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1] => 1

[1,4,8,2,6,7,5,3] => [.,[[.,[.,.]],[[[.,.],[.,.]],.]]] => [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2] => 1

[1,7,3,2,4,5,6,8] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1,1] => 0

[1,7,3,2,4,5,8,6] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1,1] => 0

[1,6,4,3,2,5,7,8] => [.,[[[[.,.],.],[.,.]],[.,[.,.]]]] => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2,1] => 1

[1,3,5,8,6,2,7,4] => [.,[[.,.],[[.,.],[[.,[.,.]],.]]]] => [1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1,1] => 1

[1,3,8,5,7,4,2,6] => [.,[[.,.],[[[.,.],[[.,.],.]],.]]] => [1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1,1] => 2

[1,2,3,7,5,4,6,8] => [.,[.,[.,[[[.,.],[.,.]],[.,.]]]]] => [1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1] => 0

[1,4,2,8,6,3,5,7] => [.,[[.,[.,.]],[[[.,.],[.,.]],.]]] => [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2] => 1

[1,5,4,2,3,6,8,7] => [.,[[[.,[.,.]],.],[.,[[.,.],.]]]] => [1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2] => 2

[3,1,2,4,8,6,7,5] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,2] => 1

[2,3,5,4,8,6,1,7] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1,1,1] => 1

[2,3,6,4,7,5,1,8] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1,1] => 0

[2,3,5,7,4,8,1,6] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1,1] => 0

[2,3,7,6,1,5,8,4] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1,1,1] => 2

[4,1,5,8,6,2,3,7] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [5,3,3,3,3] => 1

[2,5,3,6,1,8,4,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1,1] => 1

[2,5,6,8,3,1,7,4] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1,1] => 1

[1,7,2,4,5,3,6,8] => [.,[[.,[[.,.],[.,[.,.]]]],[.,.]]] => [1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1] => 0

[1,7,4,5,3,2,6,8] => [.,[[[[.,.],.],[.,[.,.]]],[.,.]]] => [1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2,1] => 1

[1,6,4,7,3,5,2,8] => [.,[[[[.,.],.],[.,.]],[.,[.,.]]]] => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2,1] => 1

[1,6,4,7,5,2,3,8] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2] => 0

[1,5,2,6,7,4,3,8] => [.,[[.,[[.,.],.]],[.,[.,[.,.]]]]] => [1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1] => 1

[3,4,6,7,8,1,5,2] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2] => 0

[4,8,5,3,2,6,1,7] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [6,3,3,3,3,2,1] => 3

[2,8,4,5,3,6,1,7] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,1,1] => 1

[2,6,3,7,8,1,5,4] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1,1] => 1

[1,4,8,5,3,2,6,7] => [.,[[[.,.],.],[[.,[.,[.,.]]],.]]] => [1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,1] => 2

[3,4,7,2,1,5,8,6] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2,1] => 1

[4,1,5,6,8,2,7,3] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3] => 1

[1,7,6,4,2,3,5,8] => [.,[[[[.,[.,.]],[.,.]],.],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,2] => 1

[1,3,2,5,8,6,4,7] => [.,[[.,.],[[.,.],[[.,[.,.]],.]]]] => [1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1,1] => 1

[1,6,7,2,4,8,5,3] => [.,[[.,[[.,.],[.,.]]],[.,[.,.]]]] => [1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1] => 0

[2,8,3,6,1,7,4,5] => [[.,.],[[.,[[.,[.,.]],[.,.]]],.]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1,1,1,1] => 1

[1,8,4,5,6,2,7,3] => [.,[[[.,[.,.]],[.,[.,[.,.]]]],.]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2] => 1

[5,7,6,1,2,8,3,4] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4] => 0

[1,7,3,8,2,4,6,5] => [.,[[[.,.],[.,[[.,.],.]]],[.,.]]] => [1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1,1] => 1

[1,5,7,2,4,3,6,8] => [.,[[.,[[.,.],.]],[[.,.],[.,.]]]] => [1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1] => 1

[1,6,5,3,2,4,7,8] => [.,[[[[.,.],[.,.]],.],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,1,1] => 1

[1,7,2,4,6,5,3,8] => [.,[[.,[[.,.],[[.,.],.]]],[.,.]]] => [1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1] => 1

[1,4,7,2,6,5,3,8] => [.,[[.,[.,.]],[[[.,.],.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2] => 1

[1,2,6,8,7,4,3,5] => [.,[.,[[[.,.],[.,.]],[[.,.],.]]]] => [1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1] => 1

[1,2,7,4,3,5,8,6] => [.,[.,[[[.,.],[.,[.,.]]],[.,.]]]] => [1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1] => 0

[1,6,2,8,7,4,3,5] => [.,[[.,[[.,.],[.,.]]],[[.,.],.]]] => [1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1] => 1

[1,7,4,2,3,5,8,6] => [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2] => 0

[1,8,5,2,3,6,4,7] => [.,[[[.,[.,[.,.]]],[.,[.,.]]],.]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3] => 1

[1,7,4,8,5,2,3,6] => [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2] => 0

[1,4,7,5,2,8,6,3] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2] => 0

[1,6,3,7,4,2,8,5] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]] => [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1] => 0

[1,8,5,2,7,4,3,6] => [.,[[[.,[[.,.],.]],[[.,.],.]],.]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,3,1] => 3

[1,4,8,7,5,3,2,6] => [.,[[[.,.],.],[[[.,[.,.]],.],.]]] => [1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,1] => 3

[1,2,5,8,6,3,7,4] => [.,[.,[[.,[.,.]],[[.,[.,.]],.]]]] => [1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2] => 1

[1,2,4,7,5,8,6,3] => [.,[.,[[.,.],[[.,[.,.]],[.,.]]]]] => [1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1] => 0

[1,5,8,7,6,2,4,3] => [.,[[.,[[.,.],.]],[[[.,.],.],.]]] => [1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1] => 3

[1,3,5,8,7,6,2,4] => [.,[[.,.],[[.,.],[[[.,.],.],.]]]] => [1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1,1] => 2

[1,5,2,4,3,6,8,7] => [.,[[.,[[.,.],.]],[.,[[.,.],.]]]] => [1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1] => 2

[1,2,5,7,4,3,8,6] => [.,[.,[[[.,.],.],[[.,.],[.,.]]]]] => [1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1] => 1

[1,5,3,2,6,8,7,4] => [.,[[[.,.],[.,.]],[.,[[.,.],.]]]] => [1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1] => 1

[1,4,2,6,8,7,5,3] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2] => 1

[1,5,8,6,3,2,7,4] => [.,[[[.,.],[.,.]],[[.,[.,.]],.]]] => [1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1] => 1

[1,8,5,2,6,3,4,7] => [.,[[[.,[.,[.,.]]],[.,[.,.]]],.]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3] => 1

[1,6,3,2,8,5,4,7] => [.,[[[.,.],[[.,.],.]],[[.,.],.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,1,1] => 2

[1,3,8,6,4,2,5,7] => [.,[[.,.],[[[.,[.,.]],[.,.]],.]]] => [1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1,1] => 1

[1,5,7,4,2,3,8,6] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2] => 1

[3,4,6,5,8,2,7,1] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2,1] => 2

[1,5,8,2,6,7,4,3] => [.,[[.,[[.,.],.]],[[.,[.,.]],.]]] => [1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1] => 2

[1,4,7,5,2,3,8,6] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2] => 0

[1,2,4,6,8,5,3,7] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => [1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1] => 1

[2,5,4,6,8,1,3,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1,1] => 2

[1,5,8,7,4,2,6,3] => [.,[[[.,[.,.]],.],[[[.,.],.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,2] => 3

[3,4,5,8,6,2,7,1] => [[[.,.],.],[.,[.,[[.,[.,.]],.]]]] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,2,1] => 2

[8,1,4,7,2,3,5,6] => [[.,[[.,[.,.]],[[.,[.,.]],.]]],.] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,2,2] => 2

[1,5,3,4,7,8,6,2] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1] => 0

[5,1,7,8,6,2,3,4] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4] => 0

[7,1,2,6,4,5,8,3] => [[.,[.,[[[.,.],[.,.]],.]]],[.,.]] => [1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [6,6,3,1,1] => 1

[1,7,3,6,4,5,8,2] => [.,[[[.,.],[[.,[.,.]],.]],[.,.]]] => [1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1,1,1] => 1

[1,8,3,6,4,5,7,2] => [.,[[[.,.],[[.,[.,.]],[.,.]]],.]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1,1,1] => 1

[8,1,6,2,7,3,4,5] => [[.,[[.,[.,[.,[.,.]]]],[.,.]]],.] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [7,4,4] => 1

[8,1,6,2,5,3,4,7] => [[.,[[.,[[.,[.,.]],.]],[.,.]]],.] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [7,4,4,2] => 2

[8,1,7,2,5,3,4,6] => [[.,[[.,[[.,[.,.]],[.,.]]],.]],.] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [7,5,2,2] => 2

[8,1,2,7,4,5,6,3] => [[.,[.,[[[.,.],[.,[.,.]]],.]]],.] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,1,1] => 2

[1,8,3,7,4,5,6,2] => [.,[[[.,.],[[.,[.,[.,.]]],.]],.]] => [1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,1,1,1] => 2

[1,7,3,4,6,8,5,2] => [.,[[[.,.],[.,[[.,.],.]]],[.,.]]] => [1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1,1] => 1

[1,7,3,8,4,5,6,2] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1,1] => 0

[7,1,8,2,5,3,4,6] => [[.,[.,[[.,[.,.]],[.,.]]]],[.,.]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2] => 0

[6,1,7,2,5,3,4,8] => [[.,[.,[[.,[.,.]],.]]],[.,[.,.]]] => [1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [5,5,5,2] => 1

[5,1,7,2,6,3,4,8] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4] => 0

[5,1,8,2,6,3,4,7] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [6,4,4,4] => 1

[1,6,3,7,4,5,8,2] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]] => [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1] => 0

[2,4,7,3,5,1,6,8] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => 0

[2,4,8,6,3,5,1,7] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1,1] => 1

[2,3,7,5,4,1,6,8] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1,1] => 0

[3,4,6,2,1,5,8,7] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2,1] => 2

[2,3,6,1,5,8,4,7] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1,1] => 2

[2,3,7,1,6,5,8,4] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1,1,1] => 2

[2,4,7,1,3,6,8,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1,1] => 1

[2,4,7,1,6,3,5,8] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1,1] => 1

[2,3,7,1,6,5,4,8] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1,1,1] => 2

[2,5,7,3,1,4,6,8] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[2,4,7,1,6,3,8,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1,1] => 1

[2,4,7,1,6,8,3,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1,1] => 1

[2,8,3,7,4,5,6,1] => [[.,.],[[.,[[.,[.,[.,.]]],.]],.]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,1,1,1,1] => 2

[8,2,4,5,3,1,6,7] => [[[.,.],[[.,.],[.,[.,[.,.]]]]],.] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2,1,1] => 1

[1,6,7,4,3,2,5,8] => [.,[[[[.,.],.],[.,.]],[.,[.,.]]]] => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2,1] => 1

[1,4,5,7,3,2,6,8] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]] => [1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1] => 1

[3,5,1,6,4,2,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 0

[1,7,3,2,5,6,4,8] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]] => [1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1] => 0

[2,1,7,3,5,6,8,4] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1,1] => 0

[2,1,6,3,5,7,8,4] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1,1] => 1

[1,6,3,2,5,7,4,8] => [.,[[[.,.],[[.,.],.]],[.,[.,.]]]] => [1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1] => 1

[1,4,6,5,2,7,3,8] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2] => 0

[2,5,1,6,4,3,7,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1,1] => 1

[2,5,4,1,6,3,7,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1,1] => 1

[4,6,1,5,2,7,3,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[1,6,5,3,7,2,4,8] => [.,[[[[.,.],[.,.]],.],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,1,1] => 1

[1,2,5,3,4,8,7,6] => [.,[.,[[.,[.,.]],[[[.,.],.],.]]]] => [1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2] => 2

[1,5,8,3,6,2,7,4] => [.,[[[.,.],[.,.]],[[.,[.,.]],.]]] => [1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1] => 1

[1,2,6,4,7,3,8,5] => [.,[.,[[[.,.],[.,.]],[.,[.,.]]]]] => [1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1] => 0

[1,2,7,8,3,5,6,4] => [.,[.,[[.,[[.,.],[.,.]]],[.,.]]]] => [1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1] => 0

[1,8,2,5,6,4,7,3] => [.,[[.,[[[.,.],.],[.,[.,.]]]],.]] => [1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,1] => 2

[2,6,3,7,5,4,8,1] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1,1] => 1

[1,5,6,3,2,4,7,8] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => [1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1] => 0

[2,4,5,7,3,6,1,8] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1,1] => 0

[2,5,3,1,6,4,7,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1,1] => 0

[1,7,8,4,5,3,6,2] => [.,[[[[.,.],.],[.,[.,.]]],[.,.]]] => [1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2,1] => 1

[1,7,5,6,8,2,4,3] => [.,[[[.,[[.,.],.]],[.,.]],[.,.]]] => [1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,1] => 1

[1,7,4,5,2,8,6,3] => [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2] => 0

[7,1,2,4,5,6,3,8] => [[.,[.,[[.,.],[.,[.,.]]]]],[.,.]] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1] => 0

[2,6,7,3,1,5,4,8] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1,1] => 1

[7,1,2,3,6,8,4,5] => [[.,[.,[.,[[.,[.,.]],.]]]],[.,.]] => [1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [6,6,2] => 1

[6,1,2,3,8,4,7,5] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [6,5,5] => 1

[3,4,7,5,8,2,6,1] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2,1] => 1

[8,10,1,2,3,4,5,9,6,7] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,1,0,0] => [8,7,7] => 1

[6,1,2,3,4,5,7,8,9] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,5,5,5] => 0

[5,1,2,3,4,6,7,8,9] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,4,4,4,4] => 0

[4,1,2,3,5,6,7,8,9] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3,3] => 0

[3,4,7,8,5,1,2,6] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2] => 0

[1,7,3,6,8,4,2,5] => [.,[[[.,.],[[.,[.,.]],.]],[.,.]]] => [1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1,1,1] => 1

[2,3,6,5,1,8,7,4] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1,1] => 2

[1,7,8,2,4,3,5,6] => [.,[[.,[[.,.],[.,[.,.]]]],[.,.]]] => [1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1] => 0

[2,3,7,5,1,8,6,4] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1,1] => 0

[1,5,8,2,4,3,6,7] => [.,[[.,[[.,.],.]],[[.,[.,.]],.]]] => [1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1] => 2

[2,3,7,6,1,8,5,4] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1,1,1] => 2

[2,1,3,8,7,4,6,5] => [[.,.],[.,[[[.,[[.,.],.]],.],.]]] => [1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,1,1,1] => 3

[2,1,3,8,7,4,5,6] => [[.,.],[.,[[[.,[.,[.,.]]],.],.]]] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1,1,1,1] => 2

[1,6,8,3,2,4,7,5] => [.,[[[.,.],[.,[.,.]]],[[.,.],.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1] => 1

[1,3,2,8,7,6,4,5] => [.,[[.,.],[[[[.,[.,.]],.],.],.]]] => [1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,1,1] => 3

[2,1,3,8,7,6,4,5] => [[.,.],[.,[[[[.,[.,.]],.],.],.]]] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,1,1,1] => 3

[1,6,3,7,2,5,4,8] => [.,[[[.,.],[[.,.],.]],[.,[.,.]]]] => [1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1] => 1

[1,7,2,4,6,3,5,8] => [.,[[.,[[.,.],[[.,.],.]]],[.,.]]] => [1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1] => 1

[2,5,8,3,1,4,6,7] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1,1] => 1

[2,8,1,3,5,7,4,6] => [[.,.],[[.,[[.,.],[[.,.],.]]],.]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,1,1,1] => 2

[3,4,8,5,7,1,2,6] => [[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,2] => 2

[3,4,6,5,8,2,1,7] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2,1] => 2

[2,4,6,7,8,3,5,1] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[1,4,2,5,7,6,3,8] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2] => 0

[1,4,2,6,8,5,3,7] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2] => 1

[1,2,6,8,3,5,4,7] => [.,[.,[[.,[[.,.],.]],[[.,.],.]]]] => [1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1] => 2

[1,6,8,3,5,4,2,7] => [.,[[[.,.],[[.,.],.]],[[.,.],.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,1,1] => 2

[1,5,3,2,4,6,8,7] => [.,[[[.,.],[.,.]],[.,[[.,.],.]]]] => [1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1] => 1

[1,5,8,7,6,3,2,4] => [.,[[[.,.],[.,.]],[[[.,.],.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1,1] => 2

[1,5,7,6,3,2,4,8] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1] => 0

[1,6,3,2,4,7,5,8] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]] => [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1] => 0

[1,6,3,2,4,8,7,5] => [.,[[[.,.],[.,[.,.]]],[[.,.],.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1] => 1

[1,2,7,6,4,3,5,8] => [.,[.,[[[[.,.],[.,.]],.],[.,.]]]] => [1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1] => 1

[1,7,5,2,4,6,3,8] => [.,[[[.,[[.,.],.]],[.,.]],[.,.]]] => [1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,1] => 1

[1,7,4,2,5,3,6,8] => [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2] => 0

[1,8,4,7,5,2,6,3] => [.,[[[.,[.,.]],[[.,[.,.]],.]],.]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,2] => 2

[1,7,5,2,3,6,4,8] => [.,[[[.,[.,[.,.]]],[.,.]],[.,.]]] => [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3] => 0

[1,7,5,2,6,3,4,8] => [.,[[[.,[.,[.,.]]],[.,.]],[.,.]]] => [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3] => 0

[1,6,3,7,4,2,5,8] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]] => [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1] => 0

[1,6,3,2,7,5,4,8] => [.,[[[.,.],[[.,.],.]],[.,[.,.]]]] => [1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1] => 1

[1,4,7,5,2,6,3,8] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2] => 0

[1,3,6,4,8,7,5,2] => [.,[[.,.],[[.,[.,.]],[[.,.],.]]]] => [1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1] => 1

[1,3,7,6,4,2,5,8] => [.,[[.,.],[[[.,[.,.]],.],[.,.]]]] => [1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1,1] => 1

[1,3,2,4,8,5,7,6] => [.,[[.,.],[.,[[.,[[.,.],.]],.]]]] => [1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1,1] => 2

[1,3,8,7,5,2,4,6] => [.,[[.,.],[[[[.,.],[.,.]],.],.]]] => [1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,1,1] => 2

[1,4,6,3,2,7,5,8] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1] => 1

[1,4,6,3,2,8,7,5] => [.,[[[.,.],.],[[.,.],[[.,.],.]]]] => [1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1] => 2

[1,5,7,6,4,2,3,8] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2] => 1

[1,6,3,2,8,4,7,5] => [.,[[[.,.],[.,[.,.]]],[[.,.],.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1] => 1

[1,6,3,5,2,7,4,8] => [.,[[[.,.],[[.,.],.]],[.,[.,.]]]] => [1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1] => 1

[1,6,3,5,2,8,7,4] => [.,[[[.,.],[[.,.],.]],[[.,.],.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,1,1] => 2

[1,8,3,7,5,2,4,6] => [.,[[[.,.],[[[.,.],[.,.]],.]],.]] => [1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,1,1] => 2

[4,8,3,5,7,6,2,1] => [[[[.,.],.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,3,3,2,1] => 4

[1,3,4,2,8,5,7,6] => [.,[[.,.],[.,[[.,[[.,.],.]],.]]]] => [1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1,1] => 2

[3,2,1,4,8,5,7,6] => [[[.,.],.],[.,[[.,[[.,.],.]],.]]] => [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,2,1] => 3

[1,8,7,3,4,5,2,6] => [.,[[[[.,.],[.,[.,[.,.]]]],.],.]] => [1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,1,1,1] => 2

[1,8,7,4,5,2,3,6] => [.,[[[[.,[.,.]],[.,[.,.]]],.],.]] => [1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,2] => 2

[1,2,6,8,7,3,4,5] => [.,[.,[[.,[.,[.,.]]],[[.,.],.]]]] => [1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [4,3,3] => 1

[1,3,7,8,4,5,6,2] => [.,[[.,.],[[.,[.,[.,.]]],[.,.]]]] => [1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1,1] => 0

[2,6,3,1,7,4,8,5] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1,1] => 0

[1,4,3,7,2,8,6,5] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1] => 2

[1,8,7,4,5,3,2,6] => [.,[[[[[.,.],.],[.,[.,.]]],.],.]] => [1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,2,1] => 3

[2,8,3,1,4,5,7,6] => [[.,.],[[.,[.,[.,[[.,.],.]]]],.]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1,1,1,1] => 2

[6,1,7,2,8,4,5,3] => [[.,[.,[[.,.],[.,.]]]],[.,[.,.]]] => [1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [5,5,5,1,1] => 0

[1,4,8,2,5,6,7,3] => [.,[[.,[.,.]],[[.,[.,[.,.]]],.]]] => [1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2] => 1

[8,1,2,7,6,5,4,3] => [[.,[.,[[[[[.,.],.],.],.],.]]],.] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,1] => 5

[4,5,8,1,6,7,2,3] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [5,3,3,3,3] => 1

[1,3,2,6,8,7,4,5] => [.,[[.,.],[[.,[.,.]],[[.,.],.]]]] => [1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1] => 1

[1,3,8,2,5,4,6,7] => [.,[[.,.],[[[.,.],[.,[.,.]]],.]]] => [1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1,1] => 1

[1,6,2,5,8,7,3,4] => [.,[[.,[[.,[.,.]],.]],[[.,.],.]]] => [1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2] => 2

[1,6,8,7,2,3,5,4] => [.,[[.,[.,[[.,.],.]]],[[.,.],.]]] => [1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1] => 2

[1,6,8,7,2,5,3,4] => [.,[[.,[[.,[.,.]],.]],[[.,.],.]]] => [1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2] => 2

[1,5,2,4,8,3,6,7] => [.,[[.,[[.,.],.]],[[.,[.,.]],.]]] => [1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1] => 2

[1,2,4,5,8,6,3,7] => [.,[.,[[.,.],[.,[[.,[.,.]],.]]]]] => [1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1] => 1

[1,2,8,3,5,4,7,6] => [.,[.,[[.,[[.,.],[[.,.],.]]],.]]] => [1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1] => 2

[1,3,8,2,5,4,7,6] => [.,[[.,.],[[[.,.],[[.,.],.]],.]]] => [1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1,1] => 2

[1,6,7,5,2,4,8,3] => [.,[[[.,[[.,.],.]],.],[.,[.,.]]]] => [1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,1] => 2

[1,5,6,4,7,2,3,8] => [.,[[[.,[.,.]],.],[.,[.,[.,.]]]]] => [1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2] => 1

[1,7,4,2,5,8,3,6] => [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2] => 0

[1,6,4,3,7,5,2,8] => [.,[[[[.,.],.],[.,.]],[.,[.,.]]]] => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2,1] => 1

[1,6,5,4,7,2,3,8] => [.,[[[[.,[.,.]],.],.],[.,[.,.]]]] => [1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,2] => 2

[1,7,3,2,6,4,8,5] => [.,[[[.,.],[[.,[.,.]],.]],[.,.]]] => [1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1,1,1] => 1

[1,5,8,2,3,6,7,4] => [.,[[.,[.,[.,.]]],[[.,[.,.]],.]]] => [1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3] => 1

[1,3,2,6,8,5,4,7] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]] => [1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1] => 2

[1,6,3,2,7,4,5,8] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]] => [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1] => 0

[1,7,8,5,4,2,3,6] => [.,[[[[.,[.,.]],.],[.,.]],[.,.]]] => [1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,2] => 1

[1,8,4,2,3,6,5,7] => [.,[[[.,[.,.]],[[.,.],[.,.]]],.]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,2] => 1

[1,4,2,7,5,3,8,6] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2] => 0

[1,5,7,6,2,4,3,8] => [.,[[.,[[.,.],.]],[[.,.],[.,.]]]] => [1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1] => 1

[1,3,8,4,2,6,5,7] => [.,[[.,.],[[.,[[.,.],[.,.]]],.]]] => [1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1,1] => 1

[1,7,4,2,6,5,8,3] => [.,[[[.,[.,.]],[[.,.],.]],[.,.]]] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,2] => 1

[1,7,4,8,3,2,5,6] => [.,[[[[.,.],.],[.,[.,.]]],[.,.]]] => [1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2,1] => 1

[1,4,8,3,2,7,5,6] => [.,[[[.,.],.],[[[.,[.,.]],.],.]]] => [1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,1] => 3

[1,8,3,6,4,5,2,7] => [.,[[[.,.],[[.,[.,.]],[.,.]]],.]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1,1,1] => 1

[1,6,4,7,3,2,8,5] => [.,[[[[.,.],.],[.,.]],[.,[.,.]]]] => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2,1] => 1

[8,2,3,7,4,5,6,1] => [[[.,.],[.,[[.,[.,[.,.]]],.]]],.] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,1,1,1,1] => 2

[2,8,7,3,4,6,1,5] => [[.,.],[[[.,[.,[[.,.],.]]],.],.]] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,1,1,1] => 3

[8,1,7,3,4,5,2,6] => [[.,[[[.,.],[.,[.,[.,.]]]],.]],.] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,1,1,1] => 2

[7,1,8,3,4,5,2,6] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1,1] => 0

[1,8,5,3,4,6,2,7] => [.,[[[[.,.],[.,.]],[.,[.,.]]],.]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,1,1] => 1

[3,4,5,1,6,7,8,2,9] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2] => 0

[5,6,1,7,8,9,2,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,4,4,4,4] => 0

[3,4,8,5,7,2,1,6] => [[[.,.],.],[.,[[.,[[.,.],.]],.]]] => [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,2,1] => 3

[5,8,4,7,3,6,2,1] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,4,3,2,1] => 5

[1,2,8,4,5,7,3,6] => [.,[.,[[[.,.],[.,[[.,.],.]]],.]]] => [1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1] => 2

[1,6,2,4,8,5,7,3] => [.,[[.,[[.,.],[.,.]]],[[.,.],.]]] => [1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1] => 1

[2,7,1,3,6,4,5,8] => [[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1,1,1,1] => 1

[3,2,4,8,5,7,1,6] => [[[.,.],.],[.,[[.,[[.,.],.]],.]]] => [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,2,1] => 3

[8,1,2,4,7,5,6,3] => [[.,[.,[[.,.],[[.,[.,.]],.]]]],.] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,1,1] => 2

[2,8,3,1,4,6,7,5] => [[.,.],[[.,[.,[[.,.],[.,.]]]],.]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1,1,1,1] => 1

[1,3,8,7,6,5,2,4] => [.,[[.,.],[[[[[.,.],.],.],.],.]]] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,1] => 4

[1,8,7,2,6,3,5,4] => [.,[[[.,[[.,[[.,.],.]],.]],.],.]] => [1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1] => 4

[2,8,7,1,6,3,4,5] => [[.,.],[[[[.,[.,[.,.]]],.],.],.]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,1,1,1] => 3

[1,2,5,7,4,8,6,3] => [.,[.,[[[.,.],.],[[.,.],[.,.]]]]] => [1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1] => 1

[2,8,3,4,1,5,6,7] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1,1,1] => 1

[1,3,7,5,4,8,6,2] => [.,[[.,.],[[[.,.],[.,.]],[.,.]]]] => [1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1] => 0

[1,5,6,3,8,4,2,7] => [.,[[[.,.],[.,.]],[.,[[.,.],.]]]] => [1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1] => 1

[2,3,6,5,4,8,1,7] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1,1] => 2

[8,1,4,6,7,5,2,3] => [[.,[[.,[.,.]],[[.,.],[.,.]]]],.] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2,2] => 1

[8,1,2,6,4,7,5,3] => [[.,[.,[[[.,.],[.,.]],[.,.]]]],.] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,3,1,1] => 1

[4,5,3,6,7,1,8,2] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,2] => 1

[1,4,7,8,3,5,2,6] => [.,[[[.,.],.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1] => 1

[2,4,5,6,8,3,1,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,1,1] => 1

[3,4,5,8,6,2,1,7] => [[[.,.],.],[.,[.,[[.,[.,.]],.]]]] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,2,1] => 2

[1,8,2,3,4,5,9,6,7] => [.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [6,6] => 0

[1,5,6,3,8,2,7,4] => [.,[[[.,.],[.,.]],[.,[[.,.],.]]]] => [1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1] => 1

[2,6,3,8,4,7,1,5] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1,1] => 1

[2,6,3,5,7,8,1,4] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1,1] => 1

[1,5,6,3,7,2,8,4] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => [1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1] => 0

[1,7,5,3,6,2,8,4] => [.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,1,1] => 0

[1,5,7,3,4,2,8,6] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1] => 0

[1,5,8,3,4,2,7,6] => [.,[[[.,.],[.,.]],[[[.,.],.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1,1] => 2

[1,4,5,3,7,2,8,6] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]] => [1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1] => 1

[1,4,5,3,8,2,7,6] => [.,[[[.,.],.],[.,[[[.,.],.],.]]]] => [1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,1] => 3

[1,7,5,4,2,8,6,3] => [.,[[[[.,[.,.]],.],[.,.]],[.,.]]] => [1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,2] => 1

[1,4,8,2,6,5,3,7] => [.,[[.,[.,.]],[[[.,.],[.,.]],.]]] => [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2] => 1

[1,2,5,6,8,7,3,4] => [.,[.,[[.,[.,.]],[.,[[.,.],.]]]]] => [1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2] => 1

[1,5,6,8,2,7,4,3] => [.,[[.,[[.,.],.]],[.,[[.,.],.]]]] => [1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1] => 2

[2,6,7,3,4,1,8,5] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1,1] => 0

[1,6,5,7,8,2,4,3] => [.,[[[.,[[.,.],.]],.],[.,[.,.]]]] => [1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,1] => 2

[1,5,6,7,2,8,4,3] => [.,[[.,[[.,.],.]],[.,[.,[.,.]]]]] => [1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1] => 1

[1,3,7,2,6,4,8,5] => [.,[[.,.],[[[.,[.,.]],.],[.,.]]]] => [1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1,1] => 1

[1,5,8,6,7,3,4,2] => [.,[[[.,.],[.,.]],[[.,[.,.]],.]]] => [1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1] => 1

[1,6,5,8,7,2,4,3] => [.,[[[.,[[.,.],.]],.],[[.,.],.]]] => [1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3,1] => 3

[1,5,7,6,2,8,3,4] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3] => 0

[1,2,5,8,6,7,4,3] => [.,[.,[[[.,.],.],[[.,[.,.]],.]]]] => [1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1] => 2

[1,2,6,5,7,3,8,4] => [.,[.,[[[.,[.,.]],.],[.,[.,.]]]]] => [1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2] => 1

[1,7,5,8,6,4,2,3] => [.,[[[[.,[.,.]],.],[.,.]],[.,.]]] => [1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,2] => 1

[2,5,6,8,1,3,7,4] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1,1] => 1

[2,4,7,8,5,6,3,1] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => 0

[3,8,7,4,2,6,5,1] => [[[.,.],.],[[[.,[[.,.],.]],.],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,2,2,1] => 4

[1,3,4,7,2,6,5,8] => [.,[[.,.],[.,[[[.,.],.],[.,.]]]]] => [1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1,1] => 1

[2,5,1,4,3,6,7,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1,1] => 1

[2,7,1,3,8,5,4,6] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1,1] => 0

[7,1,2,3,4,5,8,6,9] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,6,6] => 0

[6,1,2,3,4,7,5,8,9] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,5,5,5] => 0

[5,1,2,3,6,4,7,8,9] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,4,4,4,4] => 0

[4,1,2,5,3,6,7,8,9] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3,3] => 0

[7,1,2,6,3,8,4,5] => [[.,[.,[[.,[.,[.,.]]],.]]],[.,.]] => [1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [6,6,3] => 1

[8,1,2,6,5,3,7,4] => [[.,[.,[[[.,[.,.]],.],[.,.]]]],.] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2] => 2

[8,2,3,1,6,7,4,5] => [[[.,.],[.,[[.,[.,.]],[.,.]]]],.] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,3,1,1,1,1] => 1

[1,7,4,3,2,5,6,8] => [.,[[[[.,.],.],[.,[.,.]]],[.,.]]] => [1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2,1] => 1

[3,5,6,8,4,7,1,2] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,2] => 1

[4,1,5,6,8,7,3,2] => [[.,[[.,.],.]],[.,[.,[[.,.],.]]]] => [1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3,1] => 2

[6,1,2,4,5,7,8,3] => [[.,[.,[[.,.],[.,.]]]],[.,[.,.]]] => [1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [5,5,5,1,1] => 0

[8,1,3,7,4,5,6,2] => [[.,[[.,.],[[.,[.,[.,.]]],.]]],.] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,1,1,1] => 2

[3,5,1,4,6,2,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 0

[2,5,1,4,6,7,3,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1,1] => 1

[1,7,2,4,3,5,8,6] => [.,[[.,[[.,.],[.,[.,.]]]],[.,.]]] => [1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1] => 0

[2,8,3,1,4,7,5,6] => [[.,.],[[.,[.,[[.,[.,.]],.]]],.]] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1,1,1,1] => 2

[2,7,3,1,8,4,5,6] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1,1,1] => 0

[1,2,8,3,5,6,4,7] => [.,[.,[[.,[[.,.],[.,[.,.]]]],.]]] => [1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1] => 1

[2,8,1,3,5,4,6,7] => [[.,.],[[.,[[.,.],[.,[.,.]]]],.]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,1,1,1] => 1

[1,5,2,8,6,4,3,7] => [.,[[.,[[.,.],.]],[[.,[.,.]],.]]] => [1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1] => 2

[8,1,3,5,7,4,2,6] => [[.,[[.,.],[[.,.],[[.,.],.]]]],.] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,1,1] => 2

[1,8,4,7,3,2,5,6] => [.,[[[[.,.],.],[[.,[.,.]],.]],.]] => [1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,2,1] => 3

[1,2,5,4,7,8,3,6] => [.,[.,[[[.,.],.],[[.,.],[.,.]]]]] => [1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1] => 1

[1,8,3,2,6,4,7,5] => [.,[[[.,.],[[.,[.,.]],[.,.]]],.]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1,1,1] => 1

[1,6,2,3,5,7,8,4] => [.,[[.,[.,[[.,.],.]]],[.,[.,.]]]] => [1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1] => 1

[1,3,4,8,5,2,6,7] => [.,[[.,.],[.,[[.,[.,[.,.]]],.]]]] => [1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1] => 1

[1,5,7,2,3,6,8,4] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3] => 0

[7,3,1,4,2,5,8,6] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,2,2] => 0

[4,3,5,1,6,2,7,8] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,2] => 1

[4,3,8,7,2,6,1,5] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,3,2,1] => 5

[3,8,7,2,6,4,1,5] => [[[.,.],.],[[[[.,[.,.]],.],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,2,2,1] => 4

[3,8,7,2,6,1,5,4] => [[[.,.],.],[[[[[.,.],.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,2,1] => 5

[1,8,3,7,6,5,2,4] => [.,[[[.,.],[[[[.,.],.],.],.]],.]] => [1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,1,1] => 4

[1,4,3,8,7,2,6,5] => [.,[[[.,.],.],[[[[.,.],.],.],.]]] => [1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,2,1] => 4

[2,6,8,3,1,7,4,5] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1,1] => 1

[3,4,7,8,5,1,6,2] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2] => 0

[1,5,4,8,6,2,7,3] => [.,[[[.,[.,.]],.],[[.,[.,.]],.]]] => [1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,2] => 2

[1,7,5,8,2,4,6,3] => [.,[[[.,[[.,.],.]],[.,.]],[.,.]]] => [1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,1] => 1

[5,6,8,1,2,3,7,4] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [5,4,4,4] => 1

[1,6,4,5,2,7,3,8] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2] => 0

[1,2,4,6,8,3,7,5] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => [1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1] => 1

[1,3,5,8,2,6,7,4] => [.,[[.,.],[[.,.],[[.,[.,.]],.]]]] => [1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1,1] => 1

[8,1,5,2,6,4,3,7] => [[.,[[.,[[.,.],.]],[.,[.,.]]]],.] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [7,3,3,3,1] => 2

[1,6,7,4,2,8,3,5] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2] => 0

[1,4,7,2,3,6,8,5] => [.,[[.,[.,.]],[[[.,.],.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2] => 1

[1,6,3,4,7,8,2,5] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]] => [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1] => 0

[2,4,3,7,6,1,8,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1,1] => 1

[1,4,7,6,8,3,2,5] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1] => 2

[1,2,8,4,3,7,6,5] => [.,[.,[[[.,.],[[[.,.],.],.]],.]]] => [1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,1] => 3

[1,5,4,2,8,6,3,7] => [.,[[[.,[.,.]],.],[[.,[.,.]],.]]] => [1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,2] => 2

[1,4,2,8,5,3,7,6] => [.,[[.,[.,.]],[[.,[[.,.],.]],.]]] => [1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2] => 2

[1,7,4,8,3,5,2,6] => [.,[[[[.,.],.],[.,[.,.]]],[.,.]]] => [1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2,1] => 1

[2,5,1,8,6,3,7,4] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1,1] => 1

[1,8,4,2,7,5,3,6] => [.,[[[.,[.,.]],[[.,[.,.]],.]],.]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,2] => 2

[1,2,8,7,6,4,3,5] => [.,[.,[[[[[.,.],[.,.]],.],.],.]]] => [1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,1] => 3

[1,6,5,7,8,4,2,3] => [.,[[[[.,[.,.]],.],.],[.,[.,.]]]] => [1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,2] => 2

[1,9,2,10,3,4,5,6,7,8] => [.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [7,7] => 0

[1,5,4,8,6,2,3,7] => [.,[[[.,[.,.]],.],[[.,[.,.]],.]]] => [1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,2] => 2

[2,5,6,4,8,3,7,1] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1,1] => 2

[2,3,7,8,5,1,6,4] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1,1] => 0

[1,2,6,7,4,3,5,8] => [.,[.,[[[.,.],[.,.]],[.,[.,.]]]]] => [1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1] => 0

[3,4,8,2,5,6,1,7] => [[[.,.],.],[.,[[.,[.,[.,.]]],.]]] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,2,1] => 2

[4,3,8,5,2,7,1,6] => [[[[.,.],.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,3,3,2,1] => 4

[2,8,4,5,1,6,3,7] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,1,1] => 1

[1,4,8,2,7,6,5,3] => [.,[[.,[.,.]],[[[[.,.],.],.],.]]] => [1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,2] => 3

[2,4,7,3,8,5,1,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => 0

[2,7,3,1,8,5,4,6] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1,1] => 0

[2,8,3,1,7,4,5,6] => [[.,.],[[.,[[.,[.,[.,.]]],.]],.]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,1,1,1,1] => 2

[1,2,6,8,3,4,7,5] => [.,[.,[[.,[.,[.,.]]],[[.,.],.]]]] => [1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [4,3,3] => 1

[1,8,2,7,3,5,6,4] => [.,[[.,[[.,[[.,.],[.,.]]],.]],.]] => [1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,1] => 2

[1,6,3,5,7,4,8,2] => [.,[[[.,.],[[.,.],.]],[.,[.,.]]]] => [1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1] => 1

[1,5,4,7,2,8,3,6] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2] => 1

[8,1,2,6,5,3,4,7] => [[.,[.,[[[.,[.,.]],.],[.,.]]]],.] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2] => 2

[8,1,2,6,3,5,7,4] => [[.,[.,[[.,[[.,.],.]],[.,.]]]],.] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [7,3,3,1] => 2

[3,4,2,8,5,1,6,7] => [[[.,.],.],[.,[[.,[.,[.,.]]],.]]] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,2,1] => 2

[1,8,4,5,7,6,2,3] => [.,[[[.,[.,.]],[.,[[.,.],.]]],.]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2] => 2

[3,2,8,7,1,6,4,5] => [[[.,.],.],[[[[.,[.,.]],.],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,2,2,1] => 4

[2,7,8,3,1,6,4,5] => [[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1,1,1,1] => 1

[2,7,8,1,3,6,4,5] => [[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1,1,1,1] => 1

[1,8,6,2,5,4,7,3] => [.,[[[.,[[[.,.],.],.]],[.,.]],.]] => [1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2,1] => 3

[8,3,4,5,6,1,7,2] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2,2] => 1

[2,4,8,3,7,5,6,1] => [[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,1,1] => 2

[4,8,3,7,5,6,2,1] => [[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,3,3,2,1] => 4

[2,3,8,6,4,5,7,1] => [[.,.],[.,[[[.,[.,.]],[.,.]],.]]] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1,1,1] => 1

[2,5,6,1,8,7,3,4] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1,1] => 1

[2,3,8,6,7,5,4,1] => [[.,.],[.,[[[[.,.],.],[.,.]],.]]] => [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1,1,1] => 2

[1,5,8,3,6,4,2,7] => [.,[[[.,.],[.,.]],[[.,[.,.]],.]]] => [1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1] => 1

[1,5,8,6,3,4,2,7] => [.,[[[.,.],[.,.]],[[.,[.,.]],.]]] => [1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1] => 1

[1,3,7,8,4,2,6,5] => [.,[[.,.],[[.,[[.,.],.]],[.,.]]]] => [1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1,1] => 1

[6,1,2,5,3,4,7,8] => [[.,[.,[[.,[.,.]],.]]],[.,[.,.]]] => [1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [5,5,5,2] => 1

[1,4,6,5,7,2,3,8] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2] => 0

[1,3,2,6,8,4,7,5] => [.,[[.,.],[[.,[.,.]],[[.,.],.]]]] => [1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1] => 1

[1,2,6,4,7,3,5,8] => [.,[.,[[[.,.],[.,.]],[.,[.,.]]]]] => [1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1] => 0

[1,6,4,3,7,2,5,8] => [.,[[[[.,.],.],[.,.]],[.,[.,.]]]] => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2,1] => 1

[3,4,5,6,7,1,2,8,9] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2] => 0

[2,7,3,1,4,8,6,5] => [[.,.],[[.,[.,[[.,.],.]]],[.,.]]] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1,1,1] => 1

[1,7,2,5,6,8,4,3] => [.,[[.,[[[.,.],.],[.,.]]],[.,.]]] => [1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1] => 1

[1,4,2,6,7,8,5,3] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2] => 0

[1,4,2,5,6,8,7,3] => [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => [1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2] => 1

[2,5,3,6,7,8,4,1] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1,1] => 0

[1,8,6,2,4,3,5,7] => [.,[[[.,[[.,.],[.,.]]],[.,.]],.]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,4,1,1] => 1

[3,2,4,5,7,8,1,6] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2,1] => 1

[2,3,4,7,5,8,6,1] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1,1] => 0

[1,6,2,7,8,4,5,3] => [.,[[.,[[.,.],[.,.]]],[.,[.,.]]]] => [1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1] => 0

[1,6,8,2,7,5,3,4] => [.,[[.,[[.,[.,.]],.]],[[.,.],.]]] => [1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2] => 2

[1,7,8,6,4,2,3,5] => [.,[[[[.,[.,.]],[.,.]],.],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,2] => 1

[1,5,3,7,4,2,6,8] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1] => 0

[1,7,6,4,3,2,8,5] => [.,[[[[[.,.],.],[.,.]],.],[.,.]]] => [1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,2,1] => 2

[1,7,6,3,4,2,5,8] => [.,[[[[.,.],[.,[.,.]]],.],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1,1,1] => 1

[1,2,7,4,3,8,6,5] => [.,[.,[[[.,.],[[.,.],.]],[.,.]]]] => [1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1] => 1

[1,5,4,2,3,8,7,6] => [.,[[[.,[.,.]],.],[[[.,.],.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,2] => 3

[1,5,3,2,4,6,7,8] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => [1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1] => 0

[1,5,4,2,3,7,8,6] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2] => 1

[1,2,7,6,3,5,8,4] => [.,[.,[[[.,[[.,.],.]],.],[.,.]]]] => [1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1] => 2

[8,1,3,2,6,5,7,4] => [[.,[[.,.],[[[.,.],.],[.,.]]]],.] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2,1,1] => 2

[8,1,4,3,5,2,7,6] => [[.,[[[.,.],.],[.,[[.,.],.]]]],.] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,2,1] => 3

[1,7,5,8,4,6,3,2] => [.,[[[[[.,.],.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,2,1] => 2

[8,1,2,5,3,7,6,4] => [[.,[.,[[.,[.,.]],[[.,.],.]]]],.] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2] => 2

[3,4,2,7,8,1,5,6] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2,1] => 1

[4,5,6,7,1,8,2,9,3] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3,3] => 0

[1,5,7,6,8,2,4,3] => [.,[[.,[[.,.],.]],[[.,.],[.,.]]]] => [1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1] => 1

[1,6,2,4,3,5,8,7] => [.,[[.,[[.,.],[.,.]]],[[.,.],.]]] => [1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1] => 1

[1,5,6,3,7,8,4,2] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => [1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1] => 0

[1,5,7,6,3,8,4,2] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1] => 0

[1,6,3,7,8,5,4,2] => [.,[[[.,.],[[.,.],.]],[.,[.,.]]]] => [1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1] => 1

[1,6,3,7,2,4,5,8] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]] => [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1] => 0

[1,5,3,8,4,2,7,6] => [.,[[[.,.],[.,.]],[[[.,.],.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1,1] => 2

[1,4,8,5,3,6,7,2] => [.,[[[.,.],.],[[.,[.,[.,.]]],.]]] => [1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,1] => 2

[2,5,6,3,1,8,4,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1,1] => 1

[4,5,1,2,7,8,6,3] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [4,4,3,3,3] => 0

[4,6,7,5,1,2,8,3] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[8,1,3,6,2,5,7,4] => [[.,[[.,.],[[[.,.],.],[.,.]]]],.] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2,1,1] => 2

[1,5,6,3,8,4,7,2] => [.,[[[.,.],[.,.]],[.,[[.,.],.]]]] => [1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1] => 1

[5,6,1,8,2,3,7,4] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [5,4,4,4] => 1

[1,7,8,6,3,4,2,5] => [.,[[[[.,.],[.,[.,.]]],.],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1,1,1] => 1

[1,7,3,8,6,4,2,5] => [.,[[[.,.],[[.,[.,.]],.]],[.,.]]] => [1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1,1,1] => 1

[8,1,3,5,6,4,2,7] => [[.,[[.,.],[[.,.],[.,[.,.]]]]],.] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,1,1] => 1

[1,3,8,5,6,4,2,7] => [.,[[.,.],[[[.,.],[.,[.,.]]],.]]] => [1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1,1] => 1

[1,3,5,8,6,4,2,7] => [.,[[.,.],[[.,.],[[.,[.,.]],.]]]] => [1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1,1] => 1

[1,5,7,8,6,4,2,3] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2] => 1

[1,8,2,6,5,3,4,7] => [.,[[.,[[[.,[.,.]],.],[.,.]]],.]] => [1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2] => 2

[7,6,1,2,3,8,4,5] => [[[.,[.,[.,[.,[.,.]]]]],.],[.,.]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [6,6,5] => 1

[6,8,1,2,3,7,4,5] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [6,5,5] => 1

[8,1,3,5,6,7,2,4] => [[.,[[.,.],[[.,.],[.,[.,.]]]]],.] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,1,1] => 1

[8,1,2,5,3,4,7,6] => [[.,[.,[[.,[.,.]],[[.,.],.]]]],.] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2] => 2

[1,2,8,6,4,5,3,7] => [.,[.,[[[[.,.],[.,.]],[.,.]],.]]] => [1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1] => 1

[1,5,8,7,6,3,4,2] => [.,[[[.,.],[.,.]],[[[.,.],.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1,1] => 2

[1,4,7,8,5,6,3,2] => [.,[[[.,.],.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1] => 1

[1,6,8,5,2,7,3,4] => [.,[[[.,[.,[.,.]]],.],[[.,.],.]]] => [1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3] => 2

[1,3,4,8,5,2,7,6] => [.,[[.,.],[.,[[.,[[.,.],.]],.]]]] => [1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1,1] => 2

[3,1,5,4,6,8,7,2] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,2] => 1

[1,8,4,7,2,3,6,5] => [.,[[[.,[.,.]],[[[.,.],.],.]],.]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,2] => 3

[1,8,3,7,4,6,5,2] => [.,[[[.,.],[[.,[[.,.],.]],.]],.]] => [1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,1,1] => 3

[8,2,3,1,7,4,5,6] => [[[.,.],[.,[[.,[.,[.,.]]],.]]],.] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,1,1,1,1] => 2

[2,1,5,7,6,3,8,4] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[4,1,2,5,7,6,8,3] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [4,4,3,3,3] => 0

[1,8,5,2,3,4,7,6] => [.,[[[.,[.,[.,.]]],[[.,.],.]],.]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,3] => 2

[1,5,8,2,3,4,7,6] => [.,[[.,[.,[.,.]]],[[[.,.],.],.]]] => [1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3] => 2

[1,2,7,8,4,5,6,3] => [.,[.,[[[.,.],[.,[.,.]]],[.,.]]]] => [1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1] => 0

[4,3,8,7,6,2,5,1] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,3,2,1] => 5

[2,3,6,4,1,7,5,8] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1,1] => 0

[2,3,7,1,5,8,4,6] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1,1] => 0

[2,3,6,1,7,5,8,4] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1,1] => 1

[2,3,6,5,1,7,4,8] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1,1] => 1

[3,5,6,2,1,4,7,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => 1

[1,2,5,6,8,3,7,4] => [.,[.,[[.,[.,.]],[.,[[.,.],.]]]]] => [1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2] => 1

[4,1,5,6,8,7,2,3] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3] => 1

[1,2,5,6,8,4,7,3] => [.,[.,[[[.,.],.],[.,[[.,.],.]]]]] => [1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1] => 2

[1,5,6,8,4,7,2,3] => [.,[[[.,[.,.]],.],[.,[[.,.],.]]]] => [1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2] => 2

[1,3,5,6,8,4,7,2] => [.,[[.,.],[[.,.],[.,[[.,.],.]]]]] => [1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1,1] => 1

[5,1,7,2,8,6,3,4] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4] => 0

[1,5,6,4,2,8,7,3] => [.,[[[.,[.,.]],.],[.,[[.,.],.]]]] => [1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2] => 2

[3,4,2,1,5,6,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2,1] => 1

[3,4,2,5,1,6,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2,1] => 1

[1,3,8,2,4,6,7,5] => [.,[[.,.],[[.,[[.,.],[.,.]]],.]]] => [1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1,1] => 1

[2,8,7,6,3,5,1,4] => [[.,.],[[[[.,[[.,.],.]],.],.],.]] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,1,1,1] => 4

[1,6,5,7,4,2,3,8] => [.,[[[[.,[.,.]],.],.],[.,[.,.]]]] => [1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,2] => 2

[2,3,1,8,4,6,5,7] => [[.,.],[.,[[.,[[.,.],[.,.]]],.]]] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1,1,1] => 1

[2,3,1,7,6,8,4,5] => [[.,.],[.,[[[.,[.,.]],.],[.,.]]]] => [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1,1,1] => 1

[2,3,1,8,4,6,7,5] => [[.,.],[.,[[.,[[.,.],[.,.]]],.]]] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1,1,1] => 1

[4,1,6,2,7,5,3,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[2,4,5,3,1,8,6,7] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,1,1] => 1

[2,4,8,5,6,3,1,7] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,1,1] => 1

[4,5,1,6,3,2,7,8] => [[.,[[.,.],.]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1] => 1

[4,2,5,1,6,3,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1,1] => 0

[5,1,6,2,4,3,7,8] => [[.,[.,[[.,.],.]]],[.,[.,[.,.]]]] => [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,1] => 1

[1,8,2,6,7,4,5,3] => [.,[[.,[[[.,.],[.,.]],[.,.]]],.]] => [1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1,1] => 1

[1,2,8,3,4,7,6,5] => [.,[.,[[.,[.,[[[.,.],.],.]]],.]]] => [1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,2,1] => 3

[1,4,5,8,3,2,6,7] => [.,[[[.,.],.],[.,[[.,[.,.]],.]]]] => [1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,1] => 2

[1,5,2,4,7,8,6,3] => [.,[[.,[[.,.],.]],[[.,.],[.,.]]]] => [1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1] => 1

[2,7,3,4,8,5,6,1] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1,1,1] => 0

[1,6,3,2,7,5,8,4] => [.,[[[.,.],[[.,.],.]],[.,[.,.]]]] => [1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1] => 1

[2,5,3,6,4,7,8,1] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1,1] => 0

[4,2,5,3,6,7,8,1] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1,1] => 0

[1,6,5,2,4,7,3,8] => [.,[[[.,[[.,.],.]],.],[.,[.,.]]]] => [1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,1] => 2

[1,8,7,2,4,6,3,5] => [.,[[[.,[[.,.],[[.,.],.]]],.],.]] => [1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,1] => 3

[1,8,7,2,5,4,3,6] => [.,[[[.,[[[.,.],.],[.,.]]],.],.]] => [1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,1] => 3

[1,5,4,2,7,3,6,8] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2] => 1

[1,5,4,2,8,7,3,6] => [.,[[[.,[.,.]],.],[[[.,.],.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,2] => 3

[1,6,8,3,5,2,4,7] => [.,[[[.,.],[[.,.],.]],[[.,.],.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,1,1] => 2

[1,7,6,2,3,5,8,4] => [.,[[[.,[.,[[.,.],.]]],.],[.,.]]] => [1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1] => 2

[1,2,8,3,6,5,4,7] => [.,[.,[[.,[[[.,.],.],[.,.]]],.]]] => [1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1] => 2

[1,3,8,6,5,2,4,7] => [.,[[.,.],[[[[.,.],.],[.,.]],.]]] => [1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1,1] => 2

[1,4,7,3,2,8,6,5] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1] => 2

[1,7,5,3,2,6,4,8] => [.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,1,1] => 0

[1,2,6,5,3,8,4,7] => [.,[.,[[[.,[.,.]],.],[[.,.],.]]]] => [1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2] => 2

[1,7,3,2,8,4,6,5] => [.,[[[.,.],[.,[[.,.],.]]],[.,.]]] => [1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1,1] => 1

[1,6,5,2,8,4,7,3] => [.,[[[.,[[.,.],.]],.],[[.,.],.]]] => [1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3,1] => 3

[1,8,3,7,2,4,6,5] => [.,[[[.,.],[[.,[[.,.],.]],.]],.]] => [1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,1,1] => 3

[2,4,3,6,7,8,1,5] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[6,1,2,4,3,7,8,5] => [[.,[.,[[.,.],[.,.]]]],[.,[.,.]]] => [1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [5,5,5,1,1] => 0

[7,1,2,4,6,3,8,5] => [[.,[.,[[.,.],[[.,.],.]]]],[.,.]] => [1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [6,6,2,1,1] => 1

[7,1,2,6,5,3,8,4] => [[.,[.,[[[.,[.,.]],.],.]]],[.,.]] => [1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [6,6,3,2] => 2

[1,6,7,5,8,3,4,2] => [.,[[[[.,.],[.,.]],.],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,1,1] => 1

[8,1,2,3,7,5,4,6] => [[.,[.,[.,[[[.,.],[.,.]],.]]]],.] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,1] => 2

[9,2,3,4,5,6,1,7,8] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1,1,1,1,1,1] => 1

[4,3,8,5,6,2,7,1] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [6,3,3,3,3,2,1] => 3

[3,5,1,6,4,8,2,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,2] => 1

[2,4,8,5,6,1,3,7] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,1,1] => 1

[8,1,2,7,5,6,3,4] => [[.,[.,[[[.,[.,.]],[.,.]],.]]],.] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [7,4,2,2] => 2

[1,5,6,3,2,8,7,4] => [.,[[[.,.],[.,.]],[.,[[.,.],.]]]] => [1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1] => 1

[1,3,7,6,8,4,2,5] => [.,[[.,.],[[[.,[.,.]],.],[.,.]]]] => [1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1,1] => 1

[1,6,7,3,2,8,5,4] => [.,[[[.,.],[[.,.],.]],[.,[.,.]]]] => [1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1] => 1

[1,3,8,5,2,7,6,4] => [.,[[.,.],[[[.,.],[[.,.],.]],.]]] => [1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1,1] => 2

[2,5,7,1,6,3,8,4] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[3,4,7,6,1,2,5,8] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,2] => 1

[4,1,6,5,2,7,3,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[1,5,8,4,2,3,6,7] => [.,[[[.,[.,.]],.],[[.,[.,.]],.]]] => [1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,2] => 2

[1,5,8,4,6,7,2,3] => [.,[[[.,[.,.]],.],[[.,[.,.]],.]]] => [1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,2] => 2

[1,8,6,4,5,7,2,3] => [.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2,2] => 1

[1,8,6,4,2,3,5,7] => [.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2,2] => 1

[8,1,3,6,2,4,5,7] => [[.,[[.,.],[[.,[.,.]],[.,.]]]],.] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,3,1,1,1] => 1

[1,8,4,6,7,5,2,3] => [.,[[[.,[.,.]],[[.,.],[.,.]]],.]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,2] => 1

[1,6,2,5,8,4,7,3] => [.,[[.,[[[.,.],.],.]],[[.,.],.]]] => [1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,1] => 3

[1,2,8,6,4,7,3,5] => [.,[.,[[[[.,.],[.,.]],[.,.]],.]]] => [1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1] => 1

[2,8,3,7,1,4,6,5] => [[.,.],[[.,[[.,[[.,.],.]],.]],.]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,1,1,1] => 3

[4,8,3,2,7,5,6,1] => [[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,3,3,2,1] => 4

[8,1,3,6,5,4,2,7] => [[.,[[.,.],[[[.,.],.],[.,.]]]],.] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2,1,1] => 2

[1,2,4,8,6,3,7,5] => [.,[.,[[.,.],[[[.,.],[.,.]],.]]]] => [1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1] => 1

[1,8,6,4,7,5,3,2] => [.,[[[[[.,.],.],[.,.]],[.,.]],.]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2,2,1] => 2

[1,3,8,7,6,4,2,5] => [.,[[.,.],[[[[.,[.,.]],.],.],.]]] => [1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,1,1] => 3

[1,8,6,4,7,5,2,3] => [.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2,2] => 1

[1,2,8,6,4,7,5,3] => [.,[.,[[[[.,.],[.,.]],[.,.]],.]]] => [1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1] => 1

[3,4,5,6,1,2,7,8,9] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2] => 0

[5,1,6,7,8,9,2,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,4,4,4,4] => 0

[1,2,8,6,4,3,5,7] => [.,[.,[[[[.,.],[.,.]],[.,.]],.]]] => [1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1] => 1

[1,8,2,7,5,3,4,6] => [.,[[.,[[[.,[.,.]],[.,.]],.]],.]] => [1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2] => 2

[7,1,3,2,4,5,6,8] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1,1] => 0

[1,7,6,4,2,5,3,8] => [.,[[[[.,[.,.]],[.,.]],.],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,2] => 1

[1,5,2,4,6,8,7,3] => [.,[[.,[[.,.],.]],[.,[[.,.],.]]]] => [1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1] => 2

[8,1,2,4,7,6,5,3] => [[.,[.,[[.,.],[[[.,.],.],.]]]],.] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1,1] => 3

[3,4,1,8,6,7,5,2] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,2] => 1

[1,3,8,4,7,5,2,6] => [.,[[.,.],[[.,[[.,[.,.]],.]],.]]] => [1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1,1,1] => 2

[2,8,3,1,7,6,4,5] => [[.,.],[[.,[[[.,[.,.]],.],.]],.]] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,1,1,1] => 3

[2,5,6,4,8,1,7,3] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1,1] => 2

[4,5,2,1,6,7,8,3] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1,1] => 0

[4,5,6,3,1,7,8,2] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,2] => 1

[3,5,6,7,4,1,8,2] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 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] => [4,3,3,3,2,2] => 1

[3,5,1,4,2,6,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 0

[1,3,8,4,6,2,5,7] => [.,[[.,.],[[.,[[.,.],[.,.]]],.]]] => [1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1,1] => 1

[1,8,4,2,3,7,5,6] => [.,[[[.,[.,.]],[[.,[.,.]],.]],.]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,2] => 2

[1,4,8,3,2,7,6,5] => [.,[[[.,.],.],[[[[.,.],.],.],.]]] => [1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,2,1] => 4

[1,3,7,6,5,2,4,8] => [.,[[.,.],[[[[.,.],.],.],[.,.]]]] => [1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1,1] => 2

[1,2,8,6,7,5,4,3] => [.,[.,[[[[[.,.],.],.],[.,.]],.]]] => [1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1] => 3

[1,7,5,4,3,2,6,8] => [.,[[[[[.,.],.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,2,1] => 2

[3,8,7,4,5,2,6,1] => [[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,2,2,1] => 3

[7,2,3,4,1,8,5,6] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1,1,1] => 0

[1,4,6,8,2,5,7,3] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2] => 1

[1,5,2,6,8,3,7,4] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3] => 1

[1,6,2,7,8,4,3,5] => [.,[[.,[[.,.],[.,.]]],[.,[.,.]]]] => [1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1] => 0

[1,4,7,8,6,2,5,3] => [.,[[.,[.,.]],[[[.,.],.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2] => 1

[1,6,7,8,3,2,5,4] => [.,[[[.,.],[[.,.],.]],[.,[.,.]]]] => [1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1] => 1

[1,3,2,7,8,4,6,5] => [.,[[.,.],[[.,[[.,.],.]],[.,.]]]] => [1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1,1] => 1

[4,5,7,1,8,6,2,3] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [4,4,3,3,3] => 0

[2,3,8,6,5,1,7,4] => [[.,.],[.,[[[[.,.],.],[.,.]],.]]] => [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1,1,1] => 2

[2,4,3,5,6,8,1,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,1,1] => 1

[2,5,6,3,8,4,7,1] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1,1] => 1

[1,7,6,2,8,3,5,4] => [.,[[[.,[.,[[.,.],.]]],.],[.,.]]] => [1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1] => 2

[2,4,3,8,6,5,1,7] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1,1] => 1

[3,1,4,5,8,6,2,7] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,2] => 1

[1,8,3,2,5,4,6,7] => [.,[[[.,.],[[.,.],[.,[.,.]]]],.]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,1,1] => 1

[1,7,5,8,4,3,2,6] => [.,[[[[[.,.],.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,2,1] => 2

[1,2,5,7,8,3,6,4] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => [1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2] => 0

[3,4,5,8,1,7,2,6] => [[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,2] => 2

[4,5,6,2,7,8,3,1] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1,1] => 0

[4,5,6,2,7,1,8,3] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1,1] => 0

[4,5,6,2,1,7,8,3] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1,1] => 0

[4,5,6,2,1,7,3,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1,1] => 0

[4,5,1,6,7,3,2,8] => [[.,[[.,.],.]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1] => 1

[2,3,4,6,8,1,7,5] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1,1] => 1

[2,3,5,8,1,6,7,4] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1,1,1] => 1

[2,4,7,5,6,8,1,3] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => 0

[2,7,3,6,4,1,8,5] => [[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1,1,1,1] => 1

[2,5,1,4,6,3,8,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1,1] => 2

[3,1,5,6,4,2,8,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,2] => 1

[2,1,4,7,3,6,8,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1,1] => 1

[2,1,5,3,7,8,6,4] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[8,1,4,2,6,5,7,3] => [[.,[[.,[.,.]],[[.,.],[.,.]]]],.] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2,2] => 1

[5,6,4,3,8,2,7,1] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [5,4,4,4,3,2,1] => 4

[7,1,2,4,5,6,8,3] => [[.,[.,[[.,.],[.,[.,.]]]]],[.,.]] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1] => 0

[8,7,1,3,4,5,6,2] => [[[.,[[.,.],[.,[.,[.,.]]]]],.],.] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,1,1,1] => 2

[1,7,2,5,4,6,8,3] => [.,[[.,[[[.,.],.],[.,.]]],[.,.]]] => [1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1] => 1

[2,5,3,8,1,6,7,4] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1,1] => 1

[1,6,4,2,5,7,8,3] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2] => 0

[2,5,3,1,4,7,8,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[8,1,4,5,3,6,2,7] => [[.,[[[.,.],.],[.,[.,[.,.]]]]],.] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2,1] => 2

[1,5,4,7,3,8,6,2] => [.,[[[[.,.],.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2,1] => 2

[1,6,2,7,4,5,8,3] => [.,[[.,[[.,.],[.,.]]],[.,[.,.]]]] => [1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1] => 0

[7,3,4,5,1,6,8,2] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,2,2] => 0

[3,2,4,1,5,6,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2,1] => 1

[4,1,2,6,5,3,7,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[4,6,1,2,5,3,7,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[6,1,2,4,7,3,5,8] => [[.,[.,[[.,.],[.,.]]]],[.,[.,.]]] => [1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [5,5,5,1,1] => 0

[2,4,1,3,7,8,6,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1,1] => 1

[5,1,6,4,7,8,2,3] => [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,2] => 1

[1,5,4,7,2,6,3,8] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2] => 1

[2,4,5,8,3,1,7,6] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,1,1] => 2

[1,4,7,5,8,3,6,2] => [.,[[[.,.],.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1] => 1

[4,8,7,3,5,6,2,1] => [[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,3,3,2,1] => 4

[1,3,6,2,5,8,7,4] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]] => [1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1] => 2

[4,6,5,1,2,7,3,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[5,6,4,1,2,7,3,8] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3] => 1

[8,1,5,6,2,4,3,7] => [[.,[[.,[[.,.],.]],[.,[.,.]]]],.] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [7,3,3,3,1] => 2

[1,2,6,7,8,4,5,3] => [.,[.,[[[.,.],[.,.]],[.,[.,.]]]]] => [1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1] => 0

[7,3,4,5,1,8,6,2] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,2,2] => 0

[1,5,6,7,4,8,2,3] => [.,[[[.,[.,.]],.],[.,[.,[.,.]]]]] => [1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2] => 1

[2,6,7,8,3,1,4,5] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1,1] => 0

[5,6,7,1,8,4,2,3] => [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,2] => 1

[1,7,3,2,8,6,5,4] => [.,[[[.,.],[[[.,.],.],.]],[.,.]]] => [1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,1,1] => 2

[1,8,2,4,7,6,3,5] => [.,[[.,[[.,.],[[[.,.],.],.]]],.]] => [1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,1] => 3

[1,8,2,4,6,7,5,3] => [.,[[.,[[.,.],[[.,.],[.,.]]]],.]] => [1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1,1] => 1

[2,4,5,8,1,7,6,3] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,1,1] => 2

[1,6,5,2,8,7,3,4] => [.,[[[.,[.,[.,.]]],.],[[.,.],.]]] => [1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3] => 2

[8,1,3,2,7,6,4,5] => [[.,[[.,.],[[[.,[.,.]],.],.]]],.] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [7,4,3,1,1,1] => 3

[1,6,8,4,2,5,7,3] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,2] => 1

[1,4,2,8,3,5,7,6] => [.,[[.,[.,.]],[[.,[[.,.],.]],.]]] => [1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2] => 2

[1,3,5,4,8,7,2,6] => [.,[[.,.],[[.,.],[[[.,.],.],.]]]] => [1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1,1] => 2

[1,6,2,4,8,3,7,5] => [.,[[.,[[.,.],[.,.]]],[[.,.],.]]] => [1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1] => 1

[1,7,8,5,4,2,6,3] => [.,[[[[.,[.,.]],.],[.,.]],[.,.]]] => [1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,2] => 1

[1,5,2,8,6,4,7,3] => [.,[[.,[[.,.],.]],[[.,[.,.]],.]]] => [1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1] => 2

[1,6,5,2,7,4,8,3] => [.,[[[.,[[.,.],.]],.],[.,[.,.]]]] => [1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,1] => 2

[5,1,6,7,4,2,8,3] => [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,2] => 1

[1,5,4,2,8,6,7,3] => [.,[[[.,[.,.]],.],[[.,[.,.]],.]]] => [1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,2] => 2

[1,8,5,4,6,2,7,3] => [.,[[[[.,[.,.]],.],[.,[.,.]]],.]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,2] => 2

[1,7,5,4,6,2,8,3] => [.,[[[[.,[.,.]],.],[.,.]],[.,.]]] => [1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,2] => 1

[1,7,8,6,4,5,3,2] => [.,[[[[[.,.],.],[.,.]],.],[.,.]]] => [1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,2,1] => 2

[1,6,3,4,2,7,5,8] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]] => [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1] => 0

[1,7,2,4,5,6,8,3] => [.,[[.,[[.,.],[.,[.,.]]]],[.,.]]] => [1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1] => 0

[1,8,3,2,5,6,4,7] => [.,[[[.,.],[[.,.],[.,[.,.]]]],.]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,1,1] => 1

[1,9,8,10,7,6,5,4,3,2] => [.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [7,7,6,5,4,3,2,1] => 6

[2,5,3,7,4,6,1,8] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[2,6,7,3,4,5,1,8] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1,1] => 0

[3,8,4,5,2,1,6,7] => [[[.,.],.],[[.,[.,[.,[.,.]]]],.]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,2,1] => 2

[8,1,2,3,6,4,7,5] => [[.,[.,[.,[[.,[.,.]],[.,.]]]]],.] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [7,2,2] => 1

[3,5,4,1,2,6,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 0

[2,5,3,7,8,4,6,1] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[7,1,3,8,4,5,2,6] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1,1] => 0

[7,1,8,3,4,6,2,5] => [[.,[[.,.],[.,[[.,.],.]]]],[.,.]] => [1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [6,6,2,1,1,1] => 1

[2,5,4,1,3,6,7,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1,1] => 1

[5,4,1,2,6,7,3,8] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3] => 1

[1,7,6,3,8,4,5,2] => [.,[[[[.,.],[.,[.,.]]],.],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1,1,1] => 1

[3,2,4,6,5,8,1,7] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2,1] => 2

[2,5,4,6,1,3,8,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1,1] => 2

[2,4,3,5,8,1,6,7] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,1,1] => 1

[6,1,2,4,3,5,7,8] => [[.,[.,[[.,.],[.,.]]]],[.,[.,.]]] => [1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [5,5,5,1,1] => 0

[1,7,6,8,4,3,2,5] => [.,[[[[[.,.],.],[.,.]],.],[.,.]]] => [1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,2,1] => 2

[1,7,6,5,3,8,2,4] => [.,[[[[[.,.],[.,.]],.],.],[.,.]]] => [1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3,1,1] => 2

[1,5,6,3,8,7,2,4] => [.,[[[.,.],[.,.]],[.,[[.,.],.]]]] => [1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1] => 1

[1,8,7,5,4,3,2,6] => [.,[[[[[[.,.],.],.],[.,.]],.],.]] => [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3,2,1] => 4

[3,1,4,7,6,2,5,8] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,2] => 1

[7,1,2,3,6,4,5,8] => [[.,[.,[.,[[.,[.,.]],.]]]],[.,.]] => [1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [6,6,2] => 1

[2,4,6,5,7,8,1,3] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[2,4,6,7,5,8,1,3] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[2,4,6,3,7,8,1,5] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[2,4,5,6,8,7,1,3] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,1,1] => 1

[2,4,5,6,8,3,7,1] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,1,1] => 1

[2,4,5,6,3,8,1,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,1,1] => 1

[2,3,4,6,8,5,1,7] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1,1] => 1

[1,5,2,7,6,8,4,3] => [.,[[.,[[.,.],.]],[[.,.],[.,.]]]] => [1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1] => 1

[3,4,8,5,2,1,7,6] => [[[.,.],.],[.,[[.,[[.,.],.]],.]]] => [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,2,1] => 3

[1,3,5,6,8,7,2,4] => [.,[[.,.],[[.,.],[.,[[.,.],.]]]]] => [1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1,1] => 1

[1,3,8,4,7,6,2,5] => [.,[[.,.],[[.,[[[.,.],.],.]],.]]] => [1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,1,1] => 3

[2,3,8,4,1,7,5,6] => [[.,.],[.,[[.,[[.,[.,.]],.]],.]]] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1,1,1,1] => 2

[3,4,6,7,1,5,8,2] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2] => 0

[3,4,5,7,8,1,6,2] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2] => 0

[1,8,7,4,3,5,2,6] => [.,[[[[[.,.],.],[.,[.,.]]],.],.]] => [1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,2,1] => 3

[2,4,5,8,1,3,7,6] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,1,1] => 2

[2,8,3,5,6,1,4,7] => [[.,.],[[.,[[.,.],[.,[.,.]]]],.]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,1,1,1] => 1

[1,3,6,4,2,7,5,8] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => [1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1] => 0

[2,3,7,5,8,1,4,6] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1,1] => 0

[3,4,7,5,2,8,1,6] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2,1] => 1

[2,4,7,5,8,3,1,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => 0

[1,5,4,8,7,6,2,3] => [.,[[[.,[.,.]],.],[[[.,.],.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,2] => 3

[3,2,4,5,8,1,6,7] => [[[.,.],.],[.,[.,[[.,[.,.]],.]]]] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,2,1] => 2

[4,8,3,7,6,2,1,5] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,3,2,1] => 5

[1,3,6,8,2,4,7,5] => [.,[[.,.],[[.,[.,.]],[[.,.],.]]]] => [1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1] => 1

[1,6,7,4,3,8,2,5] => [.,[[[[.,.],.],[.,.]],[.,[.,.]]]] => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2,1] => 1

[2,1,3,8,7,5,6,4] => [[.,.],[.,[[[[.,.],[.,.]],.],.]]] => [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,1,1,1] => 2

[1,6,4,7,3,8,5,2] => [.,[[[[.,.],.],[.,.]],[.,[.,.]]]] => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2,1] => 1

[3,4,5,6,7,8,2,1,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2,1] => 1

[3,4,5,6,7,2,1,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2,1] => 1

[4,5,6,7,8,1,2,3,9] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3,3] => 0

[1,7,6,2,4,8,5,3] => [.,[[[.,[[.,.],[.,.]]],.],[.,.]]] => [1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1,1] => 1

[2,7,8,3,6,4,5,1] => [[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1,1,1,1] => 1

[1,4,7,8,6,3,5,2] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1] => 2

[1,6,8,2,5,3,4,7] => [.,[[.,[[.,[.,.]],.]],[[.,.],.]]] => [1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2] => 2

[2,5,6,4,3,8,1,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1,1] => 2

[3,4,6,7,2,1,5,8] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2,1] => 1

[1,4,6,3,7,5,2,8] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1] => 1

[1,3,8,7,4,5,6,2] => [.,[[.,.],[[[.,[.,[.,.]]],.],.]]] => [1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1,1,1] => 2

[7,3,1,8,4,5,6,2] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,2,2] => 0

[3,2,8,7,4,5,6,1] => [[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,2,2,1] => 3

[1,3,2,8,7,4,6,5] => [.,[[.,.],[[[.,[[.,.],.]],.],.]]] => [1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,1,1] => 3

[4,1,5,6,3,8,7,2] => [[.,[[.,.],.]],[.,[.,[[.,.],.]]]] => [1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3,1] => 2

[2,4,5,8,3,7,6,1] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,1,1] => 2

[1,3,8,7,2,5,6,4] => [.,[[.,.],[[[[.,.],[.,.]],.],.]]] => [1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,1,1] => 2

[4,8,3,2,7,6,5,1] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,3,2,1] => 5

[1,8,7,3,4,6,5,2] => [.,[[[[.,.],[.,[[.,.],.]]],.],.]] => [1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,1,1] => 3

[1,4,3,8,5,7,2,6] => [.,[[[.,.],.],[[.,[[.,.],.]],.]]] => [1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,1] => 3

[1,5,3,7,6,4,8,2] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1] => 0

[2,7,3,4,8,6,5,1] => [[.,.],[[.,[.,[[.,.],.]]],[.,.]]] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1,1,1] => 1

[1,8,2,4,7,3,6,5] => [.,[[.,[[.,.],[[[.,.],.],.]]],.]] => [1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,1] => 3

[1,8,4,2,5,7,3,6] => [.,[[[.,[.,.]],[.,[[.,.],.]]],.]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2] => 2

[1,4,8,5,2,3,6,7] => [.,[[.,[.,.]],[[.,[.,[.,.]]],.]]] => [1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2] => 1

[1,4,8,5,2,3,7,6] => [.,[[.,[.,.]],[[.,[[.,.],.]],.]]] => [1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2] => 2

[1,5,8,7,2,4,3,6] => [.,[[.,[[.,.],.]],[[[.,.],.],.]]] => [1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1] => 3

[1,5,4,2,8,3,7,6] => [.,[[[.,[.,.]],.],[[[.,.],.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,2] => 3

[1,2,8,7,3,5,4,6] => [.,[.,[[[.,[[.,.],[.,.]]],.],.]]] => [1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1] => 2

[1,3,7,6,4,8,2,5] => [.,[[.,.],[[[.,[.,.]],.],[.,.]]]] => [1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1,1] => 1

[8,1,3,7,2,4,6,5] => [[.,[[.,.],[[.,[[.,.],.]],.]]],.] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,1,1] => 3

[2,5,6,7,1,4,8,3] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1,1] => 1

[8,1,4,2,7,5,6,3] => [[.,[[.,[.,.]],[[.,[.,.]],.]]],.] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,2,2] => 2

[1,4,7,3,6,8,2,5] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1] => 2

[2,4,7,3,6,8,1,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1,1] => 1

[1,2,6,7,4,5,8,3] => [.,[.,[[[.,.],[.,.]],[.,[.,.]]]]] => [1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1] => 0

[2,3,1,6,8,7,4,5] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1,1] => 1

[2,3,1,8,7,5,6,4] => [[.,.],[.,[[[[.,.],[.,.]],.],.]]] => [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,1,1,1] => 2

[1,5,6,7,2,4,3,8] => [.,[[.,[[.,.],.]],[.,[.,[.,.]]]]] => [1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1] => 1

[3,2,4,6,1,8,7,5] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2,1] => 2

[1,4,7,5,8,2,3,6] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2] => 0

[2,3,5,7,8,1,6,4] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1,1] => 0

[1,5,7,4,2,3,6,8] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2] => 1

[2,4,7,5,3,6,8,1] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => 0

[8,1,7,2,4,6,3,5] => [[.,[[.,[[.,.],[[.,.],.]]],.]],.] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [7,5,2,1,1] => 3

[1,2,4,7,8,6,3,5] => [.,[.,[[.,.],[[[.,.],.],[.,.]]]]] => [1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1] => 1

[2,4,7,8,3,5,1,6] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => 0

[1,3,6,2,5,8,4,7] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]] => [1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1] => 2

[1,5,3,6,8,2,4,7] => [.,[[[.,.],[.,.]],[.,[[.,.],.]]]] => [1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1] => 1

[5,8,1,2,6,3,7,4] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [6,4,4,4] => 1

[1,6,2,3,7,5,8,4] => [.,[[.,[.,[[.,.],.]]],[.,[.,.]]]] => [1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1] => 1

[4,1,2,6,5,7,8,3] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[1,8,4,2,7,3,6,5] => [.,[[[.,[.,.]],[[[.,.],.],.]],.]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,2] => 3

[1,7,5,2,3,8,6,4] => [.,[[[.,[.,[.,.]]],[.,.]],[.,.]]] => [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3] => 0

[2,6,1,8,3,7,4,5] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1,1] => 1

[2,5,1,7,6,8,3,4] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[1,2,6,3,7,5,8,4] => [.,[.,[[.,[[.,.],.]],[.,[.,.]]]]] => [1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1] => 1

[3,1,5,4,6,7,8,2] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 0

[2,6,8,7,3,1,4,5] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1,1] => 1

[2,1,7,3,8,6,4,5] => [[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1,1,1,1] => 1

[1,7,5,3,2,4,8,6] => [.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,1,1] => 0

[1,4,2,7,6,5,8,3] => [.,[[.,[.,.]],[[[.,.],.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2] => 1

[3,4,1,6,5,7,8,2] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2] => 0

[2,8,7,3,4,1,5,6] => [[.,.],[[[.,[.,[.,[.,.]]]],.],.]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,1,1,1,1] => 2

[2,8,3,1,5,4,7,6] => [[.,.],[[.,[[.,.],[[.,.],.]]],.]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,1,1,1] => 2

[3,8,4,1,5,2,7,6] => [[.,[.,.]],[[.,[.,[[.,.],.]]],.]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2,2] => 2

[1,8,6,2,4,3,7,5] => [.,[[[.,[[.,.],[.,.]]],[.,.]],.]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,4,1,1] => 1

[2,8,3,1,6,4,7,5] => [[.,.],[[.,[[.,[.,.]],[.,.]]],.]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1,1,1,1] => 1

[4,1,6,5,2,3,7,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[2,6,3,1,7,4,5,8] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1,1] => 0

[2,3,6,7,1,5,4,8] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1,1] => 1

[5,6,1,4,7,2,3,8] => [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,2] => 1

[1,2,5,7,8,6,3,4] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => [1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2] => 0

[1,2,6,7,4,5,3,8] => [.,[.,[[[.,.],[.,.]],[.,[.,.]]]]] => [1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1] => 0

[1,2,7,8,4,6,3,5] => [.,[.,[[[.,.],[[.,.],.]],[.,.]]]] => [1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1] => 1

[5,4,8,6,3,2,1,7] => [[[[[.,.],.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,4,4,3,2,1] => 4

[1,8,5,3,2,4,6,7] => [.,[[[[.,.],[.,.]],[.,[.,.]]],.]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,1,1] => 1

[1,6,7,3,4,2,5,8] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]] => [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1] => 0

[1,6,8,3,4,2,5,7] => [.,[[[.,.],[.,[.,.]]],[[.,.],.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1] => 1

[1,8,7,5,3,4,2,6] => [.,[[[[[.,.],[.,.]],[.,.]],.],.]] => [1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3,1,1] => 2

[1,7,8,5,3,4,2,6] => [.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,1,1] => 0

[1,7,6,8,4,2,3,5] => [.,[[[[.,[.,.]],[.,.]],.],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,2] => 1

[1,7,8,6,4,3,2,5] => [.,[[[[[.,.],.],[.,.]],.],[.,.]]] => [1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,2,1] => 2

[2,8,3,1,7,5,6,4] => [[.,.],[[.,[[[.,.],[.,.]],.]],.]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,1,1,1] => 2

[3,4,5,8,2,1,6,7] => [[[.,.],.],[.,[.,[[.,[.,.]],.]]]] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,2,1] => 2

[7,8,1,2,4,6,3,5] => [[.,[.,[[.,.],[[.,.],.]]]],[.,.]] => [1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [6,6,2,1,1] => 1

[7,2,8,3,4,5,1,6] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1,1,1] => 0

[2,4,3,7,8,5,6,1] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => 0

[2,3,6,8,5,1,7,4] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1,1] => 2

[2,1,3,8,4,5,7,6] => [[.,.],[.,[[.,[.,[[.,.],.]]],.]]] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1,1,1] => 2

[2,1,3,7,8,4,6,5] => [[.,.],[.,[[.,[[.,.],.]],[.,.]]]] => [1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1,1,1] => 1

[2,1,3,8,4,7,6,5] => [[.,.],[.,[[.,[[[.,.],.],.]],.]]] => [1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,1,1,1] => 3

[3,1,2,8,4,5,7,6] => [[.,[.,.]],[[.,[.,[[.,.],.]]],.]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2,2] => 2

[1,2,8,7,5,4,6,3] => [.,[.,[[[[[.,.],.],[.,.]],.],.]]] => [1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,1] => 3

[1,4,6,8,5,7,2,3] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2] => 1

[2,4,7,1,8,3,6,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1,1] => 1

[5,8,4,3,6,7,2,1] => [[[[[.,.],.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,4,4,3,2,1] => 4

[2,5,3,8,6,7,4,1] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1,1] => 1

[8,1,4,6,5,7,2,3] => [[.,[[.,[.,.]],[[.,.],[.,.]]]],.] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2,2] => 1

[2,6,3,7,8,1,4,5] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1,1] => 0

[3,2,8,7,4,6,5,1] => [[[.,.],.],[[[.,[[.,.],.]],.],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,2,2,1] => 4

[3,4,6,2,5,7,1,8] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2,1] => 1

[1,7,5,2,6,8,3,4] => [.,[[[.,[.,[.,.]]],[.,.]],[.,.]]] => [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3] => 0

[1,5,4,3,8,7,2,6] => [.,[[[[.,.],.],.],[[[.,.],.],.]]] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,2,1] => 4

[1,5,8,2,6,4,3,7] => [.,[[.,[[.,.],.]],[[.,[.,.]],.]]] => [1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1] => 2

[3,5,6,2,4,7,8,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => 1

[3,5,6,7,2,4,8,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => 1

[3,4,5,7,2,6,8,1] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2,1] => 1

[3,4,5,7,2,8,6,1] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2,1] => 1

[2,3,5,7,8,4,6,1] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1,1] => 0

[4,2,5,6,7,3,8,1] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1,1] => 0

[8,1,4,2,5,3,6,7] => [[.,[[.,[.,.]],[.,[.,[.,.]]]]],.] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2] => 1

[2,8,4,1,5,3,6,7] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,1,1] => 1

[1,4,8,6,7,2,5,3] => [.,[[.,[.,.]],[[[.,.],[.,.]],.]]] => [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2] => 1

[1,4,5,7,3,8,2,6] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]] => [1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1] => 1

[2,4,5,8,6,3,1,7] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,1,1] => 1

[1,7,3,6,5,8,2,4] => [.,[[[.,.],[[[.,.],.],.]],[.,.]]] => [1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,1,1] => 2

[5,1,2,8,6,7,3,4] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [6,4,4,4] => 1

[5,1,7,6,8,2,3,4] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4] => 0

[1,7,6,2,4,3,8,5] => [.,[[[.,[[.,.],[.,.]]],.],[.,.]]] => [1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1,1] => 1

[5,7,1,6,2,3,4,8] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4] => 0

[1,5,3,4,8,2,6,7] => [.,[[[.,.],[.,.]],[[.,[.,.]],.]]] => [1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1] => 1

[2,1,3,6,5,8,4,7] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1,1] => 2

[5,1,2,8,6,3,7,4] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [6,4,4,4] => 1

[4,6,1,5,7,2,8,3] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[1,7,3,2,4,8,6,5] => [.,[[[.,.],[.,[[.,.],.]]],[.,.]]] => [1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1,1] => 1

[1,7,5,3,8,6,2,4] => [.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,1,1] => 0

[8,1,2,4,3,5,7,6] => [[.,[.,[[.,.],[.,[[.,.],.]]]]],.] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,1,1] => 2

[2,4,3,8,1,5,7,6] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,1,1] => 2

[2,7,3,8,5,1,6,4] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1,1] => 0

[2,3,8,4,1,5,7,6] => [[.,.],[.,[[.,[.,[[.,.],.]]],.]]] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1,1,1] => 2

[8,2,3,4,1,5,7,6] => [[[.,.],[.,[.,[.,[[.,.],.]]]]],.] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,1,1,1,1] => 2

[2,5,6,3,8,1,4,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1,1] => 1

[1,3,4,5,6,7,2,8,9] => [.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 0

[1,7,8,5,6,4,3,2] => [.,[[[[[.,.],.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,2,1] => 2

[1,6,2,3,5,8,4,7] => [.,[[.,[.,[[.,.],.]]],[[.,.],.]]] => [1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1] => 2

[1,8,5,6,4,3,7,2] => [.,[[[[[.,.],.],.],[.,[.,.]]],.]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,2,1] => 3

[1,5,3,4,8,7,2,6] => [.,[[[.,.],[.,.]],[[[.,.],.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1,1] => 2

[2,5,3,6,8,4,1,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1,1] => 1

[2,3,6,5,8,4,1,7] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1,1] => 2

[2,3,5,1,7,6,4,8] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1,1] => 0

[2,3,1,7,4,8,6,5] => [[.,.],[.,[[.,[[.,.],.]],[.,.]]]] => [1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1,1,1] => 1

[1,8,3,6,4,2,7,5] => [.,[[[.,.],[[.,[.,.]],[.,.]]],.]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1,1,1] => 1

[8,1,2,5,7,4,6,3] => [[.,[.,[[[.,.],.],[[.,.],.]]]],.] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,1] => 3

[6,1,2,4,7,8,3,5] => [[.,[.,[[.,.],[.,.]]]],[.,[.,.]]] => [1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [5,5,5,1,1] => 0

[2,4,6,5,7,1,8,3] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[1,2,7,8,6,4,5,3] => [.,[.,[[[[.,.],[.,.]],.],[.,.]]]] => [1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1] => 1

[2,4,3,8,5,7,1,6] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,1,1] => 2

[2,8,3,1,4,6,5,7] => [[.,.],[[.,[.,[[.,.],[.,.]]]],.]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1,1,1,1] => 1

[1,4,6,8,7,3,5,2] => [.,[[[.,.],.],[[.,.],[[.,.],.]]]] => [1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1] => 2

[1,4,7,5,8,6,2,3] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2] => 0

[2,4,5,1,8,3,7,6] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,1,1] => 2

[2,5,6,3,4,1,8,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1,1] => 1

[2,3,5,8,7,4,1,6] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1,1,1] => 2

[2,3,5,8,7,4,6,1] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1,1,1] => 2

[2,3,5,8,1,6,4,7] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1,1,1] => 1

[1,7,4,5,8,3,6,2] => [.,[[[[.,.],.],[.,[.,.]]],[.,.]]] => [1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2,1] => 1

[2,3,7,8,1,5,4,6] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1,1] => 0

[2,3,7,5,8,4,6,1] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1,1] => 0

[2,5,6,7,1,8,4,3] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1,1] => 1

[2,3,7,8,5,4,6,1] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1,1] => 0

[1,2,8,7,4,6,5,3] => [.,[.,[[[[.,.],[[.,.],.]],.],.]]] => [1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,1] => 3

[1,3,7,6,2,4,8,5] => [.,[[.,.],[[[.,[.,.]],.],[.,.]]]] => [1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1,1] => 1

[1,3,8,2,7,4,6,5] => [.,[[.,.],[[[.,[[.,.],.]],.],.]]] => [1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,1,1] => 3

[4,3,2,8,1,7,5,6] => [[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,3,3,2,1] => 4

[1,7,3,5,2,4,8,6] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]] => [1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1] => 0

[1,6,8,7,5,2,3,4] => [.,[[[.,[.,[.,.]]],.],[[.,.],.]]] => [1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3] => 2

[1,3,6,2,5,4,8,7] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]] => [1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1] => 2

[1,6,3,8,4,7,2,5] => [.,[[[.,.],[.,[.,.]]],[[.,.],.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1] => 1

[1,3,4,8,5,6,2,7] => [.,[[.,.],[.,[[.,[.,[.,.]]],.]]]] => [1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1] => 1

[2,5,6,4,8,1,3,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1,1] => 2

[5,4,1,6,2,3,7,8] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3] => 1

[1,3,6,5,2,4,7,8] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1] => 1

[3,8,2,7,4,5,1,6] => [[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,2,2,1] => 3

[8,1,3,7,6,4,5,2] => [[.,[[.,.],[[[.,[.,.]],.],.]]],.] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [7,4,3,1,1,1] => 3

[8,1,2,6,7,5,4,3] => [[.,[.,[[[[.,.],.],.],[.,.]]]],.] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2,1] => 3

[8,1,2,7,6,4,5,3] => [[.,[.,[[[[.,.],[.,.]],.],.]]],.] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [7,4,3,1,1] => 3

[1,8,2,4,7,5,6,3] => [.,[[.,[[.,.],[[.,[.,.]],.]]],.]] => [1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1,1] => 2

[2,3,8,4,7,1,6,5] => [[.,.],[.,[[.,[[[.,.],.],.]],.]]] => [1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,1,1,1] => 3

[1,8,2,3,5,6,4,7] => [.,[[.,[.,[[.,.],[.,[.,.]]]]],.]] => [1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1] => 1

[1,4,7,6,2,3,5,8] => [.,[[.,[.,.]],[[[.,.],.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2] => 1

[1,7,6,2,3,8,4,5] => [.,[[[.,[.,[.,[.,.]]]],.],[.,.]]] => [1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,5,4] => 1

[1,8,2,3,7,6,4,5] => [.,[[.,[.,[[[.,[.,.]],.],.]]],.]] => [1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [6,3,2] => 3

[1,7,3,8,6,2,5,4] => [.,[[[.,.],[[[.,.],.],.]],[.,.]]] => [1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,1,1] => 2

[1,3,5,6,4,8,2,7] => [.,[[.,.],[[.,.],[.,[[.,.],.]]]]] => [1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1,1] => 1

[3,4,8,5,6,1,2,7] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,2] => 1

[1,7,6,2,5,4,8,3] => [.,[[[.,[[[.,.],.],.]],.],[.,.]]] => [1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,1] => 3

[3,1,5,6,4,2,7,8] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 0

[4,5,1,6,8,3,7,2] => [[.,[[.,.],.]],[.,[.,[[.,.],.]]]] => [1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3,1] => 2

[1,7,4,5,2,6,8,3] => [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2] => 0

[1,4,2,6,5,3,8,7] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2] => 1

[1,4,8,3,5,6,2,7] => [.,[[[.,.],.],[[.,[.,[.,.]]],.]]] => [1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,1] => 2

[8,2,3,4,1,6,7,5] => [[[.,.],[.,[.,[[.,.],[.,.]]]]],.] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1,1,1,1] => 1

[1,5,8,7,4,2,3,6] => [.,[[[.,[.,.]],.],[[[.,.],.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,2] => 3

[1,7,2,4,5,8,6,3] => [.,[[.,[[.,.],[.,[.,.]]]],[.,.]]] => [1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1] => 0

[1,4,6,8,7,2,5,3] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2] => 1

[1,6,2,7,5,3,4,8] => [.,[[.,[[.,[.,.]],.]],[.,[.,.]]]] => [1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2] => 1

[1,3,7,2,6,4,5,8] => [.,[[.,.],[[[.,[.,.]],.],[.,.]]]] => [1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1,1] => 1

[1,7,3,2,8,5,6,4] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]] => [1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1] => 0

[1,6,5,2,4,8,3,7] => [.,[[[.,[[.,.],.]],.],[[.,.],.]]] => [1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3,1] => 3

[1,7,3,8,4,2,5,6] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1,1] => 0

[1,6,2,4,7,5,8,3] => [.,[[.,[[.,.],[.,.]]],[.,[.,.]]]] => [1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1] => 0

[1,6,2,7,4,3,8,5] => [.,[[.,[[.,.],[.,.]]],[.,[.,.]]]] => [1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1] => 0

[1,5,8,2,3,6,4,7] => [.,[[.,[.,[.,.]]],[[.,[.,.]],.]]] => [1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3] => 1

[2,5,3,6,7,1,4,8] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1,1] => 0

[1,2,7,3,8,5,6,4] => [.,[.,[[.,[[.,.],[.,.]]],[.,.]]]] => [1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1] => 0

[1,5,7,4,3,8,6,2] => [.,[[[[.,.],.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2,1] => 2

[2,7,3,1,4,5,8,6] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1,1,1] => 0

[1,2,6,7,5,3,4,8] => [.,[.,[[[.,[.,.]],.],[.,[.,.]]]]] => [1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2] => 1

[3,4,5,6,8,2,7,1] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,2,1] => 2

[1,5,6,7,3,4,2,8] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => [1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1] => 0

[1,6,7,8,2,4,5,3] => [.,[[.,[[.,.],[.,.]]],[.,[.,.]]]] => [1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1] => 0

[1,3,5,8,7,2,6,4] => [.,[[.,.],[[.,.],[[[.,.],.],.]]]] => [1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1,1] => 2

[2,5,6,1,3,8,7,4] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1,1] => 1

[2,3,5,4,7,1,8,6] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1,1] => 0

[8,1,6,2,3,7,5,4] => [[.,[[.,[.,[[.,.],.]]],[.,.]]],.] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [7,4,4,1] => 2

[2,8,3,6,4,1,7,5] => [[.,.],[[.,[[.,[.,.]],[.,.]]],.]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1,1,1,1] => 1

[5,4,8,7,3,6,2,1] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,4,3,2,1] => 5

[3,4,5,1,2,6,7,8,9] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2] => 0

[1,7,8,3,6,5,4,2] => [.,[[[.,.],[[[.,.],.],.]],[.,.]]] => [1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,1,1] => 2

[2,5,7,3,8,1,4,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[1,6,5,7,3,8,2,4] => [.,[[[[.,.],[.,.]],.],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,1,1] => 1

[2,4,1,7,5,6,3,8] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => 0

[1,4,3,7,6,2,8,5] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1] => 2

[1,6,2,5,7,3,8,4] => [.,[[.,[[.,[.,.]],.]],[.,[.,.]]]] => [1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2] => 1

[1,4,3,8,2,5,7,6] => [.,[[[.,.],.],[[.,[[.,.],.]],.]]] => [1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,1] => 3

[1,5,7,3,6,4,2,8] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1] => 0

[1,6,7,2,4,8,3,5] => [.,[[.,[[.,.],[.,.]]],[.,[.,.]]]] => [1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1] => 0

[1,2,6,8,4,3,5,7] => [.,[.,[[[.,.],[.,.]],[[.,.],.]]]] => [1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1] => 1

[3,4,2,1,6,8,5,7] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2,1] => 2

[8,1,3,5,6,4,7,2] => [[.,[[.,.],[[.,.],[.,[.,.]]]]],.] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,1,1] => 1

[3,4,7,1,5,6,2,8] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2] => 0

[5,8,6,4,7,3,2,1] => [[[[[.,.],.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,4,4,3,2,1] => 4

[8,1,5,2,4,6,7,3] => [[.,[[.,[[.,.],.]],[.,[.,.]]]],.] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [7,3,3,3,1] => 2

[2,5,7,3,4,8,1,6] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[2,5,6,8,7,1,4,3] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1,1] => 2

[8,2,3,6,4,1,7,5] => [[[.,.],[.,[[.,[.,.]],[.,.]]]],.] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,3,1,1,1,1] => 1

[2,3,7,5,8,6,1,4] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1,1] => 0

[1,3,6,4,8,2,7,5] => [.,[[.,.],[[.,[.,.]],[[.,.],.]]]] => [1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1] => 1

[1,7,6,2,8,5,3,4] => [.,[[[.,[[.,[.,.]],.]],.],[.,.]]] => [1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2] => 2

[1,5,8,6,4,7,2,3] => [.,[[[.,[.,.]],.],[[.,[.,.]],.]]] => [1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,2] => 2

[1,6,8,3,2,4,5,7] => [.,[[[.,.],[.,[.,.]]],[[.,.],.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1] => 1

[1,6,5,7,4,2,8,3] => [.,[[[[.,[.,.]],.],.],[.,[.,.]]]] => [1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,2] => 2

[1,2,7,4,8,5,6,3] => [.,[.,[[[.,.],[.,[.,.]]],[.,.]]]] => [1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1] => 0

[9,1,2,3,4,5,8,7,6] => [[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]],.] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1] => 3

[10,1,2,3,4,5,6,9,8,7] => [[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]],.] => [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0] => [9,2,1] => 3

[8,1,4,5,7,3,6,2] => [[.,[[[.,.],.],[.,[[.,.],.]]]],.] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,2,1] => 3

[2,5,6,4,1,3,8,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1,1] => 2

[2,5,1,6,4,8,3,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1,1] => 2

[3,2,4,5,8,6,1,7] => [[[.,.],.],[.,[.,[[.,[.,.]],.]]]] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,2,1] => 2

[3,4,5,8,6,1,7,2] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,2] => 1

[3,4,5,8,6,1,2,7] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,2] => 1

[1,5,8,2,4,3,7,6] => [.,[[.,[[.,.],.]],[[[.,.],.],.]]] => [1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1] => 3

[2,4,7,8,3,6,5,1] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1,1] => 1

[1,4,8,5,7,2,3,6] => [.,[[.,[.,.]],[[.,[[.,.],.]],.]]] => [1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2] => 2

[1,8,7,3,2,4,5,6] => [.,[[[[.,.],[.,[.,[.,.]]]],.],.]] => [1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,1,1,1] => 2

[1,5,6,3,7,2,4,8] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => [1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1] => 0

[1,5,6,7,4,2,3,8] => [.,[[[.,[.,.]],.],[.,[.,[.,.]]]]] => [1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2] => 1

[1,7,8,3,6,5,2,4] => [.,[[[.,.],[[[.,.],.],.]],[.,.]]] => [1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,1,1] => 2

[4,6,7,5,1,8,2,3] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[7,1,2,8,4,6,5,3] => [[.,[.,[[.,.],[[.,.],.]]]],[.,.]] => [1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [6,6,2,1,1] => 1

[1,4,3,6,8,5,2,7] => [.,[[[.,.],.],[[.,.],[[.,.],.]]]] => [1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1] => 2

[2,3,1,8,7,4,6,5] => [[.,.],[.,[[[.,[[.,.],.]],.],.]]] => [1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,1,1,1] => 3

[3,4,5,7,2,1,6,8] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2,1] => 1

[2,4,7,8,6,5,1,3] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1,1] => 1

[1,2,4,6,5,8,3,7] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => [1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1] => 1

[5,8,6,1,7,2,3,4] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [6,4,4,4] => 1

[2,4,5,3,8,7,1,6] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,1,1] => 2

[4,1,6,7,8,2,5,3] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[8,1,4,7,5,2,6,3] => [[.,[[.,[.,.]],[[.,[.,.]],.]]],.] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,2,2] => 2

[1,4,8,6,7,3,5,2] => [.,[[[.,.],.],[[[.,.],[.,.]],.]]] => [1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1] => 2

[4,6,1,5,7,2,3,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[4,8,5,3,2,7,1,6] => [[[[.,.],.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,3,3,2,1] => 4

[3,4,7,8,6,1,2,5] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,2] => 1

[2,1,4,7,8,6,3,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1,1] => 1

[2,4,5,8,1,6,3,7] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,1,1] => 1

[3,4,6,8,2,5,7,1] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2,1] => 2

[1,8,5,6,4,2,3,7] => [.,[[[[.,[.,.]],.],[.,[.,.]]],.]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,2] => 2

[1,8,7,6,2,4,5,3] => [.,[[[[.,[[.,.],[.,.]]],.],.],.]] => [1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,1] => 3

[1,6,4,7,2,5,8,3] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2] => 0

[1,7,5,6,4,8,2,3] => [.,[[[[.,[.,.]],.],[.,.]],[.,.]]] => [1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,2] => 1

[2,4,8,5,7,3,1,6] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,1,1] => 2

[2,4,3,8,5,1,7,6] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,1,1] => 2

[2,8,3,4,1,7,6,5] => [[.,.],[[.,[.,[[[.,.],.],.]]],.]] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,1,1,1] => 3

[2,7,3,4,1,5,8,6] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1,1,1] => 0

[2,5,8,1,6,7,3,4] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1,1] => 1

[3,5,4,1,6,2,8,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,2] => 1

[2,3,6,7,1,8,5,4] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1,1] => 1

[3,1,4,5,7,6,2,8] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2] => 0

[4,5,1,3,6,8,7,2] => [[.,[[.,.],.]],[.,[.,[[.,.],.]]]] => [1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3,1] => 2

[8,1,2,4,6,3,7,5] => [[.,[.,[[.,.],[[.,.],[.,.]]]]],.] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1,1] => 1

[6,1,2,7,8,4,3,5] => [[.,[.,[[.,.],[.,.]]]],[.,[.,.]]] => [1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [5,5,5,1,1] => 0

[7,8,1,2,5,3,4,6] => [[.,[.,[[.,[.,.]],[.,.]]]],[.,.]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2] => 0

[1,8,4,7,5,2,3,6] => [.,[[[.,[.,.]],[[.,[.,.]],.]],.]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,2] => 2

[1,4,8,3,2,6,5,7] => [.,[[[.,.],.],[[[.,.],[.,.]],.]]] => [1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1] => 2

[1,3,8,4,2,7,5,6] => [.,[[.,.],[[.,[[.,[.,.]],.]],.]]] => [1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1,1,1] => 2

[7,2,8,3,1,4,5,6] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1,1,1] => 0

[8,1,3,2,7,5,4,6] => [[.,[[.,.],[[[.,.],[.,.]],.]]],.] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [7,4,2,2,1,1] => 2

[1,7,5,4,8,6,2,3] => [.,[[[[.,[.,.]],.],[.,.]],[.,.]]] => [1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,2] => 1

[4,5,1,6,8,2,7,3] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3] => 1

[1,6,3,7,2,4,8,5] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]] => [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1] => 0

[2,8,3,1,6,7,4,5] => [[.,.],[[.,[[.,[.,.]],[.,.]]],.]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1,1,1,1] => 1

[4,5,6,8,1,3,7,2] => [[.,[[.,.],.]],[.,[.,[[.,.],.]]]] => [1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3,1] => 2

[4,5,1,3,2,6,7,8] => [[.,[[.,.],.]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1] => 1

[7,1,3,4,5,6,2,8] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1,1] => 0

[2,3,6,5,8,4,7,1] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1,1] => 2

[1,3,6,7,5,2,4,8] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1] => 1

[1,5,2,6,8,7,3,4] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3] => 1

[5,8,4,3,2,6,1,7] => [[[[[.,.],.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,4,4,3,2,1] => 4

[1,5,7,4,8,6,2,3] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2] => 1

[1,2,7,8,6,4,3,5] => [.,[.,[[[[.,.],[.,.]],.],[.,.]]]] => [1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1] => 1

[5,7,8,1,6,2,3,4] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4] => 0

[1,6,4,2,7,3,8,5] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2] => 0

[1,4,2,5,8,6,3,7] => [.,[[.,[.,.]],[.,[[.,[.,.]],.]]]] => [1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2] => 1

[1,4,7,5,6,2,8,3] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2] => 0

[1,7,4,8,3,5,6,2] => [.,[[[[.,.],.],[.,[.,.]]],[.,.]]] => [1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2,1] => 1

[1,8,6,7,5,3,2,4] => [.,[[[[[.,.],[.,.]],.],[.,.]],.]] => [1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3,1,1] => 2

[1,3,7,6,8,4,5,2] => [.,[[.,.],[[[.,[.,.]],.],[.,.]]]] => [1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1,1] => 1

[1,8,7,2,5,6,3,4] => [.,[[[.,[[.,[.,.]],[.,.]]],.],.]] => [1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2] => 2

[1,8,2,6,7,4,3,5] => [.,[[.,[[[.,.],[.,.]],[.,.]]],.]] => [1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1,1] => 1

[2,5,7,1,3,6,4,8] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[1,4,7,2,5,3,6,8] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2] => 0

[2,4,3,6,7,1,5,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 0

[2,5,6,1,4,3,7,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1,1] => 1

[1,6,8,7,3,2,4,5] => [.,[[[.,.],[.,[.,.]]],[[.,.],.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1] => 1

[1,7,8,2,4,6,3,5] => [.,[[.,[[.,.],[[.,.],.]]],[.,.]]] => [1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1] => 1

[1,8,2,6,7,5,4,3] => [.,[[.,[[[[.,.],.],.],[.,.]]],.]] => [1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,1] => 3

[1,8,4,7,2,3,5,6] => [.,[[[.,[.,.]],[[.,[.,.]],.]],.]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,2] => 2

[3,4,5,6,2,1,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2,1] => 1

[3,4,5,2,1,6,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2,1] => 1

[1,6,8,2,7,3,4,5] => [.,[[.,[.,[.,[.,.]]]],[[.,.],.]]] => [1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,4,4] => 1

[1,6,8,7,3,4,2,5] => [.,[[[.,.],[.,[.,.]]],[[.,.],.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1] => 1

[4,1,2,6,7,8,5,3] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[3,4,5,6,1,7,2,8,9] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2] => 0

[3,4,5,1,6,2,7,8,9] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2] => 0

[1,5,4,7,8,3,6,2] => [.,[[[[.,.],.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2,1] => 2

[1,7,4,5,6,8,3,2] => [.,[[[[.,.],.],[.,[.,.]]],[.,.]]] => [1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2,1] => 1

[2,4,7,8,3,1,6,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1,1] => 1

[1,4,3,5,6,8,2,7] => [.,[[[.,.],.],[.,[.,[[.,.],.]]]]] => [1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,1] => 2

[1,4,6,5,8,2,7,3] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2] => 1

[1,7,3,6,4,2,8,5] => [.,[[[.,.],[[.,[.,.]],.]],[.,.]]] => [1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1,1,1] => 1

[1,6,4,2,3,5,8,7] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,2] => 1

[4,8,3,5,2,1,6,7] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [6,3,3,3,3,2,1] => 3

[7,1,8,2,4,5,3,6] => [[.,[.,[[.,.],[.,[.,.]]]]],[.,.]] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1] => 0

[2,6,3,7,5,8,4,1] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1,1] => 1

[7,3,8,4,5,1,2,6] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,2,2] => 0

[8,7,1,3,2,4,5,6] => [[[.,[[.,.],[.,[.,[.,.]]]]],.],.] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,1,1,1] => 2

[1,5,4,8,7,3,2,6] => [.,[[[[.,.],.],.],[[[.,.],.],.]]] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,2,1] => 4

[1,4,7,2,6,5,8,3] => [.,[[.,[.,.]],[[[.,.],.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2] => 1

[1,5,7,2,6,4,8,3] => [.,[[.,[[.,.],.]],[[.,.],[.,.]]]] => [1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1] => 1

[1,2,7,8,3,5,4,6] => [.,[.,[[.,[[.,.],[.,.]]],[.,.]]]] => [1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1] => 0

[1,7,6,2,8,5,4,3] => [.,[[[.,[[[.,.],.],.]],.],[.,.]]] => [1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,1] => 3

[1,2,7,8,3,4,6,5] => [.,[.,[[.,[.,[[.,.],.]]],[.,.]]]] => [1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [4,4,1] => 1

[1,7,6,8,3,4,2,5] => [.,[[[[.,.],[.,[.,.]]],.],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1,1,1] => 1

[3,4,1,7,8,6,5,2] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,2] => 1

[2,4,8,6,5,7,1,3] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1,1] => 1

[2,1,5,6,3,8,7,4] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1,1] => 1

[2,4,5,3,8,1,7,6] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,1,1] => 2

[1,8,7,3,5,2,6,4] => [.,[[[[.,.],[[.,.],[.,.]]],.],.]] => [1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,1,1] => 2

[2,4,8,3,6,5,7,1] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1,1] => 1

[1,7,3,4,8,5,2,6] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1,1] => 0

[1,7,3,8,5,4,2,6] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]] => [1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1] => 0

[1,7,3,4,8,2,5,6] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1,1] => 0

[1,5,8,3,4,6,2,7] => [.,[[[.,.],[.,.]],[[.,[.,.]],.]]] => [1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1] => 1

[1,3,8,4,2,5,7,6] => [.,[[.,.],[[.,[.,[[.,.],.]]],.]]] => [1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1,1] => 2

[1,4,7,6,2,3,8,5] => [.,[[.,[.,.]],[[[.,.],.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2] => 1

[1,8,4,6,7,2,3,5] => [.,[[[.,[.,.]],[[.,.],[.,.]]],.]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,2] => 1

[1,4,2,3,7,8,6,5] => [.,[[.,[.,.]],[[[.,.],.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2] => 1

[1,4,3,6,2,5,8,7] => [.,[[[.,.],.],[[.,.],[[.,.],.]]]] => [1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1] => 2

[1,3,6,5,8,2,4,7] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]] => [1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1] => 2

[1,4,6,3,2,8,5,7] => [.,[[[.,.],.],[[.,.],[[.,.],.]]]] => [1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1] => 2

[8,1,4,6,2,5,7,3] => [[.,[[.,[.,.]],[[.,.],[.,.]]]],.] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2,2] => 1

[4,5,8,1,6,2,7,3] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [5,3,3,3,3] => 1

[2,7,3,5,4,1,8,6] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1,1] => 0

[2,6,3,7,4,1,8,5] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1,1] => 0

[2,1,4,8,5,3,7,6] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,1,1] => 2

[2,7,3,8,4,1,6,5] => [[.,.],[[.,[.,[[.,.],.]]],[.,.]]] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1,1,1] => 1

[1,5,8,3,4,7,2,6] => [.,[[[.,.],[.,.]],[[[.,.],.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1,1] => 2

[1,6,3,2,8,7,4,5] => [.,[[[.,.],[.,[.,.]]],[[.,.],.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1] => 1

[4,8,3,2,1,7,5,6] => [[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,3,3,2,1] => 4

[1,8,4,5,6,3,2,7] => [.,[[[[.,.],.],[.,[.,[.,.]]]],.]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,1] => 2

[1,3,7,8,4,6,2,5] => [.,[[.,.],[[.,[[.,.],.]],[.,.]]]] => [1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1,1] => 1

[4,5,6,7,8,1,9,2,3] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3,3] => 0

[1,3,6,5,7,2,4,8] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1] => 1

[1,7,2,5,6,4,3,8] => [.,[[.,[[[.,.],.],[.,.]]],[.,.]]] => [1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1] => 1

[1,6,8,5,4,3,7,2] => [.,[[[[[.,.],.],.],.],[[.,.],.]]] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3,2,1] => 4

[1,3,7,6,8,5,2,4] => [.,[[.,.],[[[[.,.],.],.],[.,.]]]] => [1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1,1] => 2

[4,5,2,6,7,8,1,3] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1,1] => 0

[1,7,6,2,3,8,5,4] => [.,[[[.,[.,[[.,.],.]]],.],[.,.]]] => [1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1] => 2

[1,5,4,3,8,6,2,7] => [.,[[[[.,.],.],.],[[.,[.,.]],.]]] => [1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,2,1] => 3

[1,3,7,5,8,4,6,2] => [.,[[.,.],[[[.,.],[.,.]],[.,.]]]] => [1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1] => 0

[1,6,7,4,5,3,2,8] => [.,[[[[.,.],.],[.,.]],[.,[.,.]]]] => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2,1] => 1

[1,4,2,6,7,5,3,8] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2] => 0

[1,8,2,4,6,5,3,7] => [.,[[.,[[.,.],[[.,.],[.,.]]]],.]] => [1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1,1] => 1

[1,4,8,7,2,3,6,5] => [.,[[.,[.,.]],[[[[.,.],.],.],.]]] => [1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,2] => 3

[1,8,6,2,7,4,3,5] => [.,[[[.,[[.,.],[.,.]]],[.,.]],.]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,4,1,1] => 1

[1,6,7,5,8,4,2,3] => [.,[[[[.,[.,.]],.],.],[.,[.,.]]]] => [1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,2] => 2

[1,6,5,7,8,3,2,4] => [.,[[[[.,.],[.,.]],.],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,1,1] => 1

[7,8,1,9,2,3,4,5,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,6,6] => 0

[6,7,8,1,9,2,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,5,5,5] => 0

[5,6,7,8,1,9,2,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,4,4,4,4] => 0

[1,5,7,2,4,3,8,6] => [.,[[.,[[.,.],.]],[[.,.],[.,.]]]] => [1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1] => 1

[1,2,7,5,8,4,3,6] => [.,[.,[[[[.,.],.],[.,.]],[.,.]]]] => [1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1] => 1

[8,1,7,2,3,6,5,4] => [[.,[[.,[.,[[[.,.],.],.]]],.]],.] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [7,5,2,1] => 4

[7,1,2,6,4,3,8,5] => [[.,[.,[[[.,.],[.,.]],.]]],[.,.]] => [1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [6,6,3,1,1] => 1

[1,4,7,8,3,2,5,6] => [.,[[[.,.],.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1] => 1

[1,8,2,7,6,3,5,4] => [.,[[.,[[[.,[[.,.],.]],.],.]],.]] => [1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1] => 4

[2,8,1,3,5,6,4,7] => [[.,.],[[.,[[.,.],[.,[.,.]]]],.]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,1,1,1] => 1

[2,6,3,4,7,8,5,1] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1,1] => 0

[1,6,4,7,8,5,3,2] => [.,[[[[.,.],.],[.,.]],[.,[.,.]]]] => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2,1] => 1

[1,5,2,6,8,7,4,3] => [.,[[.,[[.,.],.]],[.,[[.,.],.]]]] => [1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1] => 2

[1,8,3,7,5,2,6,4] => [.,[[[.,.],[[[.,.],[.,.]],.]],.]] => [1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,1,1] => 2

[8,1,3,6,5,2,7,4] => [[.,[[.,.],[[[.,.],.],[.,.]]]],.] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2,1,1] => 2

[1,5,4,8,3,2,6,7] => [.,[[[[.,.],.],.],[[.,[.,.]],.]]] => [1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,2,1] => 3

[1,5,7,6,3,8,2,4] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1] => 0

[2,6,3,1,7,8,4,5] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1,1] => 0

[2,1,7,8,3,5,4,6] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1,1] => 0

[1,5,8,6,7,4,2,3] => [.,[[[.,[.,.]],.],[[.,[.,.]],.]]] => [1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,2] => 2

[7,1,2,3,4,9,5,8,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [7,6,6] => 1

[8,1,2,3,4,5,10,6,9,7] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,1,0,0] => [8,7,7] => 1

[8,1,7,3,2,4,5,6] => [[.,[[[.,.],[.,[.,[.,.]]]],.]],.] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,1,1,1] => 2

[1,6,5,2,8,7,4,3] => [.,[[[.,[[.,.],.]],.],[[.,.],.]]] => [1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3,1] => 3

[1,3,4,5,2,6,7,8,9] => [.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 0

[4,5,6,1,7,8,9,2,3] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3,3] => 0

[4,5,1,7,2,8,6,3] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [4,4,3,3,3] => 0

[1,7,2,8,5,4,6,3] => [.,[[.,[[[.,.],.],[.,.]]],[.,.]]] => [1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1] => 1

[1,2,6,3,7,8,5,4] => [.,[.,[[.,[[.,.],.]],[.,[.,.]]]]] => [1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1] => 1

[4,5,1,8,6,2,7,3] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [5,3,3,3,3] => 1

[5,6,1,8,7,2,3,4] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [5,4,4,4] => 1

[4,5,1,6,8,7,3,2] => [[.,[[.,.],.]],[.,[.,[[.,.],.]]]] => [1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3,1] => 2

[2,8,1,3,7,5,6,4] => [[.,.],[[.,[[[.,.],[.,.]],.]],.]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,1,1,1] => 2

[1,8,7,2,5,6,4,3] => [.,[[[.,[[[.,.],.],[.,.]]],.],.]] => [1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,1] => 3

[3,4,7,1,5,8,2,6] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2] => 0

[1,4,7,5,2,3,6,8] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2] => 0

[2,5,7,6,8,3,4,1] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[1,5,3,6,8,4,7,2] => [.,[[[.,.],[.,.]],[.,[[.,.],.]]]] => [1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1] => 1

[1,7,4,8,5,3,2,6] => [.,[[[[.,.],.],[.,[.,.]]],[.,.]]] => [1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2,1] => 1

[3,4,7,5,6,8,2,1] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2,1] => 1

[3,4,7,8,5,2,6,1] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2,1] => 1

[1,8,7,5,2,6,3,4] => [.,[[[[.,[.,[.,.]]],[.,.]],.],.]] => [1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3] => 2

[1,7,6,3,4,5,8,2] => [.,[[[[.,.],[.,[.,.]]],.],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1,1,1] => 1

[1,8,7,4,5,6,2,3] => [.,[[[[.,[.,.]],[.,[.,.]]],.],.]] => [1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,2] => 2

[1,8,7,3,6,4,2,5] => [.,[[[[.,.],[[.,[.,.]],.]],.],.]] => [1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1,1,1] => 3

[1,4,7,5,8,2,6,3] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2] => 0

[1,4,7,2,3,6,5,8] => [.,[[.,[.,.]],[[[.,.],.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2] => 1

[1,7,2,5,6,3,4,8] => [.,[[.,[[.,[.,.]],[.,.]]],[.,.]]] => [1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2] => 0

[1,2,6,5,8,3,4,7] => [.,[.,[[[.,[.,.]],.],[[.,.],.]]]] => [1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2] => 2

[1,5,8,2,6,3,4,7] => [.,[[.,[.,[.,.]]],[[.,[.,.]],.]]] => [1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3] => 1

[4,1,5,7,2,6,3,8] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [4,4,3,3,3] => 0

[3,5,6,7,2,4,1,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => 1

[1,5,6,4,8,3,2,7] => [.,[[[[.,.],.],.],[.,[[.,.],.]]]] => [1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1] => 3

[2,1,5,6,4,8,3,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1,1] => 2

[1,6,7,2,8,5,4,3] => [.,[[.,[[[.,.],.],.]],[.,[.,.]]]] => [1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1] => 2

[1,4,3,2,7,5,8,6] => [.,[[[.,.],.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1] => 1

[1,8,3,5,2,6,4,7] => [.,[[[.,.],[[.,.],[.,[.,.]]]],.]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,1,1] => 1

[3,4,6,1,8,5,7,2] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2] => 1

[2,3,8,7,4,5,1,6] => [[.,.],[.,[[[.,[.,[.,.]]],.],.]]] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1,1,1,1] => 2

[1,8,3,5,7,4,2,6] => [.,[[[.,.],[[.,.],[[.,.],.]]],.]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,1,1] => 2

[7,1,2,6,4,3,5,8] => [[.,[.,[[[.,.],[.,.]],.]]],[.,.]] => [1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [6,6,3,1,1] => 1

[7,1,2,6,5,3,4,8] => [[.,[.,[[[.,[.,.]],.],.]]],[.,.]] => [1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [6,6,3,2] => 2

[7,1,2,4,8,6,5,3] => [[.,[.,[[.,.],[[.,.],.]]]],[.,.]] => [1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [6,6,2,1,1] => 1

[2,8,3,6,5,7,1,4] => [[.,.],[[.,[[[.,.],.],[.,.]]],.]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,1,1,1] => 2

[3,5,1,2,6,8,7,4] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,2] => 1

[3,1,2,4,8,7,5,6] => [[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,2] => 2

[1,6,7,2,5,8,3,4] => [.,[[.,[[.,[.,.]],.]],[.,[.,.]]]] => [1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2] => 1

[8,2,1,3,7,4,6,5] => [[[.,.],[.,[[.,[[.,.],.]],.]]],.] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,1,1,1] => 3

[8,1,2,7,5,3,4,6] => [[.,[.,[[[.,[.,.]],[.,.]],.]]],.] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [7,4,2,2] => 2

[8,1,6,2,3,7,4,5] => [[.,[[.,[.,[.,[.,.]]]],[.,.]]],.] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [7,4,4] => 1

[7,1,8,2,3,6,4,5] => [[.,[.,[.,[[.,[.,.]],.]]]],[.,.]] => [1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [6,6,2] => 1

[2,4,7,6,3,8,1,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1,1] => 1

[4,6,5,7,1,2,3,8] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[3,4,7,6,1,8,2,5] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,2] => 1

[2,8,7,3,1,4,5,6] => [[.,.],[[[.,[.,[.,[.,.]]]],.],.]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,1,1,1,1] => 2

[5,6,1,2,4,7,8,3] => [[.,[.,[[.,.],.]]],[.,[.,[.,.]]]] => [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,1] => 1

[9,2,3,4,1,5,6,7,8] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1,1,1,1,1,1] => 1

[7,3,1,4,5,6,8,2] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,2,2] => 0

[2,5,3,8,6,4,1,7] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1,1] => 1

[4,5,2,1,6,7,3,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1,1] => 0

[2,5,1,6,4,3,8,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1,1] => 2

[4,1,2,5,7,6,3,8] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [4,4,3,3,3] => 0

[2,1,3,6,4,8,7,5] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1,1] => 1

[4,5,1,6,8,7,2,3] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3] => 1

[3,4,7,2,5,8,6,1] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2,1] => 1

[3,8,7,2,6,1,4,5] => [[[.,.],.],[[[[.,[.,.]],.],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,2,2,1] => 4

[2,5,1,8,3,6,4,7] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1,1] => 1

[5,8,4,7,3,2,1,6] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,4,3,2,1] => 5

[1,2,8,3,4,6,5,7] => [.,[.,[[.,[.,[[.,.],[.,.]]]],.]]] => [1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [5,1,1] => 1

[8,1,2,7,3,5,4,6] => [[.,[.,[[.,[[.,.],[.,.]]],.]]],.] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,1] => 2

[5,7,1,2,6,3,4,8] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4] => 0

[1,2,7,5,6,3,4,8] => [.,[.,[[[.,[.,.]],[.,.]],[.,.]]]] => [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2] => 0

[1,3,4,2,5,6,7,8,9] => [.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 0

[8,2,3,6,4,7,5,1] => [[[.,.],[.,[[.,[.,.]],[.,.]]]],.] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,3,1,1,1,1] => 1

[4,5,1,3,2,6,8,7] => [[.,[[.,.],.]],[.,[.,[[.,.],.]]]] => [1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3,1] => 2

[5,4,1,6,2,7,8,3] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3] => 1

[1,4,8,3,6,2,7,5] => [.,[[[.,.],.],[[[.,.],[.,.]],.]]] => [1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1] => 2

[4,5,7,6,1,2,8,3] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [4,4,3,3,3] => 0

[2,3,4,7,8,6,1,5] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1,1,1] => 1

[3,4,6,7,8,2,5,1] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2,1] => 1

[2,5,6,7,3,8,1,4] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1,1] => 0

[2,4,7,5,8,6,3,1] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => 0

[1,6,8,3,4,2,7,5] => [.,[[[.,.],[.,[.,.]]],[[.,.],.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1] => 1

[2,5,6,3,7,4,8,1] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1,1] => 0

[1,4,6,5,3,8,2,7] => [.,[[[.,.],.],[[.,.],[[.,.],.]]]] => [1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1] => 2

[2,4,5,8,7,1,3,6] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,1,1] => 2

[1,8,7,2,6,4,5,3] => [.,[[[.,[[[.,.],[.,.]],.]],.],.]] => [1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1,1] => 3

[1,8,4,7,6,2,5,3] => [.,[[[.,[.,.]],[[[.,.],.],.]],.]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,2] => 3

[4,5,6,7,1,2,8,3,9] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3,3] => 0

[4,3,8,5,2,6,1,7] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [6,3,3,3,3,2,1] => 3

[5,6,8,4,3,7,2,1] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [5,4,4,4,3,2,1] => 4

[1,4,8,7,6,2,5,3] => [.,[[.,[.,.]],[[[[.,.],.],.],.]]] => [1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,2] => 3

[1,7,4,2,8,5,6,3] => [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2] => 0

[1,5,3,4,7,2,6,8] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1] => 0

[1,3,8,6,7,2,5,4] => [.,[[.,.],[[[[.,.],.],[.,.]],.]]] => [1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1,1] => 2

[1,5,7,6,8,4,2,3] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2] => 1

[8,1,5,2,6,4,7,3] => [[.,[[.,[[.,.],.]],[.,[.,.]]]],.] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [7,3,3,3,1] => 2

[1,2,4,8,5,7,3,6] => [.,[.,[[.,.],[[.,[[.,.],.]],.]]]] => [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1] => 2

[1,5,7,8,4,6,3,2] => [.,[[[[.,.],.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2,1] => 2

[1,4,8,5,7,6,3,2] => [.,[[[.,.],.],[[.,[[.,.],.]],.]]] => [1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,1] => 3

[4,5,2,6,7,3,8,1] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1,1] => 0

[3,4,6,1,8,2,7,5] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2] => 1

[5,1,2,7,6,3,4,8] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4] => 0

[5,6,1,7,2,4,3,8] => [[.,[.,[[.,.],.]]],[.,[.,[.,.]]]] => [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,1] => 1

[3,5,6,8,1,2,7,4] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,2] => 1

[2,3,7,1,5,6,4,8] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1,1] => 0

[2,6,1,3,5,4,7,8] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1,1] => 1

[4,6,1,5,2,7,8,3] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[5,6,4,1,7,2,8,3] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3] => 1

[1,6,4,5,7,3,2,8] => [.,[[[[.,.],.],[.,.]],[.,[.,.]]]] => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2,1] => 1

[1,6,4,5,7,2,8,3] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2] => 0

[1,7,5,6,4,8,3,2] => [.,[[[[[.,.],.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,2,1] => 2

[1,5,6,7,3,2,4,8] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => [1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1] => 0

[4,5,6,1,3,8,2,7] => [[.,[[.,.],.]],[.,[.,[[.,.],.]]]] => [1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3,1] => 2

[1,3,8,6,5,2,7,4] => [.,[[.,.],[[[[.,.],.],[.,.]],.]]] => [1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1,1] => 2

[2,7,3,8,5,6,4,1] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1,1] => 0

[1,2,8,5,7,4,6,3] => [.,[.,[[[[.,.],.],[[.,.],.]],.]]] => [1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1] => 3

[5,8,4,3,7,6,2,1] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,4,3,2,1] => 5

[1,5,8,6,4,3,7,2] => [.,[[[[.,.],.],.],[[.,[.,.]],.]]] => [1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,2,1] => 3

[3,4,6,5,2,8,1,7] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2,1] => 2

[5,1,4,6,2,7,8,3] => [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,2] => 1

[1,2,5,3,7,8,6,4] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => [1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2] => 0

[2,1,3,7,5,8,4,6] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1,1] => 0

[2,3,8,7,1,4,6,5] => [[.,.],[.,[[[.,[[.,.],.]],.],.]]] => [1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,1,1,1] => 3

[9,2,3,4,5,1,6,7,8] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1,1,1,1,1,1] => 1

[8,2,3,1,6,4,7,5] => [[[.,.],[.,[[.,[.,.]],[.,.]]]],.] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,3,1,1,1,1] => 1

[1,8,7,2,3,4,6,5] => [.,[[[.,[.,[.,[[.,.],.]]]],.],.]] => [1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [6,5,1] => 3

[1,8,3,7,6,2,5,4] => [.,[[[.,.],[[[[.,.],.],.],.]],.]] => [1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,1,1] => 4

[1,3,8,2,5,6,4,7] => [.,[[.,.],[[[.,.],[.,[.,.]]],.]]] => [1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1,1] => 1

[1,3,2,7,4,6,8,5] => [.,[[.,.],[[.,[[.,.],.]],[.,.]]]] => [1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1,1] => 1

[1,3,8,4,6,2,7,5] => [.,[[.,.],[[.,[[.,.],[.,.]]],.]]] => [1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1,1] => 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] => [7,3,3,1,1,1,1] => 1

[2,5,7,6,3,8,4,1] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0

[1,2,7,5,8,6,3,4] => [.,[.,[[[.,[.,.]],[.,.]],[.,.]]]] => [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2] => 0

[2,1,9,8,7,6,5,3,4] => [[.,.],[[[[[[.,[.,.]],.],.],.],.],.]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,1,1,1] => 5

[1,7,8,4,2,6,3,5] => [.,[[[.,[.,.]],[[.,.],.]],[.,.]]] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,2] => 1

[1,7,5,8,4,3,6,2] => [.,[[[[[.,.],.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,2,1] => 2

[2,4,7,5,1,8,6,3] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => 0

[2,3,7,1,8,5,6,4] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1,1] => 0

[7,8,1,2,5,4,3,6] => [[.,[.,[[[.,.],.],[.,.]]]],[.,.]] => [1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,1] => 1

[2,8,4,3,5,1,7,6] => [[.,.],[[[.,.],[.,[[.,.],.]]],.]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2,1,1] => 2

[1,2,6,5,8,3,7,4] => [.,[.,[[[.,[.,.]],.],[[.,.],.]]]] => [1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2] => 2

[1,7,3,8,2,5,4,6] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]] => [1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1] => 0

[2,3,6,1,7,5,4,8] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1,1] => 1

[1,6,4,8,2,3,5,7] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,2] => 1

[1,4,7,3,5,8,6,2] => [.,[[[.,.],.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1] => 1

[5,1,8,6,7,2,3,4] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [6,4,4,4] => 1

[5,7,1,6,8,2,3,4] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4] => 0

[2,5,6,8,1,4,7,3] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1,1] => 2

[4,5,1,7,8,6,2,3] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [4,4,3,3,3] => 0

[1,6,4,7,5,3,2,8] => [.,[[[[.,.],.],[.,.]],[.,[.,.]]]] => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2,1] => 1

[1,6,5,3,2,7,4,8] => [.,[[[[.,.],[.,.]],.],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,1,1] => 1

[1,4,7,5,3,2,6,8] => [.,[[[.,.],.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1] => 1

[1,7,5,4,3,2,8,6] => [.,[[[[[.,.],.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,2,1] => 2

[1,4,7,5,3,2,8,6] => [.,[[[.,.],.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1] => 1

[8,1,3,6,4,5,2,7] => [[.,[[.,.],[[.,[.,.]],[.,.]]]],.] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,3,1,1,1] => 1

[7,1,2,4,8,3,5,6] => [[.,[.,[[.,.],[.,[.,.]]]]],[.,.]] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1] => 0

[2,5,3,4,6,8,1,7] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1,1] => 1

[1,2,4,7,8,5,6,3] => [.,[.,[[.,.],[[.,[.,.]],[.,.]]]]] => [1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1] => 0

[8,2,7,3,1,4,5,6] => [[[.,.],[[.,[.,[.,[.,.]]]],.]],.] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,1,1,1,1] => 2

[2,4,3,8,6,1,7,5] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1,1] => 1

[3,5,4,6,1,2,8,7] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,2] => 1

[1,8,5,6,2,3,7,4] => [.,[[[.,[.,[.,.]]],[.,[.,.]]],.]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3] => 1

[1,3,6,8,7,4,5,2] => [.,[[.,.],[[.,[.,.]],[[.,.],.]]]] => [1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1] => 1

[4,6,5,1,7,8,2,3] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[1,7,5,3,4,8,6,2] => [.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,1,1] => 0

[3,4,8,5,7,2,6,1] => [[[.,.],.],[.,[[.,[[.,.],.]],.]]] => [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,2,1] => 3

[1,5,3,8,4,7,2,6] => [.,[[[.,.],[.,.]],[[[.,.],.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1,1] => 2

[1,7,5,8,6,2,4,3] => [.,[[[.,[[.,.],.]],[.,.]],[.,.]]] => [1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,1] => 1

[7,1,2,6,4,8,3,5] => [[.,[.,[[[.,.],[.,.]],.]]],[.,.]] => [1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [6,6,3,1,1] => 1

[1,8,7,5,4,6,2,3] => [.,[[[[[.,[.,.]],.],[.,.]],.],.]] => [1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3,2] => 3

[1,8,6,2,4,7,5,3] => [.,[[[.,[[.,.],[.,.]]],[.,.]],.]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,4,1,1] => 1

[7,1,8,2,3,4,5,9,6] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,6,6] => 0

[2,1,3,8,5,4,6,7] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1,1,1] => 1

[1,7,8,6,3,2,4,5] => [.,[[[[.,.],[.,[.,.]]],.],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1,1,1] => 1

[7,1,2,5,3,8,4,6] => [[.,[.,[[.,[.,.]],[.,.]]]],[.,.]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2] => 0

[1,8,3,4,5,7,2,6] => [.,[[[.,.],[.,[.,[[.,.],.]]]],.]] => [1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1,1,1] => 2

[1,7,2,4,8,5,6,3] => [.,[[.,[[.,.],[.,[.,.]]]],[.,.]]] => [1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1] => 0

[1,7,6,8,4,5,3,2] => [.,[[[[[.,.],.],[.,.]],.],[.,.]]] => [1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,2,1] => 2

[2,7,3,1,8,5,6,4] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1,1] => 0

[1,4,7,6,8,3,5,2] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1] => 2

[1,7,2,8,6,5,3,4] => [.,[[.,[[[.,[.,.]],.],.]],[.,.]]] => [1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2] => 2

[1,7,6,2,5,3,8,4] => [.,[[[.,[[.,[.,.]],.]],.],[.,.]]] => [1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2] => 2

[1,7,5,2,4,3,8,6] => [.,[[[.,[[.,.],.]],[.,.]],[.,.]]] => [1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,1] => 1

[8,1,2,4,7,3,5,6] => [[.,[.,[[.,.],[[.,[.,.]],.]]]],.] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,1,1] => 2

[1,6,8,7,2,5,4,3] => [.,[[.,[[[.,.],.],.]],[[.,.],.]]] => [1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,1] => 3

[1,4,8,7,6,3,5,2] => [.,[[[.,.],.],[[[[.,.],.],.],.]]] => [1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,2,1] => 4

[8,1,6,2,5,7,3,4] => [[.,[[.,[[.,[.,.]],.]],[.,.]]],.] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [7,4,4,2] => 2

[2,4,7,6,1,8,3,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1,1] => 1

[1,6,2,3,8,5,7,4] => [.,[[.,[.,[[.,.],.]]],[[.,.],.]]] => [1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1] => 2

[3,4,2,6,8,5,7,1] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2,1] => 2

[6,1,7,8,9,2,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,5,5,5] => 0

[5,1,6,7,8,2,9,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,4,4,4,4] => 0

[6,8,1,2,7,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [6,5,5] => 1

[1,6,2,8,7,3,4,5] => [.,[[.,[.,[.,[.,.]]]],[[.,.],.]]] => [1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,4,4] => 1

[1,6,8,5,7,4,3,2] => [.,[[[[[.,.],.],.],.],[[.,.],.]]] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3,2,1] => 4

[1,4,5,7,3,6,8,2] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]] => [1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1] => 1

[2,3,8,1,4,6,5,7] => [[.,.],[.,[[.,[[.,.],[.,.]]],.]]] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1,1,1] => 1

[3,1,8,4,5,6,2,7] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,2] => 1

[2,3,7,4,8,1,6,5] => [[.,.],[.,[[.,[[.,.],.]],[.,.]]]] => [1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1,1,1] => 1

[1,6,3,5,8,7,4,2] => [.,[[[.,.],[[.,.],.]],[[.,.],.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,1,1] => 2

[2,4,5,7,1,6,8,3] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1,1] => 0

[4,1,5,7,8,6,2,3] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [4,4,3,3,3] => 0

[1,2,6,7,8,3,5,4] => [.,[.,[[.,[[.,.],.]],[.,[.,.]]]]] => [1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1] => 1

[1,2,4,8,6,7,3,5] => [.,[.,[[.,.],[[[.,.],[.,.]],.]]]] => [1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1] => 1

[8,1,2,6,5,7,3,4] => [[.,[.,[[[.,[.,.]],.],[.,.]]]],.] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2] => 2

[7,1,2,6,5,8,3,4] => [[.,[.,[[[.,[.,.]],.],.]]],[.,.]] => [1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [6,6,3,2] => 2

[2,3,5,6,8,4,7,1] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1,1,1] => 1

[2,4,5,8,3,6,7,1] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,1,1] => 1

[1,6,3,7,8,4,2,5] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]] => [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1] => 0

[1,4,3,5,8,2,6,7] => [.,[[[.,.],.],[.,[[.,[.,.]],.]]]] => [1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,1] => 2

[2,1,3,8,6,4,5,7] => [[.,.],[.,[[[.,[.,.]],[.,.]],.]]] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1,1,1] => 1

[1,3,6,4,5,8,2,7] => [.,[[.,.],[[.,[.,.]],[[.,.],.]]]] => [1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1] => 1

[1,4,3,8,6,2,5,7] => [.,[[[.,.],.],[[[.,.],[.,.]],.]]] => [1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1] => 2

[3,5,6,7,1,8,4,2] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 0

[2,6,3,1,4,7,8,5] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1,1] => 0

[2,9,3,4,5,6,1,7,8] => [[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1,1,1,1,1,1] => 1

[2,7,3,4,1,8,5,6] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1,1,1] => 0

[2,3,7,8,1,4,6,5] => [[.,.],[.,[[.,[[.,.],.]],[.,.]]]] => [1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1,1,1] => 1

[8,2,3,5,4,1,7,6] => [[[.,.],[.,[[.,.],[[.,.],.]]]],.] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,1,1,1] => 2

[7,1,3,8,2,4,6,5] => [[.,[[.,.],[.,[[.,.],.]]]],[.,.]] => [1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [6,6,2,1,1,1] => 1

[1,6,7,5,4,8,2,3] => [.,[[[[.,[.,.]],.],.],[.,[.,.]]]] => [1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,2] => 2

[1,8,5,4,2,6,3,7] => [.,[[[[.,[.,.]],.],[.,[.,.]]],.]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,2] => 2

[1,4,5,7,6,8,2,3] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2] => 0

[2,6,3,1,7,8,5,4] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1,1] => 1

[1,7,3,5,4,2,6,8] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]] => [1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1] => 0

[1,8,3,6,2,4,7,5] => [.,[[[.,.],[[.,[.,.]],[.,.]]],.]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1,1,1] => 1

[1,8,7,5,6,4,2,3] => [.,[[[[[.,[.,.]],.],[.,.]],.],.]] => [1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3,2] => 3

[3,4,6,7,5,1,8,2] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2] => 0

[1,5,2,4,7,6,8,3] => [.,[[.,[[.,.],.]],[[.,.],[.,.]]]] => [1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1] => 1

[8,1,2,4,6,3,5,7] => [[.,[.,[[.,.],[[.,.],[.,.]]]]],.] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1,1] => 1

[1,5,6,7,8,9,3,2,4] => [.,[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]] => [1,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3,1,1] => 0

[1,3,8,6,7,4,5,2] => [.,[[.,.],[[[.,[.,.]],[.,.]],.]]] => [1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1,1] => 1

[1,8,6,3,7,4,5,2] => [.,[[[[.,.],[.,[.,.]]],[.,.]],.]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,4,1,1,1] => 1

[4,8,7,3,2,5,6,1] => [[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,3,3,2,1] => 4

[1,4,3,8,5,6,2,7] => [.,[[[.,.],.],[[.,[.,[.,.]]],.]]] => [1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,1] => 2

[6,1,2,4,7,5,3,8] => [[.,[.,[[.,.],[.,.]]]],[.,[.,.]]] => [1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [5,5,5,1,1] => 0

[1,6,5,7,3,4,8,2] => [.,[[[[.,.],[.,.]],.],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,1,1] => 1

[1,8,5,2,7,6,4,3] => [.,[[[.,[[.,.],.]],[[.,.],.]],.]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,3,1] => 3

[1,7,6,8,2,5,4,3] => [.,[[[.,[[[.,.],.],.]],.],[.,.]]] => [1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,1] => 3

[1,7,8,6,2,5,4,3] => [.,[[[.,[[[.,.],.],.]],.],[.,.]]] => [1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,1] => 3

[4,6,5,7,1,8,2,3] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 0

[1,6,3,4,2,5,8,7] => [.,[[[.,.],[.,[.,.]]],[[.,.],.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1] => 1

[1,5,7,6,2,3,8,4] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3] => 0

[1,4,3,7,6,2,5,8] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1] => 2

[1,3,7,4,6,8,5,2] => [.,[[.,.],[[.,[[.,.],.]],[.,.]]]] => [1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1,1] => 1

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$F_{1} = 1$

$F_{2} = 1 + q$

$F_{3} = 3 + 2\ q + q^{2}$

$F_{4} = 9 + 11\ q + 3\ q^{2} + q^{3}$

$F_{5} = 39 + 48\ q + 28\ q^{2} + 4\ q^{3} + q^{4}$

$F_{6} = 189 + 297\ q + 166\ q^{2} + 62\ q^{3} + 5\ q^{4} + q^{5}$

Description

The number of singletons of an integer partition.
A singleton in an integer partition is a part that appear precisely once.

Map

binary search tree: left to right

Description

Return the shape of the binary search tree of the permutation as a non labelled binary tree.

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 partition

Description

The cut-out partition of a Dyck path.
The partition

$\lambda$ associated to a Dyck path is defined to be the complementary partition inside the staircase partition

$(n-1,\ldots,2,1)$ when cutting out

$D$ considered as a path from

$(0,0)$ to

$(n,n)$ .
In other words,

$\lambda_{i}$ is the number of down-steps before the

$(n+1-i)$ -th up-step of

$D$ .
This map is a bijection between Dyck paths of size

$n$ and partitions inside the staircase partition

$(n-1,\ldots,2,1)$ .