- FindStat

Identifier

Mp00014: Binary trees —to 132-avoiding permutation⟶ Permutations
Mp00067: Permutations —Foata bijection⟶ Permutations
Mp00204: Permutations —LLPS⟶ Integer partitions
St000183: Integer partitions ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 1778 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => [7] => 1

[.,[.,[.,[.,[.,[[.,.],.]]]]]] => [6,7,5,4,3,2,1] => [6,7,5,4,3,2,1] => [6,1] => 1

[.,[.,[.,[.,[[.,.],[.,.]]]]]] => [7,5,6,4,3,2,1] => [5,7,6,4,3,2,1] => [6,1] => 1

[.,[.,[.,[.,[[.,[.,.]],.]]]]] => [6,5,7,4,3,2,1] => [6,5,7,4,3,2,1] => [6,1] => 1

[.,[.,[.,[.,[[[.,.],.],.]]]]] => [5,6,7,4,3,2,1] => [5,6,7,4,3,2,1] => [5,1,1] => 1

[.,[.,[.,[[.,.],[.,[.,.]]]]]] => [7,6,4,5,3,2,1] => [4,7,6,5,3,2,1] => [6,1] => 1

[.,[.,[.,[[.,.],[[.,.],.]]]]] => [6,7,4,5,3,2,1] => [4,6,7,5,3,2,1] => [5,1,1] => 1

[.,[.,[.,[[.,[.,.]],[.,.]]]]] => [7,5,4,6,3,2,1] => [5,7,4,6,3,2,1] => [5,1,1] => 1

[.,[.,[.,[[[.,.],.],[.,.]]]]] => [7,4,5,6,3,2,1] => [4,5,7,6,3,2,1] => [5,1,1] => 1

[.,[.,[.,[[.,[.,[.,.]]],.]]]] => [6,5,4,7,3,2,1] => [6,5,4,7,3,2,1] => [6,1] => 1

[.,[.,[.,[[.,[[.,.],.]],.]]]] => [5,6,4,7,3,2,1] => [5,6,4,7,3,2,1] => [5,1,1] => 1

[.,[.,[.,[[[.,.],[.,.]],.]]]] => [6,4,5,7,3,2,1] => [4,6,5,7,3,2,1] => [5,1,1] => 1

[.,[.,[.,[[[.,[.,.]],.],.]]]] => [5,4,6,7,3,2,1] => [5,4,6,7,3,2,1] => [5,1,1] => 1

[.,[.,[.,[[[[.,.],.],.],.]]]] => [4,5,6,7,3,2,1] => [4,5,6,7,3,2,1] => [4,1,1,1] => 1

[.,[.,[[.,.],[.,[.,[.,.]]]]]] => [7,6,5,3,4,2,1] => [3,7,6,5,4,2,1] => [6,1] => 1

[.,[.,[[.,.],[.,[[.,.],.]]]]] => [6,7,5,3,4,2,1] => [3,6,7,5,4,2,1] => [5,1,1] => 1

[.,[.,[[.,.],[[.,.],[.,.]]]]] => [7,5,6,3,4,2,1] => [3,5,7,6,4,2,1] => [5,1,1] => 1

[.,[.,[[.,.],[[.,[.,.]],.]]]] => [6,5,7,3,4,2,1] => [3,6,5,7,4,2,1] => [5,1,1] => 1

[.,[.,[[.,.],[[[.,.],.],.]]]] => [5,6,7,3,4,2,1] => [3,5,6,7,4,2,1] => [4,1,1,1] => 1

[.,[.,[[.,[.,.]],[.,[.,.]]]]] => [7,6,4,3,5,2,1] => [4,7,6,3,5,2,1] => [5,1,1] => 1

[.,[.,[[.,[.,.]],[[.,.],.]]]] => [6,7,4,3,5,2,1] => [4,6,7,3,5,2,1] => [4,1,1,1] => 1

[.,[.,[[[.,.],.],[.,[.,.]]]]] => [7,6,3,4,5,2,1] => [3,4,7,6,5,2,1] => [5,1,1] => 1

[.,[.,[[[.,.],.],[[.,.],.]]]] => [6,7,3,4,5,2,1] => [3,4,6,7,5,2,1] => [4,1,1,1] => 1

[.,[.,[[.,[.,[.,.]]],[.,.]]]] => [7,5,4,3,6,2,1] => [5,7,4,3,6,2,1] => [5,1,1] => 1

[.,[.,[[.,[[.,.],.]],[.,.]]]] => [7,4,5,3,6,2,1] => [4,5,7,3,6,2,1] => [4,1,1,1] => 1

[.,[.,[[[.,.],[.,.]],[.,.]]]] => [7,5,3,4,6,2,1] => [3,5,7,4,6,2,1] => [4,1,1,1] => 1

[.,[.,[[[.,[.,.]],.],[.,.]]]] => [7,4,3,5,6,2,1] => [4,3,7,5,6,2,1] => [4,2,1] => 2

[.,[.,[[[[.,.],.],.],[.,.]]]] => [7,3,4,5,6,2,1] => [3,4,5,7,6,2,1] => [4,1,1,1] => 1

[.,[.,[[.,[.,[.,[.,.]]]],.]]] => [6,5,4,3,7,2,1] => [6,5,4,3,7,2,1] => [6,1] => 1

[.,[.,[[.,[.,[[.,.],.]]],.]]] => [5,6,4,3,7,2,1] => [5,6,4,3,7,2,1] => [5,1,1] => 1

[.,[.,[[.,[[.,.],[.,.]]],.]]] => [6,4,5,3,7,2,1] => [4,6,5,3,7,2,1] => [5,1,1] => 1

[.,[.,[[.,[[.,[.,.]],.]],.]]] => [5,4,6,3,7,2,1] => [5,4,6,3,7,2,1] => [5,1,1] => 1

[.,[.,[[.,[[[.,.],.],.]],.]]] => [4,5,6,3,7,2,1] => [4,5,6,3,7,2,1] => [4,1,1,1] => 1

[.,[.,[[[.,.],[.,[.,.]]],.]]] => [6,5,3,4,7,2,1] => [3,6,5,4,7,2,1] => [5,1,1] => 1

[.,[.,[[[.,.],[[.,.],.]],.]]] => [5,6,3,4,7,2,1] => [3,5,6,4,7,2,1] => [4,1,1,1] => 1

[.,[.,[[[.,[.,.]],[.,.]],.]]] => [6,4,3,5,7,2,1] => [4,6,3,5,7,2,1] => [4,1,1,1] => 1

[.,[.,[[[[.,.],.],[.,.]],.]]] => [6,3,4,5,7,2,1] => [3,4,6,5,7,2,1] => [4,1,1,1] => 1

[.,[.,[[[.,[.,[.,.]]],.],.]]] => [5,4,3,6,7,2,1] => [5,4,3,6,7,2,1] => [5,1,1] => 1

[.,[.,[[[.,[[.,.],.]],.],.]]] => [4,5,3,6,7,2,1] => [4,5,3,6,7,2,1] => [4,1,1,1] => 1

[.,[.,[[[[.,.],[.,.]],.],.]]] => [5,3,4,6,7,2,1] => [3,5,4,6,7,2,1] => [4,1,1,1] => 1

[.,[.,[[[[.,[.,.]],.],.],.]]] => [4,3,5,6,7,2,1] => [4,3,5,6,7,2,1] => [4,1,1,1] => 1

[.,[.,[[[[[.,.],.],.],.],.]]] => [3,4,5,6,7,2,1] => [3,4,5,6,7,2,1] => [3,1,1,1,1] => 1

[.,[[.,.],[.,[.,[.,[.,.]]]]]] => [7,6,5,4,2,3,1] => [2,7,6,5,4,3,1] => [6,1] => 1

[.,[[.,.],[.,[.,[[.,.],.]]]]] => [6,7,5,4,2,3,1] => [2,6,7,5,4,3,1] => [5,1,1] => 1

[.,[[.,.],[.,[[.,.],[.,.]]]]] => [7,5,6,4,2,3,1] => [2,5,7,6,4,3,1] => [5,1,1] => 1

[.,[[.,.],[.,[[.,[.,.]],.]]]] => [6,5,7,4,2,3,1] => [2,6,5,7,4,3,1] => [5,1,1] => 1

[.,[[.,.],[.,[[[.,.],.],.]]]] => [5,6,7,4,2,3,1] => [2,5,6,7,4,3,1] => [4,1,1,1] => 1

[.,[[.,.],[[.,.],[.,[.,.]]]]] => [7,6,4,5,2,3,1] => [2,4,7,6,5,3,1] => [5,1,1] => 1

[.,[[.,.],[[.,.],[[.,.],.]]]] => [6,7,4,5,2,3,1] => [2,4,6,7,5,3,1] => [4,1,1,1] => 1

[.,[[.,.],[[.,[.,.]],[.,.]]]] => [7,5,4,6,2,3,1] => [2,5,7,4,6,3,1] => [4,1,1,1] => 1

[.,[[.,.],[[[.,.],.],[.,.]]]] => [7,4,5,6,2,3,1] => [2,4,5,7,6,3,1] => [4,1,1,1] => 1

[.,[[.,.],[[.,[.,[.,.]]],.]]] => [6,5,4,7,2,3,1] => [2,6,5,4,7,3,1] => [5,1,1] => 1

[.,[[.,.],[[.,[[.,.],.]],.]]] => [5,6,4,7,2,3,1] => [2,5,6,4,7,3,1] => [4,1,1,1] => 1

[.,[[.,.],[[[.,.],[.,.]],.]]] => [6,4,5,7,2,3,1] => [2,4,6,5,7,3,1] => [4,1,1,1] => 1

[.,[[.,.],[[[.,[.,.]],.],.]]] => [5,4,6,7,2,3,1] => [2,5,4,6,7,3,1] => [4,1,1,1] => 1

[.,[[.,.],[[[[.,.],.],.],.]]] => [4,5,6,7,2,3,1] => [2,4,5,6,7,3,1] => [3,1,1,1,1] => 1

[.,[[.,[.,.]],[.,[.,[.,.]]]]] => [7,6,5,3,2,4,1] => [3,7,6,5,2,4,1] => [5,1,1] => 1

[.,[[.,[.,.]],[.,[[.,.],.]]]] => [6,7,5,3,2,4,1] => [3,6,7,5,2,4,1] => [4,1,1,1] => 1

[.,[[.,[.,.]],[[.,.],[.,.]]]] => [7,5,6,3,2,4,1] => [3,5,7,6,2,4,1] => [4,1,1,1] => 1

[.,[[.,[.,.]],[[.,[.,.]],.]]] => [6,5,7,3,2,4,1] => [3,6,5,7,2,4,1] => [4,1,1,1] => 1

[.,[[.,[.,.]],[[[.,.],.],.]]] => [5,6,7,3,2,4,1] => [3,5,6,7,2,4,1] => [3,1,1,1,1] => 1

[.,[[[.,.],.],[.,[.,[.,.]]]]] => [7,6,5,2,3,4,1] => [2,3,7,6,5,4,1] => [5,1,1] => 1

[.,[[[.,.],.],[.,[[.,.],.]]]] => [6,7,5,2,3,4,1] => [2,3,6,7,5,4,1] => [4,1,1,1] => 1

[.,[[[.,.],.],[[.,.],[.,.]]]] => [7,5,6,2,3,4,1] => [2,3,5,7,6,4,1] => [4,1,1,1] => 1

[.,[[[.,.],.],[[.,[.,.]],.]]] => [6,5,7,2,3,4,1] => [2,3,6,5,7,4,1] => [4,1,1,1] => 1

[.,[[[.,.],.],[[[.,.],.],.]]] => [5,6,7,2,3,4,1] => [2,3,5,6,7,4,1] => [3,1,1,1,1] => 1

[.,[[.,[.,[.,.]]],[.,[.,.]]]] => [7,6,4,3,2,5,1] => [4,7,6,3,2,5,1] => [5,1,1] => 1

[.,[[.,[.,[.,.]]],[[.,.],.]]] => [6,7,4,3,2,5,1] => [4,6,7,3,2,5,1] => [4,1,1,1] => 1

[.,[[.,[[.,.],.]],[.,[.,.]]]] => [7,6,3,4,2,5,1] => [3,4,7,6,2,5,1] => [4,1,1,1] => 1

[.,[[.,[[.,.],.]],[[.,.],.]]] => [6,7,3,4,2,5,1] => [3,4,6,7,2,5,1] => [3,1,1,1,1] => 1

[.,[[[.,.],[.,.]],[.,[.,.]]]] => [7,6,4,2,3,5,1] => [2,4,7,6,3,5,1] => [4,1,1,1] => 1

[.,[[[.,.],[.,.]],[[.,.],.]]] => [6,7,4,2,3,5,1] => [2,4,6,7,3,5,1] => [3,1,1,1,1] => 1

[.,[[[.,[.,.]],.],[.,[.,.]]]] => [7,6,3,2,4,5,1] => [3,2,7,6,4,5,1] => [4,2,1] => 2

[.,[[[.,[.,.]],.],[[.,.],.]]] => [6,7,3,2,4,5,1] => [3,2,6,7,4,5,1] => [3,2,1,1] => 2

[.,[[[[.,.],.],.],[.,[.,.]]]] => [7,6,2,3,4,5,1] => [2,3,4,7,6,5,1] => [4,1,1,1] => 1

[.,[[[[.,.],.],.],[[.,.],.]]] => [6,7,2,3,4,5,1] => [2,3,4,6,7,5,1] => [3,1,1,1,1] => 1

[.,[[.,[.,[.,[.,.]]]],[.,.]]] => [7,5,4,3,2,6,1] => [5,7,4,3,2,6,1] => [5,1,1] => 1

[.,[[.,[.,[[.,.],.]]],[.,.]]] => [7,4,5,3,2,6,1] => [4,5,7,3,2,6,1] => [4,1,1,1] => 1

[.,[[.,[[.,.],[.,.]]],[.,.]]] => [7,5,3,4,2,6,1] => [3,5,7,4,2,6,1] => [4,1,1,1] => 1

[.,[[.,[[.,[.,.]],.]],[.,.]]] => [7,4,3,5,2,6,1] => [4,3,7,5,2,6,1] => [4,2,1] => 2

[.,[[.,[[[.,.],.],.]],[.,.]]] => [7,3,4,5,2,6,1] => [3,4,5,7,2,6,1] => [3,1,1,1,1] => 1

[.,[[[.,.],[.,[.,.]]],[.,.]]] => [7,5,4,2,3,6,1] => [2,5,7,4,3,6,1] => [4,1,1,1] => 1

[.,[[[.,.],[[.,.],.]],[.,.]]] => [7,4,5,2,3,6,1] => [2,4,5,7,3,6,1] => [3,1,1,1,1] => 1

[.,[[[.,[.,.]],[.,.]],[.,.]]] => [7,5,3,2,4,6,1] => [3,5,7,2,4,6,1] => [3,1,1,1,1] => 1

[.,[[[[.,.],.],[.,.]],[.,.]]] => [7,5,2,3,4,6,1] => [2,3,5,7,4,6,1] => [3,1,1,1,1] => 1

[.,[[[.,[.,[.,.]]],.],[.,.]]] => [7,4,3,2,5,6,1] => [4,3,7,2,5,6,1] => [4,1,1,1] => 1

[.,[[[.,[[.,.],.]],.],[.,.]]] => [7,3,4,2,5,6,1] => [3,4,2,7,5,6,1] => [3,2,1,1] => 2

[.,[[[[.,.],[.,.]],.],[.,.]]] => [7,4,2,3,5,6,1] => [2,4,3,7,5,6,1] => [3,2,1,1] => 2

[.,[[[[.,[.,.]],.],.],[.,.]]] => [7,3,2,4,5,6,1] => [3,2,4,7,5,6,1] => [3,2,1,1] => 2

[.,[[[[[.,.],.],.],.],[.,.]]] => [7,2,3,4,5,6,1] => [2,3,4,5,7,6,1] => [3,1,1,1,1] => 1

[.,[[.,[.,[.,[.,[.,.]]]]],.]] => [6,5,4,3,2,7,1] => [6,5,4,3,2,7,1] => [6,1] => 1

[.,[[.,[.,[.,[[.,.],.]]]],.]] => [5,6,4,3,2,7,1] => [5,6,4,3,2,7,1] => [5,1,1] => 1

[.,[[.,[.,[[.,.],[.,.]]]],.]] => [6,4,5,3,2,7,1] => [4,6,5,3,2,7,1] => [5,1,1] => 1

[.,[[.,[.,[[.,[.,.]],.]]],.]] => [5,4,6,3,2,7,1] => [5,4,6,3,2,7,1] => [5,1,1] => 1

[.,[[.,[.,[[[.,.],.],.]]],.]] => [4,5,6,3,2,7,1] => [4,5,6,3,2,7,1] => [4,1,1,1] => 1

[.,[[.,[[.,.],[.,[.,.]]]],.]] => [6,5,3,4,2,7,1] => [3,6,5,4,2,7,1] => [5,1,1] => 1

[.,[[.,[[.,.],[[.,.],.]]],.]] => [5,6,3,4,2,7,1] => [3,5,6,4,2,7,1] => [4,1,1,1] => 1

[.,[[.,[[.,[.,.]],[.,.]]],.]] => [6,4,3,5,2,7,1] => [4,6,3,5,2,7,1] => [4,1,1,1] => 1

[.,[[.,[[[.,.],.],[.,.]]],.]] => [6,3,4,5,2,7,1] => [3,4,6,5,2,7,1] => [4,1,1,1] => 1

[.,[[.,[[.,[.,[.,.]]],.]],.]] => [5,4,3,6,2,7,1] => [5,4,3,6,2,7,1] => [5,1,1] => 1

[.,[[.,[[.,[[.,.],.]],.]],.]] => [4,5,3,6,2,7,1] => [4,5,3,6,2,7,1] => [4,1,1,1] => 1

[.,[[.,[[[.,.],[.,.]],.]],.]] => [5,3,4,6,2,7,1] => [3,5,4,6,2,7,1] => [4,1,1,1] => 1

[.,[[.,[[[.,[.,.]],.],.]],.]] => [4,3,5,6,2,7,1] => [4,3,5,6,2,7,1] => [4,1,1,1] => 1

[.,[[.,[[[[.,.],.],.],.]],.]] => [3,4,5,6,2,7,1] => [3,4,5,6,2,7,1] => [3,1,1,1,1] => 1

[.,[[[.,.],[.,[.,[.,.]]]],.]] => [6,5,4,2,3,7,1] => [2,6,5,4,3,7,1] => [5,1,1] => 1

[.,[[[.,.],[.,[[.,.],.]]],.]] => [5,6,4,2,3,7,1] => [2,5,6,4,3,7,1] => [4,1,1,1] => 1

[.,[[[.,.],[[.,.],[.,.]]],.]] => [6,4,5,2,3,7,1] => [2,4,6,5,3,7,1] => [4,1,1,1] => 1

[.,[[[.,.],[[.,[.,.]],.]],.]] => [5,4,6,2,3,7,1] => [2,5,4,6,3,7,1] => [4,1,1,1] => 1

[.,[[[.,.],[[[.,.],.],.]],.]] => [4,5,6,2,3,7,1] => [2,4,5,6,3,7,1] => [3,1,1,1,1] => 1

[.,[[[.,[.,.]],[.,[.,.]]],.]] => [6,5,3,2,4,7,1] => [3,6,5,2,4,7,1] => [4,1,1,1] => 1

[.,[[[.,[.,.]],[[.,.],.]],.]] => [5,6,3,2,4,7,1] => [3,5,6,2,4,7,1] => [3,1,1,1,1] => 1

[.,[[[[.,.],.],[.,[.,.]]],.]] => [6,5,2,3,4,7,1] => [2,3,6,5,4,7,1] => [4,1,1,1] => 1

[.,[[[[.,.],.],[[.,.],.]],.]] => [5,6,2,3,4,7,1] => [2,3,5,6,4,7,1] => [3,1,1,1,1] => 1

[.,[[[.,[.,[.,.]]],[.,.]],.]] => [6,4,3,2,5,7,1] => [4,6,3,2,5,7,1] => [4,1,1,1] => 1

[.,[[[.,[[.,.],.]],[.,.]],.]] => [6,3,4,2,5,7,1] => [3,4,6,2,5,7,1] => [3,1,1,1,1] => 1

[.,[[[[.,.],[.,.]],[.,.]],.]] => [6,4,2,3,5,7,1] => [2,4,6,3,5,7,1] => [3,1,1,1,1] => 1

[.,[[[[.,[.,.]],.],[.,.]],.]] => [6,3,2,4,5,7,1] => [3,2,6,4,5,7,1] => [3,2,1,1] => 2

[.,[[[[[.,.],.],.],[.,.]],.]] => [6,2,3,4,5,7,1] => [2,3,4,6,5,7,1] => [3,1,1,1,1] => 1

[.,[[[.,[.,[.,[.,.]]]],.],.]] => [5,4,3,2,6,7,1] => [5,4,3,2,6,7,1] => [5,1,1] => 1

[.,[[[.,[.,[[.,.],.]]],.],.]] => [4,5,3,2,6,7,1] => [4,5,3,2,6,7,1] => [4,1,1,1] => 1

[.,[[[.,[[.,.],[.,.]]],.],.]] => [5,3,4,2,6,7,1] => [3,5,4,2,6,7,1] => [4,1,1,1] => 1

[.,[[[.,[[.,[.,.]],.]],.],.]] => [4,3,5,2,6,7,1] => [4,3,5,2,6,7,1] => [4,1,1,1] => 1

[.,[[[.,[[[.,.],.],.]],.],.]] => [3,4,5,2,6,7,1] => [3,4,5,2,6,7,1] => [3,1,1,1,1] => 1

[.,[[[[.,.],[.,[.,.]]],.],.]] => [5,4,2,3,6,7,1] => [2,5,4,3,6,7,1] => [4,1,1,1] => 1

[.,[[[[.,.],[[.,.],.]],.],.]] => [4,5,2,3,6,7,1] => [2,4,5,3,6,7,1] => [3,1,1,1,1] => 1

[.,[[[[.,[.,.]],[.,.]],.],.]] => [5,3,2,4,6,7,1] => [3,5,2,4,6,7,1] => [3,1,1,1,1] => 1

[.,[[[[[.,.],.],[.,.]],.],.]] => [5,2,3,4,6,7,1] => [2,3,5,4,6,7,1] => [3,1,1,1,1] => 1

[.,[[[[.,[.,[.,.]]],.],.],.]] => [4,3,2,5,6,7,1] => [4,3,2,5,6,7,1] => [4,1,1,1] => 1

[.,[[[[.,[[.,.],.]],.],.],.]] => [3,4,2,5,6,7,1] => [3,4,2,5,6,7,1] => [3,1,1,1,1] => 1

[.,[[[[[.,.],[.,.]],.],.],.]] => [4,2,3,5,6,7,1] => [2,4,3,5,6,7,1] => [3,1,1,1,1] => 1

[.,[[[[[.,[.,.]],.],.],.],.]] => [3,2,4,5,6,7,1] => [3,2,4,5,6,7,1] => [3,1,1,1,1] => 1

[.,[[[[[[.,.],.],.],.],.],.]] => [2,3,4,5,6,7,1] => [2,3,4,5,6,7,1] => [2,1,1,1,1,1] => 1

[[.,.],[.,[.,[.,[.,[.,.]]]]]] => [7,6,5,4,3,1,2] => [1,7,6,5,4,3,2] => [6,1] => 1

[[.,.],[.,[.,[.,[[.,.],.]]]]] => [6,7,5,4,3,1,2] => [1,6,7,5,4,3,2] => [5,1,1] => 1

[[.,.],[.,[.,[[.,.],[.,.]]]]] => [7,5,6,4,3,1,2] => [1,5,7,6,4,3,2] => [5,1,1] => 1

[[.,.],[.,[.,[[.,[.,.]],.]]]] => [6,5,7,4,3,1,2] => [1,6,5,7,4,3,2] => [5,1,1] => 1

[[.,.],[.,[.,[[[.,.],.],.]]]] => [5,6,7,4,3,1,2] => [1,5,6,7,4,3,2] => [4,1,1,1] => 1

[[.,.],[.,[[.,.],[.,[.,.]]]]] => [7,6,4,5,3,1,2] => [1,4,7,6,5,3,2] => [5,1,1] => 1

[[.,.],[.,[[.,.],[[.,.],.]]]] => [6,7,4,5,3,1,2] => [1,4,6,7,5,3,2] => [4,1,1,1] => 1

[[.,.],[.,[[.,[.,.]],[.,.]]]] => [7,5,4,6,3,1,2] => [1,5,7,4,6,3,2] => [4,1,1,1] => 1

[[.,.],[.,[[[.,.],.],[.,.]]]] => [7,4,5,6,3,1,2] => [1,4,5,7,6,3,2] => [4,1,1,1] => 1

[[.,.],[.,[[.,[.,[.,.]]],.]]] => [6,5,4,7,3,1,2] => [1,6,5,4,7,3,2] => [5,1,1] => 1

[[.,.],[.,[[.,[[.,.],.]],.]]] => [5,6,4,7,3,1,2] => [1,5,6,4,7,3,2] => [4,1,1,1] => 1

[[.,.],[.,[[[.,.],[.,.]],.]]] => [6,4,5,7,3,1,2] => [1,4,6,5,7,3,2] => [4,1,1,1] => 1

[[.,.],[.,[[[.,[.,.]],.],.]]] => [5,4,6,7,3,1,2] => [1,5,4,6,7,3,2] => [4,1,1,1] => 1

[[.,.],[.,[[[[.,.],.],.],.]]] => [4,5,6,7,3,1,2] => [1,4,5,6,7,3,2] => [3,1,1,1,1] => 1

[[.,.],[[.,.],[.,[.,[.,.]]]]] => [7,6,5,3,4,1,2] => [1,3,7,6,5,4,2] => [5,1,1] => 1

[[.,.],[[.,.],[.,[[.,.],.]]]] => [6,7,5,3,4,1,2] => [1,3,6,7,5,4,2] => [4,1,1,1] => 1

[[.,.],[[.,.],[[.,.],[.,.]]]] => [7,5,6,3,4,1,2] => [1,3,5,7,6,4,2] => [4,1,1,1] => 1

[[.,.],[[.,.],[[.,[.,.]],.]]] => [6,5,7,3,4,1,2] => [1,3,6,5,7,4,2] => [4,1,1,1] => 1

[[.,.],[[.,.],[[[.,.],.],.]]] => [5,6,7,3,4,1,2] => [1,3,5,6,7,4,2] => [3,1,1,1,1] => 1

[[.,.],[[.,[.,.]],[.,[.,.]]]] => [7,6,4,3,5,1,2] => [1,4,7,6,3,5,2] => [4,1,1,1] => 1

[[.,.],[[.,[.,.]],[[.,.],.]]] => [6,7,4,3,5,1,2] => [1,4,6,7,3,5,2] => [3,1,1,1,1] => 1

[[.,.],[[[.,.],.],[.,[.,.]]]] => [7,6,3,4,5,1,2] => [1,3,4,7,6,5,2] => [4,1,1,1] => 1

[[.,.],[[[.,.],.],[[.,.],.]]] => [6,7,3,4,5,1,2] => [1,3,4,6,7,5,2] => [3,1,1,1,1] => 1

[[.,.],[[.,[.,[.,.]]],[.,.]]] => [7,5,4,3,6,1,2] => [1,5,7,4,3,6,2] => [4,1,1,1] => 1

[[.,.],[[.,[[.,.],.]],[.,.]]] => [7,4,5,3,6,1,2] => [1,4,5,7,3,6,2] => [3,1,1,1,1] => 1

[[.,.],[[[.,.],[.,.]],[.,.]]] => [7,5,3,4,6,1,2] => [1,3,5,7,4,6,2] => [3,1,1,1,1] => 1

[[.,.],[[[.,[.,.]],.],[.,.]]] => [7,4,3,5,6,1,2] => [1,4,3,7,5,6,2] => [3,2,1,1] => 2

[[.,.],[[[[.,.],.],.],[.,.]]] => [7,3,4,5,6,1,2] => [1,3,4,5,7,6,2] => [3,1,1,1,1] => 1

[[.,.],[[.,[.,[.,[.,.]]]],.]] => [6,5,4,3,7,1,2] => [1,6,5,4,3,7,2] => [5,1,1] => 1

[[.,.],[[.,[.,[[.,.],.]]],.]] => [5,6,4,3,7,1,2] => [1,5,6,4,3,7,2] => [4,1,1,1] => 1

[[.,.],[[.,[[.,.],[.,.]]],.]] => [6,4,5,3,7,1,2] => [1,4,6,5,3,7,2] => [4,1,1,1] => 1

[[.,.],[[.,[[.,[.,.]],.]],.]] => [5,4,6,3,7,1,2] => [1,5,4,6,3,7,2] => [4,1,1,1] => 1

[[.,.],[[.,[[[.,.],.],.]],.]] => [4,5,6,3,7,1,2] => [1,4,5,6,3,7,2] => [3,1,1,1,1] => 1

[[.,.],[[[.,.],[.,[.,.]]],.]] => [6,5,3,4,7,1,2] => [1,3,6,5,4,7,2] => [4,1,1,1] => 1

[[.,.],[[[.,.],[[.,.],.]],.]] => [5,6,3,4,7,1,2] => [1,3,5,6,4,7,2] => [3,1,1,1,1] => 1

[[.,.],[[[.,[.,.]],[.,.]],.]] => [6,4,3,5,7,1,2] => [1,4,6,3,5,7,2] => [3,1,1,1,1] => 1

[[.,.],[[[[.,.],.],[.,.]],.]] => [6,3,4,5,7,1,2] => [1,3,4,6,5,7,2] => [3,1,1,1,1] => 1

[[.,.],[[[.,[.,[.,.]]],.],.]] => [5,4,3,6,7,1,2] => [1,5,4,3,6,7,2] => [4,1,1,1] => 1

[[.,.],[[[.,[[.,.],.]],.],.]] => [4,5,3,6,7,1,2] => [1,4,5,3,6,7,2] => [3,1,1,1,1] => 1

[[.,.],[[[[.,.],[.,.]],.],.]] => [5,3,4,6,7,1,2] => [1,3,5,4,6,7,2] => [3,1,1,1,1] => 1

[[.,.],[[[[.,[.,.]],.],.],.]] => [4,3,5,6,7,1,2] => [1,4,3,5,6,7,2] => [3,1,1,1,1] => 1

[[.,.],[[[[[.,.],.],.],.],.]] => [3,4,5,6,7,1,2] => [1,3,4,5,6,7,2] => [2,1,1,1,1,1] => 1

[[.,[.,.]],[.,[.,[.,[.,.]]]]] => [7,6,5,4,2,1,3] => [2,7,6,5,4,1,3] => [5,1,1] => 1

[[.,[.,.]],[.,[.,[[.,.],.]]]] => [6,7,5,4,2,1,3] => [2,6,7,5,4,1,3] => [4,1,1,1] => 1

[[.,[.,.]],[.,[[.,.],[.,.]]]] => [7,5,6,4,2,1,3] => [2,5,7,6,4,1,3] => [4,1,1,1] => 1

[[.,[.,.]],[.,[[.,[.,.]],.]]] => [6,5,7,4,2,1,3] => [2,6,5,7,4,1,3] => [4,1,1,1] => 1

[[.,[.,.]],[.,[[[.,.],.],.]]] => [5,6,7,4,2,1,3] => [2,5,6,7,4,1,3] => [3,1,1,1,1] => 1

[[.,[.,.]],[[.,.],[.,[.,.]]]] => [7,6,4,5,2,1,3] => [2,4,7,6,5,1,3] => [4,1,1,1] => 1

[[.,[.,.]],[[.,.],[[.,.],.]]] => [6,7,4,5,2,1,3] => [2,4,6,7,5,1,3] => [3,1,1,1,1] => 1

[[.,[.,.]],[[.,[.,.]],[.,.]]] => [7,5,4,6,2,1,3] => [2,5,7,4,6,1,3] => [3,1,1,1,1] => 1

[[.,[.,.]],[[[.,.],.],[.,.]]] => [7,4,5,6,2,1,3] => [2,4,5,7,6,1,3] => [3,1,1,1,1] => 1

[[.,[.,.]],[[.,[.,[.,.]]],.]] => [6,5,4,7,2,1,3] => [2,6,5,4,7,1,3] => [4,1,1,1] => 1

[[.,[.,.]],[[.,[[.,.],.]],.]] => [5,6,4,7,2,1,3] => [2,5,6,4,7,1,3] => [3,1,1,1,1] => 1

[[.,[.,.]],[[[.,.],[.,.]],.]] => [6,4,5,7,2,1,3] => [2,4,6,5,7,1,3] => [3,1,1,1,1] => 1

[[.,[.,.]],[[[.,[.,.]],.],.]] => [5,4,6,7,2,1,3] => [2,5,4,6,7,1,3] => [3,1,1,1,1] => 1

[[.,[.,.]],[[[[.,.],.],.],.]] => [4,5,6,7,2,1,3] => [2,4,5,6,7,1,3] => [2,1,1,1,1,1] => 1

[[[.,.],.],[.,[.,[.,[.,.]]]]] => [7,6,5,4,1,2,3] => [1,2,7,6,5,4,3] => [5,1,1] => 1

[[[.,.],.],[.,[.,[[.,.],.]]]] => [6,7,5,4,1,2,3] => [1,2,6,7,5,4,3] => [4,1,1,1] => 1

[[[.,.],.],[.,[[.,.],[.,.]]]] => [7,5,6,4,1,2,3] => [1,2,5,7,6,4,3] => [4,1,1,1] => 1

[[[.,.],.],[.,[[.,[.,.]],.]]] => [6,5,7,4,1,2,3] => [1,2,6,5,7,4,3] => [4,1,1,1] => 1

[[[.,.],.],[.,[[[.,.],.],.]]] => [5,6,7,4,1,2,3] => [1,2,5,6,7,4,3] => [3,1,1,1,1] => 1

[[[.,.],.],[[.,.],[.,[.,.]]]] => [7,6,4,5,1,2,3] => [1,2,4,7,6,5,3] => [4,1,1,1] => 1

[[[.,.],.],[[.,.],[[.,.],.]]] => [6,7,4,5,1,2,3] => [1,2,4,6,7,5,3] => [3,1,1,1,1] => 1

[[[.,.],.],[[.,[.,.]],[.,.]]] => [7,5,4,6,1,2,3] => [1,2,5,7,4,6,3] => [3,1,1,1,1] => 1

[[[.,.],.],[[[.,.],.],[.,.]]] => [7,4,5,6,1,2,3] => [1,2,4,5,7,6,3] => [3,1,1,1,1] => 1

[[[.,.],.],[[.,[.,[.,.]]],.]] => [6,5,4,7,1,2,3] => [1,2,6,5,4,7,3] => [4,1,1,1] => 1

[[[.,.],.],[[.,[[.,.],.]],.]] => [5,6,4,7,1,2,3] => [1,2,5,6,4,7,3] => [3,1,1,1,1] => 1

[[[.,.],.],[[[.,.],[.,.]],.]] => [6,4,5,7,1,2,3] => [1,2,4,6,5,7,3] => [3,1,1,1,1] => 1

[[[.,.],.],[[[.,[.,.]],.],.]] => [5,4,6,7,1,2,3] => [1,2,5,4,6,7,3] => [3,1,1,1,1] => 1

[[[.,.],.],[[[[.,.],.],.],.]] => [4,5,6,7,1,2,3] => [1,2,4,5,6,7,3] => [2,1,1,1,1,1] => 1

[[.,[.,[.,.]]],[.,[.,[.,.]]]] => [7,6,5,3,2,1,4] => [3,7,6,5,2,1,4] => [5,1,1] => 1

[[.,[.,[.,.]]],[.,[[.,.],.]]] => [6,7,5,3,2,1,4] => [3,6,7,5,2,1,4] => [4,1,1,1] => 1

[[.,[.,[.,.]]],[[.,.],[.,.]]] => [7,5,6,3,2,1,4] => [3,5,7,6,2,1,4] => [4,1,1,1] => 1

[[.,[.,[.,.]]],[[.,[.,.]],.]] => [6,5,7,3,2,1,4] => [3,6,5,7,2,1,4] => [4,1,1,1] => 1

[[.,[.,[.,.]]],[[[.,.],.],.]] => [5,6,7,3,2,1,4] => [3,5,6,7,2,1,4] => [3,1,1,1,1] => 1

[[.,[[.,.],.]],[.,[.,[.,.]]]] => [7,6,5,2,3,1,4] => [2,3,7,6,5,1,4] => [4,1,1,1] => 1

[[.,[[.,.],.]],[.,[[.,.],.]]] => [6,7,5,2,3,1,4] => [2,3,6,7,5,1,4] => [3,1,1,1,1] => 1

[[.,[[.,.],.]],[[.,.],[.,.]]] => [7,5,6,2,3,1,4] => [2,3,5,7,6,1,4] => [3,1,1,1,1] => 1

[[.,[[.,.],.]],[[.,[.,.]],.]] => [6,5,7,2,3,1,4] => [2,3,6,5,7,1,4] => [3,1,1,1,1] => 1

[[.,[[.,.],.]],[[[.,.],.],.]] => [5,6,7,2,3,1,4] => [2,3,5,6,7,1,4] => [2,1,1,1,1,1] => 1

[[[.,.],[.,.]],[.,[.,[.,.]]]] => [7,6,5,3,1,2,4] => [1,3,7,6,5,2,4] => [4,1,1,1] => 1

[[[.,.],[.,.]],[.,[[.,.],.]]] => [6,7,5,3,1,2,4] => [1,3,6,7,5,2,4] => [3,1,1,1,1] => 1

[[[.,.],[.,.]],[[.,.],[.,.]]] => [7,5,6,3,1,2,4] => [1,3,5,7,6,2,4] => [3,1,1,1,1] => 1

[[[.,.],[.,.]],[[.,[.,.]],.]] => [6,5,7,3,1,2,4] => [1,3,6,5,7,2,4] => [3,1,1,1,1] => 1

[[[.,.],[.,.]],[[[.,.],.],.]] => [5,6,7,3,1,2,4] => [1,3,5,6,7,2,4] => [2,1,1,1,1,1] => 1

[[[.,[.,.]],.],[.,[.,[.,.]]]] => [7,6,5,2,1,3,4] => [2,1,7,6,5,3,4] => [4,2,1] => 2

[[[.,[.,.]],.],[.,[[.,.],.]]] => [6,7,5,2,1,3,4] => [2,1,6,7,5,3,4] => [3,2,1,1] => 2

[[[.,[.,.]],.],[[.,.],[.,.]]] => [7,5,6,2,1,3,4] => [2,1,5,7,6,3,4] => [3,2,1,1] => 2

[[[.,[.,.]],.],[[.,[.,.]],.]] => [6,5,7,2,1,3,4] => [2,1,6,5,7,3,4] => [3,2,1,1] => 2

[[[.,[.,.]],.],[[[.,.],.],.]] => [5,6,7,2,1,3,4] => [2,1,5,6,7,3,4] => [2,2,1,1,1] => 2

[[[[.,.],.],.],[.,[.,[.,.]]]] => [7,6,5,1,2,3,4] => [1,2,3,7,6,5,4] => [4,1,1,1] => 1

[[[[.,.],.],.],[.,[[.,.],.]]] => [6,7,5,1,2,3,4] => [1,2,3,6,7,5,4] => [3,1,1,1,1] => 1

[[[[.,.],.],.],[[.,.],[.,.]]] => [7,5,6,1,2,3,4] => [1,2,3,5,7,6,4] => [3,1,1,1,1] => 1

[[[[.,.],.],.],[[.,[.,.]],.]] => [6,5,7,1,2,3,4] => [1,2,3,6,5,7,4] => [3,1,1,1,1] => 1

[[[[.,.],.],.],[[[.,.],.],.]] => [5,6,7,1,2,3,4] => [1,2,3,5,6,7,4] => [2,1,1,1,1,1] => 1

[[.,[.,[.,[.,.]]]],[.,[.,.]]] => [7,6,4,3,2,1,5] => [4,7,6,3,2,1,5] => [5,1,1] => 1

[[.,[.,[.,[.,.]]]],[[.,.],.]] => [6,7,4,3,2,1,5] => [4,6,7,3,2,1,5] => [4,1,1,1] => 1

[[.,[.,[[.,.],.]]],[.,[.,.]]] => [7,6,3,4,2,1,5] => [3,4,7,6,2,1,5] => [4,1,1,1] => 1

[[.,[.,[[.,.],.]]],[[.,.],.]] => [6,7,3,4,2,1,5] => [3,4,6,7,2,1,5] => [3,1,1,1,1] => 1

[[.,[[.,.],[.,.]]],[.,[.,.]]] => [7,6,4,2,3,1,5] => [2,4,7,6,3,1,5] => [4,1,1,1] => 1

[[.,[[.,.],[.,.]]],[[.,.],.]] => [6,7,4,2,3,1,5] => [2,4,6,7,3,1,5] => [3,1,1,1,1] => 1

[[.,[[.,[.,.]],.]],[.,[.,.]]] => [7,6,3,2,4,1,5] => [3,2,7,6,4,1,5] => [4,2,1] => 2

[[.,[[.,[.,.]],.]],[[.,.],.]] => [6,7,3,2,4,1,5] => [3,2,6,7,4,1,5] => [3,2,1,1] => 2

[[.,[[[.,.],.],.]],[.,[.,.]]] => [7,6,2,3,4,1,5] => [2,3,4,7,6,1,5] => [3,1,1,1,1] => 1

[[.,[[[.,.],.],.]],[[.,.],.]] => [6,7,2,3,4,1,5] => [2,3,4,6,7,1,5] => [2,1,1,1,1,1] => 1

[[[.,.],[.,[.,.]]],[.,[.,.]]] => [7,6,4,3,1,2,5] => [1,4,7,6,3,2,5] => [4,1,1,1] => 1

[[[.,.],[.,[.,.]]],[[.,.],.]] => [6,7,4,3,1,2,5] => [1,4,6,7,3,2,5] => [3,1,1,1,1] => 1

[[[.,.],[[.,.],.]],[.,[.,.]]] => [7,6,3,4,1,2,5] => [1,3,4,7,6,2,5] => [3,1,1,1,1] => 1

[[[.,.],[[.,.],.]],[[.,.],.]] => [6,7,3,4,1,2,5] => [1,3,4,6,7,2,5] => [2,1,1,1,1,1] => 1

[[[.,[.,.]],[.,.]],[.,[.,.]]] => [7,6,4,2,1,3,5] => [2,4,7,6,1,3,5] => [3,1,1,1,1] => 1

[[[.,[.,.]],[.,.]],[[.,.],.]] => [6,7,4,2,1,3,5] => [2,4,6,7,1,3,5] => [2,1,1,1,1,1] => 1

[[[[.,.],.],[.,.]],[.,[.,.]]] => [7,6,4,1,2,3,5] => [1,2,4,7,6,3,5] => [3,1,1,1,1] => 1

[[[[.,.],.],[.,.]],[[.,.],.]] => [6,7,4,1,2,3,5] => [1,2,4,6,7,3,5] => [2,1,1,1,1,1] => 1

[[[.,[.,[.,.]]],.],[.,[.,.]]] => [7,6,3,2,1,4,5] => [3,2,7,6,1,4,5] => [3,2,1,1] => 2

[[[.,[.,[.,.]]],.],[[.,.],.]] => [6,7,3,2,1,4,5] => [3,2,6,7,1,4,5] => [3,1,1,1,1] => 1

[[[.,[[.,.],.]],.],[.,[.,.]]] => [7,6,2,3,1,4,5] => [2,3,1,7,6,4,5] => [3,2,1,1] => 2

[[[.,[[.,.],.]],.],[[.,.],.]] => [6,7,2,3,1,4,5] => [2,3,1,6,7,4,5] => [2,2,1,1,1] => 2

[[[[.,.],[.,.]],.],[.,[.,.]]] => [7,6,3,1,2,4,5] => [1,3,2,7,6,4,5] => [3,2,1,1] => 2

[[[[.,.],[.,.]],.],[[.,.],.]] => [6,7,3,1,2,4,5] => [1,3,2,6,7,4,5] => [2,2,1,1,1] => 2

[[[[.,[.,.]],.],.],[.,[.,.]]] => [7,6,2,1,3,4,5] => [2,1,3,7,6,4,5] => [3,2,1,1] => 2

[[[[.,[.,.]],.],.],[[.,.],.]] => [6,7,2,1,3,4,5] => [2,1,3,6,7,4,5] => [2,2,1,1,1] => 2

[[[[[.,.],.],.],.],[.,[.,.]]] => [7,6,1,2,3,4,5] => [1,2,3,4,7,6,5] => [3,1,1,1,1] => 1

[[[[[.,.],.],.],.],[[.,.],.]] => [6,7,1,2,3,4,5] => [1,2,3,4,6,7,5] => [2,1,1,1,1,1] => 1

[[.,[.,[.,[.,[.,.]]]]],[.,.]] => [7,5,4,3,2,1,6] => [5,7,4,3,2,1,6] => [5,1,1] => 1

[[.,[.,[.,[[.,.],.]]]],[.,.]] => [7,4,5,3,2,1,6] => [4,5,7,3,2,1,6] => [4,1,1,1] => 1

[[.,[.,[[.,.],[.,.]]]],[.,.]] => [7,5,3,4,2,1,6] => [3,5,7,4,2,1,6] => [4,1,1,1] => 1

[[.,[.,[[.,[.,.]],.]]],[.,.]] => [7,4,3,5,2,1,6] => [4,3,7,5,2,1,6] => [4,2,1] => 2

[[.,[.,[[[.,.],.],.]]],[.,.]] => [7,3,4,5,2,1,6] => [3,4,5,7,2,1,6] => [3,1,1,1,1] => 1

[[.,[[.,.],[.,[.,.]]]],[.,.]] => [7,5,4,2,3,1,6] => [2,5,7,4,3,1,6] => [4,1,1,1] => 1

[[.,[[.,.],[[.,.],.]]],[.,.]] => [7,4,5,2,3,1,6] => [2,4,5,7,3,1,6] => [3,1,1,1,1] => 1

[[.,[[.,[.,.]],[.,.]]],[.,.]] => [7,5,3,2,4,1,6] => [3,5,7,2,4,1,6] => [3,1,1,1,1] => 1

[[.,[[[.,.],.],[.,.]]],[.,.]] => [7,5,2,3,4,1,6] => [2,3,5,7,4,1,6] => [3,1,1,1,1] => 1

[[.,[[.,[.,[.,.]]],.]],[.,.]] => [7,4,3,2,5,1,6] => [4,3,7,2,5,1,6] => [4,1,1,1] => 1

[[.,[[.,[[.,.],.]],.]],[.,.]] => [7,3,4,2,5,1,6] => [3,4,2,7,5,1,6] => [3,2,1,1] => 2

[[.,[[[.,.],[.,.]],.]],[.,.]] => [7,4,2,3,5,1,6] => [2,4,3,7,5,1,6] => [3,2,1,1] => 2

[[.,[[[.,[.,.]],.],.]],[.,.]] => [7,3,2,4,5,1,6] => [3,2,4,7,5,1,6] => [3,2,1,1] => 2

[[.,[[[[.,.],.],.],.]],[.,.]] => [7,2,3,4,5,1,6] => [2,3,4,5,7,1,6] => [2,1,1,1,1,1] => 1

[[[.,.],[.,[.,[.,.]]]],[.,.]] => [7,5,4,3,1,2,6] => [1,5,7,4,3,2,6] => [4,1,1,1] => 1

[[[.,.],[.,[[.,.],.]]],[.,.]] => [7,4,5,3,1,2,6] => [1,4,5,7,3,2,6] => [3,1,1,1,1] => 1

[[[.,.],[[.,.],[.,.]]],[.,.]] => [7,5,3,4,1,2,6] => [1,3,5,7,4,2,6] => [3,1,1,1,1] => 1

[[[.,.],[[.,[.,.]],.]],[.,.]] => [7,4,3,5,1,2,6] => [1,4,3,7,5,2,6] => [3,2,1,1] => 2

[[[.,.],[[[.,.],.],.]],[.,.]] => [7,3,4,5,1,2,6] => [1,3,4,5,7,2,6] => [2,1,1,1,1,1] => 1

[[[.,[.,.]],[.,[.,.]]],[.,.]] => [7,5,4,2,1,3,6] => [2,5,7,4,1,3,6] => [3,1,1,1,1] => 1

[[[.,[.,.]],[[.,.],.]],[.,.]] => [7,4,5,2,1,3,6] => [2,4,5,7,1,3,6] => [2,1,1,1,1,1] => 1

[[[[.,.],.],[.,[.,.]]],[.,.]] => [7,5,4,1,2,3,6] => [1,2,5,7,4,3,6] => [3,1,1,1,1] => 1

[[[[.,.],.],[[.,.],.]],[.,.]] => [7,4,5,1,2,3,6] => [1,2,4,5,7,3,6] => [2,1,1,1,1,1] => 1

[[[.,[.,[.,.]]],[.,.]],[.,.]] => [7,5,3,2,1,4,6] => [3,5,7,2,1,4,6] => [3,1,1,1,1] => 1

[[[.,[[.,.],.]],[.,.]],[.,.]] => [7,5,2,3,1,4,6] => [2,3,5,7,1,4,6] => [2,1,1,1,1,1] => 1

[[[[.,.],[.,.]],[.,.]],[.,.]] => [7,5,3,1,2,4,6] => [1,3,5,7,2,4,6] => [2,1,1,1,1,1] => 1

[[[[.,[.,.]],.],[.,.]],[.,.]] => [7,5,2,1,3,4,6] => [2,1,5,7,3,4,6] => [2,2,1,1,1] => 2

[[[[[.,.],.],.],[.,.]],[.,.]] => [7,5,1,2,3,4,6] => [1,2,3,5,7,4,6] => [2,1,1,1,1,1] => 1

[[[.,[.,[.,[.,.]]]],.],[.,.]] => [7,4,3,2,1,5,6] => [4,3,7,2,1,5,6] => [4,1,1,1] => 1

[[[.,[.,[[.,.],.]]],.],[.,.]] => [7,3,4,2,1,5,6] => [3,4,2,7,1,5,6] => [3,1,1,1,1] => 1

[[[.,[[.,.],[.,.]]],.],[.,.]] => [7,4,2,3,1,5,6] => [2,4,3,7,1,5,6] => [3,1,1,1,1] => 1

[[[.,[[.,[.,.]],.]],.],[.,.]] => [7,3,2,4,1,5,6] => [3,2,4,7,1,5,6] => [3,1,1,1,1] => 1

[[[.,[[[.,.],.],.]],.],[.,.]] => [7,2,3,4,1,5,6] => [2,3,4,1,7,5,6] => [2,2,1,1,1] => 2

[[[[.,.],[.,[.,.]]],.],[.,.]] => [7,4,3,1,2,5,6] => [1,4,3,7,2,5,6] => [3,1,1,1,1] => 1

[[[[.,.],[[.,.],.]],.],[.,.]] => [7,3,4,1,2,5,6] => [1,3,4,2,7,5,6] => [2,2,1,1,1] => 2

[[[[.,[.,.]],[.,.]],.],[.,.]] => [7,4,2,1,3,5,6] => [2,4,1,7,3,5,6] => [2,2,1,1,1] => 2

[[[[[.,.],.],[.,.]],.],[.,.]] => [7,4,1,2,3,5,6] => [1,2,4,3,7,5,6] => [2,2,1,1,1] => 2

[[[[.,[.,[.,.]]],.],.],[.,.]] => [7,3,2,1,4,5,6] => [3,2,1,7,4,5,6] => [3,2,1,1] => 2

[[[[.,[[.,.],.]],.],.],[.,.]] => [7,2,3,1,4,5,6] => [2,3,1,4,7,5,6] => [2,2,1,1,1] => 2

[[[[[.,.],[.,.]],.],.],[.,.]] => [7,3,1,2,4,5,6] => [1,3,2,4,7,5,6] => [2,2,1,1,1] => 2

[[[[[.,[.,.]],.],.],.],[.,.]] => [7,2,1,3,4,5,6] => [2,1,3,4,7,5,6] => [2,2,1,1,1] => 2

[[[[[[.,.],.],.],.],.],[.,.]] => [7,1,2,3,4,5,6] => [1,2,3,4,5,7,6] => [2,1,1,1,1,1] => 1

[[.,[.,[.,[.,[.,[.,.]]]]]],.] => [6,5,4,3,2,1,7] => [6,5,4,3,2,1,7] => [6,1] => 1

[[.,[.,[.,[.,[[.,.],.]]]]],.] => [5,6,4,3,2,1,7] => [5,6,4,3,2,1,7] => [5,1,1] => 1

[[.,[.,[.,[[.,.],[.,.]]]]],.] => [6,4,5,3,2,1,7] => [4,6,5,3,2,1,7] => [5,1,1] => 1

[[.,[.,[.,[[.,[.,.]],.]]]],.] => [5,4,6,3,2,1,7] => [5,4,6,3,2,1,7] => [5,1,1] => 1

[[.,[.,[.,[[[.,.],.],.]]]],.] => [4,5,6,3,2,1,7] => [4,5,6,3,2,1,7] => [4,1,1,1] => 1

[[.,[.,[[.,.],[.,[.,.]]]]],.] => [6,5,3,4,2,1,7] => [3,6,5,4,2,1,7] => [5,1,1] => 1

[[.,[.,[[.,.],[[.,.],.]]]],.] => [5,6,3,4,2,1,7] => [3,5,6,4,2,1,7] => [4,1,1,1] => 1

[[.,[.,[[.,[.,.]],[.,.]]]],.] => [6,4,3,5,2,1,7] => [4,6,3,5,2,1,7] => [4,1,1,1] => 1

[[.,[.,[[[.,.],.],[.,.]]]],.] => [6,3,4,5,2,1,7] => [3,4,6,5,2,1,7] => [4,1,1,1] => 1

[[.,[.,[[.,[.,[.,.]]],.]]],.] => [5,4,3,6,2,1,7] => [5,4,3,6,2,1,7] => [5,1,1] => 1

[[.,[.,[[.,[[.,.],.]],.]]],.] => [4,5,3,6,2,1,7] => [4,5,3,6,2,1,7] => [4,1,1,1] => 1

[[.,[.,[[[.,.],[.,.]],.]]],.] => [5,3,4,6,2,1,7] => [3,5,4,6,2,1,7] => [4,1,1,1] => 1

[[.,[.,[[[.,[.,.]],.],.]]],.] => [4,3,5,6,2,1,7] => [4,3,5,6,2,1,7] => [4,1,1,1] => 1

[[.,[.,[[[[.,.],.],.],.]]],.] => [3,4,5,6,2,1,7] => [3,4,5,6,2,1,7] => [3,1,1,1,1] => 1

[[.,[[.,.],[.,[.,[.,.]]]]],.] => [6,5,4,2,3,1,7] => [2,6,5,4,3,1,7] => [5,1,1] => 1

[[.,[[.,.],[.,[[.,.],.]]]],.] => [5,6,4,2,3,1,7] => [2,5,6,4,3,1,7] => [4,1,1,1] => 1

[[.,[[.,.],[[.,.],[.,.]]]],.] => [6,4,5,2,3,1,7] => [2,4,6,5,3,1,7] => [4,1,1,1] => 1

[[.,[[.,.],[[.,[.,.]],.]]],.] => [5,4,6,2,3,1,7] => [2,5,4,6,3,1,7] => [4,1,1,1] => 1

[[.,[[.,.],[[[.,.],.],.]]],.] => [4,5,6,2,3,1,7] => [2,4,5,6,3,1,7] => [3,1,1,1,1] => 1

[[.,[[.,[.,.]],[.,[.,.]]]],.] => [6,5,3,2,4,1,7] => [3,6,5,2,4,1,7] => [4,1,1,1] => 1

[[.,[[.,[.,.]],[[.,.],.]]],.] => [5,6,3,2,4,1,7] => [3,5,6,2,4,1,7] => [3,1,1,1,1] => 1

[[.,[[[.,.],.],[.,[.,.]]]],.] => [6,5,2,3,4,1,7] => [2,3,6,5,4,1,7] => [4,1,1,1] => 1

[[.,[[[.,.],.],[[.,.],.]]],.] => [5,6,2,3,4,1,7] => [2,3,5,6,4,1,7] => [3,1,1,1,1] => 1

[[.,[[.,[.,[.,.]]],[.,.]]],.] => [6,4,3,2,5,1,7] => [4,6,3,2,5,1,7] => [4,1,1,1] => 1

[[.,[[.,[[.,.],.]],[.,.]]],.] => [6,3,4,2,5,1,7] => [3,4,6,2,5,1,7] => [3,1,1,1,1] => 1

[[.,[[[.,.],[.,.]],[.,.]]],.] => [6,4,2,3,5,1,7] => [2,4,6,3,5,1,7] => [3,1,1,1,1] => 1

[[.,[[[.,[.,.]],.],[.,.]]],.] => [6,3,2,4,5,1,7] => [3,2,6,4,5,1,7] => [3,2,1,1] => 2

[[.,[[[[.,.],.],.],[.,.]]],.] => [6,2,3,4,5,1,7] => [2,3,4,6,5,1,7] => [3,1,1,1,1] => 1

[[.,[[.,[.,[.,[.,.]]]],.]],.] => [5,4,3,2,6,1,7] => [5,4,3,2,6,1,7] => [5,1,1] => 1

[[.,[[.,[.,[[.,.],.]]],.]],.] => [4,5,3,2,6,1,7] => [4,5,3,2,6,1,7] => [4,1,1,1] => 1

[[.,[[.,[[.,.],[.,.]]],.]],.] => [5,3,4,2,6,1,7] => [3,5,4,2,6,1,7] => [4,1,1,1] => 1

[[.,[[.,[[.,[.,.]],.]],.]],.] => [4,3,5,2,6,1,7] => [4,3,5,2,6,1,7] => [4,1,1,1] => 1

[[.,[[.,[[[.,.],.],.]],.]],.] => [3,4,5,2,6,1,7] => [3,4,5,2,6,1,7] => [3,1,1,1,1] => 1

[[.,[[[.,.],[.,[.,.]]],.]],.] => [5,4,2,3,6,1,7] => [2,5,4,3,6,1,7] => [4,1,1,1] => 1

[[.,[[[.,.],[[.,.],.]],.]],.] => [4,5,2,3,6,1,7] => [2,4,5,3,6,1,7] => [3,1,1,1,1] => 1

[[.,[[[.,[.,.]],[.,.]],.]],.] => [5,3,2,4,6,1,7] => [3,5,2,4,6,1,7] => [3,1,1,1,1] => 1

[[.,[[[[.,.],.],[.,.]],.]],.] => [5,2,3,4,6,1,7] => [2,3,5,4,6,1,7] => [3,1,1,1,1] => 1

[[.,[[[.,[.,[.,.]]],.],.]],.] => [4,3,2,5,6,1,7] => [4,3,2,5,6,1,7] => [4,1,1,1] => 1

[[.,[[[.,[[.,.],.]],.],.]],.] => [3,4,2,5,6,1,7] => [3,4,2,5,6,1,7] => [3,1,1,1,1] => 1

[[.,[[[[.,.],[.,.]],.],.]],.] => [4,2,3,5,6,1,7] => [2,4,3,5,6,1,7] => [3,1,1,1,1] => 1

[[.,[[[[.,[.,.]],.],.],.]],.] => [3,2,4,5,6,1,7] => [3,2,4,5,6,1,7] => [3,1,1,1,1] => 1

[[.,[[[[[.,.],.],.],.],.]],.] => [2,3,4,5,6,1,7] => [2,3,4,5,6,1,7] => [2,1,1,1,1,1] => 1

[[[.,.],[.,[.,[.,[.,.]]]]],.] => [6,5,4,3,1,2,7] => [1,6,5,4,3,2,7] => [5,1,1] => 1

[[[.,.],[.,[.,[[.,.],.]]]],.] => [5,6,4,3,1,2,7] => [1,5,6,4,3,2,7] => [4,1,1,1] => 1

[[[.,.],[.,[[.,.],[.,.]]]],.] => [6,4,5,3,1,2,7] => [1,4,6,5,3,2,7] => [4,1,1,1] => 1

[[[.,.],[.,[[.,[.,.]],.]]],.] => [5,4,6,3,1,2,7] => [1,5,4,6,3,2,7] => [4,1,1,1] => 1

[[[.,.],[.,[[[.,.],.],.]]],.] => [4,5,6,3,1,2,7] => [1,4,5,6,3,2,7] => [3,1,1,1,1] => 1

[[[.,.],[[.,.],[.,[.,.]]]],.] => [6,5,3,4,1,2,7] => [1,3,6,5,4,2,7] => [4,1,1,1] => 1

[[[.,.],[[.,.],[[.,.],.]]],.] => [5,6,3,4,1,2,7] => [1,3,5,6,4,2,7] => [3,1,1,1,1] => 1

[[[.,.],[[.,[.,.]],[.,.]]],.] => [6,4,3,5,1,2,7] => [1,4,6,3,5,2,7] => [3,1,1,1,1] => 1

[[[.,.],[[[.,.],.],[.,.]]],.] => [6,3,4,5,1,2,7] => [1,3,4,6,5,2,7] => [3,1,1,1,1] => 1

[[[.,.],[[.,[.,[.,.]]],.]],.] => [5,4,3,6,1,2,7] => [1,5,4,3,6,2,7] => [4,1,1,1] => 1

[[[.,.],[[.,[[.,.],.]],.]],.] => [4,5,3,6,1,2,7] => [1,4,5,3,6,2,7] => [3,1,1,1,1] => 1

[[[.,.],[[[.,.],[.,.]],.]],.] => [5,3,4,6,1,2,7] => [1,3,5,4,6,2,7] => [3,1,1,1,1] => 1

[[[.,.],[[[.,[.,.]],.],.]],.] => [4,3,5,6,1,2,7] => [1,4,3,5,6,2,7] => [3,1,1,1,1] => 1

[[[.,.],[[[[.,.],.],.],.]],.] => [3,4,5,6,1,2,7] => [1,3,4,5,6,2,7] => [2,1,1,1,1,1] => 1

[[[.,[.,.]],[.,[.,[.,.]]]],.] => [6,5,4,2,1,3,7] => [2,6,5,4,1,3,7] => [4,1,1,1] => 1

[[[.,[.,.]],[.,[[.,.],.]]],.] => [5,6,4,2,1,3,7] => [2,5,6,4,1,3,7] => [3,1,1,1,1] => 1

[[[.,[.,.]],[[.,.],[.,.]]],.] => [6,4,5,2,1,3,7] => [2,4,6,5,1,3,7] => [3,1,1,1,1] => 1

[[[.,[.,.]],[[.,[.,.]],.]],.] => [5,4,6,2,1,3,7] => [2,5,4,6,1,3,7] => [3,1,1,1,1] => 1

[[[.,[.,.]],[[[.,.],.],.]],.] => [4,5,6,2,1,3,7] => [2,4,5,6,1,3,7] => [2,1,1,1,1,1] => 1

[[[[.,.],.],[.,[.,[.,.]]]],.] => [6,5,4,1,2,3,7] => [1,2,6,5,4,3,7] => [4,1,1,1] => 1

[[[[.,.],.],[.,[[.,.],.]]],.] => [5,6,4,1,2,3,7] => [1,2,5,6,4,3,7] => [3,1,1,1,1] => 1

[[[[.,.],.],[[.,.],[.,.]]],.] => [6,4,5,1,2,3,7] => [1,2,4,6,5,3,7] => [3,1,1,1,1] => 1

[[[[.,.],.],[[.,[.,.]],.]],.] => [5,4,6,1,2,3,7] => [1,2,5,4,6,3,7] => [3,1,1,1,1] => 1

[[[[.,.],.],[[[.,.],.],.]],.] => [4,5,6,1,2,3,7] => [1,2,4,5,6,3,7] => [2,1,1,1,1,1] => 1

[[[.,[.,[.,.]]],[.,[.,.]]],.] => [6,5,3,2,1,4,7] => [3,6,5,2,1,4,7] => [4,1,1,1] => 1

[[[.,[.,[.,.]]],[[.,.],.]],.] => [5,6,3,2,1,4,7] => [3,5,6,2,1,4,7] => [3,1,1,1,1] => 1

[[[.,[[.,.],.]],[.,[.,.]]],.] => [6,5,2,3,1,4,7] => [2,3,6,5,1,4,7] => [3,1,1,1,1] => 1

[[[.,[[.,.],.]],[[.,.],.]],.] => [5,6,2,3,1,4,7] => [2,3,5,6,1,4,7] => [2,1,1,1,1,1] => 1

[[[[.,.],[.,.]],[.,[.,.]]],.] => [6,5,3,1,2,4,7] => [1,3,6,5,2,4,7] => [3,1,1,1,1] => 1

[[[[.,.],[.,.]],[[.,.],.]],.] => [5,6,3,1,2,4,7] => [1,3,5,6,2,4,7] => [2,1,1,1,1,1] => 1

[[[[.,[.,.]],.],[.,[.,.]]],.] => [6,5,2,1,3,4,7] => [2,1,6,5,3,4,7] => [3,2,1,1] => 2

[[[[.,[.,.]],.],[[.,.],.]],.] => [5,6,2,1,3,4,7] => [2,1,5,6,3,4,7] => [2,2,1,1,1] => 2

[[[[[.,.],.],.],[.,[.,.]]],.] => [6,5,1,2,3,4,7] => [1,2,3,6,5,4,7] => [3,1,1,1,1] => 1

[[[[[.,.],.],.],[[.,.],.]],.] => [5,6,1,2,3,4,7] => [1,2,3,5,6,4,7] => [2,1,1,1,1,1] => 1

[[[.,[.,[.,[.,.]]]],[.,.]],.] => [6,4,3,2,1,5,7] => [4,6,3,2,1,5,7] => [4,1,1,1] => 1

[[[.,[.,[[.,.],.]]],[.,.]],.] => [6,3,4,2,1,5,7] => [3,4,6,2,1,5,7] => [3,1,1,1,1] => 1

[[[.,[[.,.],[.,.]]],[.,.]],.] => [6,4,2,3,1,5,7] => [2,4,6,3,1,5,7] => [3,1,1,1,1] => 1

[[[.,[[.,[.,.]],.]],[.,.]],.] => [6,3,2,4,1,5,7] => [3,2,6,4,1,5,7] => [3,2,1,1] => 2

[[[.,[[[.,.],.],.]],[.,.]],.] => [6,2,3,4,1,5,7] => [2,3,4,6,1,5,7] => [2,1,1,1,1,1] => 1

[[[[.,.],[.,[.,.]]],[.,.]],.] => [6,4,3,1,2,5,7] => [1,4,6,3,2,5,7] => [3,1,1,1,1] => 1

[[[[.,.],[[.,.],.]],[.,.]],.] => [6,3,4,1,2,5,7] => [1,3,4,6,2,5,7] => [2,1,1,1,1,1] => 1

[[[[.,[.,.]],[.,.]],[.,.]],.] => [6,4,2,1,3,5,7] => [2,4,6,1,3,5,7] => [2,1,1,1,1,1] => 1

[[[[[.,.],.],[.,.]],[.,.]],.] => [6,4,1,2,3,5,7] => [1,2,4,6,3,5,7] => [2,1,1,1,1,1] => 1

[[[[.,[.,[.,.]]],.],[.,.]],.] => [6,3,2,1,4,5,7] => [3,2,6,1,4,5,7] => [3,1,1,1,1] => 1

[[[[.,[[.,.],.]],.],[.,.]],.] => [6,2,3,1,4,5,7] => [2,3,1,6,4,5,7] => [2,2,1,1,1] => 2

[[[[[.,.],[.,.]],.],[.,.]],.] => [6,3,1,2,4,5,7] => [1,3,2,6,4,5,7] => [2,2,1,1,1] => 2

[[[[[.,[.,.]],.],.],[.,.]],.] => [6,2,1,3,4,5,7] => [2,1,3,6,4,5,7] => [2,2,1,1,1] => 2

[[[[[[.,.],.],.],.],[.,.]],.] => [6,1,2,3,4,5,7] => [1,2,3,4,6,5,7] => [2,1,1,1,1,1] => 1

[[[.,[.,[.,[.,[.,.]]]]],.],.] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => [5,1,1] => 1

[[[.,[.,[.,[[.,.],.]]]],.],.] => [4,5,3,2,1,6,7] => [4,5,3,2,1,6,7] => [4,1,1,1] => 1

[[[.,[.,[[.,.],[.,.]]]],.],.] => [5,3,4,2,1,6,7] => [3,5,4,2,1,6,7] => [4,1,1,1] => 1

[[[.,[.,[[.,[.,.]],.]]],.],.] => [4,3,5,2,1,6,7] => [4,3,5,2,1,6,7] => [4,1,1,1] => 1

[[[.,[.,[[[.,.],.],.]]],.],.] => [3,4,5,2,1,6,7] => [3,4,5,2,1,6,7] => [3,1,1,1,1] => 1

[[[.,[[.,.],[.,[.,.]]]],.],.] => [5,4,2,3,1,6,7] => [2,5,4,3,1,6,7] => [4,1,1,1] => 1

[[[.,[[.,.],[[.,.],.]]],.],.] => [4,5,2,3,1,6,7] => [2,4,5,3,1,6,7] => [3,1,1,1,1] => 1

[[[.,[[.,[.,.]],[.,.]]],.],.] => [5,3,2,4,1,6,7] => [3,5,2,4,1,6,7] => [3,1,1,1,1] => 1

[[[.,[[[.,.],.],[.,.]]],.],.] => [5,2,3,4,1,6,7] => [2,3,5,4,1,6,7] => [3,1,1,1,1] => 1

[[[.,[[.,[.,[.,.]]],.]],.],.] => [4,3,2,5,1,6,7] => [4,3,2,5,1,6,7] => [4,1,1,1] => 1

[[[.,[[.,[[.,.],.]],.]],.],.] => [3,4,2,5,1,6,7] => [3,4,2,5,1,6,7] => [3,1,1,1,1] => 1

[[[.,[[[.,.],[.,.]],.]],.],.] => [4,2,3,5,1,6,7] => [2,4,3,5,1,6,7] => [3,1,1,1,1] => 1

[[[.,[[[.,[.,.]],.],.]],.],.] => [3,2,4,5,1,6,7] => [3,2,4,5,1,6,7] => [3,1,1,1,1] => 1

[[[.,[[[[.,.],.],.],.]],.],.] => [2,3,4,5,1,6,7] => [2,3,4,5,1,6,7] => [2,1,1,1,1,1] => 1

[[[[.,.],[.,[.,[.,.]]]],.],.] => [5,4,3,1,2,6,7] => [1,5,4,3,2,6,7] => [4,1,1,1] => 1

[[[[.,.],[.,[[.,.],.]]],.],.] => [4,5,3,1,2,6,7] => [1,4,5,3,2,6,7] => [3,1,1,1,1] => 1

[[[[.,.],[[.,.],[.,.]]],.],.] => [5,3,4,1,2,6,7] => [1,3,5,4,2,6,7] => [3,1,1,1,1] => 1

[[[[.,.],[[.,[.,.]],.]],.],.] => [4,3,5,1,2,6,7] => [1,4,3,5,2,6,7] => [3,1,1,1,1] => 1

[[[[.,.],[[[.,.],.],.]],.],.] => [3,4,5,1,2,6,7] => [1,3,4,5,2,6,7] => [2,1,1,1,1,1] => 1

[[[[.,[.,.]],[.,[.,.]]],.],.] => [5,4,2,1,3,6,7] => [2,5,4,1,3,6,7] => [3,1,1,1,1] => 1

[[[[.,[.,.]],[[.,.],.]],.],.] => [4,5,2,1,3,6,7] => [2,4,5,1,3,6,7] => [2,1,1,1,1,1] => 1

[[[[[.,.],.],[.,[.,.]]],.],.] => [5,4,1,2,3,6,7] => [1,2,5,4,3,6,7] => [3,1,1,1,1] => 1

[[[[[.,.],.],[[.,.],.]],.],.] => [4,5,1,2,3,6,7] => [1,2,4,5,3,6,7] => [2,1,1,1,1,1] => 1

[[[[.,[.,[.,.]]],[.,.]],.],.] => [5,3,2,1,4,6,7] => [3,5,2,1,4,6,7] => [3,1,1,1,1] => 1

[[[[.,[[.,.],.]],[.,.]],.],.] => [5,2,3,1,4,6,7] => [2,3,5,1,4,6,7] => [2,1,1,1,1,1] => 1

[[[[[.,.],[.,.]],[.,.]],.],.] => [5,3,1,2,4,6,7] => [1,3,5,2,4,6,7] => [2,1,1,1,1,1] => 1

[[[[[.,[.,.]],.],[.,.]],.],.] => [5,2,1,3,4,6,7] => [2,1,5,3,4,6,7] => [2,2,1,1,1] => 2

[[[[[[.,.],.],.],[.,.]],.],.] => [5,1,2,3,4,6,7] => [1,2,3,5,4,6,7] => [2,1,1,1,1,1] => 1

[[[[.,[.,[.,[.,.]]]],.],.],.] => [4,3,2,1,5,6,7] => [4,3,2,1,5,6,7] => [4,1,1,1] => 1

[[[[.,[.,[[.,.],.]]],.],.],.] => [3,4,2,1,5,6,7] => [3,4,2,1,5,6,7] => [3,1,1,1,1] => 1

[[[[.,[[.,.],[.,.]]],.],.],.] => [4,2,3,1,5,6,7] => [2,4,3,1,5,6,7] => [3,1,1,1,1] => 1

[[[[.,[[.,[.,.]],.]],.],.],.] => [3,2,4,1,5,6,7] => [3,2,4,1,5,6,7] => [3,1,1,1,1] => 1

[[[[.,[[[.,.],.],.]],.],.],.] => [2,3,4,1,5,6,7] => [2,3,4,1,5,6,7] => [2,1,1,1,1,1] => 1

[[[[[.,.],[.,[.,.]]],.],.],.] => [4,3,1,2,5,6,7] => [1,4,3,2,5,6,7] => [3,1,1,1,1] => 1

[[[[[.,.],[[.,.],.]],.],.],.] => [3,4,1,2,5,6,7] => [1,3,4,2,5,6,7] => [2,1,1,1,1,1] => 1

[[[[[.,[.,.]],[.,.]],.],.],.] => [4,2,1,3,5,6,7] => [2,4,1,3,5,6,7] => [2,1,1,1,1,1] => 1

[[[[[[.,.],.],[.,.]],.],.],.] => [4,1,2,3,5,6,7] => [1,2,4,3,5,6,7] => [2,1,1,1,1,1] => 1

[[[[[.,[.,[.,.]]],.],.],.],.] => [3,2,1,4,5,6,7] => [3,2,1,4,5,6,7] => [3,1,1,1,1] => 1

[[[[[.,[[.,.],.]],.],.],.],.] => [2,3,1,4,5,6,7] => [2,3,1,4,5,6,7] => [2,1,1,1,1,1] => 1

[[[[[[.,.],[.,.]],.],.],.],.] => [3,1,2,4,5,6,7] => [1,3,2,4,5,6,7] => [2,1,1,1,1,1] => 1

[[[[[[.,[.,.]],.],.],.],.],.] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [2,1,1,1,1,1] => 1

[[[[[[[.,.],.],.],.],.],.],.] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 1

[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => [8] => 1

[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [7,8,6,5,4,3,2,1] => [7,8,6,5,4,3,2,1] => [7,1] => 1

[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [8,6,7,5,4,3,2,1] => [6,8,7,5,4,3,2,1] => [7,1] => 1

[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [7,6,8,5,4,3,2,1] => [7,6,8,5,4,3,2,1] => [7,1] => 1

[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]] => [6,7,8,5,4,3,2,1] => [6,7,8,5,4,3,2,1] => [6,1,1] => 1

[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => [8,7,5,6,4,3,2,1] => [5,8,7,6,4,3,2,1] => [7,1] => 1

[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]] => [7,8,5,6,4,3,2,1] => [5,7,8,6,4,3,2,1] => [6,1,1] => 1

[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]] => [8,6,5,7,4,3,2,1] => [6,8,5,7,4,3,2,1] => [6,1,1] => 1

[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]] => [8,5,6,7,4,3,2,1] => [5,6,8,7,4,3,2,1] => [6,1,1] => 1

[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]] => [7,6,5,8,4,3,2,1] => [7,6,5,8,4,3,2,1] => [7,1] => 1

[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]] => [6,7,5,8,4,3,2,1] => [6,7,5,8,4,3,2,1] => [6,1,1] => 1

[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]] => [7,5,6,8,4,3,2,1] => [5,7,6,8,4,3,2,1] => [6,1,1] => 1

[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]] => [6,5,7,8,4,3,2,1] => [6,5,7,8,4,3,2,1] => [6,1,1] => 1

[.,[.,[.,[.,[[[[.,.],.],.],.]]]]] => [5,6,7,8,4,3,2,1] => [5,6,7,8,4,3,2,1] => [5,1,1,1] => 1

[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => [8,7,6,4,5,3,2,1] => [4,8,7,6,5,3,2,1] => [7,1] => 1

[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] => [7,8,6,4,5,3,2,1] => [4,7,8,6,5,3,2,1] => [6,1,1] => 1

[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => [8,6,7,4,5,3,2,1] => [4,6,8,7,5,3,2,1] => [6,1,1] => 1

[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]] => [7,6,8,4,5,3,2,1] => [4,7,6,8,5,3,2,1] => [6,1,1] => 1

[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]] => [8,7,5,4,6,3,2,1] => [5,8,7,4,6,3,2,1] => [6,1,1] => 1

[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]] => [7,8,5,4,6,3,2,1] => [5,7,8,4,6,3,2,1] => [5,1,1,1] => 1

[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]] => [8,7,4,5,6,3,2,1] => [4,5,8,7,6,3,2,1] => [6,1,1] => 1

[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]] => [8,6,5,4,7,3,2,1] => [6,8,5,4,7,3,2,1] => [6,1,1] => 1

[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]] => [8,5,6,4,7,3,2,1] => [5,6,8,4,7,3,2,1] => [5,1,1,1] => 1

[.,[.,[.,[[[[.,.],.],.],[.,.]]]]] => [8,4,5,6,7,3,2,1] => [4,5,6,8,7,3,2,1] => [5,1,1,1] => 1

[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]] => [7,6,5,4,8,3,2,1] => [7,6,5,4,8,3,2,1] => [7,1] => 1

[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]] => [6,7,5,4,8,3,2,1] => [6,7,5,4,8,3,2,1] => [6,1,1] => 1

[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]] => [7,5,6,4,8,3,2,1] => [5,7,6,4,8,3,2,1] => [6,1,1] => 1

[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]] => [6,5,7,4,8,3,2,1] => [6,5,7,4,8,3,2,1] => [6,1,1] => 1

[.,[.,[.,[[.,[[[.,.],.],.]],.]]]] => [5,6,7,4,8,3,2,1] => [5,6,7,4,8,3,2,1] => [5,1,1,1] => 1

[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]] => [7,6,4,5,8,3,2,1] => [4,7,6,5,8,3,2,1] => [6,1,1] => 1

[.,[.,[.,[[[.,.],[[.,.],.]],.]]]] => [6,7,4,5,8,3,2,1] => [4,6,7,5,8,3,2,1] => [5,1,1,1] => 1

[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]] => [7,5,4,6,8,3,2,1] => [5,7,4,6,8,3,2,1] => [5,1,1,1] => 1

[.,[.,[.,[[[[.,.],.],[.,.]],.]]]] => [7,4,5,6,8,3,2,1] => [4,5,7,6,8,3,2,1] => [5,1,1,1] => 1

[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]] => [6,5,4,7,8,3,2,1] => [6,5,4,7,8,3,2,1] => [6,1,1] => 1

[.,[.,[.,[[[.,[[.,.],.]],.],.]]]] => [5,6,4,7,8,3,2,1] => [5,6,4,7,8,3,2,1] => [5,1,1,1] => 1

[.,[.,[.,[[[[.,.],[.,.]],.],.]]]] => [6,4,5,7,8,3,2,1] => [4,6,5,7,8,3,2,1] => [5,1,1,1] => 1

[.,[.,[.,[[[[.,[.,.]],.],.],.]]]] => [5,4,6,7,8,3,2,1] => [5,4,6,7,8,3,2,1] => [5,1,1,1] => 1

[.,[.,[.,[[[[[.,.],.],.],.],.]]]] => [4,5,6,7,8,3,2,1] => [4,5,6,7,8,3,2,1] => [4,1,1,1,1] => 1

[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => [8,7,6,5,3,4,2,1] => [3,8,7,6,5,4,2,1] => [7,1] => 1

[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => [7,8,6,5,3,4,2,1] => [3,7,8,6,5,4,2,1] => [6,1,1] => 1

[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => [8,6,7,5,3,4,2,1] => [3,6,8,7,5,4,2,1] => [6,1,1] => 1

[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]] => [7,6,8,5,3,4,2,1] => [3,7,6,8,5,4,2,1] => [6,1,1] => 1

[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [8,7,5,6,3,4,2,1] => [3,5,8,7,6,4,2,1] => [6,1,1] => 1

[.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => [7,8,5,6,3,4,2,1] => [3,5,7,8,6,4,2,1] => [5,1,1,1] => 1

[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]] => [8,6,5,7,3,4,2,1] => [3,6,8,5,7,4,2,1] => [5,1,1,1] => 1

[.,[.,[[.,.],[[[.,.],.],[.,.]]]]] => [8,5,6,7,3,4,2,1] => [3,5,6,8,7,4,2,1] => [5,1,1,1] => 1

[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]] => [7,6,5,8,3,4,2,1] => [3,7,6,5,8,4,2,1] => [6,1,1] => 1

[.,[.,[[.,.],[[[.,.],[.,.]],.]]]] => [7,5,6,8,3,4,2,1] => [3,5,7,6,8,4,2,1] => [5,1,1,1] => 1

[.,[.,[[.,.],[[[[.,.],.],.],.]]]] => [5,6,7,8,3,4,2,1] => [3,5,6,7,8,4,2,1] => [4,1,1,1,1] => 1

[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => [8,7,6,4,3,5,2,1] => [4,8,7,6,3,5,2,1] => [6,1,1] => 1

[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]] => [7,8,6,4,3,5,2,1] => [4,7,8,6,3,5,2,1] => [5,1,1,1] => 1

[.,[.,[[.,[.,.]],[[[.,.],.],.]]]] => [6,7,8,4,3,5,2,1] => [4,6,7,8,3,5,2,1] => [4,1,1,1,1] => 1

[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]] => [8,7,6,3,4,5,2,1] => [3,4,8,7,6,5,2,1] => [6,1,1] => 1

[.,[.,[[[.,.],.],[[[.,.],.],.]]]] => [6,7,8,3,4,5,2,1] => [3,4,6,7,8,5,2,1] => [4,1,1,1,1] => 1

[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => [8,7,5,4,3,6,2,1] => [5,8,7,4,3,6,2,1] => [6,1,1] => 1

[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]] => [7,8,5,4,3,6,2,1] => [5,7,8,4,3,6,2,1] => [5,1,1,1] => 1

[.,[.,[[.,[[.,.],.]],[.,[.,.]]]]] => [8,7,4,5,3,6,2,1] => [4,5,8,7,3,6,2,1] => [5,1,1,1] => 1

[.,[.,[[[.,.],[.,.]],[[.,.],.]]]] => [7,8,5,3,4,6,2,1] => [3,5,7,8,4,6,2,1] => [4,1,1,1,1] => 1

[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]] => [8,7,4,3,5,6,2,1] => [4,3,8,7,5,6,2,1] => [5,2,1] => 2

[.,[.,[[[.,[.,.]],.],[[.,.],.]]]] => [7,8,4,3,5,6,2,1] => [4,3,7,8,5,6,2,1] => [4,2,1,1] => 2

[.,[.,[[[[.,.],.],.],[.,[.,.]]]]] => [8,7,3,4,5,6,2,1] => [3,4,5,8,7,6,2,1] => [5,1,1,1] => 1

[.,[.,[[[[.,.],.],.],[[.,.],.]]]] => [7,8,3,4,5,6,2,1] => [3,4,5,7,8,6,2,1] => [4,1,1,1,1] => 1

[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]] => [8,6,5,4,3,7,2,1] => [6,8,5,4,3,7,2,1] => [6,1,1] => 1

[.,[.,[[.,[.,[[.,.],.]]],[.,.]]]] => [8,5,6,4,3,7,2,1] => [5,6,8,4,3,7,2,1] => [5,1,1,1] => 1

[.,[.,[[.,[[.,.],[.,.]]],[.,.]]]] => [8,6,4,5,3,7,2,1] => [4,6,8,5,3,7,2,1] => [5,1,1,1] => 1

[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]] => [8,5,4,6,3,7,2,1] => [5,4,8,6,3,7,2,1] => [5,2,1] => 2

[.,[.,[[[.,.],[[.,.],.]],[.,.]]]] => [8,5,6,3,4,7,2,1] => [3,5,6,8,4,7,2,1] => [4,1,1,1,1] => 1

[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]] => [8,6,4,3,5,7,2,1] => [4,6,8,3,5,7,2,1] => [4,1,1,1,1] => 1

[.,[.,[[[[.,.],.],[.,.]],[.,.]]]] => [8,6,3,4,5,7,2,1] => [3,4,6,8,5,7,2,1] => [4,1,1,1,1] => 1

[.,[.,[[[[.,[.,.]],.],.],[.,.]]]] => [8,4,3,5,6,7,2,1] => [4,3,5,8,6,7,2,1] => [4,2,1,1] => 2

[.,[.,[[[[[.,.],.],.],.],[.,.]]]] => [8,3,4,5,6,7,2,1] => [3,4,5,6,8,7,2,1] => [4,1,1,1,1] => 1

[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]] => [7,6,5,4,3,8,2,1] => [7,6,5,4,3,8,2,1] => [7,1] => 1

[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]] => [6,7,5,4,3,8,2,1] => [6,7,5,4,3,8,2,1] => [6,1,1] => 1

[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]] => [7,5,6,4,3,8,2,1] => [5,7,6,4,3,8,2,1] => [6,1,1] => 1

[.,[.,[[.,[.,[[[.,.],.],.]]],.]]] => [5,6,7,4,3,8,2,1] => [5,6,7,4,3,8,2,1] => [5,1,1,1] => 1

[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]] => [7,6,4,5,3,8,2,1] => [4,7,6,5,3,8,2,1] => [6,1,1] => 1

[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]] => [7,5,4,6,3,8,2,1] => [5,7,4,6,3,8,2,1] => [5,1,1,1] => 1

[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]] => [6,5,4,7,3,8,2,1] => [6,5,4,7,3,8,2,1] => [6,1,1] => 1

[.,[.,[[.,[[[.,[.,.]],.],.]],.]]] => [5,4,6,7,3,8,2,1] => [5,4,6,7,3,8,2,1] => [5,1,1,1] => 1

[.,[.,[[.,[[[[.,.],.],.],.]],.]]] => [4,5,6,7,3,8,2,1] => [4,5,6,7,3,8,2,1] => [4,1,1,1,1] => 1

[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]] => [7,6,5,3,4,8,2,1] => [3,7,6,5,4,8,2,1] => [6,1,1] => 1

[.,[.,[[[.,.],[[[.,.],.],.]],.]]] => [5,6,7,3,4,8,2,1] => [3,5,6,7,4,8,2,1] => [4,1,1,1,1] => 1

[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]] => [7,6,4,3,5,8,2,1] => [4,7,6,3,5,8,2,1] => [5,1,1,1] => 1

[.,[.,[[[[.,.],.],[.,[.,.]]],.]]] => [7,6,3,4,5,8,2,1] => [3,4,7,6,5,8,2,1] => [5,1,1,1] => 1

[.,[.,[[[.,[.,[.,.]]],[.,.]],.]]] => [7,5,4,3,6,8,2,1] => [5,7,4,3,6,8,2,1] => [5,1,1,1] => 1

[.,[.,[[[.,[[.,.],.]],[.,.]],.]]] => [7,4,5,3,6,8,2,1] => [4,5,7,3,6,8,2,1] => [4,1,1,1,1] => 1

[.,[.,[[[[.,.],[.,.]],[.,.]],.]]] => [7,5,3,4,6,8,2,1] => [3,5,7,4,6,8,2,1] => [4,1,1,1,1] => 1

[.,[.,[[[[.,[.,.]],.],[.,.]],.]]] => [7,4,3,5,6,8,2,1] => [4,3,7,5,6,8,2,1] => [4,2,1,1] => 2

[.,[.,[[[[[.,.],.],.],[.,.]],.]]] => [7,3,4,5,6,8,2,1] => [3,4,5,7,6,8,2,1] => [4,1,1,1,1] => 1

[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]] => [6,5,4,3,7,8,2,1] => [6,5,4,3,7,8,2,1] => [6,1,1] => 1

[.,[.,[[[[.,.],[.,[.,.]]],.],.]]] => [6,5,3,4,7,8,2,1] => [3,6,5,4,7,8,2,1] => [5,1,1,1] => 1

[.,[.,[[[[.,[.,.]],[.,.]],.],.]]] => [6,4,3,5,7,8,2,1] => [4,6,3,5,7,8,2,1] => [4,1,1,1,1] => 1

[.,[.,[[[[[.,.],.],[.,.]],.],.]]] => [6,3,4,5,7,8,2,1] => [3,4,6,5,7,8,2,1] => [4,1,1,1,1] => 1

[.,[.,[[[[.,[.,[.,.]]],.],.],.]]] => [5,4,3,6,7,8,2,1] => [5,4,3,6,7,8,2,1] => [5,1,1,1] => 1

[.,[.,[[[[[.,.],[.,.]],.],.],.]]] => [5,3,4,6,7,8,2,1] => [3,5,4,6,7,8,2,1] => [4,1,1,1,1] => 1

[.,[.,[[[[[.,[.,.]],.],.],.],.]]] => [4,3,5,6,7,8,2,1] => [4,3,5,6,7,8,2,1] => [4,1,1,1,1] => 1

[.,[.,[[[[[[.,.],.],.],.],.],.]]] => [3,4,5,6,7,8,2,1] => [3,4,5,6,7,8,2,1] => [3,1,1,1,1,1] => 1

[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [8,7,6,5,4,2,3,1] => [2,8,7,6,5,4,3,1] => [7,1] => 1

[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => [7,8,6,5,4,2,3,1] => [2,7,8,6,5,4,3,1] => [6,1,1] => 1

[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [8,6,7,5,4,2,3,1] => [2,6,8,7,5,4,3,1] => [6,1,1] => 1

[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]] => [7,6,8,5,4,2,3,1] => [2,7,6,8,5,4,3,1] => [6,1,1] => 1

[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [8,7,5,6,4,2,3,1] => [2,5,8,7,6,4,3,1] => [6,1,1] => 1

[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]] => [8,6,5,7,4,2,3,1] => [2,6,8,5,7,4,3,1] => [5,1,1,1] => 1

[.,[[.,.],[.,[[.,[[.,.],.]],.]]]] => [6,7,5,8,4,2,3,1] => [2,6,7,5,8,4,3,1] => [5,1,1,1] => 1

[.,[[.,.],[.,[[[.,[.,.]],.],.]]]] => [6,5,7,8,4,2,3,1] => [2,6,5,7,8,4,3,1] => [5,1,1,1] => 1

[.,[[.,.],[.,[[[[.,.],.],.],.]]]] => [5,6,7,8,4,2,3,1] => [2,5,6,7,8,4,3,1] => [4,1,1,1,1] => 1

[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [8,7,6,4,5,2,3,1] => [2,4,8,7,6,5,3,1] => [6,1,1] => 1

[.,[[.,.],[[.,.],[.,[[.,.],.]]]]] => [7,8,6,4,5,2,3,1] => [2,4,7,8,6,5,3,1] => [5,1,1,1] => 1

[.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [8,6,7,4,5,2,3,1] => [2,4,6,8,7,5,3,1] => [5,1,1,1] => 1

[.,[[.,.],[[.,.],[[[.,.],.],.]]]] => [6,7,8,4,5,2,3,1] => [2,4,6,7,8,5,3,1] => [4,1,1,1,1] => 1

[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => [8,7,5,4,6,2,3,1] => [2,5,8,7,4,6,3,1] => [5,1,1,1] => 1

[.,[[.,.],[[[.,.],.],[[.,.],.]]]] => [7,8,4,5,6,2,3,1] => [2,4,5,7,8,6,3,1] => [4,1,1,1,1] => 1

[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]] => [8,6,5,4,7,2,3,1] => [2,6,8,5,4,7,3,1] => [5,1,1,1] => 1

[.,[[.,.],[[[.,.],[.,.]],[.,.]]]] => [8,6,4,5,7,2,3,1] => [2,4,6,8,5,7,3,1] => [4,1,1,1,1] => 1

[.,[[.,.],[[[[.,.],.],.],[.,.]]]] => [8,4,5,6,7,2,3,1] => [2,4,5,6,8,7,3,1] => [4,1,1,1,1] => 1

[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]] => [7,6,5,4,8,2,3,1] => [2,7,6,5,4,8,3,1] => [6,1,1] => 1

[.,[[.,.],[[.,[.,[[.,.],.]]],.]]] => [6,7,5,4,8,2,3,1] => [2,6,7,5,4,8,3,1] => [5,1,1,1] => 1

[.,[[.,.],[[.,[[[.,.],.],.]],.]]] => [5,6,7,4,8,2,3,1] => [2,5,6,7,4,8,3,1] => [4,1,1,1,1] => 1

[.,[[.,.],[[[.,.],[.,[.,.]]],.]]] => [7,6,4,5,8,2,3,1] => [2,4,7,6,5,8,3,1] => [5,1,1,1] => 1

[.,[[.,.],[[[.,.],[[.,.],.]],.]]] => [6,7,4,5,8,2,3,1] => [2,4,6,7,5,8,3,1] => [4,1,1,1,1] => 1

[.,[[.,.],[[[.,[.,.]],[.,.]],.]]] => [7,5,4,6,8,2,3,1] => [2,5,7,4,6,8,3,1] => [4,1,1,1,1] => 1

[.,[[.,.],[[[.,[.,[.,.]]],.],.]]] => [6,5,4,7,8,2,3,1] => [2,6,5,4,7,8,3,1] => [5,1,1,1] => 1

[.,[[.,.],[[[.,[[.,.],.]],.],.]]] => [5,6,4,7,8,2,3,1] => [2,5,6,4,7,8,3,1] => [4,1,1,1,1] => 1

[.,[[.,.],[[[[.,.],[.,.]],.],.]]] => [6,4,5,7,8,2,3,1] => [2,4,6,5,7,8,3,1] => [4,1,1,1,1] => 1

[.,[[.,.],[[[[.,[.,.]],.],.],.]]] => [5,4,6,7,8,2,3,1] => [2,5,4,6,7,8,3,1] => [4,1,1,1,1] => 1

[.,[[.,.],[[[[[.,.],.],.],.],.]]] => [4,5,6,7,8,2,3,1] => [2,4,5,6,7,8,3,1] => [3,1,1,1,1,1] => 1

[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [8,7,6,5,3,2,4,1] => [3,8,7,6,5,2,4,1] => [6,1,1] => 1

[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => [7,8,6,5,3,2,4,1] => [3,7,8,6,5,2,4,1] => [5,1,1,1] => 1

[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [8,6,7,5,3,2,4,1] => [3,6,8,7,5,2,4,1] => [5,1,1,1] => 1

[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]] => [7,6,8,5,3,2,4,1] => [3,7,6,8,5,2,4,1] => [5,1,1,1] => 1

[.,[[.,[.,.]],[.,[[[.,.],.],.]]]] => [6,7,8,5,3,2,4,1] => [3,6,7,8,5,2,4,1] => [4,1,1,1,1] => 1

[.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [7,8,5,6,3,2,4,1] => [3,5,7,8,6,2,4,1] => [4,1,1,1,1] => 1

[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [8,6,5,7,3,2,4,1] => [3,6,8,5,7,2,4,1] => [4,1,1,1,1] => 1

[.,[[.,[.,.]],[[[.,.],.],[.,.]]]] => [8,5,6,7,3,2,4,1] => [3,5,6,8,7,2,4,1] => [4,1,1,1,1] => 1

[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]] => [7,6,5,8,3,2,4,1] => [3,7,6,5,8,2,4,1] => [5,1,1,1] => 1

[.,[[.,[.,.]],[[.,[[.,.],.]],.]]] => [6,7,5,8,3,2,4,1] => [3,6,7,5,8,2,4,1] => [4,1,1,1,1] => 1

[.,[[.,[.,.]],[[[.,.],[.,.]],.]]] => [7,5,6,8,3,2,4,1] => [3,5,7,6,8,2,4,1] => [4,1,1,1,1] => 1

[.,[[.,[.,.]],[[[.,[.,.]],.],.]]] => [6,5,7,8,3,2,4,1] => [3,6,5,7,8,2,4,1] => [4,1,1,1,1] => 1

[.,[[.,[.,.]],[[[[.,.],.],.],.]]] => [5,6,7,8,3,2,4,1] => [3,5,6,7,8,2,4,1] => [3,1,1,1,1,1] => 1

[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [8,7,6,5,2,3,4,1] => [2,3,8,7,6,5,4,1] => [6,1,1] => 1

[.,[[[.,.],.],[.,[[[.,.],.],.]]]] => [6,7,8,5,2,3,4,1] => [2,3,6,7,8,5,4,1] => [4,1,1,1,1] => 1

[.,[[[.,.],.],[[.,.],[[.,.],.]]]] => [7,8,5,6,2,3,4,1] => [2,3,5,7,8,6,4,1] => [4,1,1,1,1] => 1

[.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [8,5,6,7,2,3,4,1] => [2,3,5,6,8,7,4,1] => [4,1,1,1,1] => 1

[.,[[[.,.],.],[[.,[.,[.,.]]],.]]] => [7,6,5,8,2,3,4,1] => [2,3,7,6,5,8,4,1] => [5,1,1,1] => 1

[.,[[[.,.],.],[[[[.,.],.],.],.]]] => [5,6,7,8,2,3,4,1] => [2,3,5,6,7,8,4,1] => [3,1,1,1,1,1] => 1

[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [8,7,6,4,3,2,5,1] => [4,8,7,6,3,2,5,1] => [6,1,1] => 1

[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]] => [7,6,8,4,3,2,5,1] => [4,7,6,8,3,2,5,1] => [5,1,1,1] => 1

[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]] => [8,7,6,3,4,2,5,1] => [3,4,8,7,6,2,5,1] => [5,1,1,1] => 1

[.,[[.,[[.,.],.]],[.,[[.,.],.]]]] => [7,8,6,3,4,2,5,1] => [3,4,7,8,6,2,5,1] => [4,1,1,1,1] => 1

[.,[[.,[[.,.],.]],[[.,.],[.,.]]]] => [8,6,7,3,4,2,5,1] => [3,4,6,8,7,2,5,1] => [4,1,1,1,1] => 1

[.,[[.,[[.,.],.]],[[.,[.,.]],.]]] => [7,6,8,3,4,2,5,1] => [3,4,7,6,8,2,5,1] => [4,1,1,1,1] => 1

[.,[[.,[[.,.],.]],[[[.,.],.],.]]] => [6,7,8,3,4,2,5,1] => [3,4,6,7,8,2,5,1] => [3,1,1,1,1,1] => 1

[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => [8,7,6,4,2,3,5,1] => [2,4,8,7,6,3,5,1] => [5,1,1,1] => 1

[.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [8,6,7,4,2,3,5,1] => [2,4,6,8,7,3,5,1] => [4,1,1,1,1] => 1

[.,[[[.,.],[.,.]],[[.,[.,.]],.]]] => [7,6,8,4,2,3,5,1] => [2,4,7,6,8,3,5,1] => [4,1,1,1,1] => 1

[.,[[[.,.],[.,.]],[[[.,.],.],.]]] => [6,7,8,4,2,3,5,1] => [2,4,6,7,8,3,5,1] => [3,1,1,1,1,1] => 1

[.,[[[.,[.,.]],.],[.,[[.,.],.]]]] => [7,8,6,3,2,4,5,1] => [3,2,7,8,6,4,5,1] => [4,2,1,1] => 2

[.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [8,6,7,3,2,4,5,1] => [3,2,6,8,7,4,5,1] => [4,2,1,1] => 2

[.,[[[.,[.,.]],.],[[[.,.],.],.]]] => [6,7,8,3,2,4,5,1] => [3,2,6,7,8,4,5,1] => [3,2,1,1,1] => 2

[.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [8,7,6,2,3,4,5,1] => [2,3,4,8,7,6,5,1] => [5,1,1,1] => 1

[.,[[[[.,.],.],.],[[.,.],[.,.]]]] => [8,6,7,2,3,4,5,1] => [2,3,4,6,8,7,5,1] => [4,1,1,1,1] => 1

[.,[[[[.,.],.],.],[[.,[.,.]],.]]] => [7,6,8,2,3,4,5,1] => [2,3,4,7,6,8,5,1] => [4,1,1,1,1] => 1

[.,[[[[.,.],.],.],[[[.,.],.],.]]] => [6,7,8,2,3,4,5,1] => [2,3,4,6,7,8,5,1] => [3,1,1,1,1,1] => 1

[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]] => [7,8,5,4,3,2,6,1] => [5,7,8,4,3,2,6,1] => [5,1,1,1] => 1

[.,[[.,[[.,.],[.,.]]],[[.,.],.]]] => [7,8,5,3,4,2,6,1] => [3,5,7,8,4,2,6,1] => [4,1,1,1,1] => 1

[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]] => [8,7,4,3,5,2,6,1] => [4,3,8,7,5,2,6,1] => [5,2,1] => 2

[.,[[.,[[[.,.],.],.]],[[.,.],.]]] => [7,8,3,4,5,2,6,1] => [3,4,5,7,8,2,6,1] => [3,1,1,1,1,1] => 1

[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]] => [8,7,5,4,2,3,6,1] => [2,5,8,7,4,3,6,1] => [5,1,1,1] => 1

[.,[[[.,.],[.,[.,.]]],[[.,.],.]]] => [7,8,5,4,2,3,6,1] => [2,5,7,8,4,3,6,1] => [4,1,1,1,1] => 1

[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [8,7,5,3,2,4,6,1] => [3,5,8,7,2,4,6,1] => [4,1,1,1,1] => 1

[.,[[[[.,.],.],[.,.]],[[.,.],.]]] => [7,8,5,2,3,4,6,1] => [2,3,5,7,8,4,6,1] => [3,1,1,1,1,1] => 1

[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]] => [8,7,4,3,2,5,6,1] => [4,3,8,7,2,5,6,1] => [4,2,1,1] => 2

[.,[[[[.,.],[.,.]],.],[[.,.],.]]] => [7,8,4,2,3,5,6,1] => [2,4,3,7,8,5,6,1] => [3,2,1,1,1] => 2

[.,[[[[.,[.,.]],.],.],[[.,.],.]]] => [7,8,3,2,4,5,6,1] => [3,2,4,7,8,5,6,1] => [3,2,1,1,1] => 2

[.,[[[[[.,.],.],.],.],[.,[.,.]]]] => [8,7,2,3,4,5,6,1] => [2,3,4,5,8,7,6,1] => [4,1,1,1,1] => 1

[.,[[[[[.,.],.],.],.],[[.,.],.]]] => [7,8,2,3,4,5,6,1] => [2,3,4,5,7,8,6,1] => [3,1,1,1,1,1] => 1

[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]] => [8,6,5,4,3,2,7,1] => [6,8,5,4,3,2,7,1] => [6,1,1] => 1

[.,[[.,[.,[.,[[.,.],.]]]],[.,.]]] => [8,5,6,4,3,2,7,1] => [5,6,8,4,3,2,7,1] => [5,1,1,1] => 1

[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]] => [8,6,4,5,3,2,7,1] => [4,6,8,5,3,2,7,1] => [5,1,1,1] => 1

[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]] => [8,6,5,3,4,2,7,1] => [3,6,8,5,4,2,7,1] => [5,1,1,1] => 1

[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]] => [8,6,4,3,5,2,7,1] => [4,6,8,3,5,2,7,1] => [4,1,1,1,1] => 1

[.,[[.,[[[.,.],.],[.,.]]],[.,.]]] => [8,6,3,4,5,2,7,1] => [3,4,6,8,5,2,7,1] => [4,1,1,1,1] => 1

[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]] => [8,5,4,3,6,2,7,1] => [5,4,8,3,6,2,7,1] => [5,1,1,1] => 1

[.,[[.,[[.,[[.,.],.]],.]],[.,.]]] => [8,4,5,3,6,2,7,1] => [4,5,3,8,6,2,7,1] => [4,2,1,1] => 2

[.,[[.,[[[.,.],[.,.]],.]],[.,.]]] => [8,5,3,4,6,2,7,1] => [3,5,4,8,6,2,7,1] => [4,2,1,1] => 2

[.,[[.,[[[[.,.],.],.],.]],[.,.]]] => [8,3,4,5,6,2,7,1] => [3,4,5,6,8,2,7,1] => [3,1,1,1,1,1] => 1

[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [8,6,5,4,2,3,7,1] => [2,6,8,5,4,3,7,1] => [5,1,1,1] => 1

[.,[[[.,.],[.,[[.,.],.]]],[.,.]]] => [8,5,6,4,2,3,7,1] => [2,5,6,8,4,3,7,1] => [4,1,1,1,1] => 1

[.,[[[.,.],[[.,.],[.,.]]],[.,.]]] => [8,6,4,5,2,3,7,1] => [2,4,6,8,5,3,7,1] => [4,1,1,1,1] => 1

[.,[[[.,.],[[.,[.,.]],.]],[.,.]]] => [8,5,4,6,2,3,7,1] => [2,5,4,8,6,3,7,1] => [4,2,1,1] => 2

[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [8,6,5,3,2,4,7,1] => [3,6,8,5,2,4,7,1] => [4,1,1,1,1] => 1

[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]] => [8,6,4,3,2,5,7,1] => [4,6,8,3,2,5,7,1] => [4,1,1,1,1] => 1

[.,[[[.,[[.,.],.]],[.,.]],[.,.]]] => [8,6,3,4,2,5,7,1] => [3,4,6,8,2,5,7,1] => [3,1,1,1,1,1] => 1

[.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => [8,6,4,2,3,5,7,1] => [2,4,6,8,3,5,7,1] => [3,1,1,1,1,1] => 1

[.,[[[[[.,.],.],.],[.,.]],[.,.]]] => [8,6,2,3,4,5,7,1] => [2,3,4,6,8,5,7,1] => [3,1,1,1,1,1] => 1

[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]] => [8,5,4,3,2,6,7,1] => [5,4,8,3,2,6,7,1] => [5,1,1,1] => 1

[.,[[[.,[[.,.],[.,.]]],.],[.,.]]] => [8,5,3,4,2,6,7,1] => [3,5,4,8,2,6,7,1] => [4,1,1,1,1] => 1

[.,[[[[.,.],[.,[.,.]]],.],[.,.]]] => [8,5,4,2,3,6,7,1] => [2,5,4,8,3,6,7,1] => [4,1,1,1,1] => 1

[.,[[[[.,.],[[.,.],.]],.],[.,.]]] => [8,4,5,2,3,6,7,1] => [2,4,5,3,8,6,7,1] => [3,2,1,1,1] => 2

[.,[[[[[.,.],.],[.,.]],.],[.,.]]] => [8,5,2,3,4,6,7,1] => [2,3,5,4,8,6,7,1] => [3,2,1,1,1] => 2

[.,[[[[.,[.,[.,.]]],.],.],[.,.]]] => [8,4,3,2,5,6,7,1] => [4,3,2,8,5,6,7,1] => [4,2,1,1] => 2

[.,[[[[.,[[.,.],.]],.],.],[.,.]]] => [8,3,4,2,5,6,7,1] => [3,4,2,5,8,6,7,1] => [3,2,1,1,1] => 2

[.,[[[[[.,.],[.,.]],.],.],[.,.]]] => [8,4,2,3,5,6,7,1] => [2,4,3,5,8,6,7,1] => [3,2,1,1,1] => 2

[.,[[[[[.,[.,.]],.],.],.],[.,.]]] => [8,3,2,4,5,6,7,1] => [3,2,4,5,8,6,7,1] => [3,2,1,1,1] => 2

[.,[[[[[[.,.],.],.],.],.],[.,.]]] => [8,2,3,4,5,6,7,1] => [2,3,4,5,6,8,7,1] => [3,1,1,1,1,1] => 1

[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [7,6,5,4,3,2,8,1] => [7,6,5,4,3,2,8,1] => [7,1] => 1

[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]] => [6,7,5,4,3,2,8,1] => [6,7,5,4,3,2,8,1] => [6,1,1] => 1

[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]] => [7,5,6,4,3,2,8,1] => [5,7,6,4,3,2,8,1] => [6,1,1] => 1

[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]] => [6,5,7,4,3,2,8,1] => [6,5,7,4,3,2,8,1] => [6,1,1] => 1

[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]] => [7,6,4,5,3,2,8,1] => [4,7,6,5,3,2,8,1] => [6,1,1] => 1

[.,[[.,[.,[[.,.],[[.,.],.]]]],.]] => [6,7,4,5,3,2,8,1] => [4,6,7,5,3,2,8,1] => [5,1,1,1] => 1

[.,[[.,[.,[[[.,.],[.,.]],.]]],.]] => [6,4,5,7,3,2,8,1] => [4,6,5,7,3,2,8,1] => [5,1,1,1] => 1

[.,[[.,[.,[[[[.,.],.],.],.]]],.]] => [4,5,6,7,3,2,8,1] => [4,5,6,7,3,2,8,1] => [4,1,1,1,1] => 1

[.,[[.,[[.,.],[[.,.],[.,.]]]],.]] => [7,5,6,3,4,2,8,1] => [3,5,7,6,4,2,8,1] => [5,1,1,1] => 1

[.,[[.,[[.,.],[[[.,.],.],.]]],.]] => [5,6,7,3,4,2,8,1] => [3,5,6,7,4,2,8,1] => [4,1,1,1,1] => 1

[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]] => [7,6,4,3,5,2,8,1] => [4,7,6,3,5,2,8,1] => [5,1,1,1] => 1

[.,[[.,[[[.,.],.],[.,[.,.]]]],.]] => [7,6,3,4,5,2,8,1] => [3,4,7,6,5,2,8,1] => [5,1,1,1] => 1

[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]] => [7,5,4,3,6,2,8,1] => [5,7,4,3,6,2,8,1] => [5,1,1,1] => 1

[.,[[.,[[.,[[.,.],.]],[.,.]]],.]] => [7,4,5,3,6,2,8,1] => [4,5,7,3,6,2,8,1] => [4,1,1,1,1] => 1

[.,[[.,[[[.,.],[.,.]],[.,.]]],.]] => [7,5,3,4,6,2,8,1] => [3,5,7,4,6,2,8,1] => [4,1,1,1,1] => 1

[.,[[.,[[[[.,.],.],.],[.,.]]],.]] => [7,3,4,5,6,2,8,1] => [3,4,5,7,6,2,8,1] => [4,1,1,1,1] => 1

[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]] => [6,5,4,3,7,2,8,1] => [6,5,4,3,7,2,8,1] => [6,1,1] => 1

[.,[[.,[[.,[[.,.],[.,.]]],.]],.]] => [6,4,5,3,7,2,8,1] => [4,6,5,3,7,2,8,1] => [5,1,1,1] => 1

[.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => [5,4,6,3,7,2,8,1] => [5,4,6,3,7,2,8,1] => [5,1,1,1] => 1

[.,[[.,[[.,[[[.,.],.],.]],.]],.]] => [4,5,6,3,7,2,8,1] => [4,5,6,3,7,2,8,1] => [4,1,1,1,1] => 1

[.,[[.,[[[.,.],[.,[.,.]]],.]],.]] => [6,5,3,4,7,2,8,1] => [3,6,5,4,7,2,8,1] => [5,1,1,1] => 1

[.,[[.,[[[.,.],[[.,.],.]],.]],.]] => [5,6,3,4,7,2,8,1] => [3,5,6,4,7,2,8,1] => [4,1,1,1,1] => 1

[.,[[.,[[[.,[.,.]],[.,.]],.]],.]] => [6,4,3,5,7,2,8,1] => [4,6,3,5,7,2,8,1] => [4,1,1,1,1] => 1

[.,[[.,[[[[.,.],.],[.,.]],.]],.]] => [6,3,4,5,7,2,8,1] => [3,4,6,5,7,2,8,1] => [4,1,1,1,1] => 1

[.,[[.,[[[.,[.,[.,.]]],.],.]],.]] => [5,4,3,6,7,2,8,1] => [5,4,3,6,7,2,8,1] => [5,1,1,1] => 1

[.,[[.,[[[.,[[.,.],.]],.],.]],.]] => [4,5,3,6,7,2,8,1] => [4,5,3,6,7,2,8,1] => [4,1,1,1,1] => 1

[.,[[.,[[[[.,.],[.,.]],.],.]],.]] => [5,3,4,6,7,2,8,1] => [3,5,4,6,7,2,8,1] => [4,1,1,1,1] => 1

[.,[[.,[[[[[.,.],.],.],.],.]],.]] => [3,4,5,6,7,2,8,1] => [3,4,5,6,7,2,8,1] => [3,1,1,1,1,1] => 1

[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]] => [7,6,5,4,2,3,8,1] => [2,7,6,5,4,3,8,1] => [6,1,1] => 1

[.,[[[.,.],[.,[[.,[.,.]],.]]],.]] => [6,5,7,4,2,3,8,1] => [2,6,5,7,4,3,8,1] => [5,1,1,1] => 1

[.,[[[.,.],[.,[[[.,.],.],.]]],.]] => [5,6,7,4,2,3,8,1] => [2,5,6,7,4,3,8,1] => [4,1,1,1,1] => 1

[.,[[[.,.],[[.,.],[[.,.],.]]],.]] => [6,7,4,5,2,3,8,1] => [2,4,6,7,5,3,8,1] => [4,1,1,1,1] => 1

[.,[[[.,.],[[.,[.,.]],[.,.]]],.]] => [7,5,4,6,2,3,8,1] => [2,5,7,4,6,3,8,1] => [4,1,1,1,1] => 1

[.,[[[.,.],[[[.,.],[.,.]],.]],.]] => [6,4,5,7,2,3,8,1] => [2,4,6,5,7,3,8,1] => [4,1,1,1,1] => 1

[.,[[[.,.],[[[.,[.,.]],.],.]],.]] => [5,4,6,7,2,3,8,1] => [2,5,4,6,7,3,8,1] => [4,1,1,1,1] => 1

[.,[[[.,.],[[[[.,.],.],.],.]],.]] => [4,5,6,7,2,3,8,1] => [2,4,5,6,7,3,8,1] => [3,1,1,1,1,1] => 1

[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]] => [7,6,5,3,2,4,8,1] => [3,7,6,5,2,4,8,1] => [5,1,1,1] => 1

[.,[[[.,[.,.]],[.,[[.,.],.]]],.]] => [6,7,5,3,2,4,8,1] => [3,6,7,5,2,4,8,1] => [4,1,1,1,1] => 1

[.,[[[.,[.,.]],[[.,.],[.,.]]],.]] => [7,5,6,3,2,4,8,1] => [3,5,7,6,2,4,8,1] => [4,1,1,1,1] => 1

[.,[[[[.,.],.],[.,[.,[.,.]]]],.]] => [7,6,5,2,3,4,8,1] => [2,3,7,6,5,4,8,1] => [5,1,1,1] => 1

[.,[[[[.,.],.],[[.,.],[.,.]]],.]] => [7,5,6,2,3,4,8,1] => [2,3,5,7,6,4,8,1] => [4,1,1,1,1] => 1

[.,[[[[.,.],.],[[[.,.],.],.]],.]] => [5,6,7,2,3,4,8,1] => [2,3,5,6,7,4,8,1] => [3,1,1,1,1,1] => 1

[.,[[[.,[.,[.,.]]],[[.,.],.]],.]] => [6,7,4,3,2,5,8,1] => [4,6,7,3,2,5,8,1] => [4,1,1,1,1] => 1

[.,[[[.,[[.,.],.]],[.,[.,.]]],.]] => [7,6,3,4,2,5,8,1] => [3,4,7,6,2,5,8,1] => [4,1,1,1,1] => 1

[.,[[[[.,[.,.]],.],[.,[.,.]]],.]] => [7,6,3,2,4,5,8,1] => [3,2,7,6,4,5,8,1] => [4,2,1,1] => 2

[.,[[[[[.,.],.],.],[.,[.,.]]],.]] => [7,6,2,3,4,5,8,1] => [2,3,4,7,6,5,8,1] => [4,1,1,1,1] => 1

[.,[[[[[.,.],.],.],[[.,.],.]],.]] => [6,7,2,3,4,5,8,1] => [2,3,4,6,7,5,8,1] => [3,1,1,1,1,1] => 1

[.,[[[.,[.,[[.,.],.]]],[.,.]],.]] => [7,4,5,3,2,6,8,1] => [4,5,7,3,2,6,8,1] => [4,1,1,1,1] => 1

[.,[[[.,[[.,.],[.,.]]],[.,.]],.]] => [7,5,3,4,2,6,8,1] => [3,5,7,4,2,6,8,1] => [4,1,1,1,1] => 1

[.,[[[.,[[[.,.],.],.]],[.,.]],.]] => [7,3,4,5,2,6,8,1] => [3,4,5,7,2,6,8,1] => [3,1,1,1,1,1] => 1

[.,[[[[.,.],[[.,.],.]],[.,.]],.]] => [7,4,5,2,3,6,8,1] => [2,4,5,7,3,6,8,1] => [3,1,1,1,1,1] => 1

[.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => [7,5,3,2,4,6,8,1] => [3,5,7,2,4,6,8,1] => [3,1,1,1,1,1] => 1

[.,[[[[[.,.],.],[.,.]],[.,.]],.]] => [7,5,2,3,4,6,8,1] => [2,3,5,7,4,6,8,1] => [3,1,1,1,1,1] => 1

[.,[[[[.,[.,[.,.]]],.],[.,.]],.]] => [7,4,3,2,5,6,8,1] => [4,3,7,2,5,6,8,1] => [4,1,1,1,1] => 1

[.,[[[[[.,.],[.,.]],.],[.,.]],.]] => [7,4,2,3,5,6,8,1] => [2,4,3,7,5,6,8,1] => [3,2,1,1,1] => 2

[.,[[[[[.,[.,.]],.],.],[.,.]],.]] => [7,3,2,4,5,6,8,1] => [3,2,4,7,5,6,8,1] => [3,2,1,1,1] => 2

[.,[[[[[[.,.],.],.],.],[.,.]],.]] => [7,2,3,4,5,6,8,1] => [2,3,4,5,7,6,8,1] => [3,1,1,1,1,1] => 1

[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]] => [6,5,4,3,2,7,8,1] => [6,5,4,3,2,7,8,1] => [6,1,1] => 1

[.,[[[.,[.,[[.,[.,.]],.]]],.],.]] => [5,4,6,3,2,7,8,1] => [5,4,6,3,2,7,8,1] => [5,1,1,1] => 1

[.,[[[.,[.,[[[.,.],.],.]]],.],.]] => [4,5,6,3,2,7,8,1] => [4,5,6,3,2,7,8,1] => [4,1,1,1,1] => 1

[.,[[[.,[[.,.],[.,[.,.]]]],.],.]] => [6,5,3,4,2,7,8,1] => [3,6,5,4,2,7,8,1] => [5,1,1,1] => 1

[.,[[[.,[[.,.],[[.,.],.]]],.],.]] => [5,6,3,4,2,7,8,1] => [3,5,6,4,2,7,8,1] => [4,1,1,1,1] => 1

[.,[[[.,[[[.,.],.],[.,.]]],.],.]] => [6,3,4,5,2,7,8,1] => [3,4,6,5,2,7,8,1] => [4,1,1,1,1] => 1

[.,[[[.,[[.,[.,[.,.]]],.]],.],.]] => [5,4,3,6,2,7,8,1] => [5,4,3,6,2,7,8,1] => [5,1,1,1] => 1

[.,[[[.,[[[.,.],[.,.]],.]],.],.]] => [5,3,4,6,2,7,8,1] => [3,5,4,6,2,7,8,1] => [4,1,1,1,1] => 1

[.,[[[.,[[[.,[.,.]],.],.]],.],.]] => [4,3,5,6,2,7,8,1] => [4,3,5,6,2,7,8,1] => [4,1,1,1,1] => 1

[.,[[[.,[[[[.,.],.],.],.]],.],.]] => [3,4,5,6,2,7,8,1] => [3,4,5,6,2,7,8,1] => [3,1,1,1,1,1] => 1

[.,[[[[.,.],[.,[.,[.,.]]]],.],.]] => [6,5,4,2,3,7,8,1] => [2,6,5,4,3,7,8,1] => [5,1,1,1] => 1

[.,[[[[.,.],[.,[[.,.],.]]],.],.]] => [5,6,4,2,3,7,8,1] => [2,5,6,4,3,7,8,1] => [4,1,1,1,1] => 1

[.,[[[[.,.],[[.,.],[.,.]]],.],.]] => [6,4,5,2,3,7,8,1] => [2,4,6,5,3,7,8,1] => [4,1,1,1,1] => 1

[.,[[[[.,.],[[.,[.,.]],.]],.],.]] => [5,4,6,2,3,7,8,1] => [2,5,4,6,3,7,8,1] => [4,1,1,1,1] => 1

[.,[[[[.,.],[[[.,.],.],.]],.],.]] => [4,5,6,2,3,7,8,1] => [2,4,5,6,3,7,8,1] => [3,1,1,1,1,1] => 1

[.,[[[[.,[.,.]],[.,[.,.]]],.],.]] => [6,5,3,2,4,7,8,1] => [3,6,5,2,4,7,8,1] => [4,1,1,1,1] => 1

[.,[[[[[.,.],.],[.,[.,.]]],.],.]] => [6,5,2,3,4,7,8,1] => [2,3,6,5,4,7,8,1] => [4,1,1,1,1] => 1

[.,[[[[[.,.],.],[[.,.],.]],.],.]] => [5,6,2,3,4,7,8,1] => [2,3,5,6,4,7,8,1] => [3,1,1,1,1,1] => 1

[.,[[[[[.,.],[.,.]],[.,.]],.],.]] => [6,4,2,3,5,7,8,1] => [2,4,6,3,5,7,8,1] => [3,1,1,1,1,1] => 1

[.,[[[[[[.,.],.],.],[.,.]],.],.]] => [6,2,3,4,5,7,8,1] => [2,3,4,6,5,7,8,1] => [3,1,1,1,1,1] => 1

[.,[[[[.,[.,[.,[.,.]]]],.],.],.]] => [5,4,3,2,6,7,8,1] => [5,4,3,2,6,7,8,1] => [5,1,1,1] => 1

[.,[[[[.,[.,[[.,.],.]]],.],.],.]] => [4,5,3,2,6,7,8,1] => [4,5,3,2,6,7,8,1] => [4,1,1,1,1] => 1

[.,[[[[.,[[.,.],[.,.]]],.],.],.]] => [5,3,4,2,6,7,8,1] => [3,5,4,2,6,7,8,1] => [4,1,1,1,1] => 1

[.,[[[[.,[[.,[.,.]],.]],.],.],.]] => [4,3,5,2,6,7,8,1] => [4,3,5,2,6,7,8,1] => [4,1,1,1,1] => 1

[.,[[[[.,[[[.,.],.],.]],.],.],.]] => [3,4,5,2,6,7,8,1] => [3,4,5,2,6,7,8,1] => [3,1,1,1,1,1] => 1

[.,[[[[[.,.],[[.,.],.]],.],.],.]] => [4,5,2,3,6,7,8,1] => [2,4,5,3,6,7,8,1] => [3,1,1,1,1,1] => 1

[.,[[[[[.,[.,.]],[.,.]],.],.],.]] => [5,3,2,4,6,7,8,1] => [3,5,2,4,6,7,8,1] => [3,1,1,1,1,1] => 1

[.,[[[[[[.,.],.],[.,.]],.],.],.]] => [5,2,3,4,6,7,8,1] => [2,3,5,4,6,7,8,1] => [3,1,1,1,1,1] => 1

[.,[[[[[.,[.,[.,.]]],.],.],.],.]] => [4,3,2,5,6,7,8,1] => [4,3,2,5,6,7,8,1] => [4,1,1,1,1] => 1

[.,[[[[[.,[[.,.],.]],.],.],.],.]] => [3,4,2,5,6,7,8,1] => [3,4,2,5,6,7,8,1] => [3,1,1,1,1,1] => 1

[.,[[[[[[.,.],[.,.]],.],.],.],.]] => [4,2,3,5,6,7,8,1] => [2,4,3,5,6,7,8,1] => [3,1,1,1,1,1] => 1

[.,[[[[[[.,[.,.]],.],.],.],.],.]] => [3,2,4,5,6,7,8,1] => [3,2,4,5,6,7,8,1] => [3,1,1,1,1,1] => 1

[.,[[[[[[[.,.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,1] => [2,3,4,5,6,7,8,1] => [2,1,1,1,1,1,1] => 1

[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [8,7,6,5,4,3,1,2] => [1,8,7,6,5,4,3,2] => [7,1] => 1

[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [7,8,6,5,4,3,1,2] => [1,7,8,6,5,4,3,2] => [6,1,1] => 1

[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [8,6,7,5,4,3,1,2] => [1,6,8,7,5,4,3,2] => [6,1,1] => 1

[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [7,6,8,5,4,3,1,2] => [1,7,6,8,5,4,3,2] => [6,1,1] => 1

[[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => [6,7,8,5,4,3,1,2] => [1,6,7,8,5,4,3,2] => [5,1,1,1] => 1

[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [8,7,5,6,4,3,1,2] => [1,5,8,7,6,4,3,2] => [6,1,1] => 1

[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [8,6,5,7,4,3,1,2] => [1,6,8,5,7,4,3,2] => [5,1,1,1] => 1

[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [7,6,5,8,4,3,1,2] => [1,7,6,5,8,4,3,2] => [6,1,1] => 1

[[.,.],[.,[.,[[.,[[.,.],.]],.]]]] => [6,7,5,8,4,3,1,2] => [1,6,7,5,8,4,3,2] => [5,1,1,1] => 1

[[.,.],[.,[.,[[[.,.],[.,.]],.]]]] => [7,5,6,8,4,3,1,2] => [1,5,7,6,8,4,3,2] => [5,1,1,1] => 1

[[.,.],[.,[.,[[[.,[.,.]],.],.]]]] => [6,5,7,8,4,3,1,2] => [1,6,5,7,8,4,3,2] => [5,1,1,1] => 1

[[.,.],[.,[.,[[[[.,.],.],.],.]]]] => [5,6,7,8,4,3,1,2] => [1,5,6,7,8,4,3,2] => [4,1,1,1,1] => 1

[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [8,7,6,4,5,3,1,2] => [1,4,8,7,6,5,3,2] => [6,1,1] => 1

[[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [7,8,6,4,5,3,1,2] => [1,4,7,8,6,5,3,2] => [5,1,1,1] => 1

[[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [8,6,7,4,5,3,1,2] => [1,4,6,8,7,5,3,2] => [5,1,1,1] => 1

[[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [6,7,8,4,5,3,1,2] => [1,4,6,7,8,5,3,2] => [4,1,1,1,1] => 1

[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [8,7,5,4,6,3,1,2] => [1,5,8,7,4,6,3,2] => [5,1,1,1] => 1

[[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [8,7,4,5,6,3,1,2] => [1,4,5,8,7,6,3,2] => [5,1,1,1] => 1

[[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [7,8,4,5,6,3,1,2] => [1,4,5,7,8,6,3,2] => [4,1,1,1,1] => 1

[[.,.],[.,[[.,[[.,.],.]],[.,.]]]] => [8,5,6,4,7,3,1,2] => [1,5,6,8,4,7,3,2] => [4,1,1,1,1] => 1

[[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [8,6,4,5,7,3,1,2] => [1,4,6,8,5,7,3,2] => [4,1,1,1,1] => 1

[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]] => [7,6,5,4,8,3,1,2] => [1,7,6,5,4,8,3,2] => [6,1,1] => 1

[[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => [7,6,4,5,8,3,1,2] => [1,4,7,6,5,8,3,2] => [5,1,1,1] => 1

[[.,.],[.,[[[.,.],[[.,.],.]],.]]] => [6,7,4,5,8,3,1,2] => [1,4,6,7,5,8,3,2] => [4,1,1,1,1] => 1

[[.,.],[.,[[[.,[.,.]],[.,.]],.]]] => [7,5,4,6,8,3,1,2] => [1,5,7,4,6,8,3,2] => [4,1,1,1,1] => 1

[[.,.],[.,[[[.,[.,[.,.]]],.],.]]] => [6,5,4,7,8,3,1,2] => [1,6,5,4,7,8,3,2] => [5,1,1,1] => 1

[[.,.],[.,[[[[[.,.],.],.],.],.]]] => [4,5,6,7,8,3,1,2] => [1,4,5,6,7,8,3,2] => [3,1,1,1,1,1] => 1

[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [8,7,6,5,3,4,1,2] => [1,3,8,7,6,5,4,2] => [6,1,1] => 1

[[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [7,8,6,5,3,4,1,2] => [1,3,7,8,6,5,4,2] => [5,1,1,1] => 1

[[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [8,6,7,5,3,4,1,2] => [1,3,6,8,7,5,4,2] => [5,1,1,1] => 1

[[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [6,7,8,5,3,4,1,2] => [1,3,6,7,8,5,4,2] => [4,1,1,1,1] => 1

[[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [8,7,5,6,3,4,1,2] => [1,3,5,8,7,6,4,2] => [5,1,1,1] => 1

[[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [7,8,5,6,3,4,1,2] => [1,3,5,7,8,6,4,2] => [4,1,1,1,1] => 1

[[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [8,5,6,7,3,4,1,2] => [1,3,5,6,8,7,4,2] => [4,1,1,1,1] => 1

[[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [6,7,5,8,3,4,1,2] => [1,3,6,7,5,8,4,2] => [4,1,1,1,1] => 1

[[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [7,5,6,8,3,4,1,2] => [1,3,5,7,6,8,4,2] => [4,1,1,1,1] => 1

[[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [6,5,7,8,3,4,1,2] => [1,3,6,5,7,8,4,2] => [4,1,1,1,1] => 1

[[.,.],[[.,.],[[[[.,.],.],.],.]]] => [5,6,7,8,3,4,1,2] => [1,3,5,6,7,8,4,2] => [3,1,1,1,1,1] => 1

[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [8,7,6,4,3,5,1,2] => [1,4,8,7,6,3,5,2] => [5,1,1,1] => 1

[[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [7,8,6,4,3,5,1,2] => [1,4,7,8,6,3,5,2] => [4,1,1,1,1] => 1

[[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [8,6,7,4,3,5,1,2] => [1,4,6,8,7,3,5,2] => [4,1,1,1,1] => 1

[[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [7,6,8,4,3,5,1,2] => [1,4,7,6,8,3,5,2] => [4,1,1,1,1] => 1

[[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [6,7,8,4,3,5,1,2] => [1,4,6,7,8,3,5,2] => [3,1,1,1,1,1] => 1

[[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [8,7,6,3,4,5,1,2] => [1,3,4,8,7,6,5,2] => [5,1,1,1] => 1

[[.,.],[[[.,.],.],[[[.,.],.],.]]] => [6,7,8,3,4,5,1,2] => [1,3,4,6,7,8,5,2] => [3,1,1,1,1,1] => 1

[[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [7,8,5,4,3,6,1,2] => [1,5,7,8,4,3,6,2] => [4,1,1,1,1] => 1

[[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [8,7,4,5,3,6,1,2] => [1,4,5,8,7,3,6,2] => [4,1,1,1,1] => 1

[[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [7,8,4,5,3,6,1,2] => [1,4,5,7,8,3,6,2] => [3,1,1,1,1,1] => 1

[[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [7,8,5,3,4,6,1,2] => [1,3,5,7,8,4,6,2] => [3,1,1,1,1,1] => 1

[[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [8,7,4,3,5,6,1,2] => [1,4,3,8,7,5,6,2] => [4,2,1,1] => 2

[[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [7,8,4,3,5,6,1,2] => [1,4,3,7,8,5,6,2] => [3,2,1,1,1] => 2

[[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [8,7,3,4,5,6,1,2] => [1,3,4,5,8,7,6,2] => [4,1,1,1,1] => 1

[[.,.],[[[[.,.],.],.],[[.,.],.]]] => [7,8,3,4,5,6,1,2] => [1,3,4,5,7,8,6,2] => [3,1,1,1,1,1] => 1

[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [8,6,5,4,3,7,1,2] => [1,6,8,5,4,3,7,2] => [5,1,1,1] => 1

[[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => [8,5,4,6,3,7,1,2] => [1,5,4,8,6,3,7,2] => [4,2,1,1] => 2

[[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [8,5,6,3,4,7,1,2] => [1,3,5,6,8,4,7,2] => [3,1,1,1,1,1] => 1

[[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [8,6,4,3,5,7,1,2] => [1,4,6,8,3,5,7,2] => [3,1,1,1,1,1] => 1

[[.,.],[[[[.,[.,.]],.],.],[.,.]]] => [8,4,3,5,6,7,1,2] => [1,4,3,5,8,6,7,2] => [3,2,1,1,1] => 2

[[.,.],[[[[[.,.],.],.],.],[.,.]]] => [8,3,4,5,6,7,1,2] => [1,3,4,5,6,8,7,2] => [3,1,1,1,1,1] => 1

[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => [7,6,5,4,3,8,1,2] => [1,7,6,5,4,3,8,2] => [6,1,1] => 1

[[.,.],[[.,[.,[.,[[.,.],.]]]],.]] => [6,7,5,4,3,8,1,2] => [1,6,7,5,4,3,8,2] => [5,1,1,1] => 1

[[.,.],[[.,[.,[[.,[.,.]],.]]],.]] => [6,5,7,4,3,8,1,2] => [1,6,5,7,4,3,8,2] => [5,1,1,1] => 1

[[.,.],[[.,[[.,.],[[.,.],.]]],.]] => [6,7,4,5,3,8,1,2] => [1,4,6,7,5,3,8,2] => [4,1,1,1,1] => 1

[[.,.],[[.,[[.,[[.,.],.]],.]],.]] => [5,6,4,7,3,8,1,2] => [1,5,6,4,7,3,8,2] => [4,1,1,1,1] => 1

[[.,.],[[.,[[[.,.],[.,.]],.]],.]] => [6,4,5,7,3,8,1,2] => [1,4,6,5,7,3,8,2] => [4,1,1,1,1] => 1

[[.,.],[[.,[[[.,[.,.]],.],.]],.]] => [5,4,6,7,3,8,1,2] => [1,5,4,6,7,3,8,2] => [4,1,1,1,1] => 1

[[.,.],[[.,[[[[.,.],.],.],.]],.]] => [4,5,6,7,3,8,1,2] => [1,4,5,6,7,3,8,2] => [3,1,1,1,1,1] => 1

[[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [7,5,6,3,4,8,1,2] => [1,3,5,7,6,4,8,2] => [4,1,1,1,1] => 1

[[.,.],[[[.,.],[[.,[.,.]],.]],.]] => [6,5,7,3,4,8,1,2] => [1,3,6,5,7,4,8,2] => [4,1,1,1,1] => 1

[[.,.],[[[.,.],[[[.,.],.],.]],.]] => [5,6,7,3,4,8,1,2] => [1,3,5,6,7,4,8,2] => [3,1,1,1,1,1] => 1

[[.,.],[[[.,[.,.]],[[.,.],.]],.]] => [6,7,4,3,5,8,1,2] => [1,4,6,7,3,5,8,2] => [3,1,1,1,1,1] => 1

[[.,.],[[[[.,.],.],[.,[.,.]]],.]] => [7,6,3,4,5,8,1,2] => [1,3,4,7,6,5,8,2] => [4,1,1,1,1] => 1

[[.,.],[[[[.,.],.],[[.,.],.]],.]] => [6,7,3,4,5,8,1,2] => [1,3,4,6,7,5,8,2] => [3,1,1,1,1,1] => 1

[[.,.],[[[.,[[.,.],.]],[.,.]],.]] => [7,4,5,3,6,8,1,2] => [1,4,5,7,3,6,8,2] => [3,1,1,1,1,1] => 1

[[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [7,5,3,4,6,8,1,2] => [1,3,5,7,4,6,8,2] => [3,1,1,1,1,1] => 1

[[.,.],[[[[[.,.],.],.],[.,.]],.]] => [7,3,4,5,6,8,1,2] => [1,3,4,5,7,6,8,2] => [3,1,1,1,1,1] => 1

[[.,.],[[[.,[.,[.,[.,.]]]],.],.]] => [6,5,4,3,7,8,1,2] => [1,6,5,4,3,7,8,2] => [5,1,1,1] => 1

[[.,.],[[[.,[[.,[.,.]],.]],.],.]] => [5,4,6,3,7,8,1,2] => [1,5,4,6,3,7,8,2] => [4,1,1,1,1] => 1

[[.,.],[[[[.,.],[[.,.],.]],.],.]] => [5,6,3,4,7,8,1,2] => [1,3,5,6,4,7,8,2] => [3,1,1,1,1,1] => 1

[[.,.],[[[[.,[.,.]],[.,.]],.],.]] => [6,4,3,5,7,8,1,2] => [1,4,6,3,5,7,8,2] => [3,1,1,1,1,1] => 1

[[.,.],[[[[[.,.],.],[.,.]],.],.]] => [6,3,4,5,7,8,1,2] => [1,3,4,6,5,7,8,2] => [3,1,1,1,1,1] => 1

[[.,.],[[[[.,[.,[.,.]]],.],.],.]] => [5,4,3,6,7,8,1,2] => [1,5,4,3,6,7,8,2] => [4,1,1,1,1] => 1

[[.,.],[[[[.,[[.,.],.]],.],.],.]] => [4,5,3,6,7,8,1,2] => [1,4,5,3,6,7,8,2] => [3,1,1,1,1,1] => 1

[[.,.],[[[[[.,.],[.,.]],.],.],.]] => [5,3,4,6,7,8,1,2] => [1,3,5,4,6,7,8,2] => [3,1,1,1,1,1] => 1

[[.,.],[[[[[.,[.,.]],.],.],.],.]] => [4,3,5,6,7,8,1,2] => [1,4,3,5,6,7,8,2] => [3,1,1,1,1,1] => 1

[[.,.],[[[[[[.,.],.],.],.],.],.]] => [3,4,5,6,7,8,1,2] => [1,3,4,5,6,7,8,2] => [2,1,1,1,1,1,1] => 1

[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [8,7,6,5,4,2,1,3] => [2,8,7,6,5,4,1,3] => [6,1,1] => 1

[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [7,8,6,5,4,2,1,3] => [2,7,8,6,5,4,1,3] => [5,1,1,1] => 1

[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [8,6,7,5,4,2,1,3] => [2,6,8,7,5,4,1,3] => [5,1,1,1] => 1

[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [7,6,8,5,4,2,1,3] => [2,7,6,8,5,4,1,3] => [5,1,1,1] => 1

[[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [7,8,5,6,4,2,1,3] => [2,5,7,8,6,4,1,3] => [4,1,1,1,1] => 1

[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [8,6,5,7,4,2,1,3] => [2,6,8,5,7,4,1,3] => [4,1,1,1,1] => 1

[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [7,6,5,8,4,2,1,3] => [2,7,6,5,8,4,1,3] => [5,1,1,1] => 1

[[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => [6,5,7,8,4,2,1,3] => [2,6,5,7,8,4,1,3] => [4,1,1,1,1] => 1

[[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [5,6,7,8,4,2,1,3] => [2,5,6,7,8,4,1,3] => [3,1,1,1,1,1] => 1

[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [8,7,6,4,5,2,1,3] => [2,4,8,7,6,5,1,3] => [5,1,1,1] => 1

[[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [7,8,6,4,5,2,1,3] => [2,4,7,8,6,5,1,3] => [4,1,1,1,1] => 1

[[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [8,6,7,4,5,2,1,3] => [2,4,6,8,7,5,1,3] => [4,1,1,1,1] => 1

[[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [7,6,8,4,5,2,1,3] => [2,4,7,6,8,5,1,3] => [4,1,1,1,1] => 1

[[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [6,7,8,4,5,2,1,3] => [2,4,6,7,8,5,1,3] => [3,1,1,1,1,1] => 1

[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [8,7,5,4,6,2,1,3] => [2,5,8,7,4,6,1,3] => [4,1,1,1,1] => 1

[[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [7,8,5,4,6,2,1,3] => [2,5,7,8,4,6,1,3] => [3,1,1,1,1,1] => 1

[[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [8,7,4,5,6,2,1,3] => [2,4,5,8,7,6,1,3] => [4,1,1,1,1] => 1

[[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [8,6,4,5,7,2,1,3] => [2,4,6,8,5,7,1,3] => [3,1,1,1,1,1] => 1

[[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [8,4,5,6,7,2,1,3] => [2,4,5,6,8,7,1,3] => [3,1,1,1,1,1] => 1

[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [7,6,5,4,8,2,1,3] => [2,7,6,5,4,8,1,3] => [5,1,1,1] => 1

[[.,[.,.]],[[.,[.,[[.,.],.]]],.]] => [6,7,5,4,8,2,1,3] => [2,6,7,5,4,8,1,3] => [4,1,1,1,1] => 1

[[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [7,6,4,5,8,2,1,3] => [2,4,7,6,5,8,1,3] => [4,1,1,1,1] => 1

[[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [6,7,4,5,8,2,1,3] => [2,4,6,7,5,8,1,3] => [3,1,1,1,1,1] => 1

[[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [7,5,4,6,8,2,1,3] => [2,5,7,4,6,8,1,3] => [3,1,1,1,1,1] => 1

[[.,[.,.]],[[[[[.,.],.],.],.],.]] => [4,5,6,7,8,2,1,3] => [2,4,5,6,7,8,1,3] => [2,1,1,1,1,1,1] => 1

[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [8,7,6,5,4,1,2,3] => [1,2,8,7,6,5,4,3] => [6,1,1] => 1

[[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [7,8,6,5,4,1,2,3] => [1,2,7,8,6,5,4,3] => [5,1,1,1] => 1

[[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [6,7,8,5,4,1,2,3] => [1,2,6,7,8,5,4,3] => [4,1,1,1,1] => 1

[[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [8,6,5,7,4,1,2,3] => [1,2,6,8,5,7,4,3] => [4,1,1,1,1] => 1

[[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [8,5,6,7,4,1,2,3] => [1,2,5,6,8,7,4,3] => [4,1,1,1,1] => 1

[[[.,.],.],[.,[[.,[.,[.,.]]],.]]] => [7,6,5,8,4,1,2,3] => [1,2,7,6,5,8,4,3] => [5,1,1,1] => 1

[[[.,.],.],[.,[[[.,.],[.,.]],.]]] => [7,5,6,8,4,1,2,3] => [1,2,5,7,6,8,4,3] => [4,1,1,1,1] => 1

[[[.,.],.],[.,[[[.,[.,.]],.],.]]] => [6,5,7,8,4,1,2,3] => [1,2,6,5,7,8,4,3] => [4,1,1,1,1] => 1

[[[.,.],.],[.,[[[[.,.],.],.],.]]] => [5,6,7,8,4,1,2,3] => [1,2,5,6,7,8,4,3] => [3,1,1,1,1,1] => 1

[[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [8,7,6,4,5,1,2,3] => [1,2,4,8,7,6,5,3] => [5,1,1,1] => 1

[[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [8,6,7,4,5,1,2,3] => [1,2,4,6,8,7,5,3] => [4,1,1,1,1] => 1

[[[.,.],.],[[.,.],[[[.,.],.],.]]] => [6,7,8,4,5,1,2,3] => [1,2,4,6,7,8,5,3] => [3,1,1,1,1,1] => 1

[[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [8,7,5,4,6,1,2,3] => [1,2,5,8,7,4,6,3] => [4,1,1,1,1] => 1

[[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [7,8,5,4,6,1,2,3] => [1,2,5,7,8,4,6,3] => [3,1,1,1,1,1] => 1

[[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [8,7,4,5,6,1,2,3] => [1,2,4,5,8,7,6,3] => [4,1,1,1,1] => 1

[[[.,.],.],[[[.,.],.],[[.,.],.]]] => [7,8,4,5,6,1,2,3] => [1,2,4,5,7,8,6,3] => [3,1,1,1,1,1] => 1

[[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [8,6,5,4,7,1,2,3] => [1,2,6,8,5,4,7,3] => [4,1,1,1,1] => 1

[[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [8,5,6,4,7,1,2,3] => [1,2,5,6,8,4,7,3] => [3,1,1,1,1,1] => 1

[[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [8,6,4,5,7,1,2,3] => [1,2,4,6,8,5,7,3] => [3,1,1,1,1,1] => 1

[[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [8,5,4,6,7,1,2,3] => [1,2,5,4,8,6,7,3] => [3,2,1,1,1] => 2

[[[.,.],.],[[[[.,.],.],.],[.,.]]] => [8,4,5,6,7,1,2,3] => [1,2,4,5,6,8,7,3] => [3,1,1,1,1,1] => 1

[[[.,.],.],[[.,[.,[.,[.,.]]]],.]] => [7,6,5,4,8,1,2,3] => [1,2,7,6,5,4,8,3] => [5,1,1,1] => 1

[[[.,.],.],[[.,[[[.,.],.],.]],.]] => [5,6,7,4,8,1,2,3] => [1,2,5,6,7,4,8,3] => [3,1,1,1,1,1] => 1

[[[.,.],.],[[[.,.],[.,[.,.]]],.]] => [7,6,4,5,8,1,2,3] => [1,2,4,7,6,5,8,3] => [4,1,1,1,1] => 1

[[[.,.],.],[[[.,[.,.]],[.,.]],.]] => [7,5,4,6,8,1,2,3] => [1,2,5,7,4,6,8,3] => [3,1,1,1,1,1] => 1

[[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [6,5,4,7,8,1,2,3] => [1,2,6,5,4,7,8,3] => [4,1,1,1,1] => 1

[[[.,.],.],[[[[.,[.,.]],.],.],.]] => [5,4,6,7,8,1,2,3] => [1,2,5,4,6,7,8,3] => [3,1,1,1,1,1] => 1

[[[.,.],.],[[[[[.,.],.],.],.],.]] => [4,5,6,7,8,1,2,3] => [1,2,4,5,6,7,8,3] => [2,1,1,1,1,1,1] => 1

[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [8,7,6,5,3,2,1,4] => [3,8,7,6,5,2,1,4] => [6,1,1] => 1

[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [7,8,6,5,3,2,1,4] => [3,7,8,6,5,2,1,4] => [5,1,1,1] => 1

[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [8,6,7,5,3,2,1,4] => [3,6,8,7,5,2,1,4] => [5,1,1,1] => 1

[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [7,6,8,5,3,2,1,4] => [3,7,6,8,5,2,1,4] => [5,1,1,1] => 1

[[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => [6,7,8,5,3,2,1,4] => [3,6,7,8,5,2,1,4] => [4,1,1,1,1] => 1

[[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [7,8,5,6,3,2,1,4] => [3,5,7,8,6,2,1,4] => [4,1,1,1,1] => 1

[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [8,6,5,7,3,2,1,4] => [3,6,8,5,7,2,1,4] => [4,1,1,1,1] => 1

[[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [8,5,6,7,3,2,1,4] => [3,5,6,8,7,2,1,4] => [4,1,1,1,1] => 1

[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [7,6,5,8,3,2,1,4] => [3,7,6,5,8,2,1,4] => [5,1,1,1] => 1

[[.,[.,[.,.]]],[[.,[[.,.],.]],.]] => [6,7,5,8,3,2,1,4] => [3,6,7,5,8,2,1,4] => [4,1,1,1,1] => 1

[[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [7,5,6,8,3,2,1,4] => [3,5,7,6,8,2,1,4] => [4,1,1,1,1] => 1

[[.,[.,[.,.]]],[[[.,[.,.]],.],.]] => [6,5,7,8,3,2,1,4] => [3,6,5,7,8,2,1,4] => [4,1,1,1,1] => 1

[[.,[.,[.,.]]],[[[[.,.],.],.],.]] => [5,6,7,8,3,2,1,4] => [3,5,6,7,8,2,1,4] => [3,1,1,1,1,1] => 1

[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]] => [8,7,6,5,2,3,1,4] => [2,3,8,7,6,5,1,4] => [5,1,1,1] => 1

[[.,[[.,.],.]],[.,[[.,.],[.,.]]]] => [8,6,7,5,2,3,1,4] => [2,3,6,8,7,5,1,4] => [4,1,1,1,1] => 1

[[.,[[.,.],.]],[.,[[.,[.,.]],.]]] => [7,6,8,5,2,3,1,4] => [2,3,7,6,8,5,1,4] => [4,1,1,1,1] => 1

[[.,[[.,.],.]],[.,[[[.,.],.],.]]] => [6,7,8,5,2,3,1,4] => [2,3,6,7,8,5,1,4] => [3,1,1,1,1,1] => 1

[[.,[[.,.],.]],[[.,[.,[.,.]]],.]] => [7,6,5,8,2,3,1,4] => [2,3,7,6,5,8,1,4] => [4,1,1,1,1] => 1

[[.,[[.,.],.]],[[.,[[.,.],.]],.]] => [6,7,5,8,2,3,1,4] => [2,3,6,7,5,8,1,4] => [3,1,1,1,1,1] => 1

[[.,[[.,.],.]],[[[.,.],[.,.]],.]] => [7,5,6,8,2,3,1,4] => [2,3,5,7,6,8,1,4] => [3,1,1,1,1,1] => 1

[[.,[[.,.],.]],[[[.,[.,.]],.],.]] => [6,5,7,8,2,3,1,4] => [2,3,6,5,7,8,1,4] => [3,1,1,1,1,1] => 1

[[.,[[.,.],.]],[[[[.,.],.],.],.]] => [5,6,7,8,2,3,1,4] => [2,3,5,6,7,8,1,4] => [2,1,1,1,1,1,1] => 1

[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [8,7,6,5,3,1,2,4] => [1,3,8,7,6,5,2,4] => [5,1,1,1] => 1

[[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [8,6,7,5,3,1,2,4] => [1,3,6,8,7,5,2,4] => [4,1,1,1,1] => 1

[[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [7,6,8,5,3,1,2,4] => [1,3,7,6,8,5,2,4] => [4,1,1,1,1] => 1

[[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [8,7,5,6,3,1,2,4] => [1,3,5,8,7,6,2,4] => [4,1,1,1,1] => 1

[[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [7,8,5,6,3,1,2,4] => [1,3,5,7,8,6,2,4] => [3,1,1,1,1,1] => 1

[[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [8,6,5,7,3,1,2,4] => [1,3,6,8,5,7,2,4] => [3,1,1,1,1,1] => 1

[[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [8,5,6,7,3,1,2,4] => [1,3,5,6,8,7,2,4] => [3,1,1,1,1,1] => 1

[[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [7,6,5,8,3,1,2,4] => [1,3,7,6,5,8,2,4] => [4,1,1,1,1] => 1

[[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [6,7,5,8,3,1,2,4] => [1,3,6,7,5,8,2,4] => [3,1,1,1,1,1] => 1

[[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [7,5,6,8,3,1,2,4] => [1,3,5,7,6,8,2,4] => [3,1,1,1,1,1] => 1

[[[.,.],[.,.]],[[[.,[.,.]],.],.]] => [6,5,7,8,3,1,2,4] => [1,3,6,5,7,8,2,4] => [3,1,1,1,1,1] => 1

[[[.,.],[.,.]],[[[[.,.],.],.],.]] => [5,6,7,8,3,1,2,4] => [1,3,5,6,7,8,2,4] => [2,1,1,1,1,1,1] => 1

[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [8,7,6,5,2,1,3,4] => [2,1,8,7,6,5,3,4] => [5,2,1] => 2

[[[.,[.,.]],.],[.,[.,[[.,.],.]]]] => [7,8,6,5,2,1,3,4] => [2,1,7,8,6,5,3,4] => [4,2,1,1] => 2

[[[.,[.,.]],.],[.,[[.,.],[.,.]]]] => [8,6,7,5,2,1,3,4] => [2,1,6,8,7,5,3,4] => [4,2,1,1] => 2

[[[.,[.,.]],.],[.,[[.,[.,.]],.]]] => [7,6,8,5,2,1,3,4] => [2,1,7,6,8,5,3,4] => [4,2,1,1] => 2

[[[.,[.,.]],.],[.,[[[.,.],.],.]]] => [6,7,8,5,2,1,3,4] => [2,1,6,7,8,5,3,4] => [3,2,1,1,1] => 2

[[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [8,7,5,6,2,1,3,4] => [2,1,5,8,7,6,3,4] => [4,2,1,1] => 2

[[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [7,8,5,6,2,1,3,4] => [2,1,5,7,8,6,3,4] => [3,2,1,1,1] => 2

[[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [8,6,5,7,2,1,3,4] => [2,1,6,8,5,7,3,4] => [3,2,1,1,1] => 2

[[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [8,5,6,7,2,1,3,4] => [2,1,5,6,8,7,3,4] => [3,2,1,1,1] => 2

[[[.,[.,.]],.],[[.,[.,[.,.]]],.]] => [7,6,5,8,2,1,3,4] => [2,1,7,6,5,8,3,4] => [4,2,1,1] => 2

[[[.,[.,.]],.],[[.,[[.,.],.]],.]] => [6,7,5,8,2,1,3,4] => [2,1,6,7,5,8,3,4] => [3,2,1,1,1] => 2

[[[.,[.,.]],.],[[[.,[.,.]],.],.]] => [6,5,7,8,2,1,3,4] => [2,1,6,5,7,8,3,4] => [3,2,1,1,1] => 2

[[[.,[.,.]],.],[[[[.,.],.],.],.]] => [5,6,7,8,2,1,3,4] => [2,1,5,6,7,8,3,4] => [2,2,1,1,1,1] => 2

[[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [8,7,6,5,1,2,3,4] => [1,2,3,8,7,6,5,4] => [5,1,1,1] => 1

[[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [7,8,6,5,1,2,3,4] => [1,2,3,7,8,6,5,4] => [4,1,1,1,1] => 1

[[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [8,6,7,5,1,2,3,4] => [1,2,3,6,8,7,5,4] => [4,1,1,1,1] => 1

[[[[.,.],.],.],[.,[[.,[.,.]],.]]] => [7,6,8,5,1,2,3,4] => [1,2,3,7,6,8,5,4] => [4,1,1,1,1] => 1

[[[[.,.],.],.],[.,[[[.,.],.],.]]] => [6,7,8,5,1,2,3,4] => [1,2,3,6,7,8,5,4] => [3,1,1,1,1,1] => 1

[[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [8,7,5,6,1,2,3,4] => [1,2,3,5,8,7,6,4] => [4,1,1,1,1] => 1

[[[[.,.],.],.],[[.,.],[[.,.],.]]] => [7,8,5,6,1,2,3,4] => [1,2,3,5,7,8,6,4] => [3,1,1,1,1,1] => 1

[[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [8,6,5,7,1,2,3,4] => [1,2,3,6,8,5,7,4] => [3,1,1,1,1,1] => 1

[[[[.,.],.],.],[[[.,.],.],[.,.]]] => [8,5,6,7,1,2,3,4] => [1,2,3,5,6,8,7,4] => [3,1,1,1,1,1] => 1

[[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [7,6,5,8,1,2,3,4] => [1,2,3,7,6,5,8,4] => [4,1,1,1,1] => 1

[[[[.,.],.],.],[[.,[[.,.],.]],.]] => [6,7,5,8,1,2,3,4] => [1,2,3,6,7,5,8,4] => [3,1,1,1,1,1] => 1

[[[[.,.],.],.],[[[.,.],[.,.]],.]] => [7,5,6,8,1,2,3,4] => [1,2,3,5,7,6,8,4] => [3,1,1,1,1,1] => 1

[[[[.,.],.],.],[[[.,[.,.]],.],.]] => [6,5,7,8,1,2,3,4] => [1,2,3,6,5,7,8,4] => [3,1,1,1,1,1] => 1

[[[[.,.],.],.],[[[[.,.],.],.],.]] => [5,6,7,8,1,2,3,4] => [1,2,3,5,6,7,8,4] => [2,1,1,1,1,1,1] => 1

[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [8,7,6,4,3,2,1,5] => [4,8,7,6,3,2,1,5] => [6,1,1] => 1

[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [7,8,6,4,3,2,1,5] => [4,7,8,6,3,2,1,5] => [5,1,1,1] => 1

[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [8,6,7,4,3,2,1,5] => [4,6,8,7,3,2,1,5] => [5,1,1,1] => 1

[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [7,6,8,4,3,2,1,5] => [4,7,6,8,3,2,1,5] => [5,1,1,1] => 1

[[.,[.,[.,[.,.]]]],[[[.,.],.],.]] => [6,7,8,4,3,2,1,5] => [4,6,7,8,3,2,1,5] => [4,1,1,1,1] => 1

[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]] => [8,7,6,3,4,2,1,5] => [3,4,8,7,6,2,1,5] => [5,1,1,1] => 1

[[.,[.,[[.,.],.]]],[.,[[.,.],.]]] => [7,8,6,3,4,2,1,5] => [3,4,7,8,6,2,1,5] => [4,1,1,1,1] => 1

[[.,[.,[[.,.],.]]],[[.,.],[.,.]]] => [8,6,7,3,4,2,1,5] => [3,4,6,8,7,2,1,5] => [4,1,1,1,1] => 1

[[.,[.,[[.,.],.]]],[[[.,.],.],.]] => [6,7,8,3,4,2,1,5] => [3,4,6,7,8,2,1,5] => [3,1,1,1,1,1] => 1

[[.,[[.,.],[.,.]]],[[.,.],[.,.]]] => [8,6,7,4,2,3,1,5] => [2,4,6,8,7,3,1,5] => [4,1,1,1,1] => 1

[[.,[[.,.],[.,.]]],[[.,[.,.]],.]] => [7,6,8,4,2,3,1,5] => [2,4,7,6,8,3,1,5] => [4,1,1,1,1] => 1

[[.,[[.,.],[.,.]]],[[[.,.],.],.]] => [6,7,8,4,2,3,1,5] => [2,4,6,7,8,3,1,5] => [3,1,1,1,1,1] => 1

[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [8,7,6,3,2,4,1,5] => [3,2,8,7,6,4,1,5] => [5,2,1] => 2

[[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [8,6,7,3,2,4,1,5] => [3,2,6,8,7,4,1,5] => [4,2,1,1] => 2

[[.,[[.,[.,.]],.]],[[.,[.,.]],.]] => [7,6,8,3,2,4,1,5] => [3,2,7,6,8,4,1,5] => [4,2,1,1] => 2

[[.,[[.,[.,.]],.]],[[[.,.],.],.]] => [6,7,8,3,2,4,1,5] => [3,2,6,7,8,4,1,5] => [3,2,1,1,1] => 2

[[.,[[[.,.],.],.]],[.,[.,[.,.]]]] => [8,7,6,2,3,4,1,5] => [2,3,4,8,7,6,1,5] => [4,1,1,1,1] => 1

[[.,[[[.,.],.],.]],[.,[[.,.],.]]] => [7,8,6,2,3,4,1,5] => [2,3,4,7,8,6,1,5] => [3,1,1,1,1,1] => 1

[[.,[[[.,.],.],.]],[[.,.],[.,.]]] => [8,6,7,2,3,4,1,5] => [2,3,4,6,8,7,1,5] => [3,1,1,1,1,1] => 1

[[.,[[[.,.],.],.]],[[.,[.,.]],.]] => [7,6,8,2,3,4,1,5] => [2,3,4,7,6,8,1,5] => [3,1,1,1,1,1] => 1

[[.,[[[.,.],.],.]],[[[.,.],.],.]] => [6,7,8,2,3,4,1,5] => [2,3,4,6,7,8,1,5] => [2,1,1,1,1,1,1] => 1

[[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [7,6,8,4,3,1,2,5] => [1,4,7,6,8,3,2,5] => [4,1,1,1,1] => 1

[[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [6,7,8,4,3,1,2,5] => [1,4,6,7,8,3,2,5] => [3,1,1,1,1,1] => 1

[[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [8,7,6,3,4,1,2,5] => [1,3,4,8,7,6,2,5] => [4,1,1,1,1] => 1

[[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [7,6,8,3,4,1,2,5] => [1,3,4,7,6,8,2,5] => [3,1,1,1,1,1] => 1

[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [8,7,6,4,2,1,3,5] => [2,4,8,7,6,1,3,5] => [4,1,1,1,1] => 1

[[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [7,8,6,4,2,1,3,5] => [2,4,7,8,6,1,3,5] => [3,1,1,1,1,1] => 1

[[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [8,6,7,4,2,1,3,5] => [2,4,6,8,7,1,3,5] => [3,1,1,1,1,1] => 1

[[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [6,7,8,4,2,1,3,5] => [2,4,6,7,8,1,3,5] => [2,1,1,1,1,1,1] => 1

[[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [8,7,6,4,1,2,3,5] => [1,2,4,8,7,6,3,5] => [4,1,1,1,1] => 1

[[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [7,8,6,4,1,2,3,5] => [1,2,4,7,8,6,3,5] => [3,1,1,1,1,1] => 1

[[[[.,.],.],[.,.]],[[[.,.],.],.]] => [6,7,8,4,1,2,3,5] => [1,2,4,6,7,8,3,5] => [2,1,1,1,1,1,1] => 1

[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [8,7,6,3,2,1,4,5] => [3,2,8,7,6,1,4,5] => [4,2,1,1] => 2

[[[.,[.,[.,.]]],.],[.,[[.,.],.]]] => [7,8,6,3,2,1,4,5] => [3,2,7,8,6,1,4,5] => [3,2,1,1,1] => 2

[[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [8,6,7,3,2,1,4,5] => [3,2,6,8,7,1,4,5] => [3,2,1,1,1] => 2

[[[.,[.,[.,.]]],.],[[.,[.,.]],.]] => [7,6,8,3,2,1,4,5] => [3,2,7,6,8,1,4,5] => [3,2,1,1,1] => 2

[[[.,[.,[.,.]]],.],[[[.,.],.],.]] => [6,7,8,3,2,1,4,5] => [3,2,6,7,8,1,4,5] => [3,1,1,1,1,1] => 1

[[[.,[[.,.],.]],.],[.,[.,[.,.]]]] => [8,7,6,2,3,1,4,5] => [2,3,1,8,7,6,4,5] => [4,2,1,1] => 2

[[[.,[[.,.],.]],.],[.,[[.,.],.]]] => [7,8,6,2,3,1,4,5] => [2,3,1,7,8,6,4,5] => [3,2,1,1,1] => 2

[[[.,[[.,.],.]],.],[[[.,.],.],.]] => [6,7,8,2,3,1,4,5] => [2,3,1,6,7,8,4,5] => [2,2,1,1,1,1] => 2

[[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [8,7,6,3,1,2,4,5] => [1,3,2,8,7,6,4,5] => [4,2,1,1] => 2

[[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [8,6,7,3,1,2,4,5] => [1,3,2,6,8,7,4,5] => [3,2,1,1,1] => 2

[[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [7,6,8,3,1,2,4,5] => [1,3,2,7,6,8,4,5] => [3,2,1,1,1] => 2

[[[[.,.],[.,.]],.],[[[.,.],.],.]] => [6,7,8,3,1,2,4,5] => [1,3,2,6,7,8,4,5] => [2,2,1,1,1,1] => 2

[[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [8,7,6,2,1,3,4,5] => [2,1,3,8,7,6,4,5] => [4,2,1,1] => 2

[[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [7,8,6,2,1,3,4,5] => [2,1,3,7,8,6,4,5] => [3,2,1,1,1] => 2

[[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [8,6,7,2,1,3,4,5] => [2,1,3,6,8,7,4,5] => [3,2,1,1,1] => 2

[[[[.,[.,.]],.],.],[[[.,.],.],.]] => [6,7,8,2,1,3,4,5] => [2,1,3,6,7,8,4,5] => [2,2,1,1,1,1] => 2

[[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [8,7,6,1,2,3,4,5] => [1,2,3,4,8,7,6,5] => [4,1,1,1,1] => 1

[[[[[.,.],.],.],.],[.,[[.,.],.]]] => [7,8,6,1,2,3,4,5] => [1,2,3,4,7,8,6,5] => [3,1,1,1,1,1] => 1

[[[[[.,.],.],.],.],[[.,.],[.,.]]] => [8,6,7,1,2,3,4,5] => [1,2,3,4,6,8,7,5] => [3,1,1,1,1,1] => 1

[[[[[.,.],.],.],.],[[.,[.,.]],.]] => [7,6,8,1,2,3,4,5] => [1,2,3,4,7,6,8,5] => [3,1,1,1,1,1] => 1

[[[[[.,.],.],.],.],[[[.,.],.],.]] => [6,7,8,1,2,3,4,5] => [1,2,3,4,6,7,8,5] => [2,1,1,1,1,1,1] => 1

[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [8,7,5,4,3,2,1,6] => [5,8,7,4,3,2,1,6] => [6,1,1] => 1

[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [7,8,5,4,3,2,1,6] => [5,7,8,4,3,2,1,6] => [5,1,1,1] => 1

[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]] => [8,7,4,5,3,2,1,6] => [4,5,8,7,3,2,1,6] => [5,1,1,1] => 1

[[.,[.,[.,[[.,.],.]]]],[[.,.],.]] => [7,8,4,5,3,2,1,6] => [4,5,7,8,3,2,1,6] => [4,1,1,1,1] => 1

[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]] => [8,7,4,3,5,2,1,6] => [4,3,8,7,5,2,1,6] => [5,2,1] => 2

[[.,[.,[[.,[.,.]],.]]],[[.,.],.]] => [7,8,4,3,5,2,1,6] => [4,3,7,8,5,2,1,6] => [4,2,1,1] => 2

[[.,[.,[[[.,.],.],.]]],[.,[.,.]]] => [8,7,3,4,5,2,1,6] => [3,4,5,8,7,2,1,6] => [4,1,1,1,1] => 1

[[.,[[.,.],[[.,.],.]]],[.,[.,.]]] => [8,7,4,5,2,3,1,6] => [2,4,5,8,7,3,1,6] => [4,1,1,1,1] => 1

[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [8,7,5,3,2,4,1,6] => [3,5,8,7,2,4,1,6] => [4,1,1,1,1] => 1

[[.,[[.,[.,.]],[.,.]]],[[.,.],.]] => [7,8,5,3,2,4,1,6] => [3,5,7,8,2,4,1,6] => [3,1,1,1,1,1] => 1

[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]] => [8,7,4,3,2,5,1,6] => [4,3,8,7,2,5,1,6] => [4,2,1,1] => 2

[[.,[[.,[.,[.,.]]],.]],[[.,.],.]] => [7,8,4,3,2,5,1,6] => [4,3,7,8,2,5,1,6] => [4,1,1,1,1] => 1

[[.,[[.,[[.,.],.]],.]],[.,[.,.]]] => [8,7,3,4,2,5,1,6] => [3,4,2,8,7,5,1,6] => [4,2,1,1] => 2

[[.,[[[[.,.],.],.],.]],[.,[.,.]]] => [8,7,2,3,4,5,1,6] => [2,3,4,5,8,7,1,6] => [3,1,1,1,1,1] => 1

[[.,[[[[.,.],.],.],.]],[[.,.],.]] => [7,8,2,3,4,5,1,6] => [2,3,4,5,7,8,1,6] => [2,1,1,1,1,1,1] => 1

[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [8,7,5,4,3,1,2,6] => [1,5,8,7,4,3,2,6] => [5,1,1,1] => 1

[[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [7,8,5,4,3,1,2,6] => [1,5,7,8,4,3,2,6] => [4,1,1,1,1] => 1

[[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [7,8,5,3,4,1,2,6] => [1,3,5,7,8,4,2,6] => [3,1,1,1,1,1] => 1

[[[.,.],[[.,[.,.]],.]],[[.,.],.]] => [7,8,4,3,5,1,2,6] => [1,4,3,7,8,5,2,6] => [3,2,1,1,1] => 2

[[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [8,7,3,4,5,1,2,6] => [1,3,4,5,8,7,2,6] => [3,1,1,1,1,1] => 1

[[[.,.],[[[.,.],.],.]],[[.,.],.]] => [7,8,3,4,5,1,2,6] => [1,3,4,5,7,8,2,6] => [2,1,1,1,1,1,1] => 1

[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [8,7,5,4,2,1,3,6] => [2,5,8,7,4,1,3,6] => [4,1,1,1,1] => 1

[[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [7,8,5,4,2,1,3,6] => [2,5,7,8,4,1,3,6] => [3,1,1,1,1,1] => 1

[[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [7,8,4,5,2,1,3,6] => [2,4,5,7,8,1,3,6] => [2,1,1,1,1,1,1] => 1

[[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [8,7,5,4,1,2,3,6] => [1,2,5,8,7,4,3,6] => [4,1,1,1,1] => 1

[[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [7,8,5,4,1,2,3,6] => [1,2,5,7,8,4,3,6] => [3,1,1,1,1,1] => 1

[[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [8,7,4,5,1,2,3,6] => [1,2,4,5,8,7,3,6] => [3,1,1,1,1,1] => 1

[[[[.,.],.],[[.,.],.]],[[.,.],.]] => [7,8,4,5,1,2,3,6] => [1,2,4,5,7,8,3,6] => [2,1,1,1,1,1,1] => 1

[[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [7,8,5,3,2,1,4,6] => [3,5,7,8,2,1,4,6] => [3,1,1,1,1,1] => 1

[[[.,[[.,.],.]],[.,.]],[[.,.],.]] => [7,8,5,2,3,1,4,6] => [2,3,5,7,8,1,4,6] => [2,1,1,1,1,1,1] => 1

[[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [8,7,5,3,1,2,4,6] => [1,3,5,8,7,2,4,6] => [3,1,1,1,1,1] => 1

[[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [7,8,5,3,1,2,4,6] => [1,3,5,7,8,2,4,6] => [2,1,1,1,1,1,1] => 1

[[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [8,7,5,2,1,3,4,6] => [2,1,5,8,7,3,4,6] => [3,2,1,1,1] => 2

[[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [7,8,5,2,1,3,4,6] => [2,1,5,7,8,3,4,6] => [2,2,1,1,1,1] => 2

[[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [8,7,5,1,2,3,4,6] => [1,2,3,5,8,7,4,6] => [3,1,1,1,1,1] => 1

[[[[[.,.],.],.],[.,.]],[[.,.],.]] => [7,8,5,1,2,3,4,6] => [1,2,3,5,7,8,4,6] => [2,1,1,1,1,1,1] => 1

[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] => [8,7,4,3,2,1,5,6] => [4,3,8,7,2,1,5,6] => [4,2,1,1] => 2

[[[.,[.,[.,[.,.]]]],.],[[.,.],.]] => [7,8,4,3,2,1,5,6] => [4,3,7,8,2,1,5,6] => [4,1,1,1,1] => 1

[[[.,[.,[[.,.],.]]],.],[[.,.],.]] => [7,8,3,4,2,1,5,6] => [3,4,2,7,8,1,5,6] => [3,1,1,1,1,1] => 1

[[[.,[[.,.],[.,.]]],.],[[.,.],.]] => [7,8,4,2,3,1,5,6] => [2,4,3,7,8,1,5,6] => [3,1,1,1,1,1] => 1

[[[.,[[.,[.,.]],.]],.],[.,[.,.]]] => [8,7,3,2,4,1,5,6] => [3,2,4,8,7,1,5,6] => [3,2,1,1,1] => 2

[[[.,[[.,[.,.]],.]],.],[[.,.],.]] => [7,8,3,2,4,1,5,6] => [3,2,4,7,8,1,5,6] => [3,1,1,1,1,1] => 1

[[[.,[[[.,.],.],.]],.],[.,[.,.]]] => [8,7,2,3,4,1,5,6] => [2,3,4,1,8,7,5,6] => [3,2,1,1,1] => 2

[[[.,[[[.,.],.],.]],.],[[.,.],.]] => [7,8,2,3,4,1,5,6] => [2,3,4,1,7,8,5,6] => [2,2,1,1,1,1] => 2

[[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [8,7,4,3,1,2,5,6] => [1,4,3,8,7,2,5,6] => [3,2,1,1,1] => 2

[[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [7,8,4,3,1,2,5,6] => [1,4,3,7,8,2,5,6] => [3,1,1,1,1,1] => 1

[[[[.,.],[[.,.],.]],.],[[.,.],.]] => [7,8,3,4,1,2,5,6] => [1,3,4,2,7,8,5,6] => [2,2,1,1,1,1] => 2

[[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [8,7,4,2,1,3,5,6] => [2,4,1,8,7,3,5,6] => [3,2,1,1,1] => 2

[[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [7,8,4,2,1,3,5,6] => [2,4,1,7,8,3,5,6] => [2,2,1,1,1,1] => 2

[[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [8,7,4,1,2,3,5,6] => [1,2,4,3,8,7,5,6] => [3,2,1,1,1] => 2

[[[[[.,.],.],[.,.]],.],[[.,.],.]] => [7,8,4,1,2,3,5,6] => [1,2,4,3,7,8,5,6] => [2,2,1,1,1,1] => 2

[[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [8,7,3,2,1,4,5,6] => [3,2,1,8,7,4,5,6] => [3,3,1,1] => 2

[[[[.,[.,[.,.]]],.],.],[[.,.],.]] => [7,8,3,2,1,4,5,6] => [3,2,1,7,8,4,5,6] => [3,2,1,1,1] => 2

[[[[.,[[.,.],.]],.],.],[[.,.],.]] => [7,8,2,3,1,4,5,6] => [2,3,1,4,7,8,5,6] => [2,2,1,1,1,1] => 2

[[[[[.,.],[.,.]],.],.],[[.,.],.]] => [7,8,3,1,2,4,5,6] => [1,3,2,4,7,8,5,6] => [2,2,1,1,1,1] => 2

[[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [8,7,2,1,3,4,5,6] => [2,1,3,4,8,7,5,6] => [3,2,1,1,1] => 2

[[[[[.,[.,.]],.],.],.],[[.,.],.]] => [7,8,2,1,3,4,5,6] => [2,1,3,4,7,8,5,6] => [2,2,1,1,1,1] => 2

[[[[[[.,.],.],.],.],.],[.,[.,.]]] => [8,7,1,2,3,4,5,6] => [1,2,3,4,5,8,7,6] => [3,1,1,1,1,1] => 1

[[[[[[.,.],.],.],.],.],[[.,.],.]] => [7,8,1,2,3,4,5,6] => [1,2,3,4,5,7,8,6] => [2,1,1,1,1,1,1] => 1

[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [8,6,5,4,3,2,1,7] => [6,8,5,4,3,2,1,7] => [6,1,1] => 1

[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]] => [8,5,6,4,3,2,1,7] => [5,6,8,4,3,2,1,7] => [5,1,1,1] => 1

[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]] => [8,6,4,5,3,2,1,7] => [4,6,8,5,3,2,1,7] => [5,1,1,1] => 1

[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]] => [8,5,4,6,3,2,1,7] => [5,4,8,6,3,2,1,7] => [5,2,1] => 2

[[.,[.,[.,[[[.,.],.],.]]]],[.,.]] => [8,4,5,6,3,2,1,7] => [4,5,6,8,3,2,1,7] => [4,1,1,1,1] => 1

[[.,[.,[[.,.],[[.,.],.]]]],[.,.]] => [8,5,6,3,4,2,1,7] => [3,5,6,8,4,2,1,7] => [4,1,1,1,1] => 1

[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]] => [8,5,4,3,6,2,1,7] => [5,4,8,3,6,2,1,7] => [5,1,1,1] => 1

[[.,[[.,.],[.,[[.,.],.]]]],[.,.]] => [8,5,6,4,2,3,1,7] => [2,5,6,8,4,3,1,7] => [4,1,1,1,1] => 1

[[.,[[.,.],[[.,.],[.,.]]]],[.,.]] => [8,6,4,5,2,3,1,7] => [2,4,6,8,5,3,1,7] => [4,1,1,1,1] => 1

[[.,[[.,.],[[[.,.],.],.]]],[.,.]] => [8,4,5,6,2,3,1,7] => [2,4,5,6,8,3,1,7] => [3,1,1,1,1,1] => 1

[[.,[[[.,.],[.,.]],[.,.]]],[.,.]] => [8,6,4,2,3,5,1,7] => [2,4,6,8,3,5,1,7] => [3,1,1,1,1,1] => 1

[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]] => [8,5,4,3,2,6,1,7] => [5,4,8,3,2,6,1,7] => [5,1,1,1] => 1

[[.,[[.,[.,[[.,.],.]]],.]],[.,.]] => [8,4,5,3,2,6,1,7] => [4,5,3,8,2,6,1,7] => [4,1,1,1,1] => 1

[[.,[[.,[[.,.],[.,.]]],.]],[.,.]] => [8,5,3,4,2,6,1,7] => [3,5,4,8,2,6,1,7] => [4,1,1,1,1] => 1

[[.,[[[.,.],[.,[.,.]]],.]],[.,.]] => [8,5,4,2,3,6,1,7] => [2,5,4,8,3,6,1,7] => [4,1,1,1,1] => 1

[[.,[[[.,.],[[.,.],.]],.]],[.,.]] => [8,4,5,2,3,6,1,7] => [2,4,5,3,8,6,1,7] => [3,2,1,1,1] => 2

[[.,[[[.,[.,.]],[.,.]],.]],[.,.]] => [8,5,3,2,4,6,1,7] => [3,5,2,8,4,6,1,7] => [3,2,1,1,1] => 2

[[.,[[[[.,[.,.]],.],.],.]],[.,.]] => [8,3,2,4,5,6,1,7] => [3,2,4,5,8,6,1,7] => [3,2,1,1,1] => 2

[[.,[[[[[.,.],.],.],.],.]],[.,.]] => [8,2,3,4,5,6,1,7] => [2,3,4,5,6,8,1,7] => [2,1,1,1,1,1,1] => 1

[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [8,6,5,4,3,1,2,7] => [1,6,8,5,4,3,2,7] => [5,1,1,1] => 1

[[[.,.],[.,[[.,[.,.]],.]]],[.,.]] => [8,5,4,6,3,1,2,7] => [1,5,4,8,6,3,2,7] => [4,2,1,1] => 2

[[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [8,6,5,3,4,1,2,7] => [1,3,6,8,5,4,2,7] => [4,1,1,1,1] => 1

[[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [8,5,6,3,4,1,2,7] => [1,3,5,6,8,4,2,7] => [3,1,1,1,1,1] => 1

[[[.,.],[[.,[.,.]],[.,.]]],[.,.]] => [8,6,4,3,5,1,2,7] => [1,4,6,8,3,5,2,7] => [3,1,1,1,1,1] => 1

[[[.,.],[[[.,.],[.,.]],.]],[.,.]] => [8,5,3,4,6,1,2,7] => [1,3,5,4,8,6,2,7] => [3,2,1,1,1] => 2

[[[.,.],[[[[.,.],.],.],.]],[.,.]] => [8,3,4,5,6,1,2,7] => [1,3,4,5,6,8,2,7] => [2,1,1,1,1,1,1] => 1

[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [8,6,5,4,2,1,3,7] => [2,6,8,5,4,1,3,7] => [4,1,1,1,1] => 1

[[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [8,6,4,5,2,1,3,7] => [2,4,6,8,5,1,3,7] => [3,1,1,1,1,1] => 1

[[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [8,4,5,6,2,1,3,7] => [2,4,5,6,8,1,3,7] => [2,1,1,1,1,1,1] => 1

[[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [8,6,5,4,1,2,3,7] => [1,2,6,8,5,4,3,7] => [4,1,1,1,1] => 1

[[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [8,6,4,5,1,2,3,7] => [1,2,4,6,8,5,3,7] => [3,1,1,1,1,1] => 1

[[[[.,.],.],[[.,[.,.]],.]],[.,.]] => [8,5,4,6,1,2,3,7] => [1,2,5,4,8,6,3,7] => [3,2,1,1,1] => 2

[[[[.,.],.],[[[.,.],.],.]],[.,.]] => [8,4,5,6,1,2,3,7] => [1,2,4,5,6,8,3,7] => [2,1,1,1,1,1,1] => 1

[[[.,[.,[.,.]]],[[.,.],.]],[.,.]] => [8,5,6,3,2,1,4,7] => [3,5,6,8,2,1,4,7] => [3,1,1,1,1,1] => 1

[[[.,[[.,.],.]],[.,[.,.]]],[.,.]] => [8,6,5,2,3,1,4,7] => [2,3,6,8,5,1,4,7] => [3,1,1,1,1,1] => 1

[[[.,[[.,.],.]],[[.,.],.]],[.,.]] => [8,5,6,2,3,1,4,7] => [2,3,5,6,8,1,4,7] => [2,1,1,1,1,1,1] => 1

[[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [8,6,5,3,1,2,4,7] => [1,3,6,8,5,2,4,7] => [3,1,1,1,1,1] => 1

[[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [8,5,6,3,1,2,4,7] => [1,3,5,6,8,2,4,7] => [2,1,1,1,1,1,1] => 1

[[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [8,5,6,2,1,3,4,7] => [2,1,5,6,8,3,4,7] => [2,2,1,1,1,1] => 2

[[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [8,6,5,1,2,3,4,7] => [1,2,3,6,8,5,4,7] => [3,1,1,1,1,1] => 1

[[[[[.,.],.],.],[[.,.],.]],[.,.]] => [8,5,6,1,2,3,4,7] => [1,2,3,5,6,8,4,7] => [2,1,1,1,1,1,1] => 1

[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [8,6,4,3,2,1,5,7] => [4,6,8,3,2,1,5,7] => [4,1,1,1,1] => 1

[[[.,[.,[[.,.],.]]],[.,.]],[.,.]] => [8,6,3,4,2,1,5,7] => [3,4,6,8,2,1,5,7] => [3,1,1,1,1,1] => 1

[[[.,[[.,.],[.,.]]],[.,.]],[.,.]] => [8,6,4,2,3,1,5,7] => [2,4,6,8,3,1,5,7] => [3,1,1,1,1,1] => 1

[[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => [8,6,3,2,4,1,5,7] => [3,2,6,8,4,1,5,7] => [3,2,1,1,1] => 2

[[[.,[[[.,.],.],.]],[.,.]],[.,.]] => [8,6,2,3,4,1,5,7] => [2,3,4,6,8,1,5,7] => [2,1,1,1,1,1,1] => 1

[[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [8,6,4,3,1,2,5,7] => [1,4,6,8,3,2,5,7] => [3,1,1,1,1,1] => 1

[[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [8,6,3,4,1,2,5,7] => [1,3,4,6,8,2,5,7] => [2,1,1,1,1,1,1] => 1

[[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [8,6,4,2,1,3,5,7] => [2,4,6,8,1,3,5,7] => [2,1,1,1,1,1,1] => 1

[[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [8,6,4,1,2,3,5,7] => [1,2,4,6,8,3,5,7] => [2,1,1,1,1,1,1] => 1

[[[[.,[[.,.],.]],.],[.,.]],[.,.]] => [8,6,2,3,1,4,5,7] => [2,3,1,6,8,4,5,7] => [2,2,1,1,1,1] => 2

[[[[[[.,.],.],.],.],[.,.]],[.,.]] => [8,6,1,2,3,4,5,7] => [1,2,3,4,6,8,5,7] => [2,1,1,1,1,1,1] => 1

[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]] => [8,5,4,3,2,1,6,7] => [5,4,8,3,2,1,6,7] => [5,1,1,1] => 1

[[[.,[.,[.,[[.,.],.]]]],.],[.,.]] => [8,4,5,3,2,1,6,7] => [4,5,3,8,2,1,6,7] => [4,1,1,1,1] => 1

[[[.,[.,[[.,[.,.]],.]]],.],[.,.]] => [8,4,3,5,2,1,6,7] => [4,3,5,8,2,1,6,7] => [4,1,1,1,1] => 1

[[[.,[[.,.],[.,[.,.]]]],.],[.,.]] => [8,5,4,2,3,1,6,7] => [2,5,4,8,3,1,6,7] => [4,1,1,1,1] => 1

[[[.,[[[.,.],[.,.]],.]],.],[.,.]] => [8,4,2,3,5,1,6,7] => [2,4,3,5,8,1,6,7] => [3,1,1,1,1,1] => 1

[[[.,[[[.,[.,.]],.],.]],.],[.,.]] => [8,3,2,4,5,1,6,7] => [3,2,4,5,8,1,6,7] => [3,1,1,1,1,1] => 1

[[[.,[[[[.,.],.],.],.]],.],[.,.]] => [8,2,3,4,5,1,6,7] => [2,3,4,5,1,8,6,7] => [2,2,1,1,1,1] => 2

[[[[.,.],[.,[.,[.,.]]]],.],[.,.]] => [8,5,4,3,1,2,6,7] => [1,5,4,8,3,2,6,7] => [4,1,1,1,1] => 1

[[[[.,.],[[.,.],[.,.]]],.],[.,.]] => [8,5,3,4,1,2,6,7] => [1,3,5,4,8,2,6,7] => [3,1,1,1,1,1] => 1

[[[[.,.],[[.,[.,.]],.]],.],[.,.]] => [8,4,3,5,1,2,6,7] => [1,4,3,5,8,2,6,7] => [3,1,1,1,1,1] => 1

[[[[.,.],[[[.,.],.],.]],.],[.,.]] => [8,3,4,5,1,2,6,7] => [1,3,4,5,2,8,6,7] => [2,2,1,1,1,1] => 2

[[[[.,[.,.]],[[.,.],.]],.],[.,.]] => [8,4,5,2,1,3,6,7] => [2,4,5,1,8,3,6,7] => [2,2,1,1,1,1] => 2

[[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [8,5,4,1,2,3,6,7] => [1,2,5,4,8,3,6,7] => [3,1,1,1,1,1] => 1

[[[[[.,.],.],[[.,.],.]],.],[.,.]] => [8,4,5,1,2,3,6,7] => [1,2,4,5,3,8,6,7] => [2,2,1,1,1,1] => 2

[[[[.,[[.,.],.]],[.,.]],.],[.,.]] => [8,5,2,3,1,4,6,7] => [2,3,5,1,8,4,6,7] => [2,2,1,1,1,1] => 2

[[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [8,5,3,1,2,4,6,7] => [1,3,5,2,8,4,6,7] => [2,2,1,1,1,1] => 2

[[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [8,5,2,1,3,4,6,7] => [2,1,5,3,8,4,6,7] => [2,2,2,1,1] => 2

[[[[[[.,.],.],.],[.,.]],.],[.,.]] => [8,5,1,2,3,4,6,7] => [1,2,3,5,4,8,6,7] => [2,2,1,1,1,1] => 2

[[[[.,[.,[.,[.,.]]]],.],.],[.,.]] => [8,4,3,2,1,5,6,7] => [4,3,2,8,1,5,6,7] => [4,1,1,1,1] => 1

[[[[.,[.,[[.,.],.]]],.],.],[.,.]] => [8,3,4,2,1,5,6,7] => [3,4,2,1,8,5,6,7] => [3,2,1,1,1] => 2

[[[[.,[[.,.],[.,.]]],.],.],[.,.]] => [8,4,2,3,1,5,6,7] => [2,4,3,1,8,5,6,7] => [3,2,1,1,1] => 2

[[[[.,[[.,[.,.]],.]],.],.],[.,.]] => [8,3,2,4,1,5,6,7] => [3,2,4,1,8,5,6,7] => [3,2,1,1,1] => 2

[[[[.,[[[.,.],.],.]],.],.],[.,.]] => [8,2,3,4,1,5,6,7] => [2,3,4,1,5,8,6,7] => [2,2,1,1,1,1] => 2

[[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [8,4,3,1,2,5,6,7] => [1,4,3,2,8,5,6,7] => [3,2,1,1,1] => 2

[[[[[.,.],[[.,.],.]],.],.],[.,.]] => [8,3,4,1,2,5,6,7] => [1,3,4,2,5,8,6,7] => [2,2,1,1,1,1] => 2

[[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [8,4,2,1,3,5,6,7] => [2,4,1,3,8,5,6,7] => [2,2,1,1,1,1] => 2

[[[[[[.,.],.],[.,.]],.],.],[.,.]] => [8,4,1,2,3,5,6,7] => [1,2,4,3,5,8,6,7] => [2,2,1,1,1,1] => 2

[[[[[.,[.,[.,.]]],.],.],.],[.,.]] => [8,3,2,1,4,5,6,7] => [3,2,1,4,8,5,6,7] => [3,2,1,1,1] => 2

[[[[[.,[[.,.],.]],.],.],.],[.,.]] => [8,2,3,1,4,5,6,7] => [2,3,1,4,5,8,6,7] => [2,2,1,1,1,1] => 2

[[[[[[.,.],[.,.]],.],.],.],[.,.]] => [8,3,1,2,4,5,6,7] => [1,3,2,4,5,8,6,7] => [2,2,1,1,1,1] => 2

[[[[[[.,[.,.]],.],.],.],.],[.,.]] => [8,2,1,3,4,5,6,7] => [2,1,3,4,5,8,6,7] => [2,2,1,1,1,1] => 2

[[[[[[[.,.],.],.],.],.],.],[.,.]] => [8,1,2,3,4,5,6,7] => [1,2,3,4,5,6,8,7] => [2,1,1,1,1,1,1] => 1

[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [7,6,5,4,3,2,1,8] => [7,6,5,4,3,2,1,8] => [7,1] => 1

[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => [6,7,5,4,3,2,1,8] => [6,7,5,4,3,2,1,8] => [6,1,1] => 1

[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.] => [7,5,6,4,3,2,1,8] => [5,7,6,4,3,2,1,8] => [6,1,1] => 1

[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => [6,5,7,4,3,2,1,8] => [6,5,7,4,3,2,1,8] => [6,1,1] => 1

[[.,[.,[.,[.,[[[.,.],.],.]]]]],.] => [5,6,7,4,3,2,1,8] => [5,6,7,4,3,2,1,8] => [5,1,1,1] => 1

[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => [7,6,4,5,3,2,1,8] => [4,7,6,5,3,2,1,8] => [6,1,1] => 1

[[.,[.,[.,[[.,.],[[.,.],.]]]]],.] => [6,7,4,5,3,2,1,8] => [4,6,7,5,3,2,1,8] => [5,1,1,1] => 1

[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.] => [7,5,4,6,3,2,1,8] => [5,7,4,6,3,2,1,8] => [5,1,1,1] => 1

[[.,[.,[.,[[[.,.],.],[.,.]]]]],.] => [7,4,5,6,3,2,1,8] => [4,5,7,6,3,2,1,8] => [5,1,1,1] => 1

[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => [6,5,4,7,3,2,1,8] => [6,5,4,7,3,2,1,8] => [6,1,1] => 1

[[.,[.,[.,[[.,[[.,.],.]],.]]]],.] => [5,6,4,7,3,2,1,8] => [5,6,4,7,3,2,1,8] => [5,1,1,1] => 1

[[.,[.,[.,[[[.,.],[.,.]],.]]]],.] => [6,4,5,7,3,2,1,8] => [4,6,5,7,3,2,1,8] => [5,1,1,1] => 1

[[.,[.,[.,[[[.,[.,.]],.],.]]]],.] => [5,4,6,7,3,2,1,8] => [5,4,6,7,3,2,1,8] => [5,1,1,1] => 1

[[.,[.,[.,[[[[.,.],.],.],.]]]],.] => [4,5,6,7,3,2,1,8] => [4,5,6,7,3,2,1,8] => [4,1,1,1,1] => 1

[[.,[.,[[.,.],[[.,.],[.,.]]]]],.] => [7,5,6,3,4,2,1,8] => [3,5,7,6,4,2,1,8] => [5,1,1,1] => 1

[[.,[.,[[.,.],[[[.,.],.],.]]]],.] => [5,6,7,3,4,2,1,8] => [3,5,6,7,4,2,1,8] => [4,1,1,1,1] => 1

[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.] => [7,6,4,3,5,2,1,8] => [4,7,6,3,5,2,1,8] => [5,1,1,1] => 1

[[.,[.,[[[.,.],.],[.,[.,.]]]]],.] => [7,6,3,4,5,2,1,8] => [3,4,7,6,5,2,1,8] => [5,1,1,1] => 1

[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.] => [7,5,4,3,6,2,1,8] => [5,7,4,3,6,2,1,8] => [5,1,1,1] => 1

[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.] => [6,5,4,3,7,2,1,8] => [6,5,4,3,7,2,1,8] => [6,1,1] => 1

[[.,[.,[[.,[.,[[.,.],.]]],.]]],.] => [5,6,4,3,7,2,1,8] => [5,6,4,3,7,2,1,8] => [5,1,1,1] => 1

[[.,[.,[[.,[[.,[.,.]],.]],.]]],.] => [5,4,6,3,7,2,1,8] => [5,4,6,3,7,2,1,8] => [5,1,1,1] => 1

[[.,[.,[[[.,.],[.,[.,.]]],.]]],.] => [6,5,3,4,7,2,1,8] => [3,6,5,4,7,2,1,8] => [5,1,1,1] => 1

[[.,[.,[[[.,.],[[.,.],.]],.]]],.] => [5,6,3,4,7,2,1,8] => [3,5,6,4,7,2,1,8] => [4,1,1,1,1] => 1

[[.,[.,[[[.,[.,[.,.]]],.],.]]],.] => [5,4,3,6,7,2,1,8] => [5,4,3,6,7,2,1,8] => [5,1,1,1] => 1

[[.,[.,[[[[[.,.],.],.],.],.]]],.] => [3,4,5,6,7,2,1,8] => [3,4,5,6,7,2,1,8] => [3,1,1,1,1,1] => 1

[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.] => [7,6,5,4,2,3,1,8] => [2,7,6,5,4,3,1,8] => [6,1,1] => 1

[[.,[[.,.],[.,[.,[[.,.],.]]]]],.] => [6,7,5,4,2,3,1,8] => [2,6,7,5,4,3,1,8] => [5,1,1,1] => 1

[[.,[[.,.],[.,[[.,.],[.,.]]]]],.] => [7,5,6,4,2,3,1,8] => [2,5,7,6,4,3,1,8] => [5,1,1,1] => 1

[[.,[[.,.],[.,[[[.,.],.],.]]]],.] => [5,6,7,4,2,3,1,8] => [2,5,6,7,4,3,1,8] => [4,1,1,1,1] => 1

[[.,[[.,.],[[.,.],[[.,.],.]]]],.] => [6,7,4,5,2,3,1,8] => [2,4,6,7,5,3,1,8] => [4,1,1,1,1] => 1

[[.,[[.,.],[[.,[[.,.],.]],.]]],.] => [5,6,4,7,2,3,1,8] => [2,5,6,4,7,3,1,8] => [4,1,1,1,1] => 1

[[.,[[.,.],[[[.,[.,.]],.],.]]],.] => [5,4,6,7,2,3,1,8] => [2,5,4,6,7,3,1,8] => [4,1,1,1,1] => 1

[[.,[[.,.],[[[[.,.],.],.],.]]],.] => [4,5,6,7,2,3,1,8] => [2,4,5,6,7,3,1,8] => [3,1,1,1,1,1] => 1

[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.] => [7,6,5,3,2,4,1,8] => [3,7,6,5,2,4,1,8] => [5,1,1,1] => 1

[[.,[[.,[.,.]],[[.,.],[.,.]]]],.] => [7,5,6,3,2,4,1,8] => [3,5,7,6,2,4,1,8] => [4,1,1,1,1] => 1

[[.,[[.,[.,.]],[[.,[.,.]],.]]],.] => [6,5,7,3,2,4,1,8] => [3,6,5,7,2,4,1,8] => [4,1,1,1,1] => 1

[[.,[[.,[.,.]],[[[.,.],.],.]]],.] => [5,6,7,3,2,4,1,8] => [3,5,6,7,2,4,1,8] => [3,1,1,1,1,1] => 1

[[.,[[[.,.],.],[.,[.,[.,.]]]]],.] => [7,6,5,2,3,4,1,8] => [2,3,7,6,5,4,1,8] => [5,1,1,1] => 1

[[.,[[[.,.],.],[.,[[.,.],.]]]],.] => [6,7,5,2,3,4,1,8] => [2,3,6,7,5,4,1,8] => [4,1,1,1,1] => 1

[[.,[[[.,.],.],[[.,.],[.,.]]]],.] => [7,5,6,2,3,4,1,8] => [2,3,5,7,6,4,1,8] => [4,1,1,1,1] => 1

[[.,[[[.,.],.],[[.,[.,.]],.]]],.] => [6,5,7,2,3,4,1,8] => [2,3,6,5,7,4,1,8] => [4,1,1,1,1] => 1

[[.,[[[.,.],.],[[[.,.],.],.]]],.] => [5,6,7,2,3,4,1,8] => [2,3,5,6,7,4,1,8] => [3,1,1,1,1,1] => 1

[[.,[[[.,[.,.]],.],[.,[.,.]]]],.] => [7,6,3,2,4,5,1,8] => [3,2,7,6,4,5,1,8] => [4,2,1,1] => 2

[[.,[[[.,[.,.]],.],[[.,.],.]]],.] => [6,7,3,2,4,5,1,8] => [3,2,6,7,4,5,1,8] => [3,2,1,1,1] => 2

[[.,[[[[.,.],.],.],[.,[.,.]]]],.] => [7,6,2,3,4,5,1,8] => [2,3,4,7,6,5,1,8] => [4,1,1,1,1] => 1

[[.,[[[[.,.],.],.],[[.,.],.]]],.] => [6,7,2,3,4,5,1,8] => [2,3,4,6,7,5,1,8] => [3,1,1,1,1,1] => 1

[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.] => [7,5,4,3,2,6,1,8] => [5,7,4,3,2,6,1,8] => [5,1,1,1] => 1

[[.,[[.,[[.,.],[.,.]]],[.,.]]],.] => [7,5,3,4,2,6,1,8] => [3,5,7,4,2,6,1,8] => [4,1,1,1,1] => 1

[[.,[[[.,.],[[.,.],.]],[.,.]]],.] => [7,4,5,2,3,6,1,8] => [2,4,5,7,3,6,1,8] => [3,1,1,1,1,1] => 1

[[.,[[[.,[.,.]],[.,.]],[.,.]]],.] => [7,5,3,2,4,6,1,8] => [3,5,7,2,4,6,1,8] => [3,1,1,1,1,1] => 1

[[.,[[[.,[.,[.,.]]],.],[.,.]]],.] => [7,4,3,2,5,6,1,8] => [4,3,7,2,5,6,1,8] => [4,1,1,1,1] => 1

[[.,[[[[[.,.],.],.],.],[.,.]]],.] => [7,2,3,4,5,6,1,8] => [2,3,4,5,7,6,1,8] => [3,1,1,1,1,1] => 1

[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.] => [6,5,4,3,2,7,1,8] => [6,5,4,3,2,7,1,8] => [6,1,1] => 1

[[.,[[.,[.,[.,[[.,.],.]]]],.]],.] => [5,6,4,3,2,7,1,8] => [5,6,4,3,2,7,1,8] => [5,1,1,1] => 1

[[.,[[.,[.,[[.,[.,.]],.]]],.]],.] => [5,4,6,3,2,7,1,8] => [5,4,6,3,2,7,1,8] => [5,1,1,1] => 1

[[.,[[.,[[.,.],[[.,.],.]]],.]],.] => [5,6,3,4,2,7,1,8] => [3,5,6,4,2,7,1,8] => [4,1,1,1,1] => 1

[[.,[[.,[[.,[.,.]],[.,.]]],.]],.] => [6,4,3,5,2,7,1,8] => [4,6,3,5,2,7,1,8] => [4,1,1,1,1] => 1

[[.,[[.,[[[.,.],.],[.,.]]],.]],.] => [6,3,4,5,2,7,1,8] => [3,4,6,5,2,7,1,8] => [4,1,1,1,1] => 1

[[.,[[.,[[.,[.,[.,.]]],.]],.]],.] => [5,4,3,6,2,7,1,8] => [5,4,3,6,2,7,1,8] => [5,1,1,1] => 1

[[.,[[.,[[.,[[.,.],.]],.]],.]],.] => [4,5,3,6,2,7,1,8] => [4,5,3,6,2,7,1,8] => [4,1,1,1,1] => 1

[[.,[[.,[[[.,.],[.,.]],.]],.]],.] => [5,3,4,6,2,7,1,8] => [3,5,4,6,2,7,1,8] => [4,1,1,1,1] => 1

[[.,[[.,[[[.,[.,.]],.],.]],.]],.] => [4,3,5,6,2,7,1,8] => [4,3,5,6,2,7,1,8] => [4,1,1,1,1] => 1

[[.,[[.,[[[[.,.],.],.],.]],.]],.] => [3,4,5,6,2,7,1,8] => [3,4,5,6,2,7,1,8] => [3,1,1,1,1,1] => 1

[[.,[[[.,.],[[.,[.,.]],.]],.]],.] => [5,4,6,2,3,7,1,8] => [2,5,4,6,3,7,1,8] => [4,1,1,1,1] => 1

[[.,[[[.,[.,.]],[.,[.,.]]],.]],.] => [6,5,3,2,4,7,1,8] => [3,6,5,2,4,7,1,8] => [4,1,1,1,1] => 1

[[.,[[[.,[.,.]],[[.,.],.]],.]],.] => [5,6,3,2,4,7,1,8] => [3,5,6,2,4,7,1,8] => [3,1,1,1,1,1] => 1

[[.,[[[[.,.],.],[[.,.],.]],.]],.] => [5,6,2,3,4,7,1,8] => [2,3,5,6,4,7,1,8] => [3,1,1,1,1,1] => 1

[[.,[[[.,[[.,.],.]],[.,.]],.]],.] => [6,3,4,2,5,7,1,8] => [3,4,6,2,5,7,1,8] => [3,1,1,1,1,1] => 1

[[.,[[[[.,.],[.,.]],[.,.]],.]],.] => [6,4,2,3,5,7,1,8] => [2,4,6,3,5,7,1,8] => [3,1,1,1,1,1] => 1

[[.,[[[[.,[.,.]],.],[.,.]],.]],.] => [6,3,2,4,5,7,1,8] => [3,2,6,4,5,7,1,8] => [3,2,1,1,1] => 2

[[.,[[[[[.,.],.],.],[.,.]],.]],.] => [6,2,3,4,5,7,1,8] => [2,3,4,6,5,7,1,8] => [3,1,1,1,1,1] => 1

[[.,[[[.,[.,[.,[.,.]]]],.],.]],.] => [5,4,3,2,6,7,1,8] => [5,4,3,2,6,7,1,8] => [5,1,1,1] => 1

[[.,[[[[.,.],[.,[.,.]]],.],.]],.] => [5,4,2,3,6,7,1,8] => [2,5,4,3,6,7,1,8] => [4,1,1,1,1] => 1

[[.,[[[[[.,.],.],[.,.]],.],.]],.] => [5,2,3,4,6,7,1,8] => [2,3,5,4,6,7,1,8] => [3,1,1,1,1,1] => 1

[[.,[[[[.,[.,[.,.]]],.],.],.]],.] => [4,3,2,5,6,7,1,8] => [4,3,2,5,6,7,1,8] => [4,1,1,1,1] => 1

[[.,[[[[.,[[.,.],.]],.],.],.]],.] => [3,4,2,5,6,7,1,8] => [3,4,2,5,6,7,1,8] => [3,1,1,1,1,1] => 1

[[.,[[[[[.,[.,.]],.],.],.],.]],.] => [3,2,4,5,6,7,1,8] => [3,2,4,5,6,7,1,8] => [3,1,1,1,1,1] => 1

[[.,[[[[[[.,.],.],.],.],.],.]],.] => [2,3,4,5,6,7,1,8] => [2,3,4,5,6,7,1,8] => [2,1,1,1,1,1,1] => 1

[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [7,6,5,4,3,1,2,8] => [1,7,6,5,4,3,2,8] => [6,1,1] => 1

[[[.,.],[.,[.,[.,[[.,.],.]]]]],.] => [6,7,5,4,3,1,2,8] => [1,6,7,5,4,3,2,8] => [5,1,1,1] => 1

[[[.,.],[.,[.,[[.,[.,.]],.]]]],.] => [6,5,7,4,3,1,2,8] => [1,6,5,7,4,3,2,8] => [5,1,1,1] => 1

[[[.,.],[.,[.,[[[.,.],.],.]]]],.] => [5,6,7,4,3,1,2,8] => [1,5,6,7,4,3,2,8] => [4,1,1,1,1] => 1

[[[.,.],[.,[[.,.],[.,[.,.]]]]],.] => [7,6,4,5,3,1,2,8] => [1,4,7,6,5,3,2,8] => [5,1,1,1] => 1

[[[.,.],[.,[[.,[.,.]],[.,.]]]],.] => [7,5,4,6,3,1,2,8] => [1,5,7,4,6,3,2,8] => [4,1,1,1,1] => 1

[[[.,.],[.,[[[.,[.,.]],.],.]]],.] => [5,4,6,7,3,1,2,8] => [1,5,4,6,7,3,2,8] => [4,1,1,1,1] => 1

[[[.,.],[[.,.],[.,[.,[.,.]]]]],.] => [7,6,5,3,4,1,2,8] => [1,3,7,6,5,4,2,8] => [5,1,1,1] => 1

[[[.,.],[[.,.],[.,[[.,.],.]]]],.] => [6,7,5,3,4,1,2,8] => [1,3,6,7,5,4,2,8] => [4,1,1,1,1] => 1

[[[.,.],[[.,.],[[.,.],[.,.]]]],.] => [7,5,6,3,4,1,2,8] => [1,3,5,7,6,4,2,8] => [4,1,1,1,1] => 1

[[[.,.],[[.,.],[[.,[.,.]],.]]],.] => [6,5,7,3,4,1,2,8] => [1,3,6,5,7,4,2,8] => [4,1,1,1,1] => 1

[[[.,.],[[.,.],[[[.,.],.],.]]],.] => [5,6,7,3,4,1,2,8] => [1,3,5,6,7,4,2,8] => [3,1,1,1,1,1] => 1

[[[.,.],[[.,[.,.]],[[.,.],.]]],.] => [6,7,4,3,5,1,2,8] => [1,4,6,7,3,5,2,8] => [3,1,1,1,1,1] => 1

[[[.,.],[[[.,.],.],[[.,.],.]]],.] => [6,7,3,4,5,1,2,8] => [1,3,4,6,7,5,2,8] => [3,1,1,1,1,1] => 1

[[[.,.],[[.,[.,[.,.]]],[.,.]]],.] => [7,5,4,3,6,1,2,8] => [1,5,7,4,3,6,2,8] => [4,1,1,1,1] => 1

[[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [7,5,3,4,6,1,2,8] => [1,3,5,7,4,6,2,8] => [3,1,1,1,1,1] => 1

[[[.,.],[[[[.,.],.],.],[.,.]]],.] => [7,3,4,5,6,1,2,8] => [1,3,4,5,7,6,2,8] => [3,1,1,1,1,1] => 1

[[[.,.],[[[.,.],[.,[.,.]]],.]],.] => [6,5,3,4,7,1,2,8] => [1,3,6,5,4,7,2,8] => [4,1,1,1,1] => 1

[[[.,.],[[[.,.],[[.,.],.]],.]],.] => [5,6,3,4,7,1,2,8] => [1,3,5,6,4,7,2,8] => [3,1,1,1,1,1] => 1

[[[.,.],[[[[.,.],.],[.,.]],.]],.] => [6,3,4,5,7,1,2,8] => [1,3,4,6,5,7,2,8] => [3,1,1,1,1,1] => 1

[[[.,.],[[[.,[[.,.],.]],.],.]],.] => [4,5,3,6,7,1,2,8] => [1,4,5,3,6,7,2,8] => [3,1,1,1,1,1] => 1

[[[.,.],[[[[.,.],[.,.]],.],.]],.] => [5,3,4,6,7,1,2,8] => [1,3,5,4,6,7,2,8] => [3,1,1,1,1,1] => 1

[[[.,.],[[[[[.,.],.],.],.],.]],.] => [3,4,5,6,7,1,2,8] => [1,3,4,5,6,7,2,8] => [2,1,1,1,1,1,1] => 1

[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [7,6,5,4,2,1,3,8] => [2,7,6,5,4,1,3,8] => [5,1,1,1] => 1

[[[.,[.,.]],[.,[.,[[.,.],.]]]],.] => [6,7,5,4,2,1,3,8] => [2,6,7,5,4,1,3,8] => [4,1,1,1,1] => 1

[[[.,[.,.]],[.,[[.,[.,.]],.]]],.] => [6,5,7,4,2,1,3,8] => [2,6,5,7,4,1,3,8] => [4,1,1,1,1] => 1

[[[.,[.,.]],[[.,[.,.]],[.,.]]],.] => [7,5,4,6,2,1,3,8] => [2,5,7,4,6,1,3,8] => [3,1,1,1,1,1] => 1

[[[.,[.,.]],[[.,[.,[.,.]]],.]],.] => [6,5,4,7,2,1,3,8] => [2,6,5,4,7,1,3,8] => [4,1,1,1,1] => 1

[[[.,[.,.]],[[.,[[.,.],.]],.]],.] => [5,6,4,7,2,1,3,8] => [2,5,6,4,7,1,3,8] => [3,1,1,1,1,1] => 1

[[[.,[.,.]],[[[.,[.,.]],.],.]],.] => [5,4,6,7,2,1,3,8] => [2,5,4,6,7,1,3,8] => [3,1,1,1,1,1] => 1

[[[.,[.,.]],[[[[.,.],.],.],.]],.] => [4,5,6,7,2,1,3,8] => [2,4,5,6,7,1,3,8] => [2,1,1,1,1,1,1] => 1

[[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [7,6,5,4,1,2,3,8] => [1,2,7,6,5,4,3,8] => [5,1,1,1] => 1

[[[[.,.],.],[.,[.,[[.,.],.]]]],.] => [6,7,5,4,1,2,3,8] => [1,2,6,7,5,4,3,8] => [4,1,1,1,1] => 1

[[[[.,.],.],[.,[[.,.],[.,.]]]],.] => [7,5,6,4,1,2,3,8] => [1,2,5,7,6,4,3,8] => [4,1,1,1,1] => 1

[[[[.,.],.],[.,[[[.,.],.],.]]],.] => [5,6,7,4,1,2,3,8] => [1,2,5,6,7,4,3,8] => [3,1,1,1,1,1] => 1

[[[[.,.],.],[[.,.],[[.,.],.]]],.] => [6,7,4,5,1,2,3,8] => [1,2,4,6,7,5,3,8] => [3,1,1,1,1,1] => 1

[[[[.,.],.],[[.,[[.,.],.]],.]],.] => [5,6,4,7,1,2,3,8] => [1,2,5,6,4,7,3,8] => [3,1,1,1,1,1] => 1

[[[[.,.],.],[[[.,[.,.]],.],.]],.] => [5,4,6,7,1,2,3,8] => [1,2,5,4,6,7,3,8] => [3,1,1,1,1,1] => 1

[[[[.,.],.],[[[[.,.],.],.],.]],.] => [4,5,6,7,1,2,3,8] => [1,2,4,5,6,7,3,8] => [2,1,1,1,1,1,1] => 1

[[[.,[.,[.,.]]],[.,[[.,.],.]]],.] => [6,7,5,3,2,1,4,8] => [3,6,7,5,2,1,4,8] => [4,1,1,1,1] => 1

[[[.,[.,[.,.]]],[[.,.],[.,.]]],.] => [7,5,6,3,2,1,4,8] => [3,5,7,6,2,1,4,8] => [4,1,1,1,1] => 1

[[[.,[[.,.],.]],[.,[.,[.,.]]]],.] => [7,6,5,2,3,1,4,8] => [2,3,7,6,5,1,4,8] => [4,1,1,1,1] => 1

[[[.,[[.,.],.]],[[[.,.],.],.]],.] => [5,6,7,2,3,1,4,8] => [2,3,5,6,7,1,4,8] => [2,1,1,1,1,1,1] => 1

[[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [7,6,5,3,1,2,4,8] => [1,3,7,6,5,2,4,8] => [4,1,1,1,1] => 1

[[[[.,.],[.,.]],[.,[[.,.],.]]],.] => [6,7,5,3,1,2,4,8] => [1,3,6,7,5,2,4,8] => [3,1,1,1,1,1] => 1

[[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [7,5,6,3,1,2,4,8] => [1,3,5,7,6,2,4,8] => [3,1,1,1,1,1] => 1

[[[[.,.],[.,.]],[[[.,.],.],.]],.] => [5,6,7,3,1,2,4,8] => [1,3,5,6,7,2,4,8] => [2,1,1,1,1,1,1] => 1

[[[[.,[.,.]],.],[.,[.,[.,.]]]],.] => [7,6,5,2,1,3,4,8] => [2,1,7,6,5,3,4,8] => [4,2,1,1] => 2

[[[[.,[.,.]],.],[[[.,.],.],.]],.] => [5,6,7,2,1,3,4,8] => [2,1,5,6,7,3,4,8] => [2,2,1,1,1,1] => 2

[[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [7,6,5,1,2,3,4,8] => [1,2,3,7,6,5,4,8] => [4,1,1,1,1] => 1

[[[[[.,.],.],.],[.,[[.,.],.]]],.] => [6,7,5,1,2,3,4,8] => [1,2,3,6,7,5,4,8] => [3,1,1,1,1,1] => 1

[[[[[.,.],.],.],[[.,.],[.,.]]],.] => [7,5,6,1,2,3,4,8] => [1,2,3,5,7,6,4,8] => [3,1,1,1,1,1] => 1

[[[[[.,.],.],.],[[.,[.,.]],.]],.] => [6,5,7,1,2,3,4,8] => [1,2,3,6,5,7,4,8] => [3,1,1,1,1,1] => 1

[[[[[.,.],.],.],[[[.,.],.],.]],.] => [5,6,7,1,2,3,4,8] => [1,2,3,5,6,7,4,8] => [2,1,1,1,1,1,1] => 1

[[[.,[.,[[.,.],.]]],[[.,.],.]],.] => [6,7,3,4,2,1,5,8] => [3,4,6,7,2,1,5,8] => [3,1,1,1,1,1] => 1

[[[.,[[.,[.,.]],.]],[.,[.,.]]],.] => [7,6,3,2,4,1,5,8] => [3,2,7,6,4,1,5,8] => [4,2,1,1] => 2

[[[.,[[[.,.],.],.]],[.,[.,.]]],.] => [7,6,2,3,4,1,5,8] => [2,3,4,7,6,1,5,8] => [3,1,1,1,1,1] => 1

[[[.,[[[.,.],.],.]],[[.,.],.]],.] => [6,7,2,3,4,1,5,8] => [2,3,4,6,7,1,5,8] => [2,1,1,1,1,1,1] => 1

[[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [7,6,4,3,1,2,5,8] => [1,4,7,6,3,2,5,8] => [4,1,1,1,1] => 1

[[[[.,.],[[.,.],.]],[[.,.],.]],.] => [6,7,3,4,1,2,5,8] => [1,3,4,6,7,2,5,8] => [2,1,1,1,1,1,1] => 1

[[[[.,[.,[.,.]]],.],[.,[.,.]]],.] => [7,6,3,2,1,4,5,8] => [3,2,7,6,1,4,5,8] => [3,2,1,1,1] => 2

[[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [7,6,3,1,2,4,5,8] => [1,3,2,7,6,4,5,8] => [3,2,1,1,1] => 2

[[[[[.,.],[.,.]],.],[[.,.],.]],.] => [6,7,3,1,2,4,5,8] => [1,3,2,6,7,4,5,8] => [2,2,1,1,1,1] => 2

[[[[[[.,.],.],.],.],[.,[.,.]]],.] => [7,6,1,2,3,4,5,8] => [1,2,3,4,7,6,5,8] => [3,1,1,1,1,1] => 1

[[[[[[.,.],.],.],.],[[.,.],.]],.] => [6,7,1,2,3,4,5,8] => [1,2,3,4,6,7,5,8] => [2,1,1,1,1,1,1] => 1

[[[.,[.,[[.,.],[.,.]]]],[.,.]],.] => [7,5,3,4,2,1,6,8] => [3,5,7,4,2,1,6,8] => [4,1,1,1,1] => 1

[[[.,[.,[[.,[.,.]],.]]],[.,.]],.] => [7,4,3,5,2,1,6,8] => [4,3,7,5,2,1,6,8] => [4,2,1,1] => 2

[[[.,[[.,.],[.,[.,.]]]],[.,.]],.] => [7,5,4,2,3,1,6,8] => [2,5,7,4,3,1,6,8] => [4,1,1,1,1] => 1

[[[.,[[.,[.,.]],[.,.]]],[.,.]],.] => [7,5,3,2,4,1,6,8] => [3,5,7,2,4,1,6,8] => [3,1,1,1,1,1] => 1

[[[.,[[.,[.,[.,.]]],.]],[.,.]],.] => [7,4,3,2,5,1,6,8] => [4,3,7,2,5,1,6,8] => [4,1,1,1,1] => 1

[[[.,[[[[.,.],.],.],.]],[.,.]],.] => [7,2,3,4,5,1,6,8] => [2,3,4,5,7,1,6,8] => [2,1,1,1,1,1,1] => 1

[[[[.,.],[.,[[.,.],.]]],[.,.]],.] => [7,4,5,3,1,2,6,8] => [1,4,5,7,3,2,6,8] => [3,1,1,1,1,1] => 1

[[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [7,5,3,4,1,2,6,8] => [1,3,5,7,4,2,6,8] => [3,1,1,1,1,1] => 1

[[[[.,.],[[[.,.],.],.]],[.,.]],.] => [7,3,4,5,1,2,6,8] => [1,3,4,5,7,2,6,8] => [2,1,1,1,1,1,1] => 1

[[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [7,5,4,1,2,3,6,8] => [1,2,5,7,4,3,6,8] => [3,1,1,1,1,1] => 1

[[[[[.,.],.],[[.,.],.]],[.,.]],.] => [7,4,5,1,2,3,6,8] => [1,2,4,5,7,3,6,8] => [2,1,1,1,1,1,1] => 1

[[[[.,[.,[.,.]]],[.,.]],[.,.]],.] => [7,5,3,2,1,4,6,8] => [3,5,7,2,1,4,6,8] => [3,1,1,1,1,1] => 1

[[[[.,[[.,.],.]],[.,.]],[.,.]],.] => [7,5,2,3,1,4,6,8] => [2,3,5,7,1,4,6,8] => [2,1,1,1,1,1,1] => 1

[[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [7,5,3,1,2,4,6,8] => [1,3,5,7,2,4,6,8] => [2,1,1,1,1,1,1] => 1

[[[[[.,[.,.]],.],[.,.]],[.,.]],.] => [7,5,2,1,3,4,6,8] => [2,1,5,7,3,4,6,8] => [2,2,1,1,1,1] => 2

[[[[[[.,.],.],.],[.,.]],[.,.]],.] => [7,5,1,2,3,4,6,8] => [1,2,3,5,7,4,6,8] => [2,1,1,1,1,1,1] => 1

[[[[.,[.,[.,[.,.]]]],.],[.,.]],.] => [7,4,3,2,1,5,6,8] => [4,3,7,2,1,5,6,8] => [4,1,1,1,1] => 1

[[[[.,[.,[[.,.],.]]],.],[.,.]],.] => [7,3,4,2,1,5,6,8] => [3,4,2,7,1,5,6,8] => [3,1,1,1,1,1] => 1

[[[[.,[[[.,.],.],.]],.],[.,.]],.] => [7,2,3,4,1,5,6,8] => [2,3,4,1,7,5,6,8] => [2,2,1,1,1,1] => 2

[[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [7,4,3,1,2,5,6,8] => [1,4,3,7,2,5,6,8] => [3,1,1,1,1,1] => 1

[[[[[[.,.],.],[.,.]],.],[.,.]],.] => [7,4,1,2,3,5,6,8] => [1,2,4,3,7,5,6,8] => [2,2,1,1,1,1] => 2

[[[[[.,[.,[.,.]]],.],.],[.,.]],.] => [7,3,2,1,4,5,6,8] => [3,2,1,7,4,5,6,8] => [3,2,1,1,1] => 2

[[[[[.,[[.,.],.]],.],.],[.,.]],.] => [7,2,3,1,4,5,6,8] => [2,3,1,4,7,5,6,8] => [2,2,1,1,1,1] => 2

[[[[[[.,[.,.]],.],.],.],[.,.]],.] => [7,2,1,3,4,5,6,8] => [2,1,3,4,7,5,6,8] => [2,2,1,1,1,1] => 2

[[[[[[[.,.],.],.],.],.],[.,.]],.] => [7,1,2,3,4,5,6,8] => [1,2,3,4,5,7,6,8] => [2,1,1,1,1,1,1] => 1

[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.] => [6,5,4,3,2,1,7,8] => [6,5,4,3,2,1,7,8] => [6,1,1] => 1

[[[.,[.,[.,[.,[[.,.],.]]]]],.],.] => [5,6,4,3,2,1,7,8] => [5,6,4,3,2,1,7,8] => [5,1,1,1] => 1

[[[.,[.,[.,[[.,[.,.]],.]]]],.],.] => [5,4,6,3,2,1,7,8] => [5,4,6,3,2,1,7,8] => [5,1,1,1] => 1

[[[.,[.,[.,[[[.,.],.],.]]]],.],.] => [4,5,6,3,2,1,7,8] => [4,5,6,3,2,1,7,8] => [4,1,1,1,1] => 1

[[[.,[.,[[.,.],[.,[.,.]]]]],.],.] => [6,5,3,4,2,1,7,8] => [3,6,5,4,2,1,7,8] => [5,1,1,1] => 1

[[[.,[.,[[.,[.,[.,.]]],.]]],.],.] => [5,4,3,6,2,1,7,8] => [5,4,3,6,2,1,7,8] => [5,1,1,1] => 1

[[[.,[[.,.],[[.,.],[.,.]]]],.],.] => [6,4,5,2,3,1,7,8] => [2,4,6,5,3,1,7,8] => [4,1,1,1,1] => 1

[[[.,[[.,.],[[[.,.],.],.]]],.],.] => [4,5,6,2,3,1,7,8] => [2,4,5,6,3,1,7,8] => [3,1,1,1,1,1] => 1

[[[.,[[.,[.,.]],[.,[.,.]]]],.],.] => [6,5,3,2,4,1,7,8] => [3,6,5,2,4,1,7,8] => [4,1,1,1,1] => 1

[[[.,[[.,[.,.]],[[.,.],.]]],.],.] => [5,6,3,2,4,1,7,8] => [3,5,6,2,4,1,7,8] => [3,1,1,1,1,1] => 1

[[[.,[[[.,.],.],[[.,.],.]]],.],.] => [5,6,2,3,4,1,7,8] => [2,3,5,6,4,1,7,8] => [3,1,1,1,1,1] => 1

[[[.,[[.,[.,[.,.]]],[.,.]]],.],.] => [6,4,3,2,5,1,7,8] => [4,6,3,2,5,1,7,8] => [4,1,1,1,1] => 1

[[[.,[[.,[[.,.],.]],[.,.]]],.],.] => [6,3,4,2,5,1,7,8] => [3,4,6,2,5,1,7,8] => [3,1,1,1,1,1] => 1

[[[.,[[[.,.],[.,.]],[.,.]]],.],.] => [6,4,2,3,5,1,7,8] => [2,4,6,3,5,1,7,8] => [3,1,1,1,1,1] => 1

[[[.,[[[[.,.],.],.],[.,.]]],.],.] => [6,2,3,4,5,1,7,8] => [2,3,4,6,5,1,7,8] => [3,1,1,1,1,1] => 1

[[[.,[[.,[.,[.,[.,.]]]],.]],.],.] => [5,4,3,2,6,1,7,8] => [5,4,3,2,6,1,7,8] => [5,1,1,1] => 1

[[[.,[[.,[.,[[.,.],.]]],.]],.],.] => [4,5,3,2,6,1,7,8] => [4,5,3,2,6,1,7,8] => [4,1,1,1,1] => 1

[[[.,[[.,[[.,.],[.,.]]],.]],.],.] => [5,3,4,2,6,1,7,8] => [3,5,4,2,6,1,7,8] => [4,1,1,1,1] => 1

[[[.,[[.,[[.,[.,.]],.]],.]],.],.] => [4,3,5,2,6,1,7,8] => [4,3,5,2,6,1,7,8] => [4,1,1,1,1] => 1

[[[.,[[.,[[[.,.],.],.]],.]],.],.] => [3,4,5,2,6,1,7,8] => [3,4,5,2,6,1,7,8] => [3,1,1,1,1,1] => 1

[[[.,[[[[.,.],.],[.,.]],.]],.],.] => [5,2,3,4,6,1,7,8] => [2,3,5,4,6,1,7,8] => [3,1,1,1,1,1] => 1

[[[.,[[[.,[.,[.,.]]],.],.]],.],.] => [4,3,2,5,6,1,7,8] => [4,3,2,5,6,1,7,8] => [4,1,1,1,1] => 1

[[[.,[[[.,[[.,.],.]],.],.]],.],.] => [3,4,2,5,6,1,7,8] => [3,4,2,5,6,1,7,8] => [3,1,1,1,1,1] => 1

[[[.,[[[[.,[.,.]],.],.],.]],.],.] => [3,2,4,5,6,1,7,8] => [3,2,4,5,6,1,7,8] => [3,1,1,1,1,1] => 1

[[[.,[[[[[.,.],.],.],.],.]],.],.] => [2,3,4,5,6,1,7,8] => [2,3,4,5,6,1,7,8] => [2,1,1,1,1,1,1] => 1

[[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => [6,5,4,3,1,2,7,8] => [1,6,5,4,3,2,7,8] => [5,1,1,1] => 1

[[[[.,.],[.,[.,[[.,.],.]]]],.],.] => [5,6,4,3,1,2,7,8] => [1,5,6,4,3,2,7,8] => [4,1,1,1,1] => 1

[[[[.,.],[.,[[.,.],[.,.]]]],.],.] => [6,4,5,3,1,2,7,8] => [1,4,6,5,3,2,7,8] => [4,1,1,1,1] => 1

[[[[.,.],[.,[[.,[.,.]],.]]],.],.] => [5,4,6,3,1,2,7,8] => [1,5,4,6,3,2,7,8] => [4,1,1,1,1] => 1

[[[[.,.],[.,[[[.,.],.],.]]],.],.] => [4,5,6,3,1,2,7,8] => [1,4,5,6,3,2,7,8] => [3,1,1,1,1,1] => 1

[[[[.,.],[[.,.],[[.,.],.]]],.],.] => [5,6,3,4,1,2,7,8] => [1,3,5,6,4,2,7,8] => [3,1,1,1,1,1] => 1

[[[[.,.],[[.,[.,[.,.]]],.]],.],.] => [5,4,3,6,1,2,7,8] => [1,5,4,3,6,2,7,8] => [4,1,1,1,1] => 1

[[[[.,.],[[.,[[.,.],.]],.]],.],.] => [4,5,3,6,1,2,7,8] => [1,4,5,3,6,2,7,8] => [3,1,1,1,1,1] => 1

[[[[.,.],[[[.,.],[.,.]],.]],.],.] => [5,3,4,6,1,2,7,8] => [1,3,5,4,6,2,7,8] => [3,1,1,1,1,1] => 1

[[[[.,.],[[[.,[.,.]],.],.]],.],.] => [4,3,5,6,1,2,7,8] => [1,4,3,5,6,2,7,8] => [3,1,1,1,1,1] => 1

[[[[.,.],[[[[.,.],.],.],.]],.],.] => [3,4,5,6,1,2,7,8] => [1,3,4,5,6,2,7,8] => [2,1,1,1,1,1,1] => 1

[[[[.,[.,.]],[.,[.,[.,.]]]],.],.] => [6,5,4,2,1,3,7,8] => [2,6,5,4,1,3,7,8] => [4,1,1,1,1] => 1

[[[[.,[.,.]],[.,[[.,.],.]]],.],.] => [5,6,4,2,1,3,7,8] => [2,5,6,4,1,3,7,8] => [3,1,1,1,1,1] => 1

[[[[.,[.,.]],[[.,[.,.]],.]],.],.] => [5,4,6,2,1,3,7,8] => [2,5,4,6,1,3,7,8] => [3,1,1,1,1,1] => 1

[[[[.,[.,.]],[[[.,.],.],.]],.],.] => [4,5,6,2,1,3,7,8] => [2,4,5,6,1,3,7,8] => [2,1,1,1,1,1,1] => 1

[[[[[.,.],.],[.,[.,[.,.]]]],.],.] => [6,5,4,1,2,3,7,8] => [1,2,6,5,4,3,7,8] => [4,1,1,1,1] => 1

[[[[[.,.],.],[.,[[.,.],.]]],.],.] => [5,6,4,1,2,3,7,8] => [1,2,5,6,4,3,7,8] => [3,1,1,1,1,1] => 1

[[[[[.,.],.],[[.,.],[.,.]]],.],.] => [6,4,5,1,2,3,7,8] => [1,2,4,6,5,3,7,8] => [3,1,1,1,1,1] => 1

[[[[[.,.],.],[[[.,.],.],.]],.],.] => [4,5,6,1,2,3,7,8] => [1,2,4,5,6,3,7,8] => [2,1,1,1,1,1,1] => 1

[[[[.,[.,[.,.]]],[.,[.,.]]],.],.] => [6,5,3,2,1,4,7,8] => [3,6,5,2,1,4,7,8] => [4,1,1,1,1] => 1

[[[[.,[.,[.,.]]],[[.,.],.]],.],.] => [5,6,3,2,1,4,7,8] => [3,5,6,2,1,4,7,8] => [3,1,1,1,1,1] => 1

[[[[.,[[.,.],.]],[[.,.],.]],.],.] => [5,6,2,3,1,4,7,8] => [2,3,5,6,1,4,7,8] => [2,1,1,1,1,1,1] => 1

[[[[[.,.],[.,.]],[.,[.,.]]],.],.] => [6,5,3,1,2,4,7,8] => [1,3,6,5,2,4,7,8] => [3,1,1,1,1,1] => 1

[[[[[.,.],[.,.]],[[.,.],.]],.],.] => [5,6,3,1,2,4,7,8] => [1,3,5,6,2,4,7,8] => [2,1,1,1,1,1,1] => 1

[[[[[.,[.,.]],.],[[.,.],.]],.],.] => [5,6,2,1,3,4,7,8] => [2,1,5,6,3,4,7,8] => [2,2,1,1,1,1] => 2

[[[[[[.,.],.],.],[.,[.,.]]],.],.] => [6,5,1,2,3,4,7,8] => [1,2,3,6,5,4,7,8] => [3,1,1,1,1,1] => 1

[[[[[[.,.],.],.],[[.,.],.]],.],.] => [5,6,1,2,3,4,7,8] => [1,2,3,5,6,4,7,8] => [2,1,1,1,1,1,1] => 1

[[[[.,[[.,[.,.]],.]],[.,.]],.],.] => [6,3,2,4,1,5,7,8] => [3,2,6,4,1,5,7,8] => [3,2,1,1,1] => 2

[[[[.,[[[.,.],.],.]],[.,.]],.],.] => [6,2,3,4,1,5,7,8] => [2,3,4,6,1,5,7,8] => [2,1,1,1,1,1,1] => 1

[[[[[.,.],[[.,.],.]],[.,.]],.],.] => [6,3,4,1,2,5,7,8] => [1,3,4,6,2,5,7,8] => [2,1,1,1,1,1,1] => 1

[[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [6,4,2,1,3,5,7,8] => [2,4,6,1,3,5,7,8] => [2,1,1,1,1,1,1] => 1

[[[[[[.,.],.],[.,.]],[.,.]],.],.] => [6,4,1,2,3,5,7,8] => [1,2,4,6,3,5,7,8] => [2,1,1,1,1,1,1] => 1

[[[[[.,[.,[.,.]]],.],[.,.]],.],.] => [6,3,2,1,4,5,7,8] => [3,2,6,1,4,5,7,8] => [3,1,1,1,1,1] => 1

[[[[[.,[[.,.],.]],.],[.,.]],.],.] => [6,2,3,1,4,5,7,8] => [2,3,1,6,4,5,7,8] => [2,2,1,1,1,1] => 2

[[[[[[.,.],[.,.]],.],[.,.]],.],.] => [6,3,1,2,4,5,7,8] => [1,3,2,6,4,5,7,8] => [2,2,1,1,1,1] => 2

[[[[[[.,[.,.]],.],.],[.,.]],.],.] => [6,2,1,3,4,5,7,8] => [2,1,3,6,4,5,7,8] => [2,2,1,1,1,1] => 2

[[[[[[[.,.],.],.],.],[.,.]],.],.] => [6,1,2,3,4,5,7,8] => [1,2,3,4,6,5,7,8] => [2,1,1,1,1,1,1] => 1

[[[[.,[.,[.,[.,[.,.]]]]],.],.],.] => [5,4,3,2,1,6,7,8] => [5,4,3,2,1,6,7,8] => [5,1,1,1] => 1

[[[[.,[.,[.,[[.,.],.]]]],.],.],.] => [4,5,3,2,1,6,7,8] => [4,5,3,2,1,6,7,8] => [4,1,1,1,1] => 1

[[[[.,[.,[[.,.],[.,.]]]],.],.],.] => [5,3,4,2,1,6,7,8] => [3,5,4,2,1,6,7,8] => [4,1,1,1,1] => 1

[[[[.,[.,[[.,[.,.]],.]]],.],.],.] => [4,3,5,2,1,6,7,8] => [4,3,5,2,1,6,7,8] => [4,1,1,1,1] => 1

[[[[.,[.,[[[.,.],.],.]]],.],.],.] => [3,4,5,2,1,6,7,8] => [3,4,5,2,1,6,7,8] => [3,1,1,1,1,1] => 1

[[[[.,[[.,.],[.,[.,.]]]],.],.],.] => [5,4,2,3,1,6,7,8] => [2,5,4,3,1,6,7,8] => [4,1,1,1,1] => 1

[[[[.,[[.,.],[[.,.],.]]],.],.],.] => [4,5,2,3,1,6,7,8] => [2,4,5,3,1,6,7,8] => [3,1,1,1,1,1] => 1

[[[[.,[[.,[.,.]],[.,.]]],.],.],.] => [5,3,2,4,1,6,7,8] => [3,5,2,4,1,6,7,8] => [3,1,1,1,1,1] => 1

[[[[.,[[[.,.],.],[.,.]]],.],.],.] => [5,2,3,4,1,6,7,8] => [2,3,5,4,1,6,7,8] => [3,1,1,1,1,1] => 1

[[[[.,[[.,[.,[.,.]]],.]],.],.],.] => [4,3,2,5,1,6,7,8] => [4,3,2,5,1,6,7,8] => [4,1,1,1,1] => 1

[[[[.,[[.,[[.,.],.]],.]],.],.],.] => [3,4,2,5,1,6,7,8] => [3,4,2,5,1,6,7,8] => [3,1,1,1,1,1] => 1

[[[[.,[[[.,.],[.,.]],.]],.],.],.] => [4,2,3,5,1,6,7,8] => [2,4,3,5,1,6,7,8] => [3,1,1,1,1,1] => 1

[[[[.,[[[.,[.,.]],.],.]],.],.],.] => [3,2,4,5,1,6,7,8] => [3,2,4,5,1,6,7,8] => [3,1,1,1,1,1] => 1

[[[[.,[[[[.,.],.],.],.]],.],.],.] => [2,3,4,5,1,6,7,8] => [2,3,4,5,1,6,7,8] => [2,1,1,1,1,1,1] => 1

[[[[[.,.],[.,[.,[.,.]]]],.],.],.] => [5,4,3,1,2,6,7,8] => [1,5,4,3,2,6,7,8] => [4,1,1,1,1] => 1

[[[[[.,.],[.,[[.,.],.]]],.],.],.] => [4,5,3,1,2,6,7,8] => [1,4,5,3,2,6,7,8] => [3,1,1,1,1,1] => 1

[[[[[.,.],[[.,.],[.,.]]],.],.],.] => [5,3,4,1,2,6,7,8] => [1,3,5,4,2,6,7,8] => [3,1,1,1,1,1] => 1

[[[[[.,.],[[[.,.],.],.]],.],.],.] => [3,4,5,1,2,6,7,8] => [1,3,4,5,2,6,7,8] => [2,1,1,1,1,1,1] => 1

[[[[[.,[.,.]],[.,[.,.]]],.],.],.] => [5,4,2,1,3,6,7,8] => [2,5,4,1,3,6,7,8] => [3,1,1,1,1,1] => 1

[[[[[.,[.,.]],[[.,.],.]],.],.],.] => [4,5,2,1,3,6,7,8] => [2,4,5,1,3,6,7,8] => [2,1,1,1,1,1,1] => 1

[[[[[[.,.],.],[.,[.,.]]],.],.],.] => [5,4,1,2,3,6,7,8] => [1,2,5,4,3,6,7,8] => [3,1,1,1,1,1] => 1

[[[[[.,[.,[.,.]]],[.,.]],.],.],.] => [5,3,2,1,4,6,7,8] => [3,5,2,1,4,6,7,8] => [3,1,1,1,1,1] => 1

[[[[[.,[[.,.],.]],[.,.]],.],.],.] => [5,2,3,1,4,6,7,8] => [2,3,5,1,4,6,7,8] => [2,1,1,1,1,1,1] => 1

[[[[[[.,.],[.,.]],[.,.]],.],.],.] => [5,3,1,2,4,6,7,8] => [1,3,5,2,4,6,7,8] => [2,1,1,1,1,1,1] => 1

[[[[[[.,[.,.]],.],[.,.]],.],.],.] => [5,2,1,3,4,6,7,8] => [2,1,5,3,4,6,7,8] => [2,2,1,1,1,1] => 2

[[[[[[[.,.],.],.],[.,.]],.],.],.] => [5,1,2,3,4,6,7,8] => [1,2,3,5,4,6,7,8] => [2,1,1,1,1,1,1] => 1

[[[[[.,[.,[.,[.,.]]]],.],.],.],.] => [4,3,2,1,5,6,7,8] => [4,3,2,1,5,6,7,8] => [4,1,1,1,1] => 1

[[[[[.,[.,[[.,.],.]]],.],.],.],.] => [3,4,2,1,5,6,7,8] => [3,4,2,1,5,6,7,8] => [3,1,1,1,1,1] => 1

[[[[[.,[[.,.],[.,.]]],.],.],.],.] => [4,2,3,1,5,6,7,8] => [2,4,3,1,5,6,7,8] => [3,1,1,1,1,1] => 1

[[[[[.,[[.,[.,.]],.]],.],.],.],.] => [3,2,4,1,5,6,7,8] => [3,2,4,1,5,6,7,8] => [3,1,1,1,1,1] => 1

[[[[[.,[[[.,.],.],.]],.],.],.],.] => [2,3,4,1,5,6,7,8] => [2,3,4,1,5,6,7,8] => [2,1,1,1,1,1,1] => 1

[[[[[[.,.],[.,[.,.]]],.],.],.],.] => [4,3,1,2,5,6,7,8] => [1,4,3,2,5,6,7,8] => [3,1,1,1,1,1] => 1

[[[[[[.,.],[[.,.],.]],.],.],.],.] => [3,4,1,2,5,6,7,8] => [1,3,4,2,5,6,7,8] => [2,1,1,1,1,1,1] => 1

[[[[[[.,[.,.]],[.,.]],.],.],.],.] => [4,2,1,3,5,6,7,8] => [2,4,1,3,5,6,7,8] => [2,1,1,1,1,1,1] => 1

[[[[[[[.,.],.],[.,.]],.],.],.],.] => [4,1,2,3,5,6,7,8] => [1,2,4,3,5,6,7,8] => [2,1,1,1,1,1,1] => 1

[[[[[[.,[.,[.,.]]],.],.],.],.],.] => [3,2,1,4,5,6,7,8] => [3,2,1,4,5,6,7,8] => [3,1,1,1,1,1] => 1

[[[[[[.,[[.,.],.]],.],.],.],.],.] => [2,3,1,4,5,6,7,8] => [2,3,1,4,5,6,7,8] => [2,1,1,1,1,1,1] => 1

[[[[[[[.,.],[.,.]],.],.],.],.],.] => [3,1,2,4,5,6,7,8] => [1,3,2,4,5,6,7,8] => [2,1,1,1,1,1,1] => 1

[[[[[[[.,[.,.]],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7,8] => [2,1,1,1,1,1,1] => 1

[[[[[[[[.,.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => 1

[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => [9] => 1

[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [8,9,7,6,5,4,3,2,1] => [8,9,7,6,5,4,3,2,1] => [8,1] => 1

[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]] => [7,8,9,6,5,4,3,2,1] => [7,8,9,6,5,4,3,2,1] => [7,1,1] => 1

[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]] => [6,7,8,9,5,4,3,2,1] => [6,7,8,9,5,4,3,2,1] => [6,1,1,1] => 1

[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]] => [5,6,7,8,9,4,3,2,1] => [5,6,7,8,9,4,3,2,1] => [5,1,1,1,1] => 1

[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]] => [4,5,6,7,8,9,3,2,1] => [4,5,6,7,8,9,3,2,1] => [4,1,1,1,1,1] => 1

[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]] => [3,4,5,6,7,8,9,2,1] => [3,4,5,6,7,8,9,2,1] => [3,1,1,1,1,1,1] => 1

[.,[[[[[[[[.,.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,1] => [2,3,4,5,6,7,8,9,1] => [2,1,1,1,1,1,1,1] => 1

[[[[[[[[[.,.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1] => 1

[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [10,9,8,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,3,2,1] => [10] => 1

[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]] => [9,10,8,7,6,5,4,3,2,1] => [9,10,8,7,6,5,4,3,2,1] => [9,1] => 1

[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]] => [9,7,8,6,5,4,3,2,1] => [7,9,8,6,5,4,3,2,1] => [8,1] => 1

[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]] => [8,9,10,7,6,5,4,3,2,1] => [8,9,10,7,6,5,4,3,2,1] => [8,1,1] => 1

[.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]] => [7,8,9,10,6,5,4,3,2,1] => [7,8,9,10,6,5,4,3,2,1] => [7,1,1,1] => 1

[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]] => [6,7,8,9,10,5,4,3,2,1] => [6,7,8,9,10,5,4,3,2,1] => [6,1,1,1,1] => 1

[.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]] => [5,6,7,8,9,10,4,3,2,1] => [5,6,7,8,9,10,4,3,2,1] => [5,1,1,1,1,1] => 1

[.,[.,[[.,.],[[[[[.,.],.],.],.],.]]]] => [5,6,7,8,9,3,4,2,1] => [3,5,6,7,8,9,4,2,1] => [4,1,1,1,1,1] => 1

[.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]] => [4,5,6,7,8,9,10,3,2,1] => [4,5,6,7,8,9,10,3,2,1] => [4,1,1,1,1,1,1] => 1

[.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]] => [3,4,5,6,7,8,9,10,2,1] => [3,4,5,6,7,8,9,10,2,1] => [3,1,1,1,1,1,1,1] => 1

[[.,.],[[[[[[[.,.],.],.],.],.],.],.]] => [3,4,5,6,7,8,9,1,2] => [1,3,4,5,6,7,8,9,2] => [2,1,1,1,1,1,1,1] => 1

[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,10,1] => [2,3,4,5,6,7,8,9,10,1] => [2,1,1,1,1,1,1,1,1] => 1

[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1] => 1

[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]] => [8,7,9,6,5,4,3,2,1] => [8,7,9,6,5,4,3,2,1] => [8,1] => 1

[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]] => [8,7,6,9,5,4,3,2,1] => [8,7,6,9,5,4,3,2,1] => [8,1] => 1

[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]] => [8,7,6,5,9,4,3,2,1] => [8,7,6,5,9,4,3,2,1] => [8,1] => 1

[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]] => [8,7,6,5,4,9,3,2,1] => [8,7,6,5,4,9,3,2,1] => [8,1] => 1

[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]] => [8,7,6,5,4,3,9,2,1] => [8,7,6,5,4,3,9,2,1] => [8,1] => 1

[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]] => [8,7,6,5,4,3,2,9,1] => [8,7,6,5,4,3,2,9,1] => [8,1] => 1

[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [8,7,6,5,4,3,2,1,9] => [8,7,6,5,4,3,2,1,9] => [8,1] => 1

[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]] => [9,8,10,7,6,5,4,3,2,1] => [9,8,10,7,6,5,4,3,2,1] => [9,1] => 1

[.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]] => [8,6,7,9,5,4,3,2,1] => [6,8,7,9,5,4,3,2,1] => [7,1,1] => 1

[.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]] => [9,8,7,10,6,5,4,3,2,1] => [9,8,7,10,6,5,4,3,2,1] => [9,1] => 1

[.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]] => [8,7,5,6,9,4,3,2,1] => [5,8,7,6,9,4,3,2,1] => [7,1,1] => 1

[.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]] => [9,8,7,6,10,5,4,3,2,1] => [9,8,7,6,10,5,4,3,2,1] => [9,1] => 1

[.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]] => [8,7,6,4,5,9,3,2,1] => [4,8,7,6,5,9,3,2,1] => [7,1,1] => 1

[.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]] => [9,8,7,6,5,10,4,3,2,1] => [9,8,7,6,5,10,4,3,2,1] => [9,1] => 1

[.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]] => [8,7,6,5,3,4,9,2,1] => [3,8,7,6,5,4,9,2,1] => [7,1,1] => 1

[.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]] => [9,8,7,6,5,4,10,3,2,1] => [9,8,7,6,5,4,10,3,2,1] => [9,1] => 1

[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]] => [8,7,6,5,4,2,3,9,1] => [2,8,7,6,5,4,3,9,1] => [7,1,1] => 1

[.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]] => [9,8,7,6,5,4,3,10,2,1] => [9,8,7,6,5,4,3,10,2,1] => [9,1] => 1

[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [8,7,6,5,4,3,1,2,9] => [1,8,7,6,5,4,3,2,9] => [7,1,1] => 1

[.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]] => [9,8,7,6,5,4,3,2,10,1] => [9,8,7,6,5,4,3,2,10,1] => [9,1] => 1

[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => [9,8,7,6,5,4,3,2,1,10] => [9,8,7,6,5,4,3,2,1,10] => [9,1] => 1

[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [9,10,7,8,5,6,3,4,1,2] => [1,3,5,7,9,10,8,6,4,2] => [5,1,1,1,1,1] => 1

[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]] => [6,7,5,8,4,9,3,10,1,2] => [1,6,7,5,8,4,9,3,10,2] => [5,1,1,1,1,1] => 1

[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.] => [5,6,4,7,3,8,2,9,1,10] => [5,6,4,7,3,8,2,9,1,10] => [5,1,1,1,1,1] => 1

[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [10,8,6,4,2,1,3,5,7,9] => [2,4,6,8,10,1,3,5,7,9] => [2,1,1,1,1,1,1,1,1] => 1

[[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [9,1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,9,8] => [2,1,1,1,1,1,1,1] => 1

[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [10,1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,10,9] => [2,1,1,1,1,1,1,1,1] => 1

[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]] => [9,2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,9,7,8] => [2,2,1,1,1,1,1] => 2

[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]] => [3,2,4,5,6,7,8,9,1] => [3,2,4,5,6,7,8,9,1] => [3,1,1,1,1,1,1] => 1

[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]] => [11,1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,11,10] => [2,1,1,1,1,1,1,1,1,1] => 1

[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]] => [10,2,1,3,4,5,6,7,8,9] => [2,1,3,4,5,6,7,10,8,9] => [2,2,1,1,1,1,1,1] => 2

[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]] => [9,3,1,2,4,5,6,7,8] => [1,3,2,4,5,6,9,7,8] => [2,2,1,1,1,1,1] => 2

[[[[[[.,[[.,.],.]],.],.],.],.],[.,.]] => [9,2,3,1,4,5,6,7,8] => [2,3,1,4,5,6,9,7,8] => [2,2,1,1,1,1,1] => 2

[.,[[[[[[[.,.],[.,.]],.],.],.],.],.]] => [4,2,3,5,6,7,8,9,1] => [2,4,3,5,6,7,8,9,1] => [3,1,1,1,1,1,1] => 1

[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]] => [3,4,2,5,6,7,8,9,1] => [3,4,2,5,6,7,8,9,1] => [3,1,1,1,1,1,1] => 1

[.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]] => [3,2,4,5,6,7,8,9,10,1] => [3,2,4,5,6,7,8,9,10,1] => [3,1,1,1,1,1,1,1] => 1

[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,10,11,1] => [2,3,4,5,6,7,8,9,10,11,1] => [2,1,1,1,1,1,1,1,1,1] => 1

[[[[[[[.,.],.],.],.],.],.],[[.,.],.]] => [8,9,1,2,3,4,5,6,7] => [1,2,3,4,5,6,8,9,7] => [2,1,1,1,1,1,1,1] => 1

[[[[[[.,.],.],.],.],.],[[[.,.],.],.]] => [7,8,9,1,2,3,4,5,6] => [1,2,3,4,5,7,8,9,6] => [2,1,1,1,1,1,1,1] => 1

[[[[[.,.],.],.],.],[[[[.,.],.],.],.]] => [6,7,8,9,1,2,3,4,5] => [1,2,3,4,6,7,8,9,5] => [2,1,1,1,1,1,1,1] => 1

[[[[.,.],.],.],[[[[[.,.],.],.],.],.]] => [5,6,7,8,9,1,2,3,4] => [1,2,3,5,6,7,8,9,4] => [2,1,1,1,1,1,1,1] => 1

[[[.,.],.],[[[[[[.,.],.],.],.],.],.]] => [4,5,6,7,8,9,1,2,3] => [1,2,4,5,6,7,8,9,3] => [2,1,1,1,1,1,1,1] => 1

[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => [9,8,1,2,3,4,5,6,7] => [1,2,3,4,5,6,9,8,7] => [3,1,1,1,1,1,1] => 1

[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]] => [9,10,1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,9,10,8] => [2,1,1,1,1,1,1,1,1] => 1

[[[[[[.,.],.],.],.],.],[[.,[.,.]],.]] => [8,7,9,1,2,3,4,5,6] => [1,2,3,4,5,8,7,9,6] => [3,1,1,1,1,1,1] => 1

[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]] => [8,9,10,1,2,3,4,5,6,7] => [1,2,3,4,5,6,8,9,10,7] => [2,1,1,1,1,1,1,1,1] => 1

[[[[[.,.],.],.],.],[[[.,[.,.]],.],.]] => [7,6,8,9,1,2,3,4,5] => [1,2,3,4,7,6,8,9,5] => [3,1,1,1,1,1,1] => 1

[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]] => [7,8,9,10,1,2,3,4,5,6] => [1,2,3,4,5,7,8,9,10,6] => [2,1,1,1,1,1,1,1,1] => 1

[[[[.,.],.],.],[[[[.,[.,.]],.],.],.]] => [6,5,7,8,9,1,2,3,4] => [1,2,3,6,5,7,8,9,4] => [3,1,1,1,1,1,1] => 1

[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]] => [6,7,8,9,10,1,2,3,4,5] => [1,2,3,4,6,7,8,9,10,5] => [2,1,1,1,1,1,1,1,1] => 1

[[[.,.],.],[[[[[.,[.,.]],.],.],.],.]] => [5,4,6,7,8,9,1,2,3] => [1,2,5,4,6,7,8,9,3] => [3,1,1,1,1,1,1] => 1

[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]] => [5,6,7,8,9,10,1,2,3,4] => [1,2,3,5,6,7,8,9,10,4] => [2,1,1,1,1,1,1,1,1] => 1

[[.,.],[[[[[[.,[.,.]],.],.],.],.],.]] => [4,3,5,6,7,8,9,1,2] => [1,4,3,5,6,7,8,9,2] => [3,1,1,1,1,1,1] => 1

[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]] => [4,5,6,7,8,9,10,1,2,3] => [1,2,4,5,6,7,8,9,10,3] => [2,1,1,1,1,1,1,1,1] => 1

[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]] => [3,4,5,6,7,8,9,10,1,2] => [1,3,4,5,6,7,8,9,10,2] => [2,1,1,1,1,1,1,1,1] => 1

[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [9,8,7,6,5,4,3,1,2] => [1,9,8,7,6,5,4,3,2] => [8,1] => 1

[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.] => [7,8,6,5,4,3,2,1,9] => [7,8,6,5,4,3,2,1,9] => [7,1,1] => 1

[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [10,9,8,7,6,5,4,3,1,2] => [1,10,9,8,7,6,5,4,3,2] => [9,1] => 1

[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.] => [10,9,8,7,6,5,4,3,2,1,11] => [10,9,8,7,6,5,4,3,2,1,11] => [10,1] => 1

[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.] => [8,9,7,6,5,4,3,2,1,10] => [8,9,7,6,5,4,3,2,1,10] => [8,1,1] => 1

[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.] => [7,6,8,5,4,3,2,1,9] => [7,6,8,5,4,3,2,1,9] => [7,1,1] => 1

[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [11,10,9,8,7,6,5,4,3,1,2] => [1,11,10,9,8,7,6,5,4,3,2] => [10,1] => 1

[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]] => [6,5,7,4,8,3,9,2,10,1] => [6,5,7,4,8,3,9,2,10,1] => [6,1,1,1,1] => 1

[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [9,8,7,6,5,4,2,1,3] => [2,9,8,7,6,5,4,1,3] => [7,1,1] => 1

[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]] => [9,8,7,5,4,3,2,1,6] => [5,9,8,7,4,3,2,1,6] => [7,1,1] => 1

[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] => [9,8,6,5,4,3,2,1,7] => [6,9,8,5,4,3,2,1,7] => [7,1,1] => 1

[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => [9,7,6,5,4,3,2,1,8] => [7,9,6,5,4,3,2,1,8] => [7,1,1] => 1

[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [9,8,7,6,5,4,1,2,3] => [1,2,9,8,7,6,5,4,3] => [7,1,1] => 1

[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [10,9,8,7,6,5,4,2,1,3] => [2,10,9,8,7,6,5,4,1,3] => [8,1,1] => 1

[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]] => [10,9,7,6,5,4,3,2,1,8] => [7,10,9,6,5,4,3,2,1,8] => [8,1,1] => 1

[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]] => [10,8,7,6,5,4,3,2,1,9] => [8,10,7,6,5,4,3,2,1,9] => [8,1,1] => 1

[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.] => [7,6,5,4,3,2,1,8,9] => [7,6,5,4,3,2,1,8,9] => [7,1,1] => 1

[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.] => [6,5,4,3,2,1,7,8,9] => [6,5,4,3,2,1,7,8,9] => [6,1,1,1] => 1

[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.] => [5,4,3,2,1,6,7,8,9] => [5,4,3,2,1,6,7,8,9] => [5,1,1,1,1] => 1

[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.] => [4,3,2,1,5,6,7,8,9] => [4,3,2,1,5,6,7,8,9] => [4,1,1,1,1,1] => 1

[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.] => [3,2,1,4,5,6,7,8,9] => [3,2,1,4,5,6,7,8,9] => [3,1,1,1,1,1,1] => 1

[[[[[[[[.,[.,.]],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9] => [2,1,3,4,5,6,7,8,9] => [2,1,1,1,1,1,1,1] => 1

[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.] => [8,7,6,5,4,3,2,1,9,10] => [8,7,6,5,4,3,2,1,9,10] => [8,1,1] => 1

[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.] => [7,6,5,4,3,2,1,8,9,10] => [7,6,5,4,3,2,1,8,9,10] => [7,1,1,1] => 1

[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.] => [6,5,4,3,2,1,7,8,9,10] => [6,5,4,3,2,1,7,8,9,10] => [6,1,1,1,1] => 1

[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.] => [5,4,3,2,1,6,7,8,9,10] => [5,4,3,2,1,6,7,8,9,10] => [5,1,1,1,1,1] => 1

[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.] => [4,3,2,1,5,6,7,8,9,10] => [4,3,2,1,5,6,7,8,9,10] => [4,1,1,1,1,1,1] => 1

[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.] => [4,3,1,2,5,6,7,8,9] => [1,4,3,2,5,6,7,8,9] => [3,1,1,1,1,1,1] => 1

[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.] => [3,2,1,4,5,6,7,8,9,10] => [3,2,1,4,5,6,7,8,9,10] => [3,1,1,1,1,1,1,1] => 1

[[[[[[[[.,.],[.,.]],.],.],.],.],.],.] => [3,1,2,4,5,6,7,8,9] => [1,3,2,4,5,6,7,8,9] => [2,1,1,1,1,1,1,1] => 1

[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9,10] => [2,1,3,4,5,6,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => 1

[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]] => [9,8,7,5,6,4,3,2,1] => [5,9,8,7,6,4,3,2,1] => [8,1] => 1

[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]] => [9,8,7,6,4,5,3,2,1] => [4,9,8,7,6,5,3,2,1] => [8,1] => 1

[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]] => [9,8,7,6,5,3,4,2,1] => [3,9,8,7,6,5,4,2,1] => [8,1] => 1

[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]] => [9,8,7,6,5,4,2,3,1] => [2,9,8,7,6,5,4,3,1] => [8,1] => 1

[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]] => [10,8,9,7,6,5,4,3,2,1] => [8,10,9,7,6,5,4,3,2,1] => [9,1] => 1

[.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]] => [10,9,8,6,7,5,4,3,2,1] => [6,10,9,8,7,5,4,3,2,1] => [9,1] => 1

[.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]] => [10,9,8,7,5,6,4,3,2,1] => [5,10,9,8,7,6,4,3,2,1] => [9,1] => 1

[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [10,9,8,7,6,5,4,2,3,1] => [2,10,9,8,7,6,5,4,3,1] => [9,1] => 1

[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]] => [9,2,3,4,5,6,7,8,1] => [2,3,4,5,6,7,9,8,1] => [3,1,1,1,1,1,1] => 1

[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9,10,11] => [2,1,3,4,5,6,7,8,9,10,11] => [2,1,1,1,1,1,1,1,1,1] => 1

[[[[[[[.,[.,.]],.],.],.],.],[.,.]],.] => [8,2,1,3,4,5,6,7,9] => [2,1,3,4,5,8,6,7,9] => [2,2,1,1,1,1,1] => 2

[.,[[[[[[[.,.],.],.],.],.],[.,.]],.]] => [8,2,3,4,5,6,7,9,1] => [2,3,4,5,6,8,7,9,1] => [3,1,1,1,1,1,1] => 1

[.,[[[[[[.,.],.],.],.],.],[[.,.],.]]] => [8,9,2,3,4,5,6,7,1] => [2,3,4,5,6,8,9,7,1] => [3,1,1,1,1,1,1] => 1

[.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]] => [10,2,3,4,5,6,7,8,9,1] => [2,3,4,5,6,7,8,10,9,1] => [3,1,1,1,1,1,1,1] => 1

[[[[[[[.,[.,.]],[.,.]],.],.],.],.],.] => [4,2,1,3,5,6,7,8,9] => [2,4,1,3,5,6,7,8,9] => [2,1,1,1,1,1,1,1] => 1

[.,[[.,[[[[[[.,.],.],.],.],.],.]],.]] => [3,4,5,6,7,8,2,9,1] => [3,4,5,6,7,8,2,9,1] => [3,1,1,1,1,1,1] => 1

[[.,[[[[[[[.,.],.],.],.],.],.],.]],.] => [2,3,4,5,6,7,8,1,9] => [2,3,4,5,6,7,8,1,9] => [2,1,1,1,1,1,1,1] => 1

[[[[[[[.,[[.,.],.]],.],.],.],.],.],.] => [2,3,1,4,5,6,7,8,9] => [2,3,1,4,5,6,7,8,9] => [2,1,1,1,1,1,1,1] => 1

[[[[[.,[[[[.,.],.],.],.]],.],.],.],.] => [2,3,4,5,1,6,7,8,9] => [2,3,4,5,1,6,7,8,9] => [2,1,1,1,1,1,1,1] => 1

[[[.,[[[[[[.,.],.],.],.],.],.]],.],.] => [2,3,4,5,6,7,1,8,9] => [2,3,4,5,6,7,1,8,9] => [2,1,1,1,1,1,1,1] => 1

[[[[[[.,[[.,.],[.,.]]],.],.],.],.],.] => [4,2,3,1,5,6,7,8,9] => [2,4,3,1,5,6,7,8,9] => [3,1,1,1,1,1,1] => 1

[[.,[[[[[[.,.],.],.],.],.],[.,.]]],.] => [8,2,3,4,5,6,7,1,9] => [2,3,4,5,6,8,7,1,9] => [3,1,1,1,1,1,1] => 1

[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.] => [2,3,4,5,6,7,8,9,1,10] => [2,3,4,5,6,7,8,9,1,10] => [2,1,1,1,1,1,1,1,1] => 1

[[[[[[[[.,.],.],[.,.]],.],.],.],.],.] => [4,1,2,3,5,6,7,8,9] => [1,2,4,3,5,6,7,8,9] => [2,1,1,1,1,1,1,1] => 1

[[[[[[[[.,.],.],.],[.,.]],.],.],.],.] => [5,1,2,3,4,6,7,8,9] => [1,2,3,5,4,6,7,8,9] => [2,1,1,1,1,1,1,1] => 1

[[[[[[[[.,.],.],.],.],[.,.]],.],.],.] => [6,1,2,3,4,5,7,8,9] => [1,2,3,4,6,5,7,8,9] => [2,1,1,1,1,1,1,1] => 1

[[[[[[[[.,.],.],.],.],.],[.,.]],.],.] => [7,1,2,3,4,5,6,8,9] => [1,2,3,4,5,7,6,8,9] => [2,1,1,1,1,1,1,1] => 1

[[[[[[[[.,.],.],.],.],.],.],[.,.]],.] => [8,1,2,3,4,5,6,7,9] => [1,2,3,4,5,6,8,7,9] => [2,1,1,1,1,1,1,1] => 1

[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.] => [3,1,2,4,5,6,7,8,9,10] => [1,3,2,4,5,6,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => 1

[[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.] => [4,1,2,3,5,6,7,8,9,10] => [1,2,4,3,5,6,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => 1

[[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.] => [5,1,2,3,4,6,7,8,9,10] => [1,2,3,5,4,6,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => 1

[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.] => [6,1,2,3,4,5,7,8,9,10] => [1,2,3,4,6,5,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => 1

[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.] => [7,1,2,3,4,5,6,8,9,10] => [1,2,3,4,5,7,6,8,9,10] => [2,1,1,1,1,1,1,1,1] => 1

[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.] => [8,1,2,3,4,5,6,7,9,10] => [1,2,3,4,5,6,8,7,9,10] => [2,1,1,1,1,1,1,1,1] => 1

[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.] => [9,1,2,3,4,5,6,7,8,10] => [1,2,3,4,5,6,7,9,8,10] => [2,1,1,1,1,1,1,1,1] => 1

[[.,.],[[[[[[.,.],.],.],.],.],[.,.]]] => [9,3,4,5,6,7,8,1,2] => [1,3,4,5,6,7,9,8,2] => [3,1,1,1,1,1,1] => 1

[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]] => [9,7,6,5,4,3,2,8,1] => [7,9,6,5,4,3,2,8,1] => [7,1,1] => 1

[.,[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]] => [6,5,4,3,2,7,8,9,1] => [6,5,4,3,2,7,8,9,1] => [6,1,1,1] => 1

[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9,10,11] => [1,2,3,4,5,6,7,8,9,10,11] => [1,1,1,1,1,1,1,1,1,1,1] => 1

[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [10,9,8,7,6,5,4,1,2,3] => [1,2,10,9,8,7,6,5,4,3] => [8,1,1] => 1

[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [9,8,7,6,5,4,3,1,2,10] => [1,9,8,7,6,5,4,3,2,10] => [8,1,1] => 1

[[[[[[.,.],[[[.,.],.],.]],.],.],.],.] => [3,4,5,1,2,6,7,8,9] => [1,3,4,5,2,6,7,8,9] => [2,1,1,1,1,1,1,1] => 1

[[[[[[[.,.],.],[[.,.],.]],.],.],.],.] => [4,5,1,2,3,6,7,8,9] => [1,2,4,5,3,6,7,8,9] => [2,1,1,1,1,1,1,1] => 1

[[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.] => [7,8,1,2,3,4,5,6,9,10] => [1,2,3,4,5,7,8,6,9,10] => [2,1,1,1,1,1,1,1,1] => 1

[[[[[[[.,.],.],.],.],.],[[[.,.],.],.]],.] => [7,8,9,1,2,3,4,5,6,10] => [1,2,3,4,5,7,8,9,6,10] => [2,1,1,1,1,1,1,1,1] => 1

[[[[[[[.,.],[.,.]],[.,.]],.],.],.],.] => [5,3,1,2,4,6,7,8,9] => [1,3,5,2,4,6,7,8,9] => [2,1,1,1,1,1,1,1] => 1

[.,[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]] => [6,2,3,4,5,7,8,9,10,1] => [2,3,4,6,5,7,8,9,10,1] => [3,1,1,1,1,1,1,1] => 1

[[.,.],[.,[[[[[[.,.],.],.],.],.],.]]] => [4,5,6,7,8,9,3,1,2] => [1,4,5,6,7,8,9,3,2] => [3,1,1,1,1,1,1] => 1

[[.,[.,.]],[[[[[[.,.],.],.],.],.],.]] => [4,5,6,7,8,9,2,1,3] => [2,4,5,6,7,8,9,1,3] => [2,1,1,1,1,1,1,1] => 1

[[[.,.],[[[[[[.,.],.],.],.],.],.]],.] => [3,4,5,6,7,8,1,2,9] => [1,3,4,5,6,7,8,2,9] => [2,1,1,1,1,1,1,1] => 1

[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => [10,9,1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,10,9,8] => [3,1,1,1,1,1,1,1] => 1

[[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]],.] => [6,7,8,5,4,3,2,1,9] => [6,7,8,5,4,3,2,1,9] => [6,1,1,1] => 1

[[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]],.] => [6,5,4,3,2,7,8,1,9] => [6,5,4,3,2,7,8,1,9] => [6,1,1,1] => 1

[[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]],.] => [7,8,9,6,5,4,3,2,1,10] => [7,8,9,6,5,4,3,2,1,10] => [7,1,1,1] => 1

[.,[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]] => [10,9,8,7,6,5,4,3,2,11,1] => [10,9,8,7,6,5,4,3,2,11,1] => [10,1] => 1

[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] => [9,8,7,1,2,3,4,5,6] => [1,2,3,4,5,9,8,7,6] => [4,1,1,1,1,1] => 1

[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => [9,8,7,6,1,2,3,4,5] => [1,2,3,4,9,8,7,6,5] => [5,1,1,1,1] => 1

[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [9,8,7,6,5,1,2,3,4] => [1,2,3,9,8,7,6,5,4] => [6,1,1,1] => 1

[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]] => [9,7,1,2,3,4,5,6,8] => [1,2,3,4,5,7,9,6,8] => [2,1,1,1,1,1,1,1] => 1

[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]] => [10,9,8,1,2,3,4,5,6,7] => [1,2,3,4,5,6,10,9,8,7] => [4,1,1,1,1,1,1] => 1

[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]] => [10,9,8,7,1,2,3,4,5,6] => [1,2,3,4,5,10,9,8,7,6] => [5,1,1,1,1,1] => 1

[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [10,9,8,7,6,1,2,3,4,5] => [1,2,3,4,10,9,8,7,6,5] => [6,1,1,1,1] => 1

[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [10,9,8,7,6,5,1,2,3,4] => [1,2,3,10,9,8,7,6,5,4] => [7,1,1,1] => 1

[[[[[[.,[[.,[.,.]],.]],.],.],.],.],.] => [3,2,4,1,5,6,7,8,9] => [3,2,4,1,5,6,7,8,9] => [3,1,1,1,1,1,1] => 1

[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]] => [10,11,9,8,7,6,5,4,3,2,1] => [10,11,9,8,7,6,5,4,3,2,1] => [10,1] => 1

[[[[[[.,[.,[[.,.],.]]],.],.],.],.],.] => [3,4,2,1,5,6,7,8,9] => [3,4,2,1,5,6,7,8,9] => [3,1,1,1,1,1,1] => 1

[[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.] => [7,6,5,4,3,2,8,1,9] => [7,6,5,4,3,2,8,1,9] => [7,1,1] => 1

[[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.],.] => [6,5,4,3,2,7,1,8,9] => [6,5,4,3,2,7,1,8,9] => [6,1,1,1] => 1

[[[[.,[[.,[.,[.,[.,.]]]],.]],.],.],.] => [5,4,3,2,6,1,7,8,9] => [5,4,3,2,6,1,7,8,9] => [5,1,1,1,1] => 1

[[[[[.,[[.,[.,[.,.]]],.]],.],.],.],.] => [4,3,2,5,1,6,7,8,9] => [4,3,2,5,1,6,7,8,9] => [4,1,1,1,1,1] => 1

[[[[[.,[.,[.,[[.,.],.]]]],.],.],.],.] => [4,5,3,2,1,6,7,8,9] => [4,5,3,2,1,6,7,8,9] => [4,1,1,1,1,1] => 1

[[.,[[[[[[.,[.,.]],.],.],.],.],.]],.] => [3,2,4,5,6,7,8,1,9] => [3,2,4,5,6,7,8,1,9] => [3,1,1,1,1,1,1] => 1

[[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.] => [8,7,6,5,4,2,3,1,9] => [2,8,7,6,5,4,3,1,9] => [7,1,1] => 1

[[.,[[[[[[.,.],.],.],.],.],.]],[.,.]] => [9,2,3,4,5,6,7,1,8] => [2,3,4,5,6,7,9,1,8] => [2,1,1,1,1,1,1,1] => 1

[[[[[[[.,.],[[.,.],.]],.],.],.],.],.] => [3,4,1,2,5,6,7,8,9] => [1,3,4,2,5,6,7,8,9] => [2,1,1,1,1,1,1,1] => 1

[[[[[[[[[.,.],.],.],.],.],.],.],.],[[.,.],.]] => [10,11,1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,10,11,9] => [2,1,1,1,1,1,1,1,1,1] => 1

[.,[[[[[[.,.],.],.],.],.],[.,[.,.]]]] => [9,8,2,3,4,5,6,7,1] => [2,3,4,5,6,9,8,7,1] => [4,1,1,1,1,1] => 1

[.,[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]] => [10,9,2,3,4,5,6,7,8,1] => [2,3,4,5,6,7,10,9,8,1] => [4,1,1,1,1,1,1] => 1

[[.,[.,[[[[[[.,.],.],.],.],.],.]]],.] => [3,4,5,6,7,8,2,1,9] => [3,4,5,6,7,8,2,1,9] => [3,1,1,1,1,1,1] => 1

[[[.,[[[[[.,.],.],.],.],.]],.],[.,.]] => [9,2,3,4,5,6,1,7,8] => [2,3,4,5,6,1,9,7,8] => [2,2,1,1,1,1,1] => 2

[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.] => [6,7,5,4,3,2,1,8,9] => [6,7,5,4,3,2,1,8,9] => [6,1,1,1] => 1

[[.,[[[[[.,.],.],.],.],.]],[.,[.,.]]] => [9,8,2,3,4,5,6,1,7] => [2,3,4,5,6,9,8,1,7] => [3,1,1,1,1,1,1] => 1

[[[[[.,[.,[[[.,.],.],.]]],.],.],.],.] => [3,4,5,2,1,6,7,8,9] => [3,4,5,2,1,6,7,8,9] => [3,1,1,1,1,1,1] => 1

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Description

The side length of the Durfee square of an integer partition.
Given a partition $\lambda = (\lambda_1,\ldots,\lambda_n)$, the Durfee square is the largest partition $(s^s)$ whose diagram fits inside the diagram of $\lambda$. In symbols, $s = \max\{ i \mid \lambda_i \geq i \}$.
This is also known as the Frobenius rank.

Map

Foata bijection

Description

Sends a permutation to its image under the Foata bijection.
The Foata bijection $\phi$ is a bijection on the set of words with no two equal letters. It can be defined by induction on the size of the word:
Given a word $w_1 w_2 ... w_n$, compute the image inductively by starting with $\phi(w_1) = w_1$.
At the $i$-th step, if $\phi(w_1 w_2 ... w_i) = v_1 v_2 ... v_i$, define $\phi(w_1 w_2 ... w_i w_{i+1})$ by placing $w_{i+1}$ on the end of the word $v_1 v_2 ... v_i$ and breaking the word up into blocks as follows.

If $w_{i+1} \geq v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} \geq v_k$.
If $w_{i+1} < v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} < v_k$.

In either case, place a vertical line at the start of the word as well. Now, within each block between vertical lines, cyclically shift the entries one place to the right.
To compute $\phi([1,4,2,5,3])$, the sequence of words is

$1$
$|1|4 \to 14$
$|14|2 \to 412$
$|4|1|2|5 \to 4125$
$|4|125|3 \to 45123.$

In total, this gives $\phi([1,4,2,5,3]) = [4,5,1,2,3]$.
This bijection sends the major index (St000004The major index of a permutation.) to the number of inversions (St000018The number of inversions of a permutation.).

Map

LLPS

Description

The Lewis-Lyu-Pylyavskyy-Sen shape of a permutation.
An ascent in a sequence $u = (u_1, u_2, \ldots)$ is an index $i$ such that $u_i < u_{i+1}$. Let $\mathrm{asc}(u)$ denote the number of ascents of $u$, and let
$$\mathrm{asc}^{*}(u) := \begin{cases} 0 &\textrm{if u is empty}, \\ 1 + \mathrm{asc}(u) &\textrm{otherwise}.\end{cases}$$
Given a permutation $w$ in the symmetric group $\mathfrak{S}_n$, define
$A'_k := \max_{u_1, \ldots, u_k} (\mathrm{asc}^{*}(u_1) + \cdots + \mathrm{asc}^{*}(u_k))$
where the maximum is taken over disjoint subsequences ${u_i}$ of $w$.
Then $A'_1, A'_2-A'_1, A'_3-A'_2,\dots$ is a partition of $n$. Its conjugate is the Lewis-Lyu-Pylyavskyy-Sen shape of a permutation.

Map

to 132-avoiding permutation

Description

Return a 132-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the maximal element of the Sylvester class.