Identifier
Mp00017:
Binary trees
—to 312-avoiding permutation⟶
Permutations
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00248: Permutations —DEX composition⟶ Integer compositions
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00248: Permutations —DEX composition⟶ Integer compositions
Images
[.,.] => [1] => [1] => [1]
[.,[.,.]] => [2,1] => [2,1] => [2]
[[.,.],.] => [1,2] => [1,2] => [2]
[.,[.,[.,.]]] => [3,2,1] => [2,3,1] => [3]
[.,[[.,.],.]] => [2,3,1] => [3,2,1] => [2,1]
[[.,.],[.,.]] => [1,3,2] => [1,3,2] => [1,2]
[[.,[.,.]],.] => [2,1,3] => [2,1,3] => [3]
[[[.,.],.],.] => [1,2,3] => [1,2,3] => [3]
[.,[.,[.,[.,.]]]] => [4,3,2,1] => [2,3,4,1] => [4]
[.,[.,[[.,.],.]]] => [3,4,2,1] => [2,4,3,1] => [3,1]
[.,[[.,.],[.,.]]] => [2,4,3,1] => [3,2,4,1] => [2,2]
[.,[[.,[.,.]],.]] => [3,2,4,1] => [4,3,2,1] => [1,2,1]
[.,[[[.,.],.],.]] => [2,3,4,1] => [4,2,3,1] => [3,1]
[[.,.],[.,[.,.]]] => [1,4,3,2] => [1,3,4,2] => [1,3]
[[.,.],[[.,.],.]] => [1,3,4,2] => [1,4,3,2] => [1,2,1]
[[.,[.,.]],[.,.]] => [2,1,4,3] => [2,1,4,3] => [2,2]
[[[.,.],.],[.,.]] => [1,2,4,3] => [1,2,4,3] => [2,2]
[[.,[.,[.,.]]],.] => [3,2,1,4] => [2,3,1,4] => [4]
[[.,[[.,.],.]],.] => [2,3,1,4] => [3,2,1,4] => [2,2]
[[[.,.],[.,.]],.] => [1,3,2,4] => [1,3,2,4] => [1,3]
[[[.,[.,.]],.],.] => [2,1,3,4] => [2,1,3,4] => [4]
[[[[.,.],.],.],.] => [1,2,3,4] => [1,2,3,4] => [4]
[.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => [2,3,4,5,1] => [5]
[.,[.,[.,[[.,.],.]]]] => [4,5,3,2,1] => [2,3,5,4,1] => [4,1]
[.,[.,[[.,.],[.,.]]]] => [3,5,4,2,1] => [2,4,3,5,1] => [3,2]
[.,[.,[[.,[.,.]],.]]] => [4,3,5,2,1] => [2,5,4,3,1] => [2,2,1]
[.,[.,[[[.,.],.],.]]] => [3,4,5,2,1] => [2,5,3,4,1] => [4,1]
[.,[[.,.],[.,[.,.]]]] => [2,5,4,3,1] => [3,2,4,5,1] => [2,3]
[.,[[.,.],[[.,.],.]]] => [2,4,5,3,1] => [3,2,5,4,1] => [2,2,1]
[.,[[.,[.,.]],[.,.]]] => [3,2,5,4,1] => [4,3,2,5,1] => [1,2,2]
[.,[[[.,.],.],[.,.]]] => [2,3,5,4,1] => [4,2,3,5,1] => [3,2]
[.,[[.,[.,[.,.]]],.]] => [4,3,2,5,1] => [5,3,4,2,1] => [1,3,1]
[.,[[.,[[.,.],.]],.]] => [3,4,2,5,1] => [5,4,3,2,1] => [1,2,1,1]
[.,[[[.,.],[.,.]],.]] => [2,4,3,5,1] => [5,2,4,3,1] => [2,2,1]
[.,[[[.,[.,.]],.],.]] => [3,2,4,5,1] => [5,3,2,4,1] => [1,3,1]
[.,[[[[.,.],.],.],.]] => [2,3,4,5,1] => [5,2,3,4,1] => [4,1]
[[.,.],[.,[.,[.,.]]]] => [1,5,4,3,2] => [1,3,4,5,2] => [1,4]
[[.,.],[.,[[.,.],.]]] => [1,4,5,3,2] => [1,3,5,4,2] => [1,3,1]
[[.,.],[[.,.],[.,.]]] => [1,3,5,4,2] => [1,4,3,5,2] => [1,2,2]
[[.,.],[[.,[.,.]],.]] => [1,4,3,5,2] => [1,5,4,3,2] => [1,1,2,1]
[[.,.],[[[.,.],.],.]] => [1,3,4,5,2] => [1,5,3,4,2] => [1,3,1]
[[.,[.,.]],[.,[.,.]]] => [2,1,5,4,3] => [2,1,4,5,3] => [2,3]
[[.,[.,.]],[[.,.],.]] => [2,1,4,5,3] => [2,1,5,4,3] => [2,2,1]
[[[.,.],.],[.,[.,.]]] => [1,2,5,4,3] => [1,2,4,5,3] => [2,3]
[[[.,.],.],[[.,.],.]] => [1,2,4,5,3] => [1,2,5,4,3] => [2,2,1]
[[.,[.,[.,.]]],[.,.]] => [3,2,1,5,4] => [2,3,1,5,4] => [3,2]
[[.,[[.,.],.]],[.,.]] => [2,3,1,5,4] => [3,2,1,5,4] => [2,1,2]
[[[.,.],[.,.]],[.,.]] => [1,3,2,5,4] => [1,3,2,5,4] => [1,2,2]
[[[.,[.,.]],.],[.,.]] => [2,1,3,5,4] => [2,1,3,5,4] => [3,2]
[[[[.,.],.],.],[.,.]] => [1,2,3,5,4] => [1,2,3,5,4] => [3,2]
[[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => [2,3,4,1,5] => [5]
[[.,[.,[[.,.],.]]],.] => [3,4,2,1,5] => [2,4,3,1,5] => [3,2]
[[.,[[.,.],[.,.]]],.] => [2,4,3,1,5] => [3,2,4,1,5] => [2,3]
[[.,[[.,[.,.]],.]],.] => [3,2,4,1,5] => [4,3,2,1,5] => [1,2,2]
[[.,[[[.,.],.],.]],.] => [2,3,4,1,5] => [4,2,3,1,5] => [3,2]
[[[.,.],[.,[.,.]]],.] => [1,4,3,2,5] => [1,3,4,2,5] => [1,4]
[[[.,.],[[.,.],.]],.] => [1,3,4,2,5] => [1,4,3,2,5] => [1,2,2]
[[[.,[.,.]],[.,.]],.] => [2,1,4,3,5] => [2,1,4,3,5] => [2,3]
[[[[.,.],.],[.,.]],.] => [1,2,4,3,5] => [1,2,4,3,5] => [2,3]
[[[.,[.,[.,.]]],.],.] => [3,2,1,4,5] => [2,3,1,4,5] => [5]
[[[.,[[.,.],.]],.],.] => [2,3,1,4,5] => [3,2,1,4,5] => [2,3]
[[[[.,.],[.,.]],.],.] => [1,3,2,4,5] => [1,3,2,4,5] => [1,4]
[[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => [2,1,3,4,5] => [5]
[[[[[.,.],.],.],.],.] => [1,2,3,4,5] => [1,2,3,4,5] => [5]
[.,[.,[.,[.,[.,[.,.]]]]]] => [6,5,4,3,2,1] => [2,3,4,5,6,1] => [6]
[.,[.,[.,[.,[[.,.],.]]]]] => [5,6,4,3,2,1] => [2,3,4,6,5,1] => [5,1]
[.,[.,[.,[[.,.],[.,.]]]]] => [4,6,5,3,2,1] => [2,3,5,4,6,1] => [4,2]
[.,[.,[.,[[.,[.,.]],.]]]] => [5,4,6,3,2,1] => [2,3,6,5,4,1] => [3,2,1]
[.,[.,[.,[[[.,.],.],.]]]] => [4,5,6,3,2,1] => [2,3,6,4,5,1] => [5,1]
[.,[.,[[.,.],[.,[.,.]]]]] => [3,6,5,4,2,1] => [2,4,3,5,6,1] => [3,3]
[.,[.,[[.,.],[[.,.],.]]]] => [3,5,6,4,2,1] => [2,4,3,6,5,1] => [3,2,1]
[.,[.,[[.,[.,.]],[.,.]]]] => [4,3,6,5,2,1] => [2,5,4,3,6,1] => [2,2,2]
[.,[.,[[[.,.],.],[.,.]]]] => [3,4,6,5,2,1] => [2,5,3,4,6,1] => [4,2]
[.,[.,[[.,[.,[.,.]]],.]]] => [5,4,3,6,2,1] => [2,6,4,5,3,1] => [2,3,1]
[.,[.,[[.,[[.,.],.]],.]]] => [4,5,3,6,2,1] => [2,6,5,4,3,1] => [2,2,1,1]
[.,[.,[[[.,.],[.,.]],.]]] => [3,5,4,6,2,1] => [2,6,3,5,4,1] => [3,2,1]
[.,[.,[[[.,[.,.]],.],.]]] => [4,3,5,6,2,1] => [2,6,4,3,5,1] => [2,3,1]
[.,[.,[[[[.,.],.],.],.]]] => [3,4,5,6,2,1] => [2,6,3,4,5,1] => [5,1]
[.,[[.,.],[.,[.,[.,.]]]]] => [2,6,5,4,3,1] => [3,2,4,5,6,1] => [2,4]
[.,[[.,.],[.,[[.,.],.]]]] => [2,5,6,4,3,1] => [3,2,4,6,5,1] => [2,3,1]
[.,[[.,.],[[.,.],[.,.]]]] => [2,4,6,5,3,1] => [3,2,5,4,6,1] => [2,2,2]
[.,[[.,.],[[.,[.,.]],.]]] => [2,5,4,6,3,1] => [3,2,6,5,4,1] => [2,1,2,1]
[.,[[.,.],[[[.,.],.],.]]] => [2,4,5,6,3,1] => [3,2,6,4,5,1] => [2,3,1]
[.,[[.,[.,.]],[.,[.,.]]]] => [3,2,6,5,4,1] => [4,3,2,5,6,1] => [1,2,3]
[.,[[.,[.,.]],[[.,.],.]]] => [3,2,5,6,4,1] => [4,3,2,6,5,1] => [1,2,2,1]
[.,[[[.,.],.],[.,[.,.]]]] => [2,3,6,5,4,1] => [4,2,3,5,6,1] => [3,3]
[.,[[[.,.],.],[[.,.],.]]] => [2,3,5,6,4,1] => [4,2,3,6,5,1] => [3,2,1]
[.,[[.,[.,[.,.]]],[.,.]]] => [4,3,2,6,5,1] => [5,3,4,2,6,1] => [1,3,2]
[.,[[.,[[.,.],.]],[.,.]]] => [3,4,2,6,5,1] => [5,4,3,2,6,1] => [1,2,1,2]
[.,[[[.,.],[.,.]],[.,.]]] => [2,4,3,6,5,1] => [5,2,4,3,6,1] => [2,2,2]
[.,[[[.,[.,.]],.],[.,.]]] => [3,2,4,6,5,1] => [5,3,2,4,6,1] => [1,3,2]
[.,[[[[.,.],.],.],[.,.]]] => [2,3,4,6,5,1] => [5,2,3,4,6,1] => [4,2]
[.,[[.,[.,[.,[.,.]]]],.]] => [5,4,3,2,6,1] => [6,3,4,5,2,1] => [1,4,1]
[.,[[.,[.,[[.,.],.]]],.]] => [4,5,3,2,6,1] => [6,3,5,4,2,1] => [1,3,1,1]
[.,[[.,[[.,.],[.,.]]],.]] => [3,5,4,2,6,1] => [6,4,3,5,2,1] => [1,2,2,1]
[.,[[.,[[.,[.,.]],.]],.]] => [4,3,5,2,6,1] => [6,5,4,3,2,1] => [1,1,2,1,1]
[.,[[.,[[[.,.],.],.]],.]] => [3,4,5,2,6,1] => [6,5,3,4,2,1] => [1,3,1,1]
[.,[[[.,.],[.,[.,.]]],.]] => [2,5,4,3,6,1] => [6,2,4,5,3,1] => [2,3,1]
[.,[[[.,.],[[.,.],.]],.]] => [2,4,5,3,6,1] => [6,2,5,4,3,1] => [2,2,1,1]
[.,[[[.,[.,.]],[.,.]],.]] => [3,2,5,4,6,1] => [6,3,2,5,4,1] => [1,2,2,1]
[.,[[[[.,.],.],[.,.]],.]] => [2,3,5,4,6,1] => [6,2,3,5,4,1] => [3,2,1]
>>> Load all 1142 entries. <<<
[.,[[[.,[.,[.,.]]],.],.]] => [4,3,2,5,6,1] => [6,3,4,2,5,1] => [1,4,1]
[.,[[[.,[[.,.],.]],.],.]] => [3,4,2,5,6,1] => [6,4,3,2,5,1] => [1,2,2,1]
[.,[[[[.,.],[.,.]],.],.]] => [2,4,3,5,6,1] => [6,2,4,3,5,1] => [2,3,1]
[.,[[[[.,[.,.]],.],.],.]] => [3,2,4,5,6,1] => [6,3,2,4,5,1] => [1,4,1]
[.,[[[[[.,.],.],.],.],.]] => [2,3,4,5,6,1] => [6,2,3,4,5,1] => [5,1]
[[.,.],[.,[.,[.,[.,.]]]]] => [1,6,5,4,3,2] => [1,3,4,5,6,2] => [1,5]
[[.,.],[.,[.,[[.,.],.]]]] => [1,5,6,4,3,2] => [1,3,4,6,5,2] => [1,4,1]
[[.,.],[.,[[.,.],[.,.]]]] => [1,4,6,5,3,2] => [1,3,5,4,6,2] => [1,3,2]
[[.,.],[.,[[.,[.,.]],.]]] => [1,5,4,6,3,2] => [1,3,6,5,4,2] => [1,2,2,1]
[[.,.],[.,[[[.,.],.],.]]] => [1,4,5,6,3,2] => [1,3,6,4,5,2] => [1,4,1]
[[.,.],[[.,.],[.,[.,.]]]] => [1,3,6,5,4,2] => [1,4,3,5,6,2] => [1,2,3]
[[.,.],[[.,.],[[.,.],.]]] => [1,3,5,6,4,2] => [1,4,3,6,5,2] => [1,2,2,1]
[[.,.],[[.,[.,.]],[.,.]]] => [1,4,3,6,5,2] => [1,5,4,3,6,2] => [1,1,2,2]
[[.,.],[[[.,.],.],[.,.]]] => [1,3,4,6,5,2] => [1,5,3,4,6,2] => [1,3,2]
[[.,.],[[.,[.,[.,.]]],.]] => [1,5,4,3,6,2] => [1,6,4,5,3,2] => [1,1,3,1]
[[.,.],[[.,[[.,.],.]],.]] => [1,4,5,3,6,2] => [1,6,5,4,3,2] => [1,1,2,1,1]
[[.,.],[[[.,.],[.,.]],.]] => [1,3,5,4,6,2] => [1,6,3,5,4,2] => [1,2,2,1]
[[.,.],[[[.,[.,.]],.],.]] => [1,4,3,5,6,2] => [1,6,4,3,5,2] => [1,1,3,1]
[[.,.],[[[[.,.],.],.],.]] => [1,3,4,5,6,2] => [1,6,3,4,5,2] => [1,4,1]
[[.,[.,.]],[.,[.,[.,.]]]] => [2,1,6,5,4,3] => [2,1,4,5,6,3] => [2,4]
[[.,[.,.]],[.,[[.,.],.]]] => [2,1,5,6,4,3] => [2,1,4,6,5,3] => [2,3,1]
[[.,[.,.]],[[.,.],[.,.]]] => [2,1,4,6,5,3] => [2,1,5,4,6,3] => [2,2,2]
[[.,[.,.]],[[.,[.,.]],.]] => [2,1,5,4,6,3] => [2,1,6,5,4,3] => [2,1,2,1]
[[.,[.,.]],[[[.,.],.],.]] => [2,1,4,5,6,3] => [2,1,6,4,5,3] => [2,3,1]
[[[.,.],.],[.,[.,[.,.]]]] => [1,2,6,5,4,3] => [1,2,4,5,6,3] => [2,4]
[[[.,.],.],[.,[[.,.],.]]] => [1,2,5,6,4,3] => [1,2,4,6,5,3] => [2,3,1]
[[[.,.],.],[[.,.],[.,.]]] => [1,2,4,6,5,3] => [1,2,5,4,6,3] => [2,2,2]
[[[.,.],.],[[.,[.,.]],.]] => [1,2,5,4,6,3] => [1,2,6,5,4,3] => [2,1,2,1]
[[[.,.],.],[[[.,.],.],.]] => [1,2,4,5,6,3] => [1,2,6,4,5,3] => [2,3,1]
[[.,[.,[.,.]]],[.,[.,.]]] => [3,2,1,6,5,4] => [2,3,1,5,6,4] => [3,3]
[[.,[.,[.,.]]],[[.,.],.]] => [3,2,1,5,6,4] => [2,3,1,6,5,4] => [3,2,1]
[[.,[[.,.],.]],[.,[.,.]]] => [2,3,1,6,5,4] => [3,2,1,5,6,4] => [2,1,3]
[[.,[[.,.],.]],[[.,.],.]] => [2,3,1,5,6,4] => [3,2,1,6,5,4] => [2,1,2,1]
[[[.,.],[.,.]],[.,[.,.]]] => [1,3,2,6,5,4] => [1,3,2,5,6,4] => [1,2,3]
[[[.,.],[.,.]],[[.,.],.]] => [1,3,2,5,6,4] => [1,3,2,6,5,4] => [1,2,2,1]
[[[.,[.,.]],.],[.,[.,.]]] => [2,1,3,6,5,4] => [2,1,3,5,6,4] => [3,3]
[[[.,[.,.]],.],[[.,.],.]] => [2,1,3,5,6,4] => [2,1,3,6,5,4] => [3,2,1]
[[[[.,.],.],.],[.,[.,.]]] => [1,2,3,6,5,4] => [1,2,3,5,6,4] => [3,3]
[[[[.,.],.],.],[[.,.],.]] => [1,2,3,5,6,4] => [1,2,3,6,5,4] => [3,2,1]
[[.,[.,[.,[.,.]]]],[.,.]] => [4,3,2,1,6,5] => [2,3,4,1,6,5] => [4,2]
[[.,[.,[[.,.],.]]],[.,.]] => [3,4,2,1,6,5] => [2,4,3,1,6,5] => [3,1,2]
[[.,[[.,.],[.,.]]],[.,.]] => [2,4,3,1,6,5] => [3,2,4,1,6,5] => [2,2,2]
[[.,[[.,[.,.]],.]],[.,.]] => [3,2,4,1,6,5] => [4,3,2,1,6,5] => [1,2,1,2]
[[.,[[[.,.],.],.]],[.,.]] => [2,3,4,1,6,5] => [4,2,3,1,6,5] => [3,1,2]
[[[.,.],[.,[.,.]]],[.,.]] => [1,4,3,2,6,5] => [1,3,4,2,6,5] => [1,3,2]
[[[.,.],[[.,.],.]],[.,.]] => [1,3,4,2,6,5] => [1,4,3,2,6,5] => [1,2,1,2]
[[[.,[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => [2,2,2]
[[[[.,.],.],[.,.]],[.,.]] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => [2,2,2]
[[[.,[.,[.,.]]],.],[.,.]] => [3,2,1,4,6,5] => [2,3,1,4,6,5] => [4,2]
[[[.,[[.,.],.]],.],[.,.]] => [2,3,1,4,6,5] => [3,2,1,4,6,5] => [2,2,2]
[[[[.,.],[.,.]],.],[.,.]] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => [1,3,2]
[[[[.,[.,.]],.],.],[.,.]] => [2,1,3,4,6,5] => [2,1,3,4,6,5] => [4,2]
[[[[[.,.],.],.],.],[.,.]] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => [4,2]
[[.,[.,[.,[.,[.,.]]]]],.] => [5,4,3,2,1,6] => [2,3,4,5,1,6] => [6]
[[.,[.,[.,[[.,.],.]]]],.] => [4,5,3,2,1,6] => [2,3,5,4,1,6] => [4,2]
[[.,[.,[[.,.],[.,.]]]],.] => [3,5,4,2,1,6] => [2,4,3,5,1,6] => [3,3]
[[.,[.,[[.,[.,.]],.]]],.] => [4,3,5,2,1,6] => [2,5,4,3,1,6] => [2,2,2]
[[.,[.,[[[.,.],.],.]]],.] => [3,4,5,2,1,6] => [2,5,3,4,1,6] => [4,2]
[[.,[[.,.],[.,[.,.]]]],.] => [2,5,4,3,1,6] => [3,2,4,5,1,6] => [2,4]
[[.,[[.,.],[[.,.],.]]],.] => [2,4,5,3,1,6] => [3,2,5,4,1,6] => [2,2,2]
[[.,[[.,[.,.]],[.,.]]],.] => [3,2,5,4,1,6] => [4,3,2,5,1,6] => [1,2,3]
[[.,[[[.,.],.],[.,.]]],.] => [2,3,5,4,1,6] => [4,2,3,5,1,6] => [3,3]
[[.,[[.,[.,[.,.]]],.]],.] => [4,3,2,5,1,6] => [5,3,4,2,1,6] => [1,3,2]
[[.,[[.,[[.,.],.]],.]],.] => [3,4,2,5,1,6] => [5,4,3,2,1,6] => [1,2,1,2]
[[.,[[[.,.],[.,.]],.]],.] => [2,4,3,5,1,6] => [5,2,4,3,1,6] => [2,2,2]
[[.,[[[.,[.,.]],.],.]],.] => [3,2,4,5,1,6] => [5,3,2,4,1,6] => [1,3,2]
[[.,[[[[.,.],.],.],.]],.] => [2,3,4,5,1,6] => [5,2,3,4,1,6] => [4,2]
[[[.,.],[.,[.,[.,.]]]],.] => [1,5,4,3,2,6] => [1,3,4,5,2,6] => [1,5]
[[[.,.],[.,[[.,.],.]]],.] => [1,4,5,3,2,6] => [1,3,5,4,2,6] => [1,3,2]
[[[.,.],[[.,.],[.,.]]],.] => [1,3,5,4,2,6] => [1,4,3,5,2,6] => [1,2,3]
[[[.,.],[[.,[.,.]],.]],.] => [1,4,3,5,2,6] => [1,5,4,3,2,6] => [1,1,2,2]
[[[.,.],[[[.,.],.],.]],.] => [1,3,4,5,2,6] => [1,5,3,4,2,6] => [1,3,2]
[[[.,[.,.]],[.,[.,.]]],.] => [2,1,5,4,3,6] => [2,1,4,5,3,6] => [2,4]
[[[.,[.,.]],[[.,.],.]],.] => [2,1,4,5,3,6] => [2,1,5,4,3,6] => [2,2,2]
[[[[.,.],.],[.,[.,.]]],.] => [1,2,5,4,3,6] => [1,2,4,5,3,6] => [2,4]
[[[[.,.],.],[[.,.],.]],.] => [1,2,4,5,3,6] => [1,2,5,4,3,6] => [2,2,2]
[[[.,[.,[.,.]]],[.,.]],.] => [3,2,1,5,4,6] => [2,3,1,5,4,6] => [3,3]
[[[.,[[.,.],.]],[.,.]],.] => [2,3,1,5,4,6] => [3,2,1,5,4,6] => [2,1,3]
[[[[.,.],[.,.]],[.,.]],.] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => [1,2,3]
[[[[.,[.,.]],.],[.,.]],.] => [2,1,3,5,4,6] => [2,1,3,5,4,6] => [3,3]
[[[[[.,.],.],.],[.,.]],.] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => [3,3]
[[[.,[.,[.,[.,.]]]],.],.] => [4,3,2,1,5,6] => [2,3,4,1,5,6] => [6]
[[[.,[.,[[.,.],.]]],.],.] => [3,4,2,1,5,6] => [2,4,3,1,5,6] => [3,3]
[[[.,[[.,.],[.,.]]],.],.] => [2,4,3,1,5,6] => [3,2,4,1,5,6] => [2,4]
[[[.,[[.,[.,.]],.]],.],.] => [3,2,4,1,5,6] => [4,3,2,1,5,6] => [1,2,3]
[[[.,[[[.,.],.],.]],.],.] => [2,3,4,1,5,6] => [4,2,3,1,5,6] => [3,3]
[[[[.,.],[.,[.,.]]],.],.] => [1,4,3,2,5,6] => [1,3,4,2,5,6] => [1,5]
[[[[.,.],[[.,.],.]],.],.] => [1,3,4,2,5,6] => [1,4,3,2,5,6] => [1,2,3]
[[[[.,[.,.]],[.,.]],.],.] => [2,1,4,3,5,6] => [2,1,4,3,5,6] => [2,4]
[[[[[.,.],.],[.,.]],.],.] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => [2,4]
[[[[.,[.,[.,.]]],.],.],.] => [3,2,1,4,5,6] => [2,3,1,4,5,6] => [6]
[[[[.,[[.,.],.]],.],.],.] => [2,3,1,4,5,6] => [3,2,1,4,5,6] => [2,4]
[[[[[.,.],[.,.]],.],.],.] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => [1,5]
[[[[[.,[.,.]],.],.],.],.] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [6]
[[[[[[.,.],.],.],.],.],.] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [6]
[.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [7,6,5,4,3,2,1] => [2,3,4,5,6,7,1] => [7]
[.,[.,[.,[.,[.,[[.,.],.]]]]]] => [6,7,5,4,3,2,1] => [2,3,4,5,7,6,1] => [6,1]
[.,[.,[.,[.,[[.,.],[.,.]]]]]] => [5,7,6,4,3,2,1] => [2,3,4,6,5,7,1] => [5,2]
[.,[.,[.,[.,[[.,[.,.]],.]]]]] => [6,5,7,4,3,2,1] => [2,3,4,7,6,5,1] => [4,2,1]
[.,[.,[.,[.,[[[.,.],.],.]]]]] => [5,6,7,4,3,2,1] => [2,3,4,7,5,6,1] => [6,1]
[.,[.,[.,[[.,.],[.,[.,.]]]]]] => [4,7,6,5,3,2,1] => [2,3,5,4,6,7,1] => [4,3]
[.,[.,[.,[[.,.],[[.,.],.]]]]] => [4,6,7,5,3,2,1] => [2,3,5,4,7,6,1] => [4,2,1]
[.,[.,[.,[[.,[.,.]],[.,.]]]]] => [5,4,7,6,3,2,1] => [2,3,6,5,4,7,1] => [3,2,2]
[.,[.,[.,[[[.,.],.],[.,.]]]]] => [4,5,7,6,3,2,1] => [2,3,6,4,5,7,1] => [5,2]
[.,[.,[.,[[.,[.,[.,.]]],.]]]] => [6,5,4,7,3,2,1] => [2,3,7,5,6,4,1] => [3,3,1]
[.,[.,[.,[[.,[[.,.],.]],.]]]] => [5,6,4,7,3,2,1] => [2,3,7,6,5,4,1] => [3,2,1,1]
[.,[.,[.,[[[.,.],[.,.]],.]]]] => [4,6,5,7,3,2,1] => [2,3,7,4,6,5,1] => [4,2,1]
[.,[.,[.,[[[.,[.,.]],.],.]]]] => [5,4,6,7,3,2,1] => [2,3,7,5,4,6,1] => [3,3,1]
[.,[.,[.,[[[[.,.],.],.],.]]]] => [4,5,6,7,3,2,1] => [2,3,7,4,5,6,1] => [6,1]
[.,[.,[[.,.],[.,[.,[.,.]]]]]] => [3,7,6,5,4,2,1] => [2,4,3,5,6,7,1] => [3,4]
[.,[.,[[.,.],[.,[[.,.],.]]]]] => [3,6,7,5,4,2,1] => [2,4,3,5,7,6,1] => [3,3,1]
[.,[.,[[.,.],[[.,.],[.,.]]]]] => [3,5,7,6,4,2,1] => [2,4,3,6,5,7,1] => [3,2,2]
[.,[.,[[.,.],[[.,[.,.]],.]]]] => [3,6,5,7,4,2,1] => [2,4,3,7,6,5,1] => [3,1,2,1]
[.,[.,[[.,.],[[[.,.],.],.]]]] => [3,5,6,7,4,2,1] => [2,4,3,7,5,6,1] => [3,3,1]
[.,[.,[[.,[.,.]],[.,[.,.]]]]] => [4,3,7,6,5,2,1] => [2,5,4,3,6,7,1] => [2,2,3]
[.,[.,[[.,[.,.]],[[.,.],.]]]] => [4,3,6,7,5,2,1] => [2,5,4,3,7,6,1] => [2,2,2,1]
[.,[.,[[[.,.],.],[.,[.,.]]]]] => [3,4,7,6,5,2,1] => [2,5,3,4,6,7,1] => [4,3]
[.,[.,[[[.,.],.],[[.,.],.]]]] => [3,4,6,7,5,2,1] => [2,5,3,4,7,6,1] => [4,2,1]
[.,[.,[[.,[.,[.,.]]],[.,.]]]] => [5,4,3,7,6,2,1] => [2,6,4,5,3,7,1] => [2,3,2]
[.,[.,[[.,[[.,.],.]],[.,.]]]] => [4,5,3,7,6,2,1] => [2,6,5,4,3,7,1] => [2,2,1,2]
[.,[.,[[[.,.],[.,.]],[.,.]]]] => [3,5,4,7,6,2,1] => [2,6,3,5,4,7,1] => [3,2,2]
[.,[.,[[[.,[.,.]],.],[.,.]]]] => [4,3,5,7,6,2,1] => [2,6,4,3,5,7,1] => [2,3,2]
[.,[.,[[[[.,.],.],.],[.,.]]]] => [3,4,5,7,6,2,1] => [2,6,3,4,5,7,1] => [5,2]
[.,[.,[[.,[.,[.,[.,.]]]],.]]] => [6,5,4,3,7,2,1] => [2,7,4,5,6,3,1] => [2,4,1]
[.,[.,[[.,[.,[[.,.],.]]],.]]] => [5,6,4,3,7,2,1] => [2,7,4,6,5,3,1] => [2,3,1,1]
[.,[.,[[.,[[.,.],[.,.]]],.]]] => [4,6,5,3,7,2,1] => [2,7,5,4,6,3,1] => [2,2,2,1]
[.,[.,[[.,[[.,[.,.]],.]],.]]] => [5,4,6,3,7,2,1] => [2,7,6,5,4,3,1] => [2,1,2,1,1]
[.,[.,[[.,[[[.,.],.],.]],.]]] => [4,5,6,3,7,2,1] => [2,7,6,4,5,3,1] => [2,3,1,1]
[.,[.,[[[.,.],[.,[.,.]]],.]]] => [3,6,5,4,7,2,1] => [2,7,3,5,6,4,1] => [3,3,1]
[.,[.,[[[.,.],[[.,.],.]],.]]] => [3,5,6,4,7,2,1] => [2,7,3,6,5,4,1] => [3,2,1,1]
[.,[.,[[[.,[.,.]],[.,.]],.]]] => [4,3,6,5,7,2,1] => [2,7,4,3,6,5,1] => [2,2,2,1]
[.,[.,[[[[.,.],.],[.,.]],.]]] => [3,4,6,5,7,2,1] => [2,7,3,4,6,5,1] => [4,2,1]
[.,[.,[[[.,[.,[.,.]]],.],.]]] => [5,4,3,6,7,2,1] => [2,7,4,5,3,6,1] => [2,4,1]
[.,[.,[[[.,[[.,.],.]],.],.]]] => [4,5,3,6,7,2,1] => [2,7,5,4,3,6,1] => [2,2,2,1]
[.,[.,[[[[.,.],[.,.]],.],.]]] => [3,5,4,6,7,2,1] => [2,7,3,5,4,6,1] => [3,3,1]
[.,[.,[[[[.,[.,.]],.],.],.]]] => [4,3,5,6,7,2,1] => [2,7,4,3,5,6,1] => [2,4,1]
[.,[.,[[[[[.,.],.],.],.],.]]] => [3,4,5,6,7,2,1] => [2,7,3,4,5,6,1] => [6,1]
[.,[[.,.],[.,[.,[.,[.,.]]]]]] => [2,7,6,5,4,3,1] => [3,2,4,5,6,7,1] => [2,5]
[.,[[.,.],[.,[.,[[.,.],.]]]]] => [2,6,7,5,4,3,1] => [3,2,4,5,7,6,1] => [2,4,1]
[.,[[.,.],[.,[[.,.],[.,.]]]]] => [2,5,7,6,4,3,1] => [3,2,4,6,5,7,1] => [2,3,2]
[.,[[.,.],[.,[[.,[.,.]],.]]]] => [2,6,5,7,4,3,1] => [3,2,4,7,6,5,1] => [2,2,2,1]
[.,[[.,.],[.,[[[.,.],.],.]]]] => [2,5,6,7,4,3,1] => [3,2,4,7,5,6,1] => [2,4,1]
[.,[[.,.],[[.,.],[.,[.,.]]]]] => [2,4,7,6,5,3,1] => [3,2,5,4,6,7,1] => [2,2,3]
[.,[[.,.],[[.,.],[[.,.],.]]]] => [2,4,6,7,5,3,1] => [3,2,5,4,7,6,1] => [2,2,2,1]
[.,[[.,.],[[.,[.,.]],[.,.]]]] => [2,5,4,7,6,3,1] => [3,2,6,5,4,7,1] => [2,1,2,2]
[.,[[.,.],[[[.,.],.],[.,.]]]] => [2,4,5,7,6,3,1] => [3,2,6,4,5,7,1] => [2,3,2]
[.,[[.,.],[[.,[.,[.,.]]],.]]] => [2,6,5,4,7,3,1] => [3,2,7,5,6,4,1] => [2,1,3,1]
[.,[[.,.],[[.,[[.,.],.]],.]]] => [2,5,6,4,7,3,1] => [3,2,7,6,5,4,1] => [2,1,2,1,1]
[.,[[.,.],[[[.,.],[.,.]],.]]] => [2,4,6,5,7,3,1] => [3,2,7,4,6,5,1] => [2,2,2,1]
[.,[[.,.],[[[.,[.,.]],.],.]]] => [2,5,4,6,7,3,1] => [3,2,7,5,4,6,1] => [2,1,3,1]
[.,[[.,.],[[[[.,.],.],.],.]]] => [2,4,5,6,7,3,1] => [3,2,7,4,5,6,1] => [2,4,1]
[.,[[.,[.,.]],[.,[.,[.,.]]]]] => [3,2,7,6,5,4,1] => [4,3,2,5,6,7,1] => [1,2,4]
[.,[[.,[.,.]],[.,[[.,.],.]]]] => [3,2,6,7,5,4,1] => [4,3,2,5,7,6,1] => [1,2,3,1]
[.,[[.,[.,.]],[[.,.],[.,.]]]] => [3,2,5,7,6,4,1] => [4,3,2,6,5,7,1] => [1,2,2,2]
[.,[[.,[.,.]],[[.,[.,.]],.]]] => [3,2,6,5,7,4,1] => [4,3,2,7,6,5,1] => [1,2,1,2,1]
[.,[[.,[.,.]],[[[.,.],.],.]]] => [3,2,5,6,7,4,1] => [4,3,2,7,5,6,1] => [1,2,3,1]
[.,[[[.,.],.],[.,[.,[.,.]]]]] => [2,3,7,6,5,4,1] => [4,2,3,5,6,7,1] => [3,4]
[.,[[[.,.],.],[.,[[.,.],.]]]] => [2,3,6,7,5,4,1] => [4,2,3,5,7,6,1] => [3,3,1]
[.,[[[.,.],.],[[.,.],[.,.]]]] => [2,3,5,7,6,4,1] => [4,2,3,6,5,7,1] => [3,2,2]
[.,[[[.,.],.],[[.,[.,.]],.]]] => [2,3,6,5,7,4,1] => [4,2,3,7,6,5,1] => [3,1,2,1]
[.,[[[.,.],.],[[[.,.],.],.]]] => [2,3,5,6,7,4,1] => [4,2,3,7,5,6,1] => [3,3,1]
[.,[[.,[.,[.,.]]],[.,[.,.]]]] => [4,3,2,7,6,5,1] => [5,3,4,2,6,7,1] => [1,3,3]
[.,[[.,[.,[.,.]]],[[.,.],.]]] => [4,3,2,6,7,5,1] => [5,3,4,2,7,6,1] => [1,3,2,1]
[.,[[.,[[.,.],.]],[.,[.,.]]]] => [3,4,2,7,6,5,1] => [5,4,3,2,6,7,1] => [1,2,1,3]
[.,[[.,[[.,.],.]],[[.,.],.]]] => [3,4,2,6,7,5,1] => [5,4,3,2,7,6,1] => [1,2,1,2,1]
[.,[[[.,.],[.,.]],[.,[.,.]]]] => [2,4,3,7,6,5,1] => [5,2,4,3,6,7,1] => [2,2,3]
[.,[[[.,.],[.,.]],[[.,.],.]]] => [2,4,3,6,7,5,1] => [5,2,4,3,7,6,1] => [2,2,2,1]
[.,[[[.,[.,.]],.],[.,[.,.]]]] => [3,2,4,7,6,5,1] => [5,3,2,4,6,7,1] => [1,3,3]
[.,[[[.,[.,.]],.],[[.,.],.]]] => [3,2,4,6,7,5,1] => [5,3,2,4,7,6,1] => [1,3,2,1]
[.,[[[[.,.],.],.],[.,[.,.]]]] => [2,3,4,7,6,5,1] => [5,2,3,4,6,7,1] => [4,3]
[.,[[[[.,.],.],.],[[.,.],.]]] => [2,3,4,6,7,5,1] => [5,2,3,4,7,6,1] => [4,2,1]
[.,[[.,[.,[.,[.,.]]]],[.,.]]] => [5,4,3,2,7,6,1] => [6,3,4,5,2,7,1] => [1,4,2]
[.,[[.,[.,[[.,.],.]]],[.,.]]] => [4,5,3,2,7,6,1] => [6,3,5,4,2,7,1] => [1,3,1,2]
[.,[[.,[[.,.],[.,.]]],[.,.]]] => [3,5,4,2,7,6,1] => [6,4,3,5,2,7,1] => [1,2,2,2]
[.,[[.,[[.,[.,.]],.]],[.,.]]] => [4,3,5,2,7,6,1] => [6,5,4,3,2,7,1] => [1,1,2,1,2]
[.,[[.,[[[.,.],.],.]],[.,.]]] => [3,4,5,2,7,6,1] => [6,5,3,4,2,7,1] => [1,3,1,2]
[.,[[[.,.],[.,[.,.]]],[.,.]]] => [2,5,4,3,7,6,1] => [6,2,4,5,3,7,1] => [2,3,2]
[.,[[[.,.],[[.,.],.]],[.,.]]] => [2,4,5,3,7,6,1] => [6,2,5,4,3,7,1] => [2,2,1,2]
[.,[[[.,[.,.]],[.,.]],[.,.]]] => [3,2,5,4,7,6,1] => [6,3,2,5,4,7,1] => [1,2,2,2]
[.,[[[[.,.],.],[.,.]],[.,.]]] => [2,3,5,4,7,6,1] => [6,2,3,5,4,7,1] => [3,2,2]
[.,[[[.,[.,[.,.]]],.],[.,.]]] => [4,3,2,5,7,6,1] => [6,3,4,2,5,7,1] => [1,4,2]
[.,[[[.,[[.,.],.]],.],[.,.]]] => [3,4,2,5,7,6,1] => [6,4,3,2,5,7,1] => [1,2,2,2]
[.,[[[[.,.],[.,.]],.],[.,.]]] => [2,4,3,5,7,6,1] => [6,2,4,3,5,7,1] => [2,3,2]
[.,[[[[.,[.,.]],.],.],[.,.]]] => [3,2,4,5,7,6,1] => [6,3,2,4,5,7,1] => [1,4,2]
[.,[[[[[.,.],.],.],.],[.,.]]] => [2,3,4,5,7,6,1] => [6,2,3,4,5,7,1] => [5,2]
[.,[[.,[.,[.,[.,[.,.]]]]],.]] => [6,5,4,3,2,7,1] => [7,3,4,5,6,2,1] => [1,5,1]
[.,[[.,[.,[.,[[.,.],.]]]],.]] => [5,6,4,3,2,7,1] => [7,3,4,6,5,2,1] => [1,4,1,1]
[.,[[.,[.,[[.,.],[.,.]]]],.]] => [4,6,5,3,2,7,1] => [7,3,5,4,6,2,1] => [1,3,2,1]
[.,[[.,[.,[[.,[.,.]],.]]],.]] => [5,4,6,3,2,7,1] => [7,3,6,5,4,2,1] => [1,2,2,1,1]
[.,[[.,[.,[[[.,.],.],.]]],.]] => [4,5,6,3,2,7,1] => [7,3,6,4,5,2,1] => [1,4,1,1]
[.,[[.,[[.,.],[.,[.,.]]]],.]] => [3,6,5,4,2,7,1] => [7,4,3,5,6,2,1] => [1,2,3,1]
[.,[[.,[[.,.],[[.,.],.]]],.]] => [3,5,6,4,2,7,1] => [7,4,3,6,5,2,1] => [1,2,2,1,1]
[.,[[.,[[.,[.,.]],[.,.]]],.]] => [4,3,6,5,2,7,1] => [7,5,4,3,6,2,1] => [1,1,2,2,1]
[.,[[.,[[[.,.],.],[.,.]]],.]] => [3,4,6,5,2,7,1] => [7,5,3,4,6,2,1] => [1,3,2,1]
[.,[[.,[[.,[.,[.,.]]],.]],.]] => [5,4,3,6,2,7,1] => [7,6,4,5,3,2,1] => [1,1,3,1,1]
[.,[[.,[[.,[[.,.],.]],.]],.]] => [4,5,3,6,2,7,1] => [7,6,5,4,3,2,1] => [1,1,2,1,1,1]
[.,[[.,[[[.,.],[.,.]],.]],.]] => [3,5,4,6,2,7,1] => [7,6,3,5,4,2,1] => [1,2,2,1,1]
[.,[[.,[[[.,[.,.]],.],.]],.]] => [4,3,5,6,2,7,1] => [7,6,4,3,5,2,1] => [1,1,3,1,1]
[.,[[.,[[[[.,.],.],.],.]],.]] => [3,4,5,6,2,7,1] => [7,6,3,4,5,2,1] => [1,4,1,1]
[.,[[[.,.],[.,[.,[.,.]]]],.]] => [2,6,5,4,3,7,1] => [7,2,4,5,6,3,1] => [2,4,1]
[.,[[[.,.],[.,[[.,.],.]]],.]] => [2,5,6,4,3,7,1] => [7,2,4,6,5,3,1] => [2,3,1,1]
[.,[[[.,.],[[.,.],[.,.]]],.]] => [2,4,6,5,3,7,1] => [7,2,5,4,6,3,1] => [2,2,2,1]
[.,[[[.,.],[[.,[.,.]],.]],.]] => [2,5,4,6,3,7,1] => [7,2,6,5,4,3,1] => [2,1,2,1,1]
[.,[[[.,.],[[[.,.],.],.]],.]] => [2,4,5,6,3,7,1] => [7,2,6,4,5,3,1] => [2,3,1,1]
[.,[[[.,[.,.]],[.,[.,.]]],.]] => [3,2,6,5,4,7,1] => [7,3,2,5,6,4,1] => [1,2,3,1]
[.,[[[.,[.,.]],[[.,.],.]],.]] => [3,2,5,6,4,7,1] => [7,3,2,6,5,4,1] => [1,2,2,1,1]
[.,[[[[.,.],.],[.,[.,.]]],.]] => [2,3,6,5,4,7,1] => [7,2,3,5,6,4,1] => [3,3,1]
[.,[[[[.,.],.],[[.,.],.]],.]] => [2,3,5,6,4,7,1] => [7,2,3,6,5,4,1] => [3,2,1,1]
[.,[[[.,[.,[.,.]]],[.,.]],.]] => [4,3,2,6,5,7,1] => [7,3,4,2,6,5,1] => [1,3,2,1]
[.,[[[.,[[.,.],.]],[.,.]],.]] => [3,4,2,6,5,7,1] => [7,4,3,2,6,5,1] => [1,2,1,2,1]
[.,[[[[.,.],[.,.]],[.,.]],.]] => [2,4,3,6,5,7,1] => [7,2,4,3,6,5,1] => [2,2,2,1]
[.,[[[[.,[.,.]],.],[.,.]],.]] => [3,2,4,6,5,7,1] => [7,3,2,4,6,5,1] => [1,3,2,1]
[.,[[[[[.,.],.],.],[.,.]],.]] => [2,3,4,6,5,7,1] => [7,2,3,4,6,5,1] => [4,2,1]
[.,[[[.,[.,[.,[.,.]]]],.],.]] => [5,4,3,2,6,7,1] => [7,3,4,5,2,6,1] => [1,5,1]
[.,[[[.,[.,[[.,.],.]]],.],.]] => [4,5,3,2,6,7,1] => [7,3,5,4,2,6,1] => [1,3,2,1]
[.,[[[.,[[.,.],[.,.]]],.],.]] => [3,5,4,2,6,7,1] => [7,4,3,5,2,6,1] => [1,2,3,1]
[.,[[[.,[[.,[.,.]],.]],.],.]] => [4,3,5,2,6,7,1] => [7,5,4,3,2,6,1] => [1,1,2,2,1]
[.,[[[.,[[[.,.],.],.]],.],.]] => [3,4,5,2,6,7,1] => [7,5,3,4,2,6,1] => [1,3,2,1]
[.,[[[[.,.],[.,[.,.]]],.],.]] => [2,5,4,3,6,7,1] => [7,2,4,5,3,6,1] => [2,4,1]
[.,[[[[.,.],[[.,.],.]],.],.]] => [2,4,5,3,6,7,1] => [7,2,5,4,3,6,1] => [2,2,2,1]
[.,[[[[.,[.,.]],[.,.]],.],.]] => [3,2,5,4,6,7,1] => [7,3,2,5,4,6,1] => [1,2,3,1]
[.,[[[[[.,.],.],[.,.]],.],.]] => [2,3,5,4,6,7,1] => [7,2,3,5,4,6,1] => [3,3,1]
[.,[[[[.,[.,[.,.]]],.],.],.]] => [4,3,2,5,6,7,1] => [7,3,4,2,5,6,1] => [1,5,1]
[.,[[[[.,[[.,.],.]],.],.],.]] => [3,4,2,5,6,7,1] => [7,4,3,2,5,6,1] => [1,2,3,1]
[.,[[[[[.,.],[.,.]],.],.],.]] => [2,4,3,5,6,7,1] => [7,2,4,3,5,6,1] => [2,4,1]
[.,[[[[[.,[.,.]],.],.],.],.]] => [3,2,4,5,6,7,1] => [7,3,2,4,5,6,1] => [1,5,1]
[.,[[[[[[.,.],.],.],.],.],.]] => [2,3,4,5,6,7,1] => [7,2,3,4,5,6,1] => [6,1]
[[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,7,6,5,4,3,2] => [1,3,4,5,6,7,2] => [1,6]
[[.,.],[.,[.,[.,[[.,.],.]]]]] => [1,6,7,5,4,3,2] => [1,3,4,5,7,6,2] => [1,5,1]
[[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,5,7,6,4,3,2] => [1,3,4,6,5,7,2] => [1,4,2]
[[.,.],[.,[.,[[.,[.,.]],.]]]] => [1,6,5,7,4,3,2] => [1,3,4,7,6,5,2] => [1,3,2,1]
[[.,.],[.,[.,[[[.,.],.],.]]]] => [1,5,6,7,4,3,2] => [1,3,4,7,5,6,2] => [1,5,1]
[[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,4,7,6,5,3,2] => [1,3,5,4,6,7,2] => [1,3,3]
[[.,.],[.,[[.,.],[[.,.],.]]]] => [1,4,6,7,5,3,2] => [1,3,5,4,7,6,2] => [1,3,2,1]
[[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,5,4,7,6,3,2] => [1,3,6,5,4,7,2] => [1,2,2,2]
[[.,.],[.,[[[.,.],.],[.,.]]]] => [1,4,5,7,6,3,2] => [1,3,6,4,5,7,2] => [1,4,2]
[[.,.],[.,[[.,[.,[.,.]]],.]]] => [1,6,5,4,7,3,2] => [1,3,7,5,6,4,2] => [1,2,3,1]
[[.,.],[.,[[.,[[.,.],.]],.]]] => [1,5,6,4,7,3,2] => [1,3,7,6,5,4,2] => [1,2,2,1,1]
[[.,.],[.,[[[.,.],[.,.]],.]]] => [1,4,6,5,7,3,2] => [1,3,7,4,6,5,2] => [1,3,2,1]
[[.,.],[.,[[[.,[.,.]],.],.]]] => [1,5,4,6,7,3,2] => [1,3,7,5,4,6,2] => [1,2,3,1]
[[.,.],[.,[[[[.,.],.],.],.]]] => [1,4,5,6,7,3,2] => [1,3,7,4,5,6,2] => [1,5,1]
[[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,3,7,6,5,4,2] => [1,4,3,5,6,7,2] => [1,2,4]
[[.,.],[[.,.],[.,[[.,.],.]]]] => [1,3,6,7,5,4,2] => [1,4,3,5,7,6,2] => [1,2,3,1]
[[.,.],[[.,.],[[.,.],[.,.]]]] => [1,3,5,7,6,4,2] => [1,4,3,6,5,7,2] => [1,2,2,2]
[[.,.],[[.,.],[[.,[.,.]],.]]] => [1,3,6,5,7,4,2] => [1,4,3,7,6,5,2] => [1,2,1,2,1]
[[.,.],[[.,.],[[[.,.],.],.]]] => [1,3,5,6,7,4,2] => [1,4,3,7,5,6,2] => [1,2,3,1]
[[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,4,3,7,6,5,2] => [1,5,4,3,6,7,2] => [1,1,2,3]
[[.,.],[[.,[.,.]],[[.,.],.]]] => [1,4,3,6,7,5,2] => [1,5,4,3,7,6,2] => [1,1,2,2,1]
[[.,.],[[[.,.],.],[.,[.,.]]]] => [1,3,4,7,6,5,2] => [1,5,3,4,6,7,2] => [1,3,3]
[[.,.],[[[.,.],.],[[.,.],.]]] => [1,3,4,6,7,5,2] => [1,5,3,4,7,6,2] => [1,3,2,1]
[[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,5,4,3,7,6,2] => [1,6,4,5,3,7,2] => [1,1,3,2]
[[.,.],[[.,[[.,.],.]],[.,.]]] => [1,4,5,3,7,6,2] => [1,6,5,4,3,7,2] => [1,1,2,1,2]
[[.,.],[[[.,.],[.,.]],[.,.]]] => [1,3,5,4,7,6,2] => [1,6,3,5,4,7,2] => [1,2,2,2]
[[.,.],[[[.,[.,.]],.],[.,.]]] => [1,4,3,5,7,6,2] => [1,6,4,3,5,7,2] => [1,1,3,2]
[[.,.],[[[[.,.],.],.],[.,.]]] => [1,3,4,5,7,6,2] => [1,6,3,4,5,7,2] => [1,4,2]
[[.,.],[[.,[.,[.,[.,.]]]],.]] => [1,6,5,4,3,7,2] => [1,7,4,5,6,3,2] => [1,1,4,1]
[[.,.],[[.,[.,[[.,.],.]]],.]] => [1,5,6,4,3,7,2] => [1,7,4,6,5,3,2] => [1,1,3,1,1]
[[.,.],[[.,[[.,.],[.,.]]],.]] => [1,4,6,5,3,7,2] => [1,7,5,4,6,3,2] => [1,1,2,2,1]
[[.,.],[[.,[[.,[.,.]],.]],.]] => [1,5,4,6,3,7,2] => [1,7,6,5,4,3,2] => [1,1,1,2,1,1]
[[.,.],[[.,[[[.,.],.],.]],.]] => [1,4,5,6,3,7,2] => [1,7,6,4,5,3,2] => [1,1,3,1,1]
[[.,.],[[[.,.],[.,[.,.]]],.]] => [1,3,6,5,4,7,2] => [1,7,3,5,6,4,2] => [1,2,3,1]
[[.,.],[[[.,.],[[.,.],.]],.]] => [1,3,5,6,4,7,2] => [1,7,3,6,5,4,2] => [1,2,2,1,1]
[[.,.],[[[.,[.,.]],[.,.]],.]] => [1,4,3,6,5,7,2] => [1,7,4,3,6,5,2] => [1,1,2,2,1]
[[.,.],[[[[.,.],.],[.,.]],.]] => [1,3,4,6,5,7,2] => [1,7,3,4,6,5,2] => [1,3,2,1]
[[.,.],[[[.,[.,[.,.]]],.],.]] => [1,5,4,3,6,7,2] => [1,7,4,5,3,6,2] => [1,1,4,1]
[[.,.],[[[.,[[.,.],.]],.],.]] => [1,4,5,3,6,7,2] => [1,7,5,4,3,6,2] => [1,1,2,2,1]
[[.,.],[[[[.,.],[.,.]],.],.]] => [1,3,5,4,6,7,2] => [1,7,3,5,4,6,2] => [1,2,3,1]
[[.,.],[[[[.,[.,.]],.],.],.]] => [1,4,3,5,6,7,2] => [1,7,4,3,5,6,2] => [1,1,4,1]
[[.,.],[[[[[.,.],.],.],.],.]] => [1,3,4,5,6,7,2] => [1,7,3,4,5,6,2] => [1,5,1]
[[.,[.,.]],[.,[.,[.,[.,.]]]]] => [2,1,7,6,5,4,3] => [2,1,4,5,6,7,3] => [2,5]
[[.,[.,.]],[.,[.,[[.,.],.]]]] => [2,1,6,7,5,4,3] => [2,1,4,5,7,6,3] => [2,4,1]
[[.,[.,.]],[.,[[.,.],[.,.]]]] => [2,1,5,7,6,4,3] => [2,1,4,6,5,7,3] => [2,3,2]
[[.,[.,.]],[.,[[.,[.,.]],.]]] => [2,1,6,5,7,4,3] => [2,1,4,7,6,5,3] => [2,2,2,1]
[[.,[.,.]],[.,[[[.,.],.],.]]] => [2,1,5,6,7,4,3] => [2,1,4,7,5,6,3] => [2,4,1]
[[.,[.,.]],[[.,.],[.,[.,.]]]] => [2,1,4,7,6,5,3] => [2,1,5,4,6,7,3] => [2,2,3]
[[.,[.,.]],[[.,.],[[.,.],.]]] => [2,1,4,6,7,5,3] => [2,1,5,4,7,6,3] => [2,2,2,1]
[[.,[.,.]],[[.,[.,.]],[.,.]]] => [2,1,5,4,7,6,3] => [2,1,6,5,4,7,3] => [2,1,2,2]
[[.,[.,.]],[[[.,.],.],[.,.]]] => [2,1,4,5,7,6,3] => [2,1,6,4,5,7,3] => [2,3,2]
[[.,[.,.]],[[.,[.,[.,.]]],.]] => [2,1,6,5,4,7,3] => [2,1,7,5,6,4,3] => [2,1,3,1]
[[.,[.,.]],[[.,[[.,.],.]],.]] => [2,1,5,6,4,7,3] => [2,1,7,6,5,4,3] => [2,1,2,1,1]
[[.,[.,.]],[[[.,.],[.,.]],.]] => [2,1,4,6,5,7,3] => [2,1,7,4,6,5,3] => [2,2,2,1]
[[.,[.,.]],[[[.,[.,.]],.],.]] => [2,1,5,4,6,7,3] => [2,1,7,5,4,6,3] => [2,1,3,1]
[[.,[.,.]],[[[[.,.],.],.],.]] => [2,1,4,5,6,7,3] => [2,1,7,4,5,6,3] => [2,4,1]
[[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,2,7,6,5,4,3] => [1,2,4,5,6,7,3] => [2,5]
[[[.,.],.],[.,[.,[[.,.],.]]]] => [1,2,6,7,5,4,3] => [1,2,4,5,7,6,3] => [2,4,1]
[[[.,.],.],[.,[[.,.],[.,.]]]] => [1,2,5,7,6,4,3] => [1,2,4,6,5,7,3] => [2,3,2]
[[[.,.],.],[.,[[.,[.,.]],.]]] => [1,2,6,5,7,4,3] => [1,2,4,7,6,5,3] => [2,2,2,1]
[[[.,.],.],[.,[[[.,.],.],.]]] => [1,2,5,6,7,4,3] => [1,2,4,7,5,6,3] => [2,4,1]
[[[.,.],.],[[.,.],[.,[.,.]]]] => [1,2,4,7,6,5,3] => [1,2,5,4,6,7,3] => [2,2,3]
[[[.,.],.],[[.,.],[[.,.],.]]] => [1,2,4,6,7,5,3] => [1,2,5,4,7,6,3] => [2,2,2,1]
[[[.,.],.],[[.,[.,.]],[.,.]]] => [1,2,5,4,7,6,3] => [1,2,6,5,4,7,3] => [2,1,2,2]
[[[.,.],.],[[[.,.],.],[.,.]]] => [1,2,4,5,7,6,3] => [1,2,6,4,5,7,3] => [2,3,2]
[[[.,.],.],[[.,[.,[.,.]]],.]] => [1,2,6,5,4,7,3] => [1,2,7,5,6,4,3] => [2,1,3,1]
[[[.,.],.],[[.,[[.,.],.]],.]] => [1,2,5,6,4,7,3] => [1,2,7,6,5,4,3] => [2,1,2,1,1]
[[[.,.],.],[[[.,.],[.,.]],.]] => [1,2,4,6,5,7,3] => [1,2,7,4,6,5,3] => [2,2,2,1]
[[[.,.],.],[[[.,[.,.]],.],.]] => [1,2,5,4,6,7,3] => [1,2,7,5,4,6,3] => [2,1,3,1]
[[[.,.],.],[[[[.,.],.],.],.]] => [1,2,4,5,6,7,3] => [1,2,7,4,5,6,3] => [2,4,1]
[[.,[.,[.,.]]],[.,[.,[.,.]]]] => [3,2,1,7,6,5,4] => [2,3,1,5,6,7,4] => [3,4]
[[.,[.,[.,.]]],[.,[[.,.],.]]] => [3,2,1,6,7,5,4] => [2,3,1,5,7,6,4] => [3,3,1]
[[.,[.,[.,.]]],[[.,.],[.,.]]] => [3,2,1,5,7,6,4] => [2,3,1,6,5,7,4] => [3,2,2]
[[.,[.,[.,.]]],[[.,[.,.]],.]] => [3,2,1,6,5,7,4] => [2,3,1,7,6,5,4] => [3,1,2,1]
[[.,[.,[.,.]]],[[[.,.],.],.]] => [3,2,1,5,6,7,4] => [2,3,1,7,5,6,4] => [3,3,1]
[[.,[[.,.],.]],[.,[.,[.,.]]]] => [2,3,1,7,6,5,4] => [3,2,1,5,6,7,4] => [2,1,4]
[[.,[[.,.],.]],[.,[[.,.],.]]] => [2,3,1,6,7,5,4] => [3,2,1,5,7,6,4] => [2,1,3,1]
[[.,[[.,.],.]],[[.,.],[.,.]]] => [2,3,1,5,7,6,4] => [3,2,1,6,5,7,4] => [2,1,2,2]
[[.,[[.,.],.]],[[.,[.,.]],.]] => [2,3,1,6,5,7,4] => [3,2,1,7,6,5,4] => [2,1,1,2,1]
[[.,[[.,.],.]],[[[.,.],.],.]] => [2,3,1,5,6,7,4] => [3,2,1,7,5,6,4] => [2,1,3,1]
[[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,3,2,7,6,5,4] => [1,3,2,5,6,7,4] => [1,2,4]
[[[.,.],[.,.]],[.,[[.,.],.]]] => [1,3,2,6,7,5,4] => [1,3,2,5,7,6,4] => [1,2,3,1]
[[[.,.],[.,.]],[[.,.],[.,.]]] => [1,3,2,5,7,6,4] => [1,3,2,6,5,7,4] => [1,2,2,2]
[[[.,.],[.,.]],[[.,[.,.]],.]] => [1,3,2,6,5,7,4] => [1,3,2,7,6,5,4] => [1,2,1,2,1]
[[[.,.],[.,.]],[[[.,.],.],.]] => [1,3,2,5,6,7,4] => [1,3,2,7,5,6,4] => [1,2,3,1]
[[[.,[.,.]],.],[.,[.,[.,.]]]] => [2,1,3,7,6,5,4] => [2,1,3,5,6,7,4] => [3,4]
[[[.,[.,.]],.],[.,[[.,.],.]]] => [2,1,3,6,7,5,4] => [2,1,3,5,7,6,4] => [3,3,1]
[[[.,[.,.]],.],[[.,.],[.,.]]] => [2,1,3,5,7,6,4] => [2,1,3,6,5,7,4] => [3,2,2]
[[[.,[.,.]],.],[[.,[.,.]],.]] => [2,1,3,6,5,7,4] => [2,1,3,7,6,5,4] => [3,1,2,1]
[[[.,[.,.]],.],[[[.,.],.],.]] => [2,1,3,5,6,7,4] => [2,1,3,7,5,6,4] => [3,3,1]
[[[[.,.],.],.],[.,[.,[.,.]]]] => [1,2,3,7,6,5,4] => [1,2,3,5,6,7,4] => [3,4]
[[[[.,.],.],.],[.,[[.,.],.]]] => [1,2,3,6,7,5,4] => [1,2,3,5,7,6,4] => [3,3,1]
[[[[.,.],.],.],[[.,.],[.,.]]] => [1,2,3,5,7,6,4] => [1,2,3,6,5,7,4] => [3,2,2]
[[[[.,.],.],.],[[.,[.,.]],.]] => [1,2,3,6,5,7,4] => [1,2,3,7,6,5,4] => [3,1,2,1]
[[[[.,.],.],.],[[[.,.],.],.]] => [1,2,3,5,6,7,4] => [1,2,3,7,5,6,4] => [3,3,1]
[[.,[.,[.,[.,.]]]],[.,[.,.]]] => [4,3,2,1,7,6,5] => [2,3,4,1,6,7,5] => [4,3]
[[.,[.,[.,[.,.]]]],[[.,.],.]] => [4,3,2,1,6,7,5] => [2,3,4,1,7,6,5] => [4,2,1]
[[.,[.,[[.,.],.]]],[.,[.,.]]] => [3,4,2,1,7,6,5] => [2,4,3,1,6,7,5] => [3,1,3]
[[.,[.,[[.,.],.]]],[[.,.],.]] => [3,4,2,1,6,7,5] => [2,4,3,1,7,6,5] => [3,1,2,1]
[[.,[[.,.],[.,.]]],[.,[.,.]]] => [2,4,3,1,7,6,5] => [3,2,4,1,6,7,5] => [2,2,3]
[[.,[[.,.],[.,.]]],[[.,.],.]] => [2,4,3,1,6,7,5] => [3,2,4,1,7,6,5] => [2,2,2,1]
[[.,[[.,[.,.]],.]],[.,[.,.]]] => [3,2,4,1,7,6,5] => [4,3,2,1,6,7,5] => [1,2,1,3]
[[.,[[.,[.,.]],.]],[[.,.],.]] => [3,2,4,1,6,7,5] => [4,3,2,1,7,6,5] => [1,2,1,2,1]
[[.,[[[.,.],.],.]],[.,[.,.]]] => [2,3,4,1,7,6,5] => [4,2,3,1,6,7,5] => [3,1,3]
[[.,[[[.,.],.],.]],[[.,.],.]] => [2,3,4,1,6,7,5] => [4,2,3,1,7,6,5] => [3,1,2,1]
[[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,4,3,2,7,6,5] => [1,3,4,2,6,7,5] => [1,3,3]
[[[.,.],[.,[.,.]]],[[.,.],.]] => [1,4,3,2,6,7,5] => [1,3,4,2,7,6,5] => [1,3,2,1]
[[[.,.],[[.,.],.]],[.,[.,.]]] => [1,3,4,2,7,6,5] => [1,4,3,2,6,7,5] => [1,2,1,3]
[[[.,.],[[.,.],.]],[[.,.],.]] => [1,3,4,2,6,7,5] => [1,4,3,2,7,6,5] => [1,2,1,2,1]
[[[.,[.,.]],[.,.]],[.,[.,.]]] => [2,1,4,3,7,6,5] => [2,1,4,3,6,7,5] => [2,2,3]
[[[.,[.,.]],[.,.]],[[.,.],.]] => [2,1,4,3,6,7,5] => [2,1,4,3,7,6,5] => [2,2,2,1]
[[[[.,.],.],[.,.]],[.,[.,.]]] => [1,2,4,3,7,6,5] => [1,2,4,3,6,7,5] => [2,2,3]
[[[[.,.],.],[.,.]],[[.,.],.]] => [1,2,4,3,6,7,5] => [1,2,4,3,7,6,5] => [2,2,2,1]
[[[.,[.,[.,.]]],.],[.,[.,.]]] => [3,2,1,4,7,6,5] => [2,3,1,4,6,7,5] => [4,3]
[[[.,[.,[.,.]]],.],[[.,.],.]] => [3,2,1,4,6,7,5] => [2,3,1,4,7,6,5] => [4,2,1]
[[[.,[[.,.],.]],.],[.,[.,.]]] => [2,3,1,4,7,6,5] => [3,2,1,4,6,7,5] => [2,2,3]
[[[.,[[.,.],.]],.],[[.,.],.]] => [2,3,1,4,6,7,5] => [3,2,1,4,7,6,5] => [2,2,2,1]
[[[[.,.],[.,.]],.],[.,[.,.]]] => [1,3,2,4,7,6,5] => [1,3,2,4,6,7,5] => [1,3,3]
[[[[.,.],[.,.]],.],[[.,.],.]] => [1,3,2,4,6,7,5] => [1,3,2,4,7,6,5] => [1,3,2,1]
[[[[.,[.,.]],.],.],[.,[.,.]]] => [2,1,3,4,7,6,5] => [2,1,3,4,6,7,5] => [4,3]
[[[[.,[.,.]],.],.],[[.,.],.]] => [2,1,3,4,6,7,5] => [2,1,3,4,7,6,5] => [4,2,1]
[[[[[.,.],.],.],.],[.,[.,.]]] => [1,2,3,4,7,6,5] => [1,2,3,4,6,7,5] => [4,3]
[[[[[.,.],.],.],.],[[.,.],.]] => [1,2,3,4,6,7,5] => [1,2,3,4,7,6,5] => [4,2,1]
[[.,[.,[.,[.,[.,.]]]]],[.,.]] => [5,4,3,2,1,7,6] => [2,3,4,5,1,7,6] => [5,2]
[[.,[.,[.,[[.,.],.]]]],[.,.]] => [4,5,3,2,1,7,6] => [2,3,5,4,1,7,6] => [4,1,2]
[[.,[.,[[.,.],[.,.]]]],[.,.]] => [3,5,4,2,1,7,6] => [2,4,3,5,1,7,6] => [3,2,2]
[[.,[.,[[.,[.,.]],.]]],[.,.]] => [4,3,5,2,1,7,6] => [2,5,4,3,1,7,6] => [2,2,1,2]
[[.,[.,[[[.,.],.],.]]],[.,.]] => [3,4,5,2,1,7,6] => [2,5,3,4,1,7,6] => [4,1,2]
[[.,[[.,.],[.,[.,.]]]],[.,.]] => [2,5,4,3,1,7,6] => [3,2,4,5,1,7,6] => [2,3,2]
[[.,[[.,.],[[.,.],.]]],[.,.]] => [2,4,5,3,1,7,6] => [3,2,5,4,1,7,6] => [2,2,1,2]
[[.,[[.,[.,.]],[.,.]]],[.,.]] => [3,2,5,4,1,7,6] => [4,3,2,5,1,7,6] => [1,2,2,2]
[[.,[[[.,.],.],[.,.]]],[.,.]] => [2,3,5,4,1,7,6] => [4,2,3,5,1,7,6] => [3,2,2]
[[.,[[.,[.,[.,.]]],.]],[.,.]] => [4,3,2,5,1,7,6] => [5,3,4,2,1,7,6] => [1,3,1,2]
[[.,[[.,[[.,.],.]],.]],[.,.]] => [3,4,2,5,1,7,6] => [5,4,3,2,1,7,6] => [1,2,1,1,2]
[[.,[[[.,.],[.,.]],.]],[.,.]] => [2,4,3,5,1,7,6] => [5,2,4,3,1,7,6] => [2,2,1,2]
[[.,[[[.,[.,.]],.],.]],[.,.]] => [3,2,4,5,1,7,6] => [5,3,2,4,1,7,6] => [1,3,1,2]
[[.,[[[[.,.],.],.],.]],[.,.]] => [2,3,4,5,1,7,6] => [5,2,3,4,1,7,6] => [4,1,2]
[[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,5,4,3,2,7,6] => [1,3,4,5,2,7,6] => [1,4,2]
[[[.,.],[.,[[.,.],.]]],[.,.]] => [1,4,5,3,2,7,6] => [1,3,5,4,2,7,6] => [1,3,1,2]
[[[.,.],[[.,.],[.,.]]],[.,.]] => [1,3,5,4,2,7,6] => [1,4,3,5,2,7,6] => [1,2,2,2]
[[[.,.],[[.,[.,.]],.]],[.,.]] => [1,4,3,5,2,7,6] => [1,5,4,3,2,7,6] => [1,1,2,1,2]
[[[.,.],[[[.,.],.],.]],[.,.]] => [1,3,4,5,2,7,6] => [1,5,3,4,2,7,6] => [1,3,1,2]
[[[.,[.,.]],[.,[.,.]]],[.,.]] => [2,1,5,4,3,7,6] => [2,1,4,5,3,7,6] => [2,3,2]
[[[.,[.,.]],[[.,.],.]],[.,.]] => [2,1,4,5,3,7,6] => [2,1,5,4,3,7,6] => [2,2,1,2]
[[[[.,.],.],[.,[.,.]]],[.,.]] => [1,2,5,4,3,7,6] => [1,2,4,5,3,7,6] => [2,3,2]
[[[[.,.],.],[[.,.],.]],[.,.]] => [1,2,4,5,3,7,6] => [1,2,5,4,3,7,6] => [2,2,1,2]
[[[.,[.,[.,.]]],[.,.]],[.,.]] => [3,2,1,5,4,7,6] => [2,3,1,5,4,7,6] => [3,2,2]
[[[.,[[.,.],.]],[.,.]],[.,.]] => [2,3,1,5,4,7,6] => [3,2,1,5,4,7,6] => [2,1,2,2]
[[[[.,.],[.,.]],[.,.]],[.,.]] => [1,3,2,5,4,7,6] => [1,3,2,5,4,7,6] => [1,2,2,2]
[[[[.,[.,.]],.],[.,.]],[.,.]] => [2,1,3,5,4,7,6] => [2,1,3,5,4,7,6] => [3,2,2]
[[[[[.,.],.],.],[.,.]],[.,.]] => [1,2,3,5,4,7,6] => [1,2,3,5,4,7,6] => [3,2,2]
[[[.,[.,[.,[.,.]]]],.],[.,.]] => [4,3,2,1,5,7,6] => [2,3,4,1,5,7,6] => [5,2]
[[[.,[.,[[.,.],.]]],.],[.,.]] => [3,4,2,1,5,7,6] => [2,4,3,1,5,7,6] => [3,2,2]
[[[.,[[.,.],[.,.]]],.],[.,.]] => [2,4,3,1,5,7,6] => [3,2,4,1,5,7,6] => [2,3,2]
[[[.,[[.,[.,.]],.]],.],[.,.]] => [3,2,4,1,5,7,6] => [4,3,2,1,5,7,6] => [1,2,2,2]
[[[.,[[[.,.],.],.]],.],[.,.]] => [2,3,4,1,5,7,6] => [4,2,3,1,5,7,6] => [3,2,2]
[[[[.,.],[.,[.,.]]],.],[.,.]] => [1,4,3,2,5,7,6] => [1,3,4,2,5,7,6] => [1,4,2]
[[[[.,.],[[.,.],.]],.],[.,.]] => [1,3,4,2,5,7,6] => [1,4,3,2,5,7,6] => [1,2,2,2]
[[[[.,[.,.]],[.,.]],.],[.,.]] => [2,1,4,3,5,7,6] => [2,1,4,3,5,7,6] => [2,3,2]
[[[[[.,.],.],[.,.]],.],[.,.]] => [1,2,4,3,5,7,6] => [1,2,4,3,5,7,6] => [2,3,2]
[[[[.,[.,[.,.]]],.],.],[.,.]] => [3,2,1,4,5,7,6] => [2,3,1,4,5,7,6] => [5,2]
[[[[.,[[.,.],.]],.],.],[.,.]] => [2,3,1,4,5,7,6] => [3,2,1,4,5,7,6] => [2,3,2]
[[[[[.,.],[.,.]],.],.],[.,.]] => [1,3,2,4,5,7,6] => [1,3,2,4,5,7,6] => [1,4,2]
[[[[[.,[.,.]],.],.],.],[.,.]] => [2,1,3,4,5,7,6] => [2,1,3,4,5,7,6] => [5,2]
[[[[[[.,.],.],.],.],.],[.,.]] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => [5,2]
[[.,[.,[.,[.,[.,[.,.]]]]]],.] => [6,5,4,3,2,1,7] => [2,3,4,5,6,1,7] => [7]
[[.,[.,[.,[.,[[.,.],.]]]]],.] => [5,6,4,3,2,1,7] => [2,3,4,6,5,1,7] => [5,2]
[[.,[.,[.,[[.,.],[.,.]]]]],.] => [4,6,5,3,2,1,7] => [2,3,5,4,6,1,7] => [4,3]
[[.,[.,[.,[[.,[.,.]],.]]]],.] => [5,4,6,3,2,1,7] => [2,3,6,5,4,1,7] => [3,2,2]
[[.,[.,[.,[[[.,.],.],.]]]],.] => [4,5,6,3,2,1,7] => [2,3,6,4,5,1,7] => [5,2]
[[.,[.,[[.,.],[.,[.,.]]]]],.] => [3,6,5,4,2,1,7] => [2,4,3,5,6,1,7] => [3,4]
[[.,[.,[[.,.],[[.,.],.]]]],.] => [3,5,6,4,2,1,7] => [2,4,3,6,5,1,7] => [3,2,2]
[[.,[.,[[.,[.,.]],[.,.]]]],.] => [4,3,6,5,2,1,7] => [2,5,4,3,6,1,7] => [2,2,3]
[[.,[.,[[[.,.],.],[.,.]]]],.] => [3,4,6,5,2,1,7] => [2,5,3,4,6,1,7] => [4,3]
[[.,[.,[[.,[.,[.,.]]],.]]],.] => [5,4,3,6,2,1,7] => [2,6,4,5,3,1,7] => [2,3,2]
[[.,[.,[[.,[[.,.],.]],.]]],.] => [4,5,3,6,2,1,7] => [2,6,5,4,3,1,7] => [2,2,1,2]
[[.,[.,[[[.,.],[.,.]],.]]],.] => [3,5,4,6,2,1,7] => [2,6,3,5,4,1,7] => [3,2,2]
[[.,[.,[[[.,[.,.]],.],.]]],.] => [4,3,5,6,2,1,7] => [2,6,4,3,5,1,7] => [2,3,2]
[[.,[.,[[[[.,.],.],.],.]]],.] => [3,4,5,6,2,1,7] => [2,6,3,4,5,1,7] => [5,2]
[[.,[[.,.],[.,[.,[.,.]]]]],.] => [2,6,5,4,3,1,7] => [3,2,4,5,6,1,7] => [2,5]
[[.,[[.,.],[.,[[.,.],.]]]],.] => [2,5,6,4,3,1,7] => [3,2,4,6,5,1,7] => [2,3,2]
[[.,[[.,.],[[.,.],[.,.]]]],.] => [2,4,6,5,3,1,7] => [3,2,5,4,6,1,7] => [2,2,3]
[[.,[[.,.],[[.,[.,.]],.]]],.] => [2,5,4,6,3,1,7] => [3,2,6,5,4,1,7] => [2,1,2,2]
[[.,[[.,.],[[[.,.],.],.]]],.] => [2,4,5,6,3,1,7] => [3,2,6,4,5,1,7] => [2,3,2]
[[.,[[.,[.,.]],[.,[.,.]]]],.] => [3,2,6,5,4,1,7] => [4,3,2,5,6,1,7] => [1,2,4]
[[.,[[.,[.,.]],[[.,.],.]]],.] => [3,2,5,6,4,1,7] => [4,3,2,6,5,1,7] => [1,2,2,2]
[[.,[[[.,.],.],[.,[.,.]]]],.] => [2,3,6,5,4,1,7] => [4,2,3,5,6,1,7] => [3,4]
[[.,[[[.,.],.],[[.,.],.]]],.] => [2,3,5,6,4,1,7] => [4,2,3,6,5,1,7] => [3,2,2]
[[.,[[.,[.,[.,.]]],[.,.]]],.] => [4,3,2,6,5,1,7] => [5,3,4,2,6,1,7] => [1,3,3]
[[.,[[.,[[.,.],.]],[.,.]]],.] => [3,4,2,6,5,1,7] => [5,4,3,2,6,1,7] => [1,2,1,3]
[[.,[[[.,.],[.,.]],[.,.]]],.] => [2,4,3,6,5,1,7] => [5,2,4,3,6,1,7] => [2,2,3]
[[.,[[[.,[.,.]],.],[.,.]]],.] => [3,2,4,6,5,1,7] => [5,3,2,4,6,1,7] => [1,3,3]
[[.,[[[[.,.],.],.],[.,.]]],.] => [2,3,4,6,5,1,7] => [5,2,3,4,6,1,7] => [4,3]
[[.,[[.,[.,[.,[.,.]]]],.]],.] => [5,4,3,2,6,1,7] => [6,3,4,5,2,1,7] => [1,4,2]
[[.,[[.,[.,[[.,.],.]]],.]],.] => [4,5,3,2,6,1,7] => [6,3,5,4,2,1,7] => [1,3,1,2]
[[.,[[.,[[.,.],[.,.]]],.]],.] => [3,5,4,2,6,1,7] => [6,4,3,5,2,1,7] => [1,2,2,2]
[[.,[[.,[[.,[.,.]],.]],.]],.] => [4,3,5,2,6,1,7] => [6,5,4,3,2,1,7] => [1,1,2,1,2]
[[.,[[.,[[[.,.],.],.]],.]],.] => [3,4,5,2,6,1,7] => [6,5,3,4,2,1,7] => [1,3,1,2]
[[.,[[[.,.],[.,[.,.]]],.]],.] => [2,5,4,3,6,1,7] => [6,2,4,5,3,1,7] => [2,3,2]
[[.,[[[.,.],[[.,.],.]],.]],.] => [2,4,5,3,6,1,7] => [6,2,5,4,3,1,7] => [2,2,1,2]
[[.,[[[.,[.,.]],[.,.]],.]],.] => [3,2,5,4,6,1,7] => [6,3,2,5,4,1,7] => [1,2,2,2]
[[.,[[[[.,.],.],[.,.]],.]],.] => [2,3,5,4,6,1,7] => [6,2,3,5,4,1,7] => [3,2,2]
[[.,[[[.,[.,[.,.]]],.],.]],.] => [4,3,2,5,6,1,7] => [6,3,4,2,5,1,7] => [1,4,2]
[[.,[[[.,[[.,.],.]],.],.]],.] => [3,4,2,5,6,1,7] => [6,4,3,2,5,1,7] => [1,2,2,2]
[[.,[[[[.,.],[.,.]],.],.]],.] => [2,4,3,5,6,1,7] => [6,2,4,3,5,1,7] => [2,3,2]
[[.,[[[[.,[.,.]],.],.],.]],.] => [3,2,4,5,6,1,7] => [6,3,2,4,5,1,7] => [1,4,2]
[[.,[[[[[.,.],.],.],.],.]],.] => [2,3,4,5,6,1,7] => [6,2,3,4,5,1,7] => [5,2]
[[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,6,5,4,3,2,7] => [1,3,4,5,6,2,7] => [1,6]
[[[.,.],[.,[.,[[.,.],.]]]],.] => [1,5,6,4,3,2,7] => [1,3,4,6,5,2,7] => [1,4,2]
[[[.,.],[.,[[.,.],[.,.]]]],.] => [1,4,6,5,3,2,7] => [1,3,5,4,6,2,7] => [1,3,3]
[[[.,.],[.,[[.,[.,.]],.]]],.] => [1,5,4,6,3,2,7] => [1,3,6,5,4,2,7] => [1,2,2,2]
[[[.,.],[.,[[[.,.],.],.]]],.] => [1,4,5,6,3,2,7] => [1,3,6,4,5,2,7] => [1,4,2]
[[[.,.],[[.,.],[.,[.,.]]]],.] => [1,3,6,5,4,2,7] => [1,4,3,5,6,2,7] => [1,2,4]
[[[.,.],[[.,.],[[.,.],.]]],.] => [1,3,5,6,4,2,7] => [1,4,3,6,5,2,7] => [1,2,2,2]
[[[.,.],[[.,[.,.]],[.,.]]],.] => [1,4,3,6,5,2,7] => [1,5,4,3,6,2,7] => [1,1,2,3]
[[[.,.],[[[.,.],.],[.,.]]],.] => [1,3,4,6,5,2,7] => [1,5,3,4,6,2,7] => [1,3,3]
[[[.,.],[[.,[.,[.,.]]],.]],.] => [1,5,4,3,6,2,7] => [1,6,4,5,3,2,7] => [1,1,3,2]
[[[.,.],[[.,[[.,.],.]],.]],.] => [1,4,5,3,6,2,7] => [1,6,5,4,3,2,7] => [1,1,2,1,2]
[[[.,.],[[[.,.],[.,.]],.]],.] => [1,3,5,4,6,2,7] => [1,6,3,5,4,2,7] => [1,2,2,2]
[[[.,.],[[[.,[.,.]],.],.]],.] => [1,4,3,5,6,2,7] => [1,6,4,3,5,2,7] => [1,1,3,2]
[[[.,.],[[[[.,.],.],.],.]],.] => [1,3,4,5,6,2,7] => [1,6,3,4,5,2,7] => [1,4,2]
[[[.,[.,.]],[.,[.,[.,.]]]],.] => [2,1,6,5,4,3,7] => [2,1,4,5,6,3,7] => [2,5]
[[[.,[.,.]],[.,[[.,.],.]]],.] => [2,1,5,6,4,3,7] => [2,1,4,6,5,3,7] => [2,3,2]
[[[.,[.,.]],[[.,.],[.,.]]],.] => [2,1,4,6,5,3,7] => [2,1,5,4,6,3,7] => [2,2,3]
[[[.,[.,.]],[[.,[.,.]],.]],.] => [2,1,5,4,6,3,7] => [2,1,6,5,4,3,7] => [2,1,2,2]
[[[.,[.,.]],[[[.,.],.],.]],.] => [2,1,4,5,6,3,7] => [2,1,6,4,5,3,7] => [2,3,2]
[[[[.,.],.],[.,[.,[.,.]]]],.] => [1,2,6,5,4,3,7] => [1,2,4,5,6,3,7] => [2,5]
[[[[.,.],.],[.,[[.,.],.]]],.] => [1,2,5,6,4,3,7] => [1,2,4,6,5,3,7] => [2,3,2]
[[[[.,.],.],[[.,.],[.,.]]],.] => [1,2,4,6,5,3,7] => [1,2,5,4,6,3,7] => [2,2,3]
[[[[.,.],.],[[.,[.,.]],.]],.] => [1,2,5,4,6,3,7] => [1,2,6,5,4,3,7] => [2,1,2,2]
[[[[.,.],.],[[[.,.],.],.]],.] => [1,2,4,5,6,3,7] => [1,2,6,4,5,3,7] => [2,3,2]
[[[.,[.,[.,.]]],[.,[.,.]]],.] => [3,2,1,6,5,4,7] => [2,3,1,5,6,4,7] => [3,4]
[[[.,[.,[.,.]]],[[.,.],.]],.] => [3,2,1,5,6,4,7] => [2,3,1,6,5,4,7] => [3,2,2]
[[[.,[[.,.],.]],[.,[.,.]]],.] => [2,3,1,6,5,4,7] => [3,2,1,5,6,4,7] => [2,1,4]
[[[.,[[.,.],.]],[[.,.],.]],.] => [2,3,1,5,6,4,7] => [3,2,1,6,5,4,7] => [2,1,2,2]
[[[[.,.],[.,.]],[.,[.,.]]],.] => [1,3,2,6,5,4,7] => [1,3,2,5,6,4,7] => [1,2,4]
[[[[.,.],[.,.]],[[.,.],.]],.] => [1,3,2,5,6,4,7] => [1,3,2,6,5,4,7] => [1,2,2,2]
[[[[.,[.,.]],.],[.,[.,.]]],.] => [2,1,3,6,5,4,7] => [2,1,3,5,6,4,7] => [3,4]
[[[[.,[.,.]],.],[[.,.],.]],.] => [2,1,3,5,6,4,7] => [2,1,3,6,5,4,7] => [3,2,2]
[[[[[.,.],.],.],[.,[.,.]]],.] => [1,2,3,6,5,4,7] => [1,2,3,5,6,4,7] => [3,4]
[[[[[.,.],.],.],[[.,.],.]],.] => [1,2,3,5,6,4,7] => [1,2,3,6,5,4,7] => [3,2,2]
[[[.,[.,[.,[.,.]]]],[.,.]],.] => [4,3,2,1,6,5,7] => [2,3,4,1,6,5,7] => [4,3]
[[[.,[.,[[.,.],.]]],[.,.]],.] => [3,4,2,1,6,5,7] => [2,4,3,1,6,5,7] => [3,1,3]
[[[.,[[.,.],[.,.]]],[.,.]],.] => [2,4,3,1,6,5,7] => [3,2,4,1,6,5,7] => [2,2,3]
[[[.,[[.,[.,.]],.]],[.,.]],.] => [3,2,4,1,6,5,7] => [4,3,2,1,6,5,7] => [1,2,1,3]
[[[.,[[[.,.],.],.]],[.,.]],.] => [2,3,4,1,6,5,7] => [4,2,3,1,6,5,7] => [3,1,3]
[[[[.,.],[.,[.,.]]],[.,.]],.] => [1,4,3,2,6,5,7] => [1,3,4,2,6,5,7] => [1,3,3]
[[[[.,.],[[.,.],.]],[.,.]],.] => [1,3,4,2,6,5,7] => [1,4,3,2,6,5,7] => [1,2,1,3]
[[[[.,[.,.]],[.,.]],[.,.]],.] => [2,1,4,3,6,5,7] => [2,1,4,3,6,5,7] => [2,2,3]
[[[[[.,.],.],[.,.]],[.,.]],.] => [1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => [2,2,3]
[[[[.,[.,[.,.]]],.],[.,.]],.] => [3,2,1,4,6,5,7] => [2,3,1,4,6,5,7] => [4,3]
[[[[.,[[.,.],.]],.],[.,.]],.] => [2,3,1,4,6,5,7] => [3,2,1,4,6,5,7] => [2,2,3]
[[[[[.,.],[.,.]],.],[.,.]],.] => [1,3,2,4,6,5,7] => [1,3,2,4,6,5,7] => [1,3,3]
[[[[[.,[.,.]],.],.],[.,.]],.] => [2,1,3,4,6,5,7] => [2,1,3,4,6,5,7] => [4,3]
[[[[[[.,.],.],.],.],[.,.]],.] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => [4,3]
[[[.,[.,[.,[.,[.,.]]]]],.],.] => [5,4,3,2,1,6,7] => [2,3,4,5,1,6,7] => [7]
[[[.,[.,[.,[[.,.],.]]]],.],.] => [4,5,3,2,1,6,7] => [2,3,5,4,1,6,7] => [4,3]
[[[.,[.,[[.,.],[.,.]]]],.],.] => [3,5,4,2,1,6,7] => [2,4,3,5,1,6,7] => [3,4]
[[[.,[.,[[.,[.,.]],.]]],.],.] => [4,3,5,2,1,6,7] => [2,5,4,3,1,6,7] => [2,2,3]
[[[.,[.,[[[.,.],.],.]]],.],.] => [3,4,5,2,1,6,7] => [2,5,3,4,1,6,7] => [4,3]
[[[.,[[.,.],[.,[.,.]]]],.],.] => [2,5,4,3,1,6,7] => [3,2,4,5,1,6,7] => [2,5]
[[[.,[[.,.],[[.,.],.]]],.],.] => [2,4,5,3,1,6,7] => [3,2,5,4,1,6,7] => [2,2,3]
[[[.,[[.,[.,.]],[.,.]]],.],.] => [3,2,5,4,1,6,7] => [4,3,2,5,1,6,7] => [1,2,4]
[[[.,[[[.,.],.],[.,.]]],.],.] => [2,3,5,4,1,6,7] => [4,2,3,5,1,6,7] => [3,4]
[[[.,[[.,[.,[.,.]]],.]],.],.] => [4,3,2,5,1,6,7] => [5,3,4,2,1,6,7] => [1,3,3]
[[[.,[[.,[[.,.],.]],.]],.],.] => [3,4,2,5,1,6,7] => [5,4,3,2,1,6,7] => [1,2,1,3]
[[[.,[[[.,.],[.,.]],.]],.],.] => [2,4,3,5,1,6,7] => [5,2,4,3,1,6,7] => [2,2,3]
[[[.,[[[.,[.,.]],.],.]],.],.] => [3,2,4,5,1,6,7] => [5,3,2,4,1,6,7] => [1,3,3]
[[[.,[[[[.,.],.],.],.]],.],.] => [2,3,4,5,1,6,7] => [5,2,3,4,1,6,7] => [4,3]
[[[[.,.],[.,[.,[.,.]]]],.],.] => [1,5,4,3,2,6,7] => [1,3,4,5,2,6,7] => [1,6]
[[[[.,.],[.,[[.,.],.]]],.],.] => [1,4,5,3,2,6,7] => [1,3,5,4,2,6,7] => [1,3,3]
[[[[.,.],[[.,.],[.,.]]],.],.] => [1,3,5,4,2,6,7] => [1,4,3,5,2,6,7] => [1,2,4]
[[[[.,.],[[.,[.,.]],.]],.],.] => [1,4,3,5,2,6,7] => [1,5,4,3,2,6,7] => [1,1,2,3]
[[[[.,.],[[[.,.],.],.]],.],.] => [1,3,4,5,2,6,7] => [1,5,3,4,2,6,7] => [1,3,3]
[[[[.,[.,.]],[.,[.,.]]],.],.] => [2,1,5,4,3,6,7] => [2,1,4,5,3,6,7] => [2,5]
[[[[.,[.,.]],[[.,.],.]],.],.] => [2,1,4,5,3,6,7] => [2,1,5,4,3,6,7] => [2,2,3]
[[[[[.,.],.],[.,[.,.]]],.],.] => [1,2,5,4,3,6,7] => [1,2,4,5,3,6,7] => [2,5]
[[[[[.,.],.],[[.,.],.]],.],.] => [1,2,4,5,3,6,7] => [1,2,5,4,3,6,7] => [2,2,3]
[[[[.,[.,[.,.]]],[.,.]],.],.] => [3,2,1,5,4,6,7] => [2,3,1,5,4,6,7] => [3,4]
[[[[.,[[.,.],.]],[.,.]],.],.] => [2,3,1,5,4,6,7] => [3,2,1,5,4,6,7] => [2,1,4]
[[[[[.,.],[.,.]],[.,.]],.],.] => [1,3,2,5,4,6,7] => [1,3,2,5,4,6,7] => [1,2,4]
[[[[[.,[.,.]],.],[.,.]],.],.] => [2,1,3,5,4,6,7] => [2,1,3,5,4,6,7] => [3,4]
[[[[[[.,.],.],.],[.,.]],.],.] => [1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => [3,4]
[[[[.,[.,[.,[.,.]]]],.],.],.] => [4,3,2,1,5,6,7] => [2,3,4,1,5,6,7] => [7]
[[[[.,[.,[[.,.],.]]],.],.],.] => [3,4,2,1,5,6,7] => [2,4,3,1,5,6,7] => [3,4]
[[[[.,[[.,.],[.,.]]],.],.],.] => [2,4,3,1,5,6,7] => [3,2,4,1,5,6,7] => [2,5]
[[[[.,[[.,[.,.]],.]],.],.],.] => [3,2,4,1,5,6,7] => [4,3,2,1,5,6,7] => [1,2,4]
[[[[.,[[[.,.],.],.]],.],.],.] => [2,3,4,1,5,6,7] => [4,2,3,1,5,6,7] => [3,4]
[[[[[.,.],[.,[.,.]]],.],.],.] => [1,4,3,2,5,6,7] => [1,3,4,2,5,6,7] => [1,6]
[[[[[.,.],[[.,.],.]],.],.],.] => [1,3,4,2,5,6,7] => [1,4,3,2,5,6,7] => [1,2,4]
[[[[[.,[.,.]],[.,.]],.],.],.] => [2,1,4,3,5,6,7] => [2,1,4,3,5,6,7] => [2,5]
[[[[[[.,.],.],[.,.]],.],.],.] => [1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => [2,5]
[[[[[.,[.,[.,.]]],.],.],.],.] => [3,2,1,4,5,6,7] => [2,3,1,4,5,6,7] => [7]
[[[[[.,[[.,.],.]],.],.],.],.] => [2,3,1,4,5,6,7] => [3,2,1,4,5,6,7] => [2,5]
[[[[[[.,.],[.,.]],.],.],.],.] => [1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => [1,6]
[[[[[[.,[.,.]],.],.],.],.],.] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [7]
[[[[[[[.,.],.],.],.],.],.],.] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [7]
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,1] => [8]
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [7,8,6,5,4,3,2,1] => [2,3,4,5,6,8,7,1] => [7,1]
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]] => [6,5,8,7,4,3,2,1] => [2,3,4,7,6,5,8,1] => [4,2,2]
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]] => [7,6,5,8,4,3,2,1] => [2,3,4,8,6,7,5,1] => [4,3,1]
[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]] => [6,7,5,8,4,3,2,1] => [2,3,4,8,7,6,5,1] => [4,2,1,1]
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]] => [5,7,6,8,4,3,2,1] => [2,3,4,8,5,7,6,1] => [5,2,1]
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]] => [6,5,7,8,4,3,2,1] => [2,3,4,8,6,5,7,1] => [4,3,1]
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]] => [5,6,7,8,4,3,2,1] => [2,3,4,8,5,6,7,1] => [7,1]
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => [4,6,8,7,5,3,2,1] => [2,3,5,4,7,6,8,1] => [4,2,2]
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]] => [4,5,6,8,7,3,2,1] => [2,3,7,4,5,6,8,1] => [6,2]
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => [3,7,8,6,5,4,2,1] => [2,4,3,5,6,8,7,1] => [3,4,1]
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [3,5,8,7,6,4,2,1] => [2,4,3,6,5,7,8,1] => [3,2,3]
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => [3,5,7,8,6,4,2,1] => [2,4,3,6,5,8,7,1] => [3,2,2,1]
[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]] => [3,6,5,8,7,4,2,1] => [2,4,3,7,6,5,8,1] => [3,1,2,2]
[.,[.,[[.,.],[[.,[[.,.],.]],.]]]] => [3,6,7,5,8,4,2,1] => [2,4,3,8,7,6,5,1] => [3,1,2,1,1]
[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => [4,3,8,7,6,5,2,1] => [2,5,4,3,6,7,8,1] => [2,2,4]
[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]] => [4,3,7,8,6,5,2,1] => [2,5,4,3,6,8,7,1] => [2,2,3,1]
[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => [4,3,6,8,7,5,2,1] => [2,5,4,3,7,6,8,1] => [2,2,2,2]
[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]] => [4,3,7,6,8,5,2,1] => [2,5,4,3,8,7,6,1] => [2,2,1,2,1]
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]] => [4,3,6,7,8,5,2,1] => [2,5,4,3,8,6,7,1] => [2,2,3,1]
[.,[.,[[[.,.],.],[[[.,.],.],.]]]] => [3,4,6,7,8,5,2,1] => [2,5,3,4,8,6,7,1] => [4,3,1]
[.,[.,[[[.,.],[.,[[.,.],.]]],.]]] => [3,6,7,5,4,8,2,1] => [2,8,3,5,7,6,4,1] => [3,3,1,1]
[.,[.,[[[[.,.],[.,.]],[.,.]],.]]] => [3,5,4,7,6,8,2,1] => [2,8,3,5,4,7,6,1] => [3,2,2,1]
[.,[.,[[[[.,[.,.]],.],[.,.]],.]]] => [4,3,5,7,6,8,2,1] => [2,8,4,3,5,7,6,1] => [2,3,2,1]
[.,[.,[[[[[[.,.],.],.],.],.],.]]] => [3,4,5,6,7,8,2,1] => [2,8,3,4,5,6,7,1] => [7,1]
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [2,8,7,6,5,4,3,1] => [3,2,4,5,6,7,8,1] => [2,6]
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [2,6,8,7,5,4,3,1] => [3,2,4,5,7,6,8,1] => [2,4,2]
[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]] => [2,6,5,8,7,4,3,1] => [3,2,4,7,6,5,8,1] => [2,2,2,2]
[.,[[.,.],[.,[[.,[[.,.],.]],.]]]] => [2,6,7,5,8,4,3,1] => [3,2,4,8,7,6,5,1] => [2,2,2,1,1]
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [2,4,6,8,7,5,3,1] => [3,2,5,4,7,6,8,1] => [2,2,2,2]
[.,[[.,.],[[.,[.,.]],[[.,.],.]]]] => [2,5,4,7,8,6,3,1] => [3,2,6,5,4,8,7,1] => [2,1,2,2,1]
[.,[[.,.],[[[.,.],[.,.]],[.,.]]]] => [2,4,6,5,8,7,3,1] => [3,2,7,4,6,5,8,1] => [2,2,2,2]
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [3,2,8,7,6,5,4,1] => [4,3,2,5,6,7,8,1] => [1,2,5]
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [3,2,6,5,8,7,4,1] => [4,3,2,7,6,5,8,1] => [1,2,1,2,2]
[.,[[.,[.,.]],[[[.,.],.],[.,.]]]] => [3,2,5,6,8,7,4,1] => [4,3,2,7,5,6,8,1] => [1,2,3,2]
[.,[[.,[.,.]],[[.,[[.,.],.]],.]]] => [3,2,6,7,5,8,4,1] => [4,3,2,8,7,6,5,1] => [1,2,1,2,1,1]
[.,[[.,[.,.]],[[[.,.],[.,.]],.]]] => [3,2,5,7,6,8,4,1] => [4,3,2,8,5,7,6,1] => [1,2,2,2,1]
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [2,3,8,7,6,5,4,1] => [4,2,3,5,6,7,8,1] => [3,5]
[.,[[[.,.],.],[[.,[.,.]],[.,.]]]] => [2,3,6,5,8,7,4,1] => [4,2,3,7,6,5,8,1] => [3,1,2,2]
[.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [2,3,5,6,8,7,4,1] => [4,2,3,7,5,6,8,1] => [3,3,2]
[.,[[[.,.],.],[[.,[[.,.],.]],.]]] => [2,3,6,7,5,8,4,1] => [4,2,3,8,7,6,5,1] => [3,1,2,1,1]
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]] => [3,4,2,8,7,6,5,1] => [5,4,3,2,6,7,8,1] => [1,2,1,4]
[.,[[.,[[.,.],.]],[.,[[.,.],.]]]] => [3,4,2,7,8,6,5,1] => [5,4,3,2,6,8,7,1] => [1,2,1,3,1]
[.,[[.,[[.,.],.]],[[.,.],[.,.]]]] => [3,4,2,6,8,7,5,1] => [5,4,3,2,7,6,8,1] => [1,2,1,2,2]
[.,[[.,[[.,.],.]],[[.,[.,.]],.]]] => [3,4,2,7,6,8,5,1] => [5,4,3,2,8,7,6,1] => [1,2,1,1,2,1]
[.,[[.,[[.,.],.]],[[[.,.],.],.]]] => [3,4,2,6,7,8,5,1] => [5,4,3,2,8,6,7,1] => [1,2,1,3,1]
[.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [2,4,3,6,8,7,5,1] => [5,2,4,3,7,6,8,1] => [2,2,2,2]
[.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [2,3,4,8,7,6,5,1] => [5,2,3,4,6,7,8,1] => [4,4]
[.,[[.,[[.,[[.,.],.]],.]],[.,.]]] => [4,5,3,6,2,8,7,1] => [7,6,5,4,3,2,8,1] => [1,1,2,1,1,2]
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => [2,4,3,6,5,8,7,1] => [7,2,4,3,6,5,8,1] => [2,2,2,2]
[.,[[.,[.,[[[.,.],[.,.]],.]]],.]] => [4,6,5,7,3,2,8,1] => [8,3,7,4,6,5,2,1] => [1,3,2,1,1]
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => [5,4,6,3,7,2,8,1] => [8,7,6,5,4,3,2,1] => [1,1,1,2,1,1,1]
[.,[[.,[[.,[[[.,.],.],.]],.]],.]] => [4,5,6,3,7,2,8,1] => [8,7,6,4,5,3,2,1] => [1,1,3,1,1,1]
[.,[[.,[[[.,.],[[.,.],.]],.]],.]] => [3,5,6,4,7,2,8,1] => [8,7,3,6,5,4,2,1] => [1,2,2,1,1,1]
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]] => [4,3,6,5,7,2,8,1] => [8,7,4,3,6,5,2,1] => [1,1,2,2,1,1]
[.,[[.,[[[.,[[.,.],.]],.],.]],.]] => [4,5,3,6,7,2,8,1] => [8,7,5,4,3,6,2,1] => [1,1,2,2,1,1]
[.,[[.,[[[[.,.],[.,.]],.],.]],.]] => [3,5,4,6,7,2,8,1] => [8,7,3,5,4,6,2,1] => [1,2,3,1,1]
[.,[[[.,.],[[[.,.],[.,.]],.]],.]] => [2,4,6,5,7,3,8,1] => [8,2,7,4,6,5,3,1] => [2,2,2,1,1]
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]] => [3,2,6,5,7,4,8,1] => [8,3,2,7,6,5,4,1] => [1,2,1,2,1,1]
[.,[[[.,[[.,[.,.]],.]],[.,.]],.]] => [4,3,5,2,7,6,8,1] => [8,5,4,3,2,7,6,1] => [1,1,2,1,2,1]
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => [3,2,5,4,7,6,8,1] => [8,3,2,5,4,7,6,1] => [1,2,2,2,1]
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,8,7,6,5,4,3,2] => [1,3,4,5,6,7,8,2] => [1,7]
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [1,7,8,6,5,4,3,2] => [1,3,4,5,6,8,7,2] => [1,6,1]
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]] => [1,6,7,5,8,4,3,2] => [1,3,4,8,7,6,5,2] => [1,3,2,1,1]
[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]] => [1,7,6,5,4,8,3,2] => [1,3,8,5,6,7,4,2] => [1,2,4,1]
[[.,.],[.,[[[[.,[.,.]],.],.],.]]] => [1,5,4,6,7,8,3,2] => [1,3,8,5,4,6,7,2] => [1,2,4,1]
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,3,8,7,6,5,4,2] => [1,4,3,5,6,7,8,2] => [1,2,5]
[[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,3,5,7,8,6,4,2] => [1,4,3,6,5,8,7,2] => [1,2,2,2,1]
[[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [1,3,6,7,5,8,4,2] => [1,4,3,8,7,6,5,2] => [1,2,1,2,1,1]
[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,4,3,8,7,6,5,2] => [1,5,4,3,6,7,8,2] => [1,1,2,4]
[[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,3,4,8,7,6,5,2] => [1,5,3,4,6,7,8,2] => [1,3,4]
[[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [1,4,5,3,7,8,6,2] => [1,6,5,4,3,8,7,2] => [1,1,2,1,2,1]
[[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,3,5,4,7,8,6,2] => [1,6,3,5,4,8,7,2] => [1,2,2,2,1]
[[.,.],[[[.,[[.,.],.]],.],[.,.]]] => [1,4,5,3,6,8,7,2] => [1,7,5,4,3,6,8,2] => [1,1,2,2,2]
[[.,.],[[.,[.,[[.,[.,.]],.]]],.]] => [1,6,5,7,4,3,8,2] => [1,8,4,7,6,5,3,2] => [1,1,2,2,1,1]
[[.,.],[[.,[[.,.],[[.,.],.]]],.]] => [1,4,6,7,5,3,8,2] => [1,8,5,4,7,6,3,2] => [1,1,2,2,1,1]
[[.,.],[[.,[[.,[.,.]],[.,.]]],.]] => [1,5,4,7,6,3,8,2] => [1,8,6,5,4,7,3,2] => [1,1,1,2,2,1]
[[.,.],[[.,[[.,[[.,.],.]],.]],.]] => [1,5,6,4,7,3,8,2] => [1,8,7,6,5,4,3,2] => [1,1,1,2,1,1,1]
[[.,.],[[.,[[[.,[.,.]],.],.]],.]] => [1,5,4,6,7,3,8,2] => [1,8,7,5,4,6,3,2] => [1,1,1,3,1,1]
[[.,.],[[.,[[[[.,.],.],.],.]],.]] => [1,4,5,6,7,3,8,2] => [1,8,7,4,5,6,3,2] => [1,1,4,1,1]
[[.,.],[[[[.,[[.,.],.]],.],.],.]] => [1,4,5,3,6,7,8,2] => [1,8,5,4,3,6,7,2] => [1,1,2,3,1]
[[.,.],[[[[[.,[.,.]],.],.],.],.]] => [1,4,3,5,6,7,8,2] => [1,8,4,3,5,6,7,2] => [1,1,5,1]
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [2,1,8,7,6,5,4,3] => [2,1,4,5,6,7,8,3] => [2,6]
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [2,1,7,6,8,5,4,3] => [2,1,4,5,8,7,6,3] => [2,3,2,1]
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [2,1,6,7,8,5,4,3] => [2,1,4,5,8,6,7,3] => [2,5,1]
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [2,1,5,7,8,6,4,3] => [2,1,4,6,5,8,7,3] => [2,3,2,1]
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => [2,1,6,7,5,8,4,3] => [2,1,4,8,7,6,5,3] => [2,2,2,1,1]
[[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [2,1,4,6,8,7,5,3] => [2,1,5,4,7,6,8,3] => [2,2,2,2]
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [2,1,4,6,5,8,7,3] => [2,1,7,4,6,5,8,3] => [2,2,2,2]
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]] => [2,1,6,5,7,4,8,3] => [2,1,8,7,6,5,4,3] => [2,1,1,2,1,1]
[[.,[.,.]],[[.,[[[.,.],.],.]],.]] => [2,1,5,6,7,4,8,3] => [2,1,8,7,5,6,4,3] => [2,1,3,1,1]
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [2,1,5,4,7,6,8,3] => [2,1,8,5,4,7,6,3] => [2,1,2,2,1]
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,2,8,7,6,5,4,3] => [1,2,4,5,6,7,8,3] => [2,6]
[[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [1,2,6,7,8,5,4,3] => [1,2,4,5,8,6,7,3] => [2,5,1]
[[[.,.],.],[.,[[.,[[.,.],.]],.]]] => [1,2,6,7,5,8,4,3] => [1,2,4,8,7,6,5,3] => [2,2,2,1,1]
[[[.,.],.],[.,[[[.,[.,.]],.],.]]] => [1,2,6,5,7,8,4,3] => [1,2,4,8,6,5,7,3] => [2,2,3,1]
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,2,4,8,7,6,5,3] => [1,2,5,4,6,7,8,3] => [2,2,4]
[[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [1,2,5,4,8,7,6,3] => [1,2,6,5,4,7,8,3] => [2,1,2,3]
[[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [1,2,4,5,8,7,6,3] => [1,2,6,4,5,7,8,3] => [2,3,3]
[[[.,.],.],[[[[.,[.,.]],.],.],.]] => [1,2,5,4,6,7,8,3] => [1,2,8,5,4,6,7,3] => [2,1,4,1]
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [3,2,1,7,6,5,8,4] => [2,3,1,8,6,7,5,4] => [3,1,3,1]
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]] => [3,2,1,6,7,5,8,4] => [2,3,1,8,7,6,5,4] => [3,1,2,1,1]
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]] => [2,3,1,8,7,6,5,4] => [3,2,1,5,6,7,8,4] => [2,1,5]
[[.,[[.,.],.]],[.,[.,[[.,.],.]]]] => [2,3,1,7,8,6,5,4] => [3,2,1,5,6,8,7,4] => [2,1,4,1]
[[.,[[.,.],.]],[.,[[.,.],[.,.]]]] => [2,3,1,6,8,7,5,4] => [3,2,1,5,7,6,8,4] => [2,1,3,2]
[[.,[[.,.],.]],[.,[[.,[.,.]],.]]] => [2,3,1,7,6,8,5,4] => [3,2,1,5,8,7,6,4] => [2,1,2,2,1]
[[.,[[.,.],.]],[.,[[[.,.],.],.]]] => [2,3,1,6,7,8,5,4] => [3,2,1,5,8,6,7,4] => [2,1,4,1]
[[.,[[.,.],.]],[[.,.],[.,[.,.]]]] => [2,3,1,5,8,7,6,4] => [3,2,1,6,5,7,8,4] => [2,1,2,3]
[[.,[[.,.],.]],[[.,.],[[.,.],.]]] => [2,3,1,5,7,8,6,4] => [3,2,1,6,5,8,7,4] => [2,1,2,2,1]
[[.,[[.,.],.]],[[.,[.,.]],[.,.]]] => [2,3,1,6,5,8,7,4] => [3,2,1,7,6,5,8,4] => [2,1,1,2,2]
[[.,[[.,.],.]],[[[.,.],.],[.,.]]] => [2,3,1,5,6,8,7,4] => [3,2,1,7,5,6,8,4] => [2,1,3,2]
[[.,[[.,.],.]],[[.,[.,[.,.]]],.]] => [2,3,1,7,6,5,8,4] => [3,2,1,8,6,7,5,4] => [2,1,1,3,1]
[[.,[[.,.],.]],[[.,[[.,.],.]],.]] => [2,3,1,6,7,5,8,4] => [3,2,1,8,7,6,5,4] => [2,1,1,2,1,1]
[[.,[[.,.],.]],[[[.,.],[.,.]],.]] => [2,3,1,5,7,6,8,4] => [3,2,1,8,5,7,6,4] => [2,1,2,2,1]
[[.,[[.,.],.]],[[[.,[.,.]],.],.]] => [2,3,1,6,5,7,8,4] => [3,2,1,8,6,5,7,4] => [2,1,1,3,1]
[[.,[[.,.],.]],[[[[.,.],.],.],.]] => [2,3,1,5,6,7,8,4] => [3,2,1,8,5,6,7,4] => [2,1,4,1]
[[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [1,3,2,6,7,5,8,4] => [1,3,2,8,7,6,5,4] => [1,2,1,2,1,1]
[[[.,.],[.,.]],[[[.,[.,.]],.],.]] => [1,3,2,6,5,7,8,4] => [1,3,2,8,6,5,7,4] => [1,2,1,3,1]
[[[.,[.,.]],.],[[.,[[.,.],.]],.]] => [2,1,3,6,7,5,8,4] => [2,1,3,8,7,6,5,4] => [3,1,2,1,1]
[[[.,[.,.]],.],[[[.,.],[.,.]],.]] => [2,1,3,5,7,6,8,4] => [2,1,3,8,5,7,6,4] => [3,2,2,1]
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,2,3,8,7,6,5,4] => [1,2,3,5,6,7,8,4] => [3,5]
[[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [1,2,3,7,8,6,5,4] => [1,2,3,5,6,8,7,4] => [3,4,1]
[[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,2,3,6,8,7,5,4] => [1,2,3,5,7,6,8,4] => [3,3,2]
[[[[.,.],.],.],[.,[[.,[.,.]],.]]] => [1,2,3,7,6,8,5,4] => [1,2,3,5,8,7,6,4] => [3,2,2,1]
[[[[.,.],.],.],[.,[[[.,.],.],.]]] => [1,2,3,6,7,8,5,4] => [1,2,3,5,8,6,7,4] => [3,4,1]
[[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [1,2,3,5,8,7,6,4] => [1,2,3,6,5,7,8,4] => [3,2,3]
[[[[.,.],.],.],[[.,.],[[.,.],.]]] => [1,2,3,5,7,8,6,4] => [1,2,3,6,5,8,7,4] => [3,2,2,1]
[[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,2,3,6,5,8,7,4] => [1,2,3,7,6,5,8,4] => [3,1,2,2]
[[[[.,.],.],.],[[[.,.],.],[.,.]]] => [1,2,3,5,6,8,7,4] => [1,2,3,7,5,6,8,4] => [3,3,2]
[[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [1,2,3,7,6,5,8,4] => [1,2,3,8,6,7,5,4] => [3,1,3,1]
[[[[.,.],.],.],[[.,[[.,.],.]],.]] => [1,2,3,6,7,5,8,4] => [1,2,3,8,7,6,5,4] => [3,1,2,1,1]
[[[[.,.],.],.],[[[.,.],[.,.]],.]] => [1,2,3,5,7,6,8,4] => [1,2,3,8,5,7,6,4] => [3,2,2,1]
[[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,2,3,6,5,7,8,4] => [1,2,3,8,6,5,7,4] => [3,1,3,1]
[[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,2,3,5,6,7,8,4] => [1,2,3,8,5,6,7,4] => [3,4,1]
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [4,3,2,1,8,7,6,5] => [2,3,4,1,6,7,8,5] => [4,4]
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [4,3,2,1,7,8,6,5] => [2,3,4,1,6,8,7,5] => [4,3,1]
[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [4,3,2,1,6,8,7,5] => [2,3,4,1,7,6,8,5] => [4,2,2]
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [4,3,2,1,7,6,8,5] => [2,3,4,1,8,7,6,5] => [4,1,2,1]
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]] => [4,3,2,1,6,7,8,5] => [2,3,4,1,8,6,7,5] => [4,3,1]
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]] => [3,4,2,1,8,7,6,5] => [2,4,3,1,6,7,8,5] => [3,1,4]
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]] => [3,4,2,1,7,8,6,5] => [2,4,3,1,6,8,7,5] => [3,1,3,1]
[[.,[.,[[.,.],.]]],[[.,.],[.,.]]] => [3,4,2,1,6,8,7,5] => [2,4,3,1,7,6,8,5] => [3,1,2,2]
[[.,[.,[[.,.],.]]],[[.,[.,.]],.]] => [3,4,2,1,7,6,8,5] => [2,4,3,1,8,7,6,5] => [3,1,1,2,1]
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [2,4,3,1,8,7,6,5] => [3,2,4,1,6,7,8,5] => [2,2,4]
[[.,[[.,.],[.,.]]],[.,[[.,.],.]]] => [2,4,3,1,7,8,6,5] => [3,2,4,1,6,8,7,5] => [2,2,3,1]
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]] => [2,4,3,1,6,8,7,5] => [3,2,4,1,7,6,8,5] => [2,2,2,2]
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]] => [2,4,3,1,7,6,8,5] => [3,2,4,1,8,7,6,5] => [2,2,1,2,1]
[[.,[[.,.],[.,.]]],[[[.,.],.],.]] => [2,4,3,1,6,7,8,5] => [3,2,4,1,8,6,7,5] => [2,2,3,1]
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [3,2,4,1,8,7,6,5] => [4,3,2,1,6,7,8,5] => [1,2,1,4]
[[.,[[.,[.,.]],.]],[.,[[.,.],.]]] => [3,2,4,1,7,8,6,5] => [4,3,2,1,6,8,7,5] => [1,2,1,3,1]
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [3,2,4,1,6,8,7,5] => [4,3,2,1,7,6,8,5] => [1,2,1,2,2]
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]] => [3,2,4,1,7,6,8,5] => [4,3,2,1,8,7,6,5] => [1,2,1,1,2,1]
[[.,[[.,[.,.]],.]],[[[.,.],.],.]] => [3,2,4,1,6,7,8,5] => [4,3,2,1,8,6,7,5] => [1,2,1,3,1]
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]] => [2,3,4,1,8,7,6,5] => [4,2,3,1,6,7,8,5] => [3,1,4]
[[.,[[[.,.],.],.]],[[.,.],[.,.]]] => [2,3,4,1,6,8,7,5] => [4,2,3,1,7,6,8,5] => [3,1,2,2]
[[.,[[[.,.],.],.]],[[.,[.,.]],.]] => [2,3,4,1,7,6,8,5] => [4,2,3,1,8,7,6,5] => [3,1,1,2,1]
[[.,[[[.,.],.],.]],[[[.,.],.],.]] => [2,3,4,1,6,7,8,5] => [4,2,3,1,8,6,7,5] => [3,1,3,1]
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,4,3,2,8,7,6,5] => [1,3,4,2,6,7,8,5] => [1,3,4]
[[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [1,4,3,2,6,8,7,5] => [1,3,4,2,7,6,8,5] => [1,3,2,2]
[[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,4,3,2,7,6,8,5] => [1,3,4,2,8,7,6,5] => [1,3,1,2,1]
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,3,4,2,8,7,6,5] => [1,4,3,2,6,7,8,5] => [1,2,1,4]
[[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [1,3,4,2,6,8,7,5] => [1,4,3,2,7,6,8,5] => [1,2,1,2,2]
[[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,3,4,2,7,6,8,5] => [1,4,3,2,8,7,6,5] => [1,2,1,1,2,1]
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [2,1,4,3,8,7,6,5] => [2,1,4,3,6,7,8,5] => [2,2,4]
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [2,1,4,3,7,8,6,5] => [2,1,4,3,6,8,7,5] => [2,2,3,1]
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [2,1,4,3,6,8,7,5] => [2,1,4,3,7,6,8,5] => [2,2,2,2]
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [2,1,4,3,7,6,8,5] => [2,1,4,3,8,7,6,5] => [2,2,1,2,1]
[[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [2,1,4,3,6,7,8,5] => [2,1,4,3,8,6,7,5] => [2,2,3,1]
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,2,4,3,8,7,6,5] => [1,2,4,3,6,7,8,5] => [2,2,4]
[[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [1,2,4,3,6,8,7,5] => [1,2,4,3,7,6,8,5] => [2,2,2,2]
[[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,2,4,3,7,6,8,5] => [1,2,4,3,8,7,6,5] => [2,2,1,2,1]
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [3,2,1,4,8,7,6,5] => [2,3,1,4,6,7,8,5] => [4,4]
[[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [3,2,1,4,6,8,7,5] => [2,3,1,4,7,6,8,5] => [4,2,2]
[[[.,[.,[.,.]]],.],[[.,[.,.]],.]] => [3,2,1,4,7,6,8,5] => [2,3,1,4,8,7,6,5] => [4,1,2,1]
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]] => [2,3,1,4,8,7,6,5] => [3,2,1,4,6,7,8,5] => [2,2,4]
[[[.,[[.,.],.]],.],[[.,.],[.,.]]] => [2,3,1,4,6,8,7,5] => [3,2,1,4,7,6,8,5] => [2,2,2,2]
[[[.,[[.,.],.]],.],[[.,[.,.]],.]] => [2,3,1,4,7,6,8,5] => [3,2,1,4,8,7,6,5] => [2,2,1,2,1]
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,3,2,4,8,7,6,5] => [1,3,2,4,6,7,8,5] => [1,3,4]
[[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [1,3,2,4,6,8,7,5] => [1,3,2,4,7,6,8,5] => [1,3,2,2]
[[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,3,2,4,7,6,8,5] => [1,3,2,4,8,7,6,5] => [1,3,1,2,1]
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [2,1,3,4,8,7,6,5] => [2,1,3,4,6,7,8,5] => [4,4]
[[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [2,1,3,4,6,8,7,5] => [2,1,3,4,7,6,8,5] => [4,2,2]
[[[[.,[.,.]],.],.],[[.,[.,.]],.]] => [2,1,3,4,7,6,8,5] => [2,1,3,4,8,7,6,5] => [4,1,2,1]
[[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,2,3,4,8,7,6,5] => [1,2,3,4,6,7,8,5] => [4,4]
[[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,2,3,4,6,8,7,5] => [1,2,3,4,7,6,8,5] => [4,2,2]
[[[[[.,.],.],.],.],[[.,[.,.]],.]] => [1,2,3,4,7,6,8,5] => [1,2,3,4,8,7,6,5] => [4,1,2,1]
[[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,2,3,4,6,7,8,5] => [1,2,3,4,8,6,7,5] => [4,3,1]
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [5,4,3,2,1,7,8,6] => [2,3,4,5,1,8,7,6] => [5,2,1]
[[.,[.,[.,[[.,.],.]]]],[[.,.],.]] => [4,5,3,2,1,7,8,6] => [2,3,5,4,1,8,7,6] => [4,1,2,1]
[[.,[.,[[.,.],[.,.]]]],[[.,.],.]] => [3,5,4,2,1,7,8,6] => [2,4,3,5,1,8,7,6] => [3,2,2,1]
[[.,[.,[[.,[.,.]],.]]],[[.,.],.]] => [4,3,5,2,1,7,8,6] => [2,5,4,3,1,8,7,6] => [2,2,1,2,1]
[[.,[.,[[[.,.],.],.]]],[[.,.],.]] => [3,4,5,2,1,7,8,6] => [2,5,3,4,1,8,7,6] => [4,1,2,1]
[[.,[[.,.],[.,[.,.]]]],[[.,.],.]] => [2,5,4,3,1,7,8,6] => [3,2,4,5,1,8,7,6] => [2,3,2,1]
[[.,[[.,.],[[.,.],.]]],[[.,.],.]] => [2,4,5,3,1,7,8,6] => [3,2,5,4,1,8,7,6] => [2,2,1,2,1]
[[.,[[.,[.,.]],[.,.]]],[[.,.],.]] => [3,2,5,4,1,7,8,6] => [4,3,2,5,1,8,7,6] => [1,2,2,2,1]
[[.,[[[.,.],.],[.,.]]],[[.,.],.]] => [2,3,5,4,1,7,8,6] => [4,2,3,5,1,8,7,6] => [3,2,2,1]
[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]] => [4,3,2,5,1,8,7,6] => [5,3,4,2,1,7,8,6] => [1,3,1,3]
[[.,[[.,[.,[.,.]]],.]],[[.,.],.]] => [4,3,2,5,1,7,8,6] => [5,3,4,2,1,8,7,6] => [1,3,1,2,1]
[[.,[[.,[[.,.],.]],.]],[.,[.,.]]] => [3,4,2,5,1,8,7,6] => [5,4,3,2,1,7,8,6] => [1,2,1,1,3]
[[.,[[.,[[.,.],.]],.]],[[.,.],.]] => [3,4,2,5,1,7,8,6] => [5,4,3,2,1,8,7,6] => [1,2,1,1,2,1]
[[.,[[[.,.],[.,.]],.]],[[.,.],.]] => [2,4,3,5,1,7,8,6] => [5,2,4,3,1,8,7,6] => [2,2,1,2,1]
[[.,[[[.,[.,.]],.],.]],[[.,.],.]] => [3,2,4,5,1,7,8,6] => [5,3,2,4,1,8,7,6] => [1,3,1,2,1]
[[.,[[[[.,.],.],.],.]],[[.,.],.]] => [2,3,4,5,1,7,8,6] => [5,2,3,4,1,8,7,6] => [4,1,2,1]
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] => [4,3,2,1,5,8,7,6] => [2,3,4,1,5,7,8,6] => [5,3]
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]] => [4,3,2,1,5,7,8,6] => [2,3,4,1,5,8,7,6] => [5,2,1]
[[[.,[[.,.],[.,.]]],.],[.,[.,.]]] => [2,4,3,1,5,8,7,6] => [3,2,4,1,5,7,8,6] => [2,3,3]
[[[.,[[.,.],[.,.]]],.],[[.,.],.]] => [2,4,3,1,5,7,8,6] => [3,2,4,1,5,8,7,6] => [2,3,2,1]
[[[.,[[.,[.,.]],.]],.],[.,[.,.]]] => [3,2,4,1,5,8,7,6] => [4,3,2,1,5,7,8,6] => [1,2,2,3]
[[[.,[[.,[.,.]],.]],.],[[.,.],.]] => [3,2,4,1,5,7,8,6] => [4,3,2,1,5,8,7,6] => [1,2,2,2,1]
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [3,2,1,4,5,8,7,6] => [2,3,1,4,5,7,8,6] => [5,3]
[[[[.,[[.,.],.]],.],.],[[.,.],.]] => [2,3,1,4,5,7,8,6] => [3,2,1,4,5,8,7,6] => [2,3,2,1]
[[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,2,3,4,5,8,7,6] => [1,2,3,4,5,7,8,6] => [5,3]
[[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,2,3,4,5,7,8,6] => [1,2,3,4,5,8,7,6] => [5,2,1]
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [6,5,4,3,2,1,8,7] => [2,3,4,5,6,1,8,7] => [6,2]
[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]] => [5,4,6,3,2,1,8,7] => [2,3,6,5,4,1,8,7] => [3,2,1,2]
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]] => [4,5,6,3,2,1,8,7] => [2,3,6,4,5,1,8,7] => [5,1,2]
[[.,[.,[[.,.],[[.,.],.]]]],[.,.]] => [3,5,6,4,2,1,8,7] => [2,4,3,6,5,1,8,7] => [3,2,1,2]
[[.,[[.,.],[[.,.],[.,.]]]],[.,.]] => [2,4,6,5,3,1,8,7] => [3,2,5,4,6,1,8,7] => [2,2,2,2]
[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]] => [3,2,6,5,4,1,8,7] => [4,3,2,5,6,1,8,7] => [1,2,3,2]
[[.,[[.,[[.,.],.]],[.,.]]],[.,.]] => [3,4,2,6,5,1,8,7] => [5,4,3,2,6,1,8,7] => [1,2,1,2,2]
[[.,[[[.,.],[.,.]],[.,.]]],[.,.]] => [2,4,3,6,5,1,8,7] => [5,2,4,3,6,1,8,7] => [2,2,2,2]
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => [4,3,5,2,6,1,8,7] => [6,5,4,3,2,1,8,7] => [1,1,2,1,1,2]
[[.,[[.,[[[.,.],.],.]],.]],[.,.]] => [3,4,5,2,6,1,8,7] => [6,5,3,4,2,1,8,7] => [1,3,1,1,2]
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]] => [3,2,5,4,6,1,8,7] => [6,3,2,5,4,1,8,7] => [1,2,2,1,2]
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [2,1,6,5,4,3,8,7] => [2,1,4,5,6,3,8,7] => [2,4,2]
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [2,1,5,6,4,3,8,7] => [2,1,4,6,5,3,8,7] => [2,3,1,2]
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [2,1,4,6,5,3,8,7] => [2,1,5,4,6,3,8,7] => [2,2,2,2]
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [2,1,5,4,6,3,8,7] => [2,1,6,5,4,3,8,7] => [2,1,2,1,2]
[[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [2,1,4,5,6,3,8,7] => [2,1,6,4,5,3,8,7] => [2,3,1,2]
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [4,3,2,1,6,5,8,7] => [2,3,4,1,6,5,8,7] => [4,2,2]
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]] => [3,4,2,1,6,5,8,7] => [2,4,3,1,6,5,8,7] => [3,1,2,2]
[[[.,[[.,.],[.,.]]],[.,.]],[.,.]] => [2,4,3,1,6,5,8,7] => [3,2,4,1,6,5,8,7] => [2,2,2,2]
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => [3,2,4,1,6,5,8,7] => [4,3,2,1,6,5,8,7] => [1,2,1,2,2]
[[[.,[[[.,.],.],.]],[.,.]],[.,.]] => [2,3,4,1,6,5,8,7] => [4,2,3,1,6,5,8,7] => [3,1,2,2]
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => [2,2,2,2]
[[[.,[[.,[[.,.],.]],.]],.],[.,.]] => [3,4,2,5,1,6,8,7] => [5,4,3,2,1,6,8,7] => [1,2,1,2,2]
[[[.,[[[.,[.,.]],.],.]],.],[.,.]] => [3,2,4,5,1,6,8,7] => [5,3,2,4,1,6,8,7] => [1,3,2,2]
[[[[.,[.,.]],[[.,.],.]],.],[.,.]] => [2,1,4,5,3,6,8,7] => [2,1,5,4,3,6,8,7] => [2,2,2,2]
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]] => [4,3,2,1,5,6,8,7] => [2,3,4,1,5,6,8,7] => [6,2]
[[[[.,[[.,.],[.,.]]],.],.],[.,.]] => [2,4,3,1,5,6,8,7] => [3,2,4,1,5,6,8,7] => [2,4,2]
[[[[.,[[.,[.,.]],.]],.],.],[.,.]] => [3,2,4,1,5,6,8,7] => [4,3,2,1,5,6,8,7] => [1,2,3,2]
[[[[[[.,[.,.]],.],.],.],.],[.,.]] => [2,1,3,4,5,6,8,7] => [2,1,3,4,5,6,8,7] => [6,2]
[[[[[[[.,.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => [6,2]
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [7,6,5,4,3,2,1,8] => [2,3,4,5,6,7,1,8] => [8]
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => [6,7,5,4,3,2,1,8] => [2,3,4,5,7,6,1,8] => [6,2]
[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.] => [2,7,6,5,4,3,1,8] => [3,2,4,5,6,7,1,8] => [2,6]
[[.,[[.,.],[[.,.],[[.,.],.]]]],.] => [2,4,6,7,5,3,1,8] => [3,2,5,4,7,6,1,8] => [2,2,2,2]
[[.,[[.,.],[[.,[[.,.],.]],.]]],.] => [2,5,6,4,7,3,1,8] => [3,2,7,6,5,4,1,8] => [2,1,2,1,2]
[[.,[[.,.],[[[.,[.,.]],.],.]]],.] => [2,5,4,6,7,3,1,8] => [3,2,7,5,4,6,1,8] => [2,1,3,2]
[[.,[[.,[[.,.],.]],[.,[.,.]]]],.] => [3,4,2,7,6,5,1,8] => [5,4,3,2,6,7,1,8] => [1,2,1,4]
[[.,[[.,[[.,.],.]],[[.,.],.]]],.] => [3,4,2,6,7,5,1,8] => [5,4,3,2,7,6,1,8] => [1,2,1,2,2]
[[.,[[.,[.,[[.,[.,.]],.]]],.]],.] => [5,4,6,3,2,7,1,8] => [7,3,6,5,4,2,1,8] => [1,2,2,1,2]
[[.,[[.,[[.,.],[[.,.],.]]],.]],.] => [3,5,6,4,2,7,1,8] => [7,4,3,6,5,2,1,8] => [1,2,2,1,2]
[[.,[[.,[[.,[.,.]],[.,.]]],.]],.] => [4,3,6,5,2,7,1,8] => [7,5,4,3,6,2,1,8] => [1,1,2,2,2]
[[.,[[.,[[.,[.,[.,.]]],.]],.]],.] => [5,4,3,6,2,7,1,8] => [7,6,4,5,3,2,1,8] => [1,1,3,1,2]
[[.,[[.,[[.,[[.,.],.]],.]],.]],.] => [4,5,3,6,2,7,1,8] => [7,6,5,4,3,2,1,8] => [1,1,2,1,1,2]
[[.,[[.,[[[.,.],[.,.]],.]],.]],.] => [3,5,4,6,2,7,1,8] => [7,6,3,5,4,2,1,8] => [1,2,2,1,2]
[[.,[[.,[[[.,[.,.]],.],.]],.]],.] => [4,3,5,6,2,7,1,8] => [7,6,4,3,5,2,1,8] => [1,1,3,1,2]
[[.,[[.,[[[[.,.],.],.],.]],.]],.] => [3,4,5,6,2,7,1,8] => [7,6,3,4,5,2,1,8] => [1,4,1,2]
[[.,[[[[.,.],.],[[.,.],.]],.]],.] => [2,3,5,6,4,7,1,8] => [7,2,3,6,5,4,1,8] => [3,2,1,2]
[[.,[[[[[.,.],.],.],[.,.]],.]],.] => [2,3,4,6,5,7,1,8] => [7,2,3,4,6,5,1,8] => [4,2,2]
[[[.,.],[.,[.,[.,[[.,.],.]]]]],.] => [1,6,7,5,4,3,2,8] => [1,3,4,5,7,6,2,8] => [1,5,2]
[[[.,.],[.,[[[[.,.],.],.],.]]],.] => [1,4,5,6,7,3,2,8] => [1,3,7,4,5,6,2,8] => [1,5,2]
[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.] => [3,2,1,7,6,5,4,8] => [2,3,1,5,6,7,4,8] => [3,5]
[[[.,[[.,.],.]],[[[.,.],.],.]],.] => [2,3,1,5,6,7,4,8] => [3,2,1,7,5,6,4,8] => [2,1,3,2]
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.] => [4,3,2,1,7,6,5,8] => [2,3,4,1,6,7,5,8] => [4,4]
[[[.,[.,[.,[.,.]]]],[[.,.],.]],.] => [4,3,2,1,6,7,5,8] => [2,3,4,1,7,6,5,8] => [4,2,2]
[[[.,[[.,[.,.]],.]],[.,[.,.]]],.] => [3,2,4,1,7,6,5,8] => [4,3,2,1,6,7,5,8] => [1,2,1,4]
[[[.,[[.,[.,.]],.]],[[.,.],.]],.] => [3,2,4,1,6,7,5,8] => [4,3,2,1,7,6,5,8] => [1,2,1,2,2]
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,4,3,2,7,6,5,8] => [1,3,4,2,6,7,5,8] => [1,3,4]
[[[[.,.],[[.,.],.]],[[.,.],.]],.] => [1,3,4,2,6,7,5,8] => [1,4,3,2,7,6,5,8] => [1,2,1,2,2]
[[[[.,[[.,.],.]],.],[[.,.],.]],.] => [2,3,1,4,6,7,5,8] => [3,2,1,4,7,6,5,8] => [2,2,2,2]
[[[.,[[.,[[.,.],.]],.]],[.,.]],.] => [3,4,2,5,1,7,6,8] => [5,4,3,2,1,7,6,8] => [1,2,1,1,3]
[[[.,[[[.,.],[.,.]],.]],[.,.]],.] => [2,4,3,5,1,7,6,8] => [5,2,4,3,1,7,6,8] => [2,2,1,3]
[[[[.,[.,[.,.]]],[.,.]],[.,.]],.] => [3,2,1,5,4,7,6,8] => [2,3,1,5,4,7,6,8] => [3,2,3]
[[[[.,[[.,.],.]],[.,.]],[.,.]],.] => [2,3,1,5,4,7,6,8] => [3,2,1,5,4,7,6,8] => [2,1,2,3]
[[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,3,2,5,4,7,6,8] => [1,3,2,5,4,7,6,8] => [1,2,2,3]
[[[[[[.,.],.],.],[.,.]],[.,.]],.] => [1,2,3,5,4,7,6,8] => [1,2,3,5,4,7,6,8] => [3,2,3]
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.] => [4,3,2,1,5,7,6,8] => [2,3,4,1,5,7,6,8] => [5,3]
[[[[.,[[.,.],[.,.]]],.],[.,.]],.] => [2,4,3,1,5,7,6,8] => [3,2,4,1,5,7,6,8] => [2,3,3]
[[[[.,[[.,[.,.]],.]],.],[.,.]],.] => [3,2,4,1,5,7,6,8] => [4,3,2,1,5,7,6,8] => [1,2,2,3]
[[[[[[.,.],[.,.]],.],.],[.,.]],.] => [1,3,2,4,5,7,6,8] => [1,3,2,4,5,7,6,8] => [1,4,3]
[[[[[[[.,.],.],.],.],.],[.,.]],.] => [1,2,3,4,5,7,6,8] => [1,2,3,4,5,7,6,8] => [5,3]
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.] => [6,5,4,3,2,1,7,8] => [2,3,4,5,6,1,7,8] => [8]
[[[.,[.,[.,[.,[[.,.],.]]]]],.],.] => [5,6,4,3,2,1,7,8] => [2,3,4,6,5,1,7,8] => [5,3]
[[[.,[[[.,.],.],[.,[.,.]]]],.],.] => [2,3,6,5,4,1,7,8] => [4,2,3,5,6,1,7,8] => [3,5]
[[[.,[[.,[[.,.],.]],[.,.]]],.],.] => [3,4,2,6,5,1,7,8] => [5,4,3,2,6,1,7,8] => [1,2,1,4]
[[[.,[[[.,.],[.,.]],[.,.]]],.],.] => [2,4,3,6,5,1,7,8] => [5,2,4,3,6,1,7,8] => [2,2,4]
[[[.,[[.,[[.,[.,.]],.]],.]],.],.] => [4,3,5,2,6,1,7,8] => [6,5,4,3,2,1,7,8] => [1,1,2,1,3]
[[[.,[[[[.,.],.],[.,.]],.]],.],.] => [2,3,5,4,6,1,7,8] => [6,2,3,5,4,1,7,8] => [3,2,3]
[[[[[.,.],.],[.,[[.,.],.]]],.],.] => [1,2,5,6,4,3,7,8] => [1,2,4,6,5,3,7,8] => [2,3,3]
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.] => [4,3,2,1,6,5,7,8] => [2,3,4,1,6,5,7,8] => [4,4]
[[[[.,[[.,.],[.,.]]],[.,.]],.],.] => [2,4,3,1,6,5,7,8] => [3,2,4,1,6,5,7,8] => [2,2,4]
[[[[.,[[.,[.,.]],.]],[.,.]],.],.] => [3,2,4,1,6,5,7,8] => [4,3,2,1,6,5,7,8] => [1,2,1,4]
[[[[[[.,.],.],[.,.]],[.,.]],.],.] => [1,2,4,3,6,5,7,8] => [1,2,4,3,6,5,7,8] => [2,2,4]
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.] => [5,4,3,2,1,6,7,8] => [2,3,4,5,1,6,7,8] => [8]
[[[[.,[[.,.],[[.,.],.]]],.],.],.] => [2,4,5,3,1,6,7,8] => [3,2,5,4,1,6,7,8] => [2,2,4]
[[[[.,[[.,[[.,.],.]],.]],.],.],.] => [3,4,2,5,1,6,7,8] => [5,4,3,2,1,6,7,8] => [1,2,1,4]
[[[[.,[[[.,.],[.,.]],.]],.],.],.] => [2,4,3,5,1,6,7,8] => [5,2,4,3,1,6,7,8] => [2,2,4]
[[[[.,[[[[.,.],.],.],.]],.],.],.] => [2,3,4,5,1,6,7,8] => [5,2,3,4,1,6,7,8] => [4,4]
[[[[[[.,.],[.,.]],[.,.]],.],.],.] => [1,3,2,5,4,6,7,8] => [1,3,2,5,4,6,7,8] => [1,2,5]
[[[[[[[.,.],.],.],[.,.]],.],.],.] => [1,2,3,5,4,6,7,8] => [1,2,3,5,4,6,7,8] => [3,5]
[[[[[.,[.,[.,[.,.]]]],.],.],.],.] => [4,3,2,1,5,6,7,8] => [2,3,4,1,5,6,7,8] => [8]
[[[[[.,[[.,.],[.,.]]],.],.],.],.] => [2,4,3,1,5,6,7,8] => [3,2,4,1,5,6,7,8] => [2,6]
[[[[[.,[[.,[.,.]],.]],.],.],.],.] => [3,2,4,1,5,6,7,8] => [4,3,2,1,5,6,7,8] => [1,2,5]
[[[[[[.,[[.,.],.]],.],.],.],.],.] => [2,3,1,4,5,6,7,8] => [3,2,1,4,5,6,7,8] => [2,6]
[[[[[[[.,.],[.,.]],.],.],.],.],.] => [1,3,2,4,5,6,7,8] => [1,3,2,4,5,6,7,8] => [1,7]
[[[[[[[.,[.,.]],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7,8] => [8]
[[[[[[[[.,.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [8]
[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [9,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,9,1] => [9]
[[[[[[[[[.,.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => [9]
[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [10,9,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,9,10,1] => [10]
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => [10]
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [8,7,6,5,4,3,2,1,9] => [2,3,4,5,6,7,8,1,9] => [9]
[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => [9,8,7,6,5,4,3,2,1,10] => [2,3,4,5,6,7,8,9,1,10] => [10]
[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]] => [1,6,7,5,8,4,9,3,10,2] => [1,10,9,8,7,6,5,4,3,2] => [1,1,1,1,2,1,1,1,1]
[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.] => [5,6,4,7,3,8,2,9,1,10] => [9,8,7,6,5,4,3,2,1,10] => [1,1,1,2,1,1,1,2]
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5,8,7,10,9] => [2,1,4,3,6,5,8,7,10,9] => [2,2,2,2,2]
[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5,8,7,10,9,12,11] => [2,1,4,3,6,5,8,7,10,9,12,11] => [2,2,2,2,2,2]
[[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,7,9,8] => [1,2,3,4,5,6,7,9,8] => [7,2]
[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,7,8,10,9] => [1,2,3,4,5,6,7,8,10,9] => [8,2]
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,7,8,9,11,10] => [1,2,3,4,5,6,7,8,9,11,10] => [9,2]
[[[[[[[.,.],.],.],.],.],.],[[.,.],.]] => [1,2,3,4,5,6,8,9,7] => [1,2,3,4,5,6,9,8,7] => [6,2,1]
[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => [1,2,3,4,5,6,9,8,7] => [1,2,3,4,5,6,8,9,7] => [6,3]
[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,9,8,7,6,5,4,3,2] => [1,3,4,5,6,7,8,9,2] => [1,8]
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [1,10,9,8,7,6,5,4,3,2] => [1,3,4,5,6,7,8,9,10,2] => [1,9]
[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]] => [6,5,7,4,8,3,9,2,10,1] => [10,9,8,7,6,5,4,3,2,1] => [1,1,1,1,2,1,1,1,1]
[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]] => [5,4,7,6,8,3,9,2,10,1] => [10,9,8,5,4,7,6,3,2,1] => [1,1,1,2,2,1,1,1]
[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]] => [4,3,7,6,8,5,9,2,10,1] => [10,9,4,3,8,7,6,5,2,1] => [1,1,2,1,2,1,1,1]
[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]] => [5,4,6,3,8,7,9,2,10,1] => [10,9,6,5,4,3,8,7,2,1] => [1,1,1,2,1,2,1,1]
[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]] => [4,3,6,5,8,7,9,2,10,1] => [10,9,4,3,6,5,8,7,2,1] => [1,1,2,2,2,1,1]
[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]] => [3,2,7,6,8,5,9,4,10,1] => [10,3,2,9,8,7,6,5,4,1] => [1,2,1,1,2,1,1,1]
[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]] => [3,2,6,5,8,7,9,4,10,1] => [10,3,2,9,6,5,8,7,4,1] => [1,2,1,2,2,1,1]
[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]] => [4,3,5,2,8,7,9,6,10,1] => [10,5,4,3,2,9,8,7,6,1] => [1,1,2,1,1,2,1,1]
[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]] => [3,2,5,4,8,7,9,6,10,1] => [10,3,2,5,4,9,8,7,6,1] => [1,2,2,1,2,1,1]
[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]] => [5,4,6,3,7,2,9,8,10,1] => [10,7,6,5,4,3,2,9,8,1] => [1,1,1,2,1,1,2,1]
[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]] => [4,3,6,5,7,2,9,8,10,1] => [10,7,4,3,6,5,2,9,8,1] => [1,1,2,2,1,2,1]
[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]] => [3,2,6,5,7,4,9,8,10,1] => [10,3,2,7,6,5,4,9,8,1] => [1,2,1,2,1,2,1]
[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]] => [4,3,5,2,7,6,9,8,10,1] => [10,5,4,3,2,7,6,9,8,1] => [1,1,2,1,2,2,1]
[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]] => [3,2,5,4,7,6,9,8,10,1] => [10,3,2,5,4,7,6,9,8,1] => [1,2,2,2,2,1]
[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]] => [2,1,7,6,8,5,9,4,10,3] => [2,1,10,9,8,7,6,5,4,3] => [2,1,1,1,2,1,1,1]
[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]] => [2,1,6,5,8,7,9,4,10,3] => [2,1,10,9,6,5,8,7,4,3] => [2,1,1,2,2,1,1]
[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]] => [2,1,5,4,8,7,9,6,10,3] => [2,1,10,5,4,9,8,7,6,3] => [2,1,2,1,2,1,1]
[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]] => [2,1,6,5,7,4,9,8,10,3] => [2,1,10,7,6,5,4,9,8,3] => [2,1,1,2,1,2,1]
[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]] => [2,1,5,4,7,6,9,8,10,3] => [2,1,10,5,4,7,6,9,8,3] => [2,1,2,2,2,1]
[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]] => [3,2,4,1,8,7,9,6,10,5] => [4,3,2,1,10,9,8,7,6,5] => [1,2,1,1,1,2,1,1]
[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]] => [3,2,4,1,7,6,9,8,10,5] => [4,3,2,1,10,7,6,9,8,5] => [1,2,1,1,2,2,1]
[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]] => [2,1,4,3,8,7,9,6,10,5] => [2,1,4,3,10,9,8,7,6,5] => [2,2,1,1,2,1,1]
[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]] => [2,1,4,3,7,6,9,8,10,5] => [2,1,4,3,10,7,6,9,8,5] => [2,2,1,2,2,1]
[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]] => [4,3,5,2,6,1,9,8,10,7] => [6,5,4,3,2,1,10,9,8,7] => [1,1,2,1,1,1,2,1]
[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]] => [3,2,5,4,6,1,9,8,10,7] => [6,3,2,5,4,1,10,9,8,7] => [1,2,2,1,1,2,1]
[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]] => [2,1,5,4,6,3,9,8,10,7] => [2,1,6,5,4,3,10,9,8,7] => [2,1,2,1,1,2,1]
[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]] => [3,2,4,1,6,5,9,8,10,7] => [4,3,2,1,6,5,10,9,8,7] => [1,2,1,2,1,2,1]
[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]] => [2,1,4,3,6,5,9,8,10,7] => [2,1,4,3,6,5,10,9,8,7] => [2,2,2,1,2,1]
[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]] => [5,4,6,3,7,2,8,1,10,9] => [8,7,6,5,4,3,2,1,10,9] => [1,1,1,2,1,1,1,2]
[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]] => [4,3,6,5,7,2,8,1,10,9] => [8,7,4,3,6,5,2,1,10,9] => [1,1,2,2,1,1,2]
[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]] => [3,2,6,5,7,4,8,1,10,9] => [8,3,2,7,6,5,4,1,10,9] => [1,2,1,2,1,1,2]
[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]] => [4,3,5,2,7,6,8,1,10,9] => [8,5,4,3,2,7,6,1,10,9] => [1,1,2,1,2,1,2]
[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]] => [3,2,5,4,7,6,8,1,10,9] => [8,3,2,5,4,7,6,1,10,9] => [1,2,2,2,1,2]
[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]] => [2,1,6,5,7,4,8,3,10,9] => [2,1,8,7,6,5,4,3,10,9] => [2,1,1,2,1,1,2]
[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]] => [2,1,5,4,7,6,8,3,10,9] => [2,1,8,5,4,7,6,3,10,9] => [2,1,2,2,1,2]
[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]] => [3,2,4,1,7,6,8,5,10,9] => [4,3,2,1,8,7,6,5,10,9] => [1,2,1,1,2,1,2]
[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]] => [2,1,4,3,7,6,8,5,10,9] => [2,1,4,3,8,7,6,5,10,9] => [2,2,1,2,1,2]
[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]] => [4,3,5,2,6,1,8,7,10,9] => [6,5,4,3,2,1,8,7,10,9] => [1,1,2,1,1,2,2]
[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]] => [3,2,5,4,6,1,8,7,10,9] => [6,3,2,5,4,1,8,7,10,9] => [1,2,2,1,2,2]
[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]] => [2,1,5,4,6,3,8,7,10,9] => [2,1,6,5,4,3,8,7,10,9] => [2,1,2,1,2,2]
[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]] => [3,2,4,1,6,5,8,7,10,9] => [4,3,2,1,6,5,8,7,10,9] => [1,2,1,2,2,2]
[.,[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],.]] => [7,6,8,5,9,4,10,3,11,2,12,1] => [12,11,10,9,8,7,6,5,4,3,2,1] => [1,1,1,1,1,2,1,1,1,1,1]
[.,[[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]],.]] => [6,5,8,7,9,4,10,3,11,2,12,1] => [12,11,10,9,6,5,8,7,4,3,2,1] => [1,1,1,1,2,2,1,1,1,1]
[.,[[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]],.]] => [5,4,8,7,9,6,10,3,11,2,12,1] => [12,11,10,5,4,9,8,7,6,3,2,1] => [1,1,1,2,1,2,1,1,1,1]
[.,[[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]],.]] => [6,5,7,4,9,8,10,3,11,2,12,1] => [12,11,10,7,6,5,4,9,8,3,2,1] => [1,1,1,1,2,1,2,1,1,1]
[.,[[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]],.]] => [5,4,7,6,9,8,10,3,11,2,12,1] => [12,11,10,5,4,7,6,9,8,3,2,1] => [1,1,1,2,2,2,1,1,1]
[.,[[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]],.]] => [4,3,8,7,9,6,10,5,11,2,12,1] => [12,11,4,3,10,9,8,7,6,5,2,1] => [1,1,2,1,1,2,1,1,1,1]
[.,[[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]],.]] => [4,3,7,6,9,8,10,5,11,2,12,1] => [12,11,4,3,10,7,6,9,8,5,2,1] => [1,1,2,1,2,2,1,1,1]
[.,[[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]],.]] => [5,4,6,3,9,8,10,7,11,2,12,1] => [12,11,6,5,4,3,10,9,8,7,2,1] => [1,1,1,2,1,1,2,1,1,1]
[.,[[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]],.]] => [4,3,6,5,9,8,10,7,11,2,12,1] => [12,11,4,3,6,5,10,9,8,7,2,1] => [1,1,2,2,1,2,1,1,1]
[.,[[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]],.]] => [6,5,7,4,8,3,10,9,11,2,12,1] => [12,11,8,7,6,5,4,3,10,9,2,1] => [1,1,1,1,2,1,1,2,1,1]
[.,[[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]],.]] => [5,4,7,6,8,3,10,9,11,2,12,1] => [12,11,8,5,4,7,6,3,10,9,2,1] => [1,1,1,2,2,1,2,1,1]
[.,[[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]],.]] => [4,3,7,6,8,5,10,9,11,2,12,1] => [12,11,4,3,8,7,6,5,10,9,2,1] => [1,1,2,1,2,1,2,1,1]
[.,[[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]],.]] => [5,4,6,3,8,7,10,9,11,2,12,1] => [12,11,6,5,4,3,8,7,10,9,2,1] => [1,1,1,2,1,2,2,1,1]
[.,[[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]],.]] => [4,3,6,5,8,7,10,9,11,2,12,1] => [12,11,4,3,6,5,8,7,10,9,2,1] => [1,1,2,2,2,2,1,1]
[.,[[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]],.]] => [3,2,8,7,9,6,10,5,11,4,12,1] => [12,3,2,11,10,9,8,7,6,5,4,1] => [1,2,1,1,1,2,1,1,1,1]
[.,[[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]],.]] => [3,2,7,6,9,8,10,5,11,4,12,1] => [12,3,2,11,10,7,6,9,8,5,4,1] => [1,2,1,1,2,2,1,1,1]
[.,[[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]],.]] => [3,2,6,5,9,8,10,7,11,4,12,1] => [12,3,2,11,6,5,10,9,8,7,4,1] => [1,2,1,2,1,2,1,1,1]
[.,[[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]],.]] => [3,2,7,6,8,5,10,9,11,4,12,1] => [12,3,2,11,8,7,6,5,10,9,4,1] => [1,2,1,1,2,1,2,1,1]
[.,[[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]],.]] => [3,2,6,5,8,7,10,9,11,4,12,1] => [12,3,2,11,6,5,8,7,10,9,4,1] => [1,2,1,2,2,2,1,1]
[.,[[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]],.]] => [4,3,5,2,9,8,10,7,11,6,12,1] => [12,5,4,3,2,11,10,9,8,7,6,1] => [1,1,2,1,1,1,2,1,1,1]
[.,[[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]],.]] => [4,3,5,2,8,7,10,9,11,6,12,1] => [12,5,4,3,2,11,8,7,10,9,6,1] => [1,1,2,1,1,2,2,1,1]
[.,[[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]],.]] => [3,2,5,4,9,8,10,7,11,6,12,1] => [12,3,2,5,4,11,10,9,8,7,6,1] => [1,2,2,1,1,2,1,1,1]
[.,[[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]],.]] => [3,2,5,4,8,7,10,9,11,6,12,1] => [12,3,2,5,4,11,8,7,10,9,6,1] => [1,2,2,1,2,2,1,1]
[.,[[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]],.]] => [5,4,6,3,7,2,10,9,11,8,12,1] => [12,7,6,5,4,3,2,11,10,9,8,1] => [1,1,1,2,1,1,1,2,1,1]
[.,[[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]],.]] => [4,3,6,5,7,2,10,9,11,8,12,1] => [12,7,4,3,6,5,2,11,10,9,8,1] => [1,1,2,2,1,1,2,1,1]
[.,[[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]],.]] => [3,2,6,5,7,4,10,9,11,8,12,1] => [12,3,2,7,6,5,4,11,10,9,8,1] => [1,2,1,2,1,1,2,1,1]
[.,[[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]],.]] => [4,3,5,2,7,6,10,9,11,8,12,1] => [12,5,4,3,2,7,6,11,10,9,8,1] => [1,1,2,1,2,1,2,1,1]
[.,[[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]],.]] => [3,2,5,4,7,6,10,9,11,8,12,1] => [12,3,2,5,4,7,6,11,10,9,8,1] => [1,2,2,2,1,2,1,1]
[.,[[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]],.]] => [6,5,7,4,8,3,9,2,11,10,12,1] => [12,9,8,7,6,5,4,3,2,11,10,1] => [1,1,1,1,2,1,1,1,2,1]
[.,[[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]],.]] => [5,4,7,6,8,3,9,2,11,10,12,1] => [12,9,8,5,4,7,6,3,2,11,10,1] => [1,1,1,2,2,1,1,2,1]
[.,[[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]],.]] => [4,3,7,6,8,5,9,2,11,10,12,1] => [12,9,4,3,8,7,6,5,2,11,10,1] => [1,1,2,1,2,1,1,2,1]
[.,[[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],.]] => [5,4,6,3,8,7,9,2,11,10,12,1] => [12,9,6,5,4,3,8,7,2,11,10,1] => [1,1,1,2,1,2,1,2,1]
[.,[[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]],.]] => [4,3,6,5,8,7,9,2,11,10,12,1] => [12,9,4,3,6,5,8,7,2,11,10,1] => [1,1,2,2,2,1,2,1]
[.,[[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]],.]] => [3,2,7,6,8,5,9,4,11,10,12,1] => [12,3,2,9,8,7,6,5,4,11,10,1] => [1,2,1,1,2,1,1,2,1]
[.,[[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]],.]] => [3,2,6,5,8,7,9,4,11,10,12,1] => [12,3,2,9,6,5,8,7,4,11,10,1] => [1,2,1,2,2,1,2,1]
[.,[[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]],.]] => [4,3,5,2,8,7,9,6,11,10,12,1] => [12,5,4,3,2,9,8,7,6,11,10,1] => [1,1,2,1,1,2,1,2,1]
[.,[[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]],.]] => [3,2,5,4,8,7,9,6,11,10,12,1] => [12,3,2,5,4,9,8,7,6,11,10,1] => [1,2,2,1,2,1,2,1]
[.,[[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]],.]] => [5,4,6,3,7,2,9,8,11,10,12,1] => [12,7,6,5,4,3,2,9,8,11,10,1] => [1,1,1,2,1,1,2,2,1]
[.,[[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]],.]] => [4,3,6,5,7,2,9,8,11,10,12,1] => [12,7,4,3,6,5,2,9,8,11,10,1] => [1,1,2,2,1,2,2,1]
[.,[[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]],.]] => [3,2,6,5,7,4,9,8,11,10,12,1] => [12,3,2,7,6,5,4,9,8,11,10,1] => [1,2,1,2,1,2,2,1]
[.,[[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]],.]] => [4,3,5,2,7,6,9,8,11,10,12,1] => [12,5,4,3,2,7,6,9,8,11,10,1] => [1,1,2,1,2,2,2,1]
[.,[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.]] => [3,2,5,4,7,6,9,8,11,10,12,1] => [12,3,2,5,4,7,6,9,8,11,10,1] => [1,2,2,2,2,2,1]
[[.,[.,.]],[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]] => [2,1,8,7,9,6,10,5,11,4,12,3] => [2,1,12,11,10,9,8,7,6,5,4,3] => [2,1,1,1,1,2,1,1,1,1]
[[.,[.,.]],[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]] => [2,1,7,6,9,8,10,5,11,4,12,3] => [2,1,12,11,10,7,6,9,8,5,4,3] => [2,1,1,1,2,2,1,1,1]
[[.,[.,.]],[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]] => [2,1,6,5,9,8,10,7,11,4,12,3] => [2,1,12,11,6,5,10,9,8,7,4,3] => [2,1,1,2,1,2,1,1,1]
[[.,[.,.]],[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]] => [2,1,7,6,8,5,10,9,11,4,12,3] => [2,1,12,11,8,7,6,5,10,9,4,3] => [2,1,1,1,2,1,2,1,1]
[[.,[.,.]],[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]] => [2,1,6,5,8,7,10,9,11,4,12,3] => [2,1,12,11,6,5,8,7,10,9,4,3] => [2,1,1,2,2,2,1,1]
[[.,[.,.]],[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]] => [2,1,5,4,9,8,10,7,11,6,12,3] => [2,1,12,5,4,11,10,9,8,7,6,3] => [2,1,2,1,1,2,1,1,1]
[[.,[.,.]],[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]] => [2,1,5,4,8,7,10,9,11,6,12,3] => [2,1,12,5,4,11,8,7,10,9,6,3] => [2,1,2,1,2,2,1,1]
[[.,[.,.]],[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]] => [2,1,6,5,7,4,10,9,11,8,12,3] => [2,1,12,7,6,5,4,11,10,9,8,3] => [2,1,1,2,1,1,2,1,1]
[[.,[.,.]],[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]] => [2,1,5,4,7,6,10,9,11,8,12,3] => [2,1,12,5,4,7,6,11,10,9,8,3] => [2,1,2,2,1,2,1,1]
[[.,[.,.]],[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]] => [2,1,7,6,8,5,9,4,11,10,12,3] => [2,1,12,9,8,7,6,5,4,11,10,3] => [2,1,1,1,2,1,1,2,1]
[[.,[.,.]],[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]] => [2,1,6,5,8,7,9,4,11,10,12,3] => [2,1,12,9,6,5,8,7,4,11,10,3] => [2,1,1,2,2,1,2,1]
[[.,[.,.]],[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]] => [2,1,5,4,8,7,9,6,11,10,12,3] => [2,1,12,5,4,9,8,7,6,11,10,3] => [2,1,2,1,2,1,2,1]
[[.,[.,.]],[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]] => [2,1,6,5,7,4,9,8,11,10,12,3] => [2,1,12,7,6,5,4,9,8,11,10,3] => [2,1,1,2,1,2,2,1]
[[.,[.,.]],[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]] => [2,1,5,4,7,6,9,8,11,10,12,3] => [2,1,12,5,4,7,6,9,8,11,10,3] => [2,1,2,2,2,2,1]
[[.,[[.,[.,.]],.]],[[.,[[.,[[.,[.,.]],.]],.]],.]] => [3,2,4,1,9,8,10,7,11,6,12,5] => [4,3,2,1,12,11,10,9,8,7,6,5] => [1,2,1,1,1,1,2,1,1,1]
[[.,[[.,[.,.]],.]],[[.,[[[.,[.,.]],[.,.]],.]],.]] => [3,2,4,1,8,7,10,9,11,6,12,5] => [4,3,2,1,12,11,8,7,10,9,6,5] => [1,2,1,1,1,2,2,1,1]
[[.,[[.,[.,.]],.]],[[[.,[.,.]],[[.,[.,.]],.]],.]] => [3,2,4,1,7,6,10,9,11,8,12,5] => [4,3,2,1,12,7,6,11,10,9,8,5] => [1,2,1,1,2,1,2,1,1]
[[.,[[.,[.,.]],.]],[[[.,[[.,[.,.]],.]],[.,.]],.]] => [3,2,4,1,8,7,9,6,11,10,12,5] => [4,3,2,1,12,9,8,7,6,11,10,5] => [1,2,1,1,1,2,1,2,1]
[[.,[[.,[.,.]],.]],[[[[.,[.,.]],[.,.]],[.,.]],.]] => [3,2,4,1,7,6,9,8,11,10,12,5] => [4,3,2,1,12,7,6,9,8,11,10,5] => [1,2,1,1,2,2,2,1]
[[[.,[.,.]],[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]] => [2,1,4,3,9,8,10,7,11,6,12,5] => [2,1,4,3,12,11,10,9,8,7,6,5] => [2,2,1,1,1,2,1,1,1]
[[[.,[.,.]],[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]] => [2,1,4,3,8,7,10,9,11,6,12,5] => [2,1,4,3,12,11,8,7,10,9,6,5] => [2,2,1,1,2,2,1,1]
[[[.,[.,.]],[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]] => [2,1,4,3,7,6,10,9,11,8,12,5] => [2,1,4,3,12,7,6,11,10,9,8,5] => [2,2,1,2,1,2,1,1]
[[[.,[.,.]],[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]] => [2,1,4,3,8,7,9,6,11,10,12,5] => [2,1,4,3,12,9,8,7,6,11,10,5] => [2,2,1,1,2,1,2,1]
[[[.,[.,.]],[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]] => [2,1,4,3,7,6,9,8,11,10,12,5] => [2,1,4,3,12,7,6,9,8,11,10,5] => [2,2,1,2,2,2,1]
[[.,[[.,[[.,[.,.]],.]],.]],[[.,[[.,[.,.]],.]],.]] => [4,3,5,2,6,1,10,9,11,8,12,7] => [6,5,4,3,2,1,12,11,10,9,8,7] => [1,1,2,1,1,1,1,2,1,1]
[[.,[[.,[[.,[.,.]],.]],.]],[[[.,[.,.]],[.,.]],.]] => [4,3,5,2,6,1,9,8,11,10,12,7] => [6,5,4,3,2,1,12,9,8,11,10,7] => [1,1,2,1,1,1,2,2,1]
[[.,[[[.,[.,.]],[.,.]],.]],[[.,[[.,[.,.]],.]],.]] => [3,2,5,4,6,1,10,9,11,8,12,7] => [6,3,2,5,4,1,12,11,10,9,8,7] => [1,2,2,1,1,1,2,1,1]
[[.,[[[.,[.,.]],[.,.]],.]],[[[.,[.,.]],[.,.]],.]] => [3,2,5,4,6,1,9,8,11,10,12,7] => [6,3,2,5,4,1,12,9,8,11,10,7] => [1,2,2,1,1,2,2,1]
[[[.,[.,.]],[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]] => [2,1,5,4,6,3,10,9,11,8,12,7] => [2,1,6,5,4,3,12,11,10,9,8,7] => [2,1,2,1,1,1,2,1,1]
[[[.,[.,.]],[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]] => [2,1,5,4,6,3,9,8,11,10,12,7] => [2,1,6,5,4,3,12,9,8,11,10,7] => [2,1,2,1,1,2,2,1]
[[[.,[[.,[.,.]],.]],[.,.]],[[.,[[.,[.,.]],.]],.]] => [3,2,4,1,6,5,10,9,11,8,12,7] => [4,3,2,1,6,5,12,11,10,9,8,7] => [1,2,1,2,1,1,2,1,1]
[[[.,[[.,[.,.]],.]],[.,.]],[[[.,[.,.]],[.,.]],.]] => [3,2,4,1,6,5,9,8,11,10,12,7] => [4,3,2,1,6,5,12,9,8,11,10,7] => [1,2,1,2,1,2,2,1]
[[[[.,[.,.]],[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]] => [2,1,4,3,6,5,10,9,11,8,12,7] => [2,1,4,3,6,5,12,11,10,9,8,7] => [2,2,2,1,1,2,1,1]
[[[[.,[.,.]],[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]] => [2,1,4,3,6,5,9,8,11,10,12,7] => [2,1,4,3,6,5,12,9,8,11,10,7] => [2,2,2,1,2,2,1]
[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[[.,[.,.]],.]] => [5,4,6,3,7,2,8,1,11,10,12,9] => [8,7,6,5,4,3,2,1,12,11,10,9] => [1,1,1,2,1,1,1,1,2,1]
[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[[.,[.,.]],.]] => [4,3,6,5,7,2,8,1,11,10,12,9] => [8,7,4,3,6,5,2,1,12,11,10,9] => [1,1,2,2,1,1,1,2,1]
[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[[.,[.,.]],.]] => [3,2,6,5,7,4,8,1,11,10,12,9] => [8,3,2,7,6,5,4,1,12,11,10,9] => [1,2,1,2,1,1,1,2,1]
[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[[.,[.,.]],.]] => [4,3,5,2,7,6,8,1,11,10,12,9] => [8,5,4,3,2,7,6,1,12,11,10,9] => [1,1,2,1,2,1,1,2,1]
[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[[.,[.,.]],.]] => [3,2,5,4,7,6,8,1,11,10,12,9] => [8,3,2,5,4,7,6,1,12,11,10,9] => [1,2,2,2,1,1,2,1]
[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]] => [2,1,6,5,7,4,8,3,11,10,12,9] => [2,1,8,7,6,5,4,3,12,11,10,9] => [2,1,1,2,1,1,1,2,1]
[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]] => [2,1,5,4,7,6,8,3,11,10,12,9] => [2,1,8,5,4,7,6,3,12,11,10,9] => [2,1,2,2,1,1,2,1]
[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[[.,[.,.]],.]] => [3,2,4,1,7,6,8,5,11,10,12,9] => [4,3,2,1,8,7,6,5,12,11,10,9] => [1,2,1,1,2,1,1,2,1]
[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]] => [2,1,4,3,7,6,8,5,11,10,12,9] => [2,1,4,3,8,7,6,5,12,11,10,9] => [2,2,1,2,1,1,2,1]
[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[[.,[.,.]],.]] => [4,3,5,2,6,1,8,7,11,10,12,9] => [6,5,4,3,2,1,8,7,12,11,10,9] => [1,1,2,1,1,2,1,2,1]
[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[[.,[.,.]],.]] => [3,2,5,4,6,1,8,7,11,10,12,9] => [6,3,2,5,4,1,8,7,12,11,10,9] => [1,2,2,1,2,1,2,1]
[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]] => [2,1,5,4,6,3,8,7,11,10,12,9] => [2,1,6,5,4,3,8,7,12,11,10,9] => [2,1,2,1,2,1,2,1]
[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[[.,[.,.]],.]] => [3,2,4,1,6,5,8,7,11,10,12,9] => [4,3,2,1,6,5,8,7,12,11,10,9] => [1,2,1,2,2,1,2,1]
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]] => [2,1,4,3,6,5,8,7,11,10,12,9] => [2,1,4,3,6,5,8,7,12,11,10,9] => [2,2,2,2,1,2,1]
[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],[.,.]] => [6,5,7,4,8,3,9,2,10,1,12,11] => [10,9,8,7,6,5,4,3,2,1,12,11] => [1,1,1,1,2,1,1,1,1,2]
[[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]],[.,.]] => [5,4,7,6,8,3,9,2,10,1,12,11] => [10,9,8,5,4,7,6,3,2,1,12,11] => [1,1,1,2,2,1,1,1,2]
[[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]],[.,.]] => [4,3,7,6,8,5,9,2,10,1,12,11] => [10,9,4,3,8,7,6,5,2,1,12,11] => [1,1,2,1,2,1,1,1,2]
[[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]],[.,.]] => [5,4,6,3,8,7,9,2,10,1,12,11] => [10,9,6,5,4,3,8,7,2,1,12,11] => [1,1,1,2,1,2,1,1,2]
[[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]],[.,.]] => [4,3,6,5,8,7,9,2,10,1,12,11] => [10,9,4,3,6,5,8,7,2,1,12,11] => [1,1,2,2,2,1,1,2]
[[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]],[.,.]] => [3,2,7,6,8,5,9,4,10,1,12,11] => [10,3,2,9,8,7,6,5,4,1,12,11] => [1,2,1,1,2,1,1,1,2]
[[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]],[.,.]] => [3,2,6,5,8,7,9,4,10,1,12,11] => [10,3,2,9,6,5,8,7,4,1,12,11] => [1,2,1,2,2,1,1,2]
[[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]],[.,.]] => [4,3,5,2,8,7,9,6,10,1,12,11] => [10,5,4,3,2,9,8,7,6,1,12,11] => [1,1,2,1,1,2,1,1,2]
[[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]],[.,.]] => [3,2,5,4,8,7,9,6,10,1,12,11] => [10,3,2,5,4,9,8,7,6,1,12,11] => [1,2,2,1,2,1,1,2]
[[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]],[.,.]] => [5,4,6,3,7,2,9,8,10,1,12,11] => [10,7,6,5,4,3,2,9,8,1,12,11] => [1,1,1,2,1,1,2,1,2]
[[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]],[.,.]] => [4,3,6,5,7,2,9,8,10,1,12,11] => [10,7,4,3,6,5,2,9,8,1,12,11] => [1,1,2,2,1,2,1,2]
[[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]],[.,.]] => [3,2,6,5,7,4,9,8,10,1,12,11] => [10,3,2,7,6,5,4,9,8,1,12,11] => [1,2,1,2,1,2,1,2]
[[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]],[.,.]] => [4,3,5,2,7,6,9,8,10,1,12,11] => [10,5,4,3,2,7,6,9,8,1,12,11] => [1,1,2,1,2,2,1,2]
[[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]],[.,.]] => [3,2,5,4,7,6,9,8,10,1,12,11] => [10,3,2,5,4,7,6,9,8,1,12,11] => [1,2,2,2,2,1,2]
[[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]] => [2,1,7,6,8,5,9,4,10,3,12,11] => [2,1,10,9,8,7,6,5,4,3,12,11] => [2,1,1,1,2,1,1,1,2]
[[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]] => [2,1,6,5,8,7,9,4,10,3,12,11] => [2,1,10,9,6,5,8,7,4,3,12,11] => [2,1,1,2,2,1,1,2]
[[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]] => [2,1,5,4,8,7,9,6,10,3,12,11] => [2,1,10,5,4,9,8,7,6,3,12,11] => [2,1,2,1,2,1,1,2]
[[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]] => [2,1,6,5,7,4,9,8,10,3,12,11] => [2,1,10,7,6,5,4,9,8,3,12,11] => [2,1,1,2,1,2,1,2]
[[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]] => [2,1,5,4,7,6,9,8,10,3,12,11] => [2,1,10,5,4,7,6,9,8,3,12,11] => [2,1,2,2,2,1,2]
[[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]],[.,.]] => [3,2,4,1,8,7,9,6,10,5,12,11] => [4,3,2,1,10,9,8,7,6,5,12,11] => [1,2,1,1,1,2,1,1,2]
[[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]],[.,.]] => [3,2,4,1,7,6,9,8,10,5,12,11] => [4,3,2,1,10,7,6,9,8,5,12,11] => [1,2,1,1,2,2,1,2]
[[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]] => [2,1,4,3,8,7,9,6,10,5,12,11] => [2,1,4,3,10,9,8,7,6,5,12,11] => [2,2,1,1,2,1,1,2]
[[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]] => [2,1,4,3,7,6,9,8,10,5,12,11] => [2,1,4,3,10,7,6,9,8,5,12,11] => [2,2,1,2,2,1,2]
[[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]],[.,.]] => [4,3,5,2,6,1,9,8,10,7,12,11] => [6,5,4,3,2,1,10,9,8,7,12,11] => [1,1,2,1,1,1,2,1,2]
[[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]],[.,.]] => [3,2,5,4,6,1,9,8,10,7,12,11] => [6,3,2,5,4,1,10,9,8,7,12,11] => [1,2,2,1,1,2,1,2]
[[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]] => [2,1,5,4,6,3,9,8,10,7,12,11] => [2,1,6,5,4,3,10,9,8,7,12,11] => [2,1,2,1,1,2,1,2]
[[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]],[.,.]] => [3,2,4,1,6,5,9,8,10,7,12,11] => [4,3,2,1,6,5,10,9,8,7,12,11] => [1,2,1,2,1,2,1,2]
[[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]] => [2,1,4,3,6,5,9,8,10,7,12,11] => [2,1,4,3,6,5,10,9,8,7,12,11] => [2,2,2,1,2,1,2]
[[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]],[.,.]] => [5,4,6,3,7,2,8,1,10,9,12,11] => [8,7,6,5,4,3,2,1,10,9,12,11] => [1,1,1,2,1,1,1,2,2]
[[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]],[.,.]] => [4,3,6,5,7,2,8,1,10,9,12,11] => [8,7,4,3,6,5,2,1,10,9,12,11] => [1,1,2,2,1,1,2,2]
[[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]],[.,.]] => [3,2,6,5,7,4,8,1,10,9,12,11] => [8,3,2,7,6,5,4,1,10,9,12,11] => [1,2,1,2,1,1,2,2]
[[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],[.,.]] => [4,3,5,2,7,6,8,1,10,9,12,11] => [8,5,4,3,2,7,6,1,10,9,12,11] => [1,1,2,1,2,1,2,2]
[[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]],[.,.]] => [3,2,5,4,7,6,8,1,10,9,12,11] => [8,3,2,5,4,7,6,1,10,9,12,11] => [1,2,2,2,1,2,2]
[[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]] => [2,1,6,5,7,4,8,3,10,9,12,11] => [2,1,8,7,6,5,4,3,10,9,12,11] => [2,1,1,2,1,1,2,2]
[[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]] => [2,1,5,4,7,6,8,3,10,9,12,11] => [2,1,8,5,4,7,6,3,10,9,12,11] => [2,1,2,2,1,2,2]
[[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]],[.,.]] => [3,2,4,1,7,6,8,5,10,9,12,11] => [4,3,2,1,8,7,6,5,10,9,12,11] => [1,2,1,1,2,1,2,2]
[[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]] => [2,1,4,3,7,6,8,5,10,9,12,11] => [2,1,4,3,8,7,6,5,10,9,12,11] => [2,2,1,2,1,2,2]
[[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]],[.,.]] => [4,3,5,2,6,1,8,7,10,9,12,11] => [6,5,4,3,2,1,8,7,10,9,12,11] => [1,1,2,1,1,2,2,2]
[[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]],[.,.]] => [3,2,5,4,6,1,8,7,10,9,12,11] => [6,3,2,5,4,1,8,7,10,9,12,11] => [1,2,2,1,2,2,2]
[[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]] => [2,1,5,4,6,3,8,7,10,9,12,11] => [2,1,6,5,4,3,8,7,10,9,12,11] => [2,1,2,1,2,2,2]
[[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]],[.,.]] => [3,2,4,1,6,5,8,7,10,9,12,11] => [4,3,2,1,6,5,8,7,10,9,12,11] => [1,2,1,2,2,2,2]
[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,2,9,8,7,6,5,4,3] => [1,2,4,5,6,7,8,9,3] => [2,7]
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.] => [7,6,5,4,3,2,1,8,9] => [2,3,4,5,6,7,1,8,9] => [9]
[[[[[[[[.,[.,.]],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9] => [2,1,3,4,5,6,7,8,9] => [9]
[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9,10] => [2,1,3,4,5,6,7,8,9,10] => [10]
[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]] => [2,9,8,7,6,5,4,3,1] => [3,2,4,5,6,7,8,9,1] => [2,7]
[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9,10,11] => [2,1,3,4,5,6,7,8,9,10,11] => [11]
[[[[[[[.,[[.,.],.]],.],.],.],.],.],.] => [2,3,1,4,5,6,7,8,9] => [3,2,1,4,5,6,7,8,9] => [2,7]
[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.] => [2,3,1,4,5,6,7,8,9,10] => [3,2,1,4,5,6,7,8,9,10] => [2,8]
[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,2,10,9,8,7,6,5,4,3] => [1,2,4,5,6,7,8,9,10,3] => [2,8]
[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => [1,2,3,4,5,6,7,10,9,8] => [1,2,3,4,5,6,7,9,10,8] => [7,3]
[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] => [1,2,3,4,5,9,8,7,6] => [1,2,3,4,5,7,8,9,6] => [5,4]
[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => [1,2,3,4,9,8,7,6,5] => [1,2,3,4,6,7,8,9,5] => [4,5]
[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,2,3,9,8,7,6,5,4] => [1,2,3,5,6,7,8,9,4] => [3,6]
[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]] => [1,2,3,4,5,6,10,9,8,7] => [1,2,3,4,5,6,8,9,10,7] => [6,4]
[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]] => [1,2,3,4,5,10,9,8,7,6] => [1,2,3,4,5,7,8,9,10,6] => [5,5]
[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,2,3,4,10,9,8,7,6,5] => [1,2,3,4,6,7,8,9,10,5] => [4,6]
[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,2,3,10,9,8,7,6,5,4] => [1,2,3,5,6,7,8,9,10,4] => [3,7]
[[[[[.,[[.,[[.,.],.]],.]],.],.],.],.] => [3,4,2,5,1,6,7,8,9] => [5,4,3,2,1,6,7,8,9] => [1,2,1,5]
[.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]] => [2,3,9,8,7,6,5,4,1] => [4,2,3,5,6,7,8,9,1] => [3,6]
Map
to 312-avoiding permutation
Description
Return a 312-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 minimal element of this Sylvester class.
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 minimal element of this Sylvester class.
Map
descent views to invisible inversion bottoms
Description
Return a permutation whose multiset of invisible inversion bottoms is the multiset of descent views of the given permutation.
An invisible inversion of a permutation σ is a pair i<j such that i<σ(j)<σ(i). The element σ(j) is then an invisible inversion bottom.
A descent view in a permutation π is an element π(j) such that π(i+1)<π(j)<π(i), and additionally the smallest element in the decreasing run containing π(i) is smaller than the smallest element in the decreasing run containing π(j).
This map is a bijection χ:Sn→Sn, such that
An invisible inversion of a permutation σ is a pair i<j such that i<σ(j)<σ(i). The element σ(j) is then an invisible inversion bottom.
A descent view in a permutation π is an element π(j) such that π(i+1)<π(j)<π(i), and additionally the smallest element in the decreasing run containing π(i) is smaller than the smallest element in the decreasing run containing π(j).
This map is a bijection χ:Sn→Sn, such that
- the multiset of descent views in π is the multiset of invisible inversion bottoms in χ(π),
- the set of left-to-right maxima of π is the set of maximal elements in the cycles of χ(π),
- the set of global ascent of π is the set of global ascent of χ(π),
- the set of maximal elements in the decreasing runs of π is the set of weak deficiency positions of χ(π), and
- the set of minimal elements in the decreasing runs of π is the set of weak deficiency values of χ(π).
Map
DEX composition
Description
The DEX composition of a permutation.
Let π be a permutation in Sn. Let ˉπ be the word in the ordered set ˉ1<⋯<ˉn<1⋯<n obtained from π by replacing every excedance π(i)>i by ¯π(i). Then the DEX set of π is the set of indices 1≤i<n such that ˉπ(i)>ˉπ(i+1). Finally, the DEX composition c1,…,ck of n corresponds to the DEX subset {c1,c1+c2,…,c1+⋯+ck−1}.
The (quasi)symmetric function
∑π∈Sλ,jFDEX(π),
where the sum is over the set of permutations of cycle type λ with j excedances, is the Eulerian quasisymmetric function.
Let π be a permutation in Sn. Let ˉπ be the word in the ordered set ˉ1<⋯<ˉn<1⋯<n obtained from π by replacing every excedance π(i)>i by ¯π(i). Then the DEX set of π is the set of indices 1≤i<n such that ˉπ(i)>ˉπ(i+1). Finally, the DEX composition c1,…,ck of n corresponds to the DEX subset {c1,c1+c2,…,c1+⋯+ck−1}.
The (quasi)symmetric function
∑π∈Sλ,jFDEX(π),
where the sum is over the set of permutations of cycle type λ with j excedances, is the Eulerian quasisymmetric function.
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