- FindStat

Identifier

Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00240: Permutations —weak exceedance partition⟶ Set partitions

Images

[.,.] => [1] => [1] => {{1}}

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 953 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[.,[.,[.,[[.,.],.]]]],[[.,.],.]] => [4,5,3,2,1,7,8,6] => [2,3,5,4,1,8,7,6] => {{1,2,3,5},{4},{6,8},{7}}

[[.,[.,[[.,.],[.,.]]]],[[.,.],.]] => [3,5,4,2,1,7,8,6] => [2,4,3,5,1,8,7,6] => {{1,2,4,5},{3},{6,8},{7}}

[[.,[.,[[.,[.,.]],.]]],[[.,.],.]] => [4,3,5,2,1,7,8,6] => [2,5,4,3,1,8,7,6] => {{1,2,5},{3,4},{6,8},{7}}

[[.,[.,[[[.,.],.],.]]],[[.,.],.]] => [3,4,5,2,1,7,8,6] => [2,5,3,4,1,8,7,6] => {{1,2,5},{3},{4},{6,8},{7}}

[[.,[[.,.],[.,[.,.]]]],[[.,.],.]] => [2,5,4,3,1,7,8,6] => [3,2,4,5,1,8,7,6] => {{1,3,4,5},{2},{6,8},{7}}

[[.,[[.,.],[[.,.],.]]],[[.,.],.]] => [2,4,5,3,1,7,8,6] => [3,2,5,4,1,8,7,6] => {{1,3,5},{2},{4},{6,8},{7}}

[[.,[[.,[.,.]],[.,.]]],[[.,.],.]] => [3,2,5,4,1,7,8,6] => [4,3,2,5,1,8,7,6] => {{1,4,5},{2,3},{6,8},{7}}

[[.,[[[.,.],.],[.,.]]],[[.,.],.]] => [2,3,5,4,1,7,8,6] => [4,2,3,5,1,8,7,6] => {{1,4,5},{2},{3},{6,8},{7}}

[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]] => [4,3,2,5,1,8,7,6] => [5,3,4,2,1,7,8,6] => {{1,5},{2,3,4},{6,7,8}}

[[.,[[.,[.,[.,.]]],.]],[[.,.],.]] => [4,3,2,5,1,7,8,6] => [5,3,4,2,1,8,7,6] => {{1,5},{2,3,4},{6,8},{7}}

[[.,[[.,[[.,.],.]],.]],[.,[.,.]]] => [3,4,2,5,1,8,7,6] => [5,4,3,2,1,7,8,6] => {{1,5},{2,4},{3},{6,7,8}}

[[.,[[.,[[.,.],.]],.]],[[.,.],.]] => [3,4,2,5,1,7,8,6] => [5,4,3,2,1,8,7,6] => {{1,5},{2,4},{3},{6,8},{7}}

[[.,[[[.,.],[.,.]],.]],[[.,.],.]] => [2,4,3,5,1,7,8,6] => [5,2,4,3,1,8,7,6] => {{1,5},{2},{3,4},{6,8},{7}}

[[.,[[[.,[.,.]],.],.]],[[.,.],.]] => [3,2,4,5,1,7,8,6] => [5,3,2,4,1,8,7,6] => {{1,5},{2,3},{4},{6,8},{7}}

[[.,[[[[.,.],.],.],.]],[[.,.],.]] => [2,3,4,5,1,7,8,6] => [5,2,3,4,1,8,7,6] => {{1,5},{2},{3},{4},{6,8},{7}}

[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] => [4,3,2,1,5,8,7,6] => [2,3,4,1,5,7,8,6] => {{1,2,3,4},{5},{6,7,8}}

[[[.,[.,[.,[.,.]]]],.],[[.,.],.]] => [4,3,2,1,5,7,8,6] => [2,3,4,1,5,8,7,6] => {{1,2,3,4},{5},{6,8},{7}}

[[[.,[[.,.],[.,.]]],.],[.,[.,.]]] => [2,4,3,1,5,8,7,6] => [3,2,4,1,5,7,8,6] => {{1,3,4},{2},{5},{6,7,8}}

[[[.,[[.,.],[.,.]]],.],[[.,.],.]] => [2,4,3,1,5,7,8,6] => [3,2,4,1,5,8,7,6] => {{1,3,4},{2},{5},{6,8},{7}}

[[[.,[[.,[.,.]],.]],.],[.,[.,.]]] => [3,2,4,1,5,8,7,6] => [4,3,2,1,5,7,8,6] => {{1,4},{2,3},{5},{6,7,8}}

[[[.,[[.,[.,.]],.]],.],[[.,.],.]] => [3,2,4,1,5,7,8,6] => [4,3,2,1,5,8,7,6] => {{1,4},{2,3},{5},{6,8},{7}}

[[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [3,2,1,4,5,8,7,6] => [2,3,1,4,5,7,8,6] => {{1,2,3},{4},{5},{6,7,8}}

[[[[.,[[.,.],.]],.],.],[[.,.],.]] => [2,3,1,4,5,7,8,6] => [3,2,1,4,5,8,7,6] => {{1,3},{2},{4},{5},{6,8},{7}}

[[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,2,3,4,5,8,7,6] => [1,2,3,4,5,7,8,6] => {{1},{2},{3},{4},{5},{6,7,8}}

[[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,2,3,4,5,7,8,6] => [1,2,3,4,5,8,7,6] => {{1},{2},{3},{4},{5},{6,8},{7}}

[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [6,5,4,3,2,1,8,7] => [2,3,4,5,6,1,8,7] => {{1,2,3,4,5,6},{7,8}}

[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]] => [5,4,6,3,2,1,8,7] => [2,3,6,5,4,1,8,7] => {{1,2,3,6},{4,5},{7,8}}

[[.,[.,[.,[[[.,.],.],.]]]],[.,.]] => [4,5,6,3,2,1,8,7] => [2,3,6,4,5,1,8,7] => {{1,2,3,6},{4},{5},{7,8}}

[[.,[.,[[.,.],[[.,.],.]]]],[.,.]] => [3,5,6,4,2,1,8,7] => [2,4,3,6,5,1,8,7] => {{1,2,4,6},{3},{5},{7,8}}

[[.,[[.,.],[[.,.],[.,.]]]],[.,.]] => [2,4,6,5,3,1,8,7] => [3,2,5,4,6,1,8,7] => {{1,3,5,6},{2},{4},{7,8}}

[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]] => [3,2,6,5,4,1,8,7] => [4,3,2,5,6,1,8,7] => {{1,4,5,6},{2,3},{7,8}}

[[.,[[.,[[.,.],.]],[.,.]]],[.,.]] => [3,4,2,6,5,1,8,7] => [5,4,3,2,6,1,8,7] => {{1,5,6},{2,4},{3},{7,8}}

[[.,[[[.,.],[.,.]],[.,.]]],[.,.]] => [2,4,3,6,5,1,8,7] => [5,2,4,3,6,1,8,7] => {{1,5,6},{2},{3,4},{7,8}}

[[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => [4,3,5,2,6,1,8,7] => [6,5,4,3,2,1,8,7] => {{1,6},{2,5},{3,4},{7,8}}

[[.,[[[.,[.,.]],[.,.]],.]],[.,.]] => [3,2,5,4,6,1,8,7] => [6,3,2,5,4,1,8,7] => {{1,6},{2,3},{4,5},{7,8}}

[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [2,1,6,5,4,3,8,7] => [2,1,4,5,6,3,8,7] => {{1,2},{3,4,5,6},{7,8}}

[[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [2,1,5,6,4,3,8,7] => [2,1,4,6,5,3,8,7] => {{1,2},{3,4,6},{5},{7,8}}

[[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [2,1,4,6,5,3,8,7] => [2,1,5,4,6,3,8,7] => {{1,2},{3,5,6},{4},{7,8}}

[[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [2,1,5,4,6,3,8,7] => [2,1,6,5,4,3,8,7] => {{1,2},{3,6},{4,5},{7,8}}

[[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [2,1,4,5,6,3,8,7] => [2,1,6,4,5,3,8,7] => {{1,2},{3,6},{4},{5},{7,8}}

[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [4,3,2,1,6,5,8,7] => [2,3,4,1,6,5,8,7] => {{1,2,3,4},{5,6},{7,8}}

[[[.,[.,[[.,.],.]]],[.,.]],[.,.]] => [3,4,2,1,6,5,8,7] => [2,4,3,1,6,5,8,7] => {{1,2,4},{3},{5,6},{7,8}}

[[[.,[[.,.],[.,.]]],[.,.]],[.,.]] => [2,4,3,1,6,5,8,7] => [3,2,4,1,6,5,8,7] => {{1,3,4},{2},{5,6},{7,8}}

[[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => [3,2,4,1,6,5,8,7] => [4,3,2,1,6,5,8,7] => {{1,4},{2,3},{5,6},{7,8}}

[[[.,[[[.,.],.],.]],[.,.]],[.,.]] => [2,3,4,1,6,5,8,7] => [4,2,3,1,6,5,8,7] => {{1,4},{2},{3},{5,6},{7,8}}

[[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => {{1,2},{3,4},{5,6},{7,8}}

[[[.,[[.,[[.,.],.]],.]],.],[.,.]] => [3,4,2,5,1,6,8,7] => [5,4,3,2,1,6,8,7] => {{1,5},{2,4},{3},{6},{7,8}}

[[[.,[[[.,[.,.]],.],.]],.],[.,.]] => [3,2,4,5,1,6,8,7] => [5,3,2,4,1,6,8,7] => {{1,5},{2,3},{4},{6},{7,8}}

[[[[.,[.,.]],[[.,.],.]],.],[.,.]] => [2,1,4,5,3,6,8,7] => [2,1,5,4,3,6,8,7] => {{1,2},{3,5},{4},{6},{7,8}}

[[[[.,[.,[.,[.,.]]]],.],.],[.,.]] => [4,3,2,1,5,6,8,7] => [2,3,4,1,5,6,8,7] => {{1,2,3,4},{5},{6},{7,8}}

[[[[.,[[.,.],[.,.]]],.],.],[.,.]] => [2,4,3,1,5,6,8,7] => [3,2,4,1,5,6,8,7] => {{1,3,4},{2},{5},{6},{7,8}}

[[[[.,[[.,[.,.]],.]],.],.],[.,.]] => [3,2,4,1,5,6,8,7] => [4,3,2,1,5,6,8,7] => {{1,4},{2,3},{5},{6},{7,8}}

[[[[[[.,[.,.]],.],.],.],.],[.,.]] => [2,1,3,4,5,6,8,7] => [2,1,3,4,5,6,8,7] => {{1,2},{3},{4},{5},{6},{7,8}}

[[[[[[[.,.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => {{1},{2},{3},{4},{5},{6},{7,8}}

[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [7,6,5,4,3,2,1,8] => [2,3,4,5,6,7,1,8] => {{1,2,3,4,5,6,7},{8}}

[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => [6,7,5,4,3,2,1,8] => [2,3,4,5,7,6,1,8] => {{1,2,3,4,5,7},{6},{8}}

[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.] => [2,7,6,5,4,3,1,8] => [3,2,4,5,6,7,1,8] => {{1,3,4,5,6,7},{2},{8}}

[[.,[[.,.],[[.,.],[[.,.],.]]]],.] => [2,4,6,7,5,3,1,8] => [3,2,5,4,7,6,1,8] => {{1,3,5,7},{2},{4},{6},{8}}

[[.,[[.,.],[[.,[[.,.],.]],.]]],.] => [2,5,6,4,7,3,1,8] => [3,2,7,6,5,4,1,8] => {{1,3,7},{2},{4,6},{5},{8}}

[[.,[[.,.],[[[.,[.,.]],.],.]]],.] => [2,5,4,6,7,3,1,8] => [3,2,7,5,4,6,1,8] => {{1,3,7},{2},{4,5},{6},{8}}

[[.,[[.,[[.,.],.]],[.,[.,.]]]],.] => [3,4,2,7,6,5,1,8] => [5,4,3,2,6,7,1,8] => {{1,5,6,7},{2,4},{3},{8}}

[[.,[[.,[[.,.],.]],[[.,.],.]]],.] => [3,4,2,6,7,5,1,8] => [5,4,3,2,7,6,1,8] => {{1,5,7},{2,4},{3},{6},{8}}

[[.,[[.,[.,[[.,[.,.]],.]]],.]],.] => [5,4,6,3,2,7,1,8] => [7,3,6,5,4,2,1,8] => {{1,7},{2,3,6},{4,5},{8}}

[[.,[[.,[[.,.],[[.,.],.]]],.]],.] => [3,5,6,4,2,7,1,8] => [7,4,3,6,5,2,1,8] => {{1,7},{2,4,6},{3},{5},{8}}

[[.,[[.,[[.,[[.,.],.]],.]],.]],.] => [4,5,3,6,2,7,1,8] => [7,6,5,4,3,2,1,8] => {{1,7},{2,6},{3,5},{4},{8}}

[[.,[[[[.,.],.],[[.,.],.]],.]],.] => [2,3,5,6,4,7,1,8] => [7,2,3,6,5,4,1,8] => {{1,7},{2},{3},{4,6},{5},{8}}

[[.,[[[[[.,.],.],.],[.,.]],.]],.] => [2,3,4,6,5,7,1,8] => [7,2,3,4,6,5,1,8] => {{1,7},{2},{3},{4},{5,6},{8}}

[[[.,.],[.,[.,[.,[[.,.],.]]]]],.] => [1,6,7,5,4,3,2,8] => [1,3,4,5,7,6,2,8] => {{1},{2,3,4,5,7},{6},{8}}

[[[.,.],[.,[[[[.,.],.],.],.]]],.] => [1,4,5,6,7,3,2,8] => [1,3,7,4,5,6,2,8] => {{1},{2,3,7},{4},{5},{6},{8}}

[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.] => [3,2,1,7,6,5,4,8] => [2,3,1,5,6,7,4,8] => {{1,2,3},{4,5,6,7},{8}}

[[[.,[[.,.],.]],[[[.,.],.],.]],.] => [2,3,1,5,6,7,4,8] => [3,2,1,7,5,6,4,8] => {{1,3},{2},{4,7},{5},{6},{8}}

[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.] => [4,3,2,1,7,6,5,8] => [2,3,4,1,6,7,5,8] => {{1,2,3,4},{5,6,7},{8}}

[[[.,[.,[.,[.,.]]]],[[.,.],.]],.] => [4,3,2,1,6,7,5,8] => [2,3,4,1,7,6,5,8] => {{1,2,3,4},{5,7},{6},{8}}

[[[.,[[.,[.,.]],.]],[.,[.,.]]],.] => [3,2,4,1,7,6,5,8] => [4,3,2,1,6,7,5,8] => {{1,4},{2,3},{5,6,7},{8}}

[[[.,[[.,[.,.]],.]],[[.,.],.]],.] => [3,2,4,1,6,7,5,8] => [4,3,2,1,7,6,5,8] => {{1,4},{2,3},{5,7},{6},{8}}

[[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,4,3,2,7,6,5,8] => [1,3,4,2,6,7,5,8] => {{1},{2,3,4},{5,6,7},{8}}

[[[[.,.],[[.,.],.]],[[.,.],.]],.] => [1,3,4,2,6,7,5,8] => [1,4,3,2,7,6,5,8] => {{1},{2,4},{3},{5,7},{6},{8}}

[[[[.,[[.,.],.]],.],[[.,.],.]],.] => [2,3,1,4,6,7,5,8] => [3,2,1,4,7,6,5,8] => {{1,3},{2},{4},{5,7},{6},{8}}

[[[.,[[.,[[.,.],.]],.]],[.,.]],.] => [3,4,2,5,1,7,6,8] => [5,4,3,2,1,7,6,8] => {{1,5},{2,4},{3},{6,7},{8}}

[[[.,[[[.,.],[.,.]],.]],[.,.]],.] => [2,4,3,5,1,7,6,8] => [5,2,4,3,1,7,6,8] => {{1,5},{2},{3,4},{6,7},{8}}

[[[[.,[.,[.,.]]],[.,.]],[.,.]],.] => [3,2,1,5,4,7,6,8] => [2,3,1,5,4,7,6,8] => {{1,2,3},{4,5},{6,7},{8}}

[[[[.,[[.,.],.]],[.,.]],[.,.]],.] => [2,3,1,5,4,7,6,8] => [3,2,1,5,4,7,6,8] => {{1,3},{2},{4,5},{6,7},{8}}

[[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,3,2,5,4,7,6,8] => [1,3,2,5,4,7,6,8] => {{1},{2,3},{4,5},{6,7},{8}}

[[[[[[.,.],.],.],[.,.]],[.,.]],.] => [1,2,3,5,4,7,6,8] => [1,2,3,5,4,7,6,8] => {{1},{2},{3},{4,5},{6,7},{8}}

[[[[.,[.,[.,[.,.]]]],.],[.,.]],.] => [4,3,2,1,5,7,6,8] => [2,3,4,1,5,7,6,8] => {{1,2,3,4},{5},{6,7},{8}}

[[[[.,[[.,.],[.,.]]],.],[.,.]],.] => [2,4,3,1,5,7,6,8] => [3,2,4,1,5,7,6,8] => {{1,3,4},{2},{5},{6,7},{8}}

[[[[.,[[.,[.,.]],.]],.],[.,.]],.] => [3,2,4,1,5,7,6,8] => [4,3,2,1,5,7,6,8] => {{1,4},{2,3},{5},{6,7},{8}}

[[[[[[.,.],[.,.]],.],.],[.,.]],.] => [1,3,2,4,5,7,6,8] => [1,3,2,4,5,7,6,8] => {{1},{2,3},{4},{5},{6,7},{8}}

[[[[[[[.,.],.],.],.],.],[.,.]],.] => [1,2,3,4,5,7,6,8] => [1,2,3,4,5,7,6,8] => {{1},{2},{3},{4},{5},{6,7},{8}}

[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.] => [6,5,4,3,2,1,7,8] => [2,3,4,5,6,1,7,8] => {{1,2,3,4,5,6},{7},{8}}

[[[.,[.,[.,[.,[[.,.],.]]]]],.],.] => [5,6,4,3,2,1,7,8] => [2,3,4,6,5,1,7,8] => {{1,2,3,4,6},{5},{7},{8}}

[[[.,[[[.,.],.],[.,[.,.]]]],.],.] => [2,3,6,5,4,1,7,8] => [4,2,3,5,6,1,7,8] => {{1,4,5,6},{2},{3},{7},{8}}

[[[.,[[.,[[.,.],.]],[.,.]]],.],.] => [3,4,2,6,5,1,7,8] => [5,4,3,2,6,1,7,8] => {{1,5,6},{2,4},{3},{7},{8}}

[[[.,[[[.,.],[.,.]],[.,.]]],.],.] => [2,4,3,6,5,1,7,8] => [5,2,4,3,6,1,7,8] => {{1,5,6},{2},{3,4},{7},{8}}

[[[.,[[.,[[.,[.,.]],.]],.]],.],.] => [4,3,5,2,6,1,7,8] => [6,5,4,3,2,1,7,8] => {{1,6},{2,5},{3,4},{7},{8}}

[[[.,[[[[.,.],.],[.,.]],.]],.],.] => [2,3,5,4,6,1,7,8] => [6,2,3,5,4,1,7,8] => {{1,6},{2},{3},{4,5},{7},{8}}

[[[[[.,.],.],[.,[[.,.],.]]],.],.] => [1,2,5,6,4,3,7,8] => [1,2,4,6,5,3,7,8] => {{1},{2},{3,4,6},{5},{7},{8}}

[[[[.,[.,[.,[.,.]]]],[.,.]],.],.] => [4,3,2,1,6,5,7,8] => [2,3,4,1,6,5,7,8] => {{1,2,3,4},{5,6},{7},{8}}

[[[[.,[[.,.],[.,.]]],[.,.]],.],.] => [2,4,3,1,6,5,7,8] => [3,2,4,1,6,5,7,8] => {{1,3,4},{2},{5,6},{7},{8}}

[[[[.,[[.,[.,.]],.]],[.,.]],.],.] => [3,2,4,1,6,5,7,8] => [4,3,2,1,6,5,7,8] => {{1,4},{2,3},{5,6},{7},{8}}

[[[[[[.,.],.],[.,.]],[.,.]],.],.] => [1,2,4,3,6,5,7,8] => [1,2,4,3,6,5,7,8] => {{1},{2},{3,4},{5,6},{7},{8}}

[[[[.,[.,[.,[.,[.,.]]]]],.],.],.] => [5,4,3,2,1,6,7,8] => [2,3,4,5,1,6,7,8] => {{1,2,3,4,5},{6},{7},{8}}

[[[[.,[[.,.],[[.,.],.]]],.],.],.] => [2,4,5,3,1,6,7,8] => [3,2,5,4,1,6,7,8] => {{1,3,5},{2},{4},{6},{7},{8}}

[[[[.,[[.,[[.,.],.]],.]],.],.],.] => [3,4,2,5,1,6,7,8] => [5,4,3,2,1,6,7,8] => {{1,5},{2,4},{3},{6},{7},{8}}

[[[[.,[[[.,.],[.,.]],.]],.],.],.] => [2,4,3,5,1,6,7,8] => [5,2,4,3,1,6,7,8] => {{1,5},{2},{3,4},{6},{7},{8}}

[[[[.,[[[[.,.],.],.],.]],.],.],.] => [2,3,4,5,1,6,7,8] => [5,2,3,4,1,6,7,8] => {{1,5},{2},{3},{4},{6},{7},{8}}

[[[[[[.,.],[.,.]],[.,.]],.],.],.] => [1,3,2,5,4,6,7,8] => [1,3,2,5,4,6,7,8] => {{1},{2,3},{4,5},{6},{7},{8}}

[[[[[[[.,.],.],.],[.,.]],.],.],.] => [1,2,3,5,4,6,7,8] => [1,2,3,5,4,6,7,8] => {{1},{2},{3},{4,5},{6},{7},{8}}

[[[[[.,[.,[.,[.,.]]]],.],.],.],.] => [4,3,2,1,5,6,7,8] => [2,3,4,1,5,6,7,8] => {{1,2,3,4},{5},{6},{7},{8}}

[[[[[.,[[.,.],[.,.]]],.],.],.],.] => [2,4,3,1,5,6,7,8] => [3,2,4,1,5,6,7,8] => {{1,3,4},{2},{5},{6},{7},{8}}

[[[[[.,[[.,[.,.]],.]],.],.],.],.] => [3,2,4,1,5,6,7,8] => [4,3,2,1,5,6,7,8] => {{1,4},{2,3},{5},{6},{7},{8}}

[[[[[[.,[[.,.],.]],.],.],.],.],.] => [2,3,1,4,5,6,7,8] => [3,2,1,4,5,6,7,8] => {{1,3},{2},{4},{5},{6},{7},{8}}

[[[[[[[.,.],[.,.]],.],.],.],.],.] => [1,3,2,4,5,6,7,8] => [1,3,2,4,5,6,7,8] => {{1},{2,3},{4},{5},{6},{7},{8}}

[[[[[[[.,[.,.]],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7,8] => {{1,2},{3},{4},{5},{6},{7},{8}}

[[[[[[[[.,.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => {{1},{2},{3},{4},{5},{6},{7},{8}}

[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [9,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,9,1] => {{1,2,3,4,5,6,7,8,9}}

[[[[[[[[[.,.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => {{1},{2},{3},{4},{5},{6},{7},{8},{9}}

[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [10,9,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,9,10,1] => {{1,2,3,4,5,6,7,8,9,10}}

[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => {{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}

[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [8,7,6,5,4,3,2,1,9] => [2,3,4,5,6,7,8,1,9] => {{1,2,3,4,5,6,7,8},{9}}

[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => [9,8,7,6,5,4,3,2,1,10] => [2,3,4,5,6,7,8,9,1,10] => {{1,2,3,4,5,6,7,8,9},{10}}

[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]] => [1,6,7,5,8,4,9,3,10,2] => [1,10,9,8,7,6,5,4,3,2] => {{1},{2,10},{3,9},{4,8},{5,7},{6}}

[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.] => [5,6,4,7,3,8,2,9,1,10] => [9,8,7,6,5,4,3,2,1,10] => {{1,9},{2,8},{3,7},{4,6},{5},{10}}

[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5,8,7,10,9] => [2,1,4,3,6,5,8,7,10,9] => {{1,2},{3,4},{5,6},{7,8},{9,10}}

[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5,8,7,10,9,12,11] => [2,1,4,3,6,5,8,7,10,9,12,11] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}

[[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,7,9,8] => [1,2,3,4,5,6,7,9,8] => {{1},{2},{3},{4},{5},{6},{7},{8,9}}

[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,7,8,10,9] => [1,2,3,4,5,6,7,8,10,9] => {{1},{2},{3},{4},{5},{6},{7},{8},{9,10}}

[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,7,8,9,11,10] => [1,2,3,4,5,6,7,8,9,11,10] => {{1},{2},{3},{4},{5},{6},{7},{8},{9},{10,11}}

[[[[[[[.,.],.],.],.],.],.],[[.,.],.]] => [1,2,3,4,5,6,8,9,7] => [1,2,3,4,5,6,9,8,7] => {{1},{2},{3},{4},{5},{6},{7,9},{8}}

[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => [1,2,3,4,5,6,9,8,7] => [1,2,3,4,5,6,8,9,7] => {{1},{2},{3},{4},{5},{6},{7,8,9}}

[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,9,8,7,6,5,4,3,2] => [1,3,4,5,6,7,8,9,2] => {{1},{2,3,4,5,6,7,8,9}}

[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [1,10,9,8,7,6,5,4,3,2] => [1,3,4,5,6,7,8,9,10,2] => {{1},{2,3,4,5,6,7,8,9,10}}

[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]] => [6,5,7,4,8,3,9,2,10,1] => [10,9,8,7,6,5,4,3,2,1] => {{1,10},{2,9},{3,8},{4,7},{5,6}}

[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,2,9,8,7,6,5,4,3] => [1,2,4,5,6,7,8,9,3] => {{1},{2},{3,4,5,6,7,8,9}}

[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.] => [7,6,5,4,3,2,1,8,9] => [2,3,4,5,6,7,1,8,9] => {{1,2,3,4,5,6,7},{8},{9}}

[[[[[[[[.,[.,.]],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9] => [2,1,3,4,5,6,7,8,9] => {{1,2},{3},{4},{5},{6},{7},{8},{9}}

[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9,10] => [2,1,3,4,5,6,7,8,9,10] => {{1,2},{3},{4},{5},{6},{7},{8},{9},{10}}

[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]] => [2,9,8,7,6,5,4,3,1] => [3,2,4,5,6,7,8,9,1] => {{1,3,4,5,6,7,8,9},{2}}

[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9,10,11] => [2,1,3,4,5,6,7,8,9,10,11] => {{1,2},{3},{4},{5},{6},{7},{8},{9},{10},{11}}

[[[[[[[.,[[.,.],.]],.],.],.],.],.],.] => [2,3,1,4,5,6,7,8,9] => [3,2,1,4,5,6,7,8,9] => {{1,3},{2},{4},{5},{6},{7},{8},{9}}

[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.] => [2,3,1,4,5,6,7,8,9,10] => [3,2,1,4,5,6,7,8,9,10] => {{1,3},{2},{4},{5},{6},{7},{8},{9},{10}}

[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,2,10,9,8,7,6,5,4,3] => [1,2,4,5,6,7,8,9,10,3] => {{1},{2},{3,4,5,6,7,8,9,10}}

[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => [1,2,3,4,5,6,7,10,9,8] => [1,2,3,4,5,6,7,9,10,8] => {{1},{2},{3},{4},{5},{6},{7},{8,9,10}}

[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] => [1,2,3,4,5,9,8,7,6] => [1,2,3,4,5,7,8,9,6] => {{1},{2},{3},{4},{5},{6,7,8,9}}

[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => [1,2,3,4,9,8,7,6,5] => [1,2,3,4,6,7,8,9,5] => {{1},{2},{3},{4},{5,6,7,8,9}}

[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,2,3,9,8,7,6,5,4] => [1,2,3,5,6,7,8,9,4] => {{1},{2},{3},{4,5,6,7,8,9}}

[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]] => [1,2,3,4,5,6,10,9,8,7] => [1,2,3,4,5,6,8,9,10,7] => {{1},{2},{3},{4},{5},{6},{7,8,9,10}}

[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]] => [1,2,3,4,5,10,9,8,7,6] => [1,2,3,4,5,7,8,9,10,6] => {{1},{2},{3},{4},{5},{6,7,8,9,10}}

[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,2,3,4,10,9,8,7,6,5] => [1,2,3,4,6,7,8,9,10,5] => {{1},{2},{3},{4},{5,6,7,8,9,10}}

[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,2,3,10,9,8,7,6,5,4] => [1,2,3,5,6,7,8,9,10,4] => {{1},{2},{3},{4,5,6,7,8,9,10}}

[[[[[.,[[.,[[.,.],.]],.]],.],.],.],.] => [3,4,2,5,1,6,7,8,9] => [5,4,3,2,1,6,7,8,9] => {{1,5},{2,4},{3},{6},{7},{8},{9}}

[.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]] => [2,3,9,8,7,6,5,4,1] => [4,2,3,5,6,7,8,9,1] => {{1,4,5,6,7,8,9},{2},{3}}

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.

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 $\sigma$ is a pair $i < j$ such that $i < \sigma(j) < \sigma(i)$. The element $\sigma(j)$ is then an invisible inversion bottom.
A descent view in a permutation $\pi$ is an element $\pi(j)$ such that $\pi(i+1) < \pi(j) < \pi(i)$, and additionally the smallest element in the decreasing run containing $\pi(i)$ is smaller than the smallest element in the decreasing run containing $\pi(j)$.
This map is a bijection $\chi:\mathfrak S_n \to \mathfrak S_n$, such that

the multiset of descent views in $\pi$ is the multiset of invisible inversion bottoms in $\chi(\pi)$,
the set of left-to-right maxima of $\pi$ is the set of maximal elements in the cycles of $\chi(\pi)$,
the set of global ascent of $\pi$ is the set of global ascent of $\chi(\pi)$,
the set of maximal elements in the decreasing runs of $\pi$ is the set of weak deficiency positions of $\chi(\pi)$, and
the set of minimal elements in the decreasing runs of $\pi$ is the set of weak deficiency values of $\chi(\pi)$.

Map

weak exceedance partition

Description

The set partition induced by the weak exceedances of a permutation.
This is the coarsest set partition that contains all arcs $(i, \pi(i))$ with $i\leq\pi(i)$.