Identifier
Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations
Mp00086: Permutations —first fundamental transformation⟶ Permutations
Mp00277: Permutations —catalanization⟶ Permutations
Images
[.,.] => [1] => [1] => [1]
[.,[.,.]] => [2,1] => [2,1] => [2,1]
[[.,.],.] => [1,2] => [1,2] => [1,2]
[.,[.,[.,.]]] => [3,2,1] => [3,1,2] => [2,3,1]
[.,[[.,.],.]] => [2,3,1] => [3,2,1] => [3,2,1]
[[.,.],[.,.]] => [1,3,2] => [1,3,2] => [1,3,2]
[[.,[.,.]],.] => [2,1,3] => [2,1,3] => [2,1,3]
[[[.,.],.],.] => [1,2,3] => [1,2,3] => [1,2,3]
[.,[.,[.,[.,.]]]] => [4,3,2,1] => [4,1,2,3] => [2,3,4,1]
[.,[.,[[.,.],.]]] => [3,4,2,1] => [4,1,3,2] => [2,4,3,1]
[.,[[.,.],[.,.]]] => [2,4,3,1] => [4,2,1,3] => [3,2,4,1]
[.,[[.,[.,.]],.]] => [3,2,4,1] => [4,3,2,1] => [4,3,2,1]
[.,[[[.,.],.],.]] => [2,3,4,1] => [4,2,3,1] => [3,4,2,1]
[[.,.],[.,[.,.]]] => [1,4,3,2] => [1,4,2,3] => [1,3,4,2]
[[.,.],[[.,.],.]] => [1,3,4,2] => [1,4,3,2] => [1,4,3,2]
[[.,[.,.]],[.,.]] => [2,1,4,3] => [2,1,4,3] => [2,1,4,3]
[[[.,.],.],[.,.]] => [1,2,4,3] => [1,2,4,3] => [1,2,4,3]
[[.,[.,[.,.]]],.] => [3,2,1,4] => [3,1,2,4] => [2,3,1,4]
[[.,[[.,.],.]],.] => [2,3,1,4] => [3,2,1,4] => [3,2,1,4]
[[[.,.],[.,.]],.] => [1,3,2,4] => [1,3,2,4] => [1,3,2,4]
[[[.,[.,.]],.],.] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4]
[[[[.,.],.],.],.] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4]
[.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => [5,1,2,3,4] => [2,3,4,5,1]
[.,[.,[.,[[.,.],.]]]] => [4,5,3,2,1] => [5,1,2,4,3] => [2,3,5,4,1]
[.,[.,[[.,.],[.,.]]]] => [3,5,4,2,1] => [5,1,3,2,4] => [2,4,3,5,1]
[.,[.,[[.,[.,.]],.]]] => [4,3,5,2,1] => [5,1,4,3,2] => [2,5,4,3,1]
[.,[.,[[[.,.],.],.]]] => [3,4,5,2,1] => [5,1,3,4,2] => [2,4,5,3,1]
[.,[[.,.],[.,[.,.]]]] => [2,5,4,3,1] => [5,2,1,3,4] => [3,2,4,5,1]
[.,[[.,.],[[.,.],.]]] => [2,4,5,3,1] => [5,2,1,4,3] => [3,2,5,4,1]
[.,[[.,[.,.]],[.,.]]] => [3,2,5,4,1] => [5,3,2,1,4] => [4,3,2,5,1]
[.,[[[.,.],.],[.,.]]] => [2,3,5,4,1] => [5,2,3,1,4] => [3,4,2,5,1]
[.,[[.,[.,[.,.]]],.]] => [4,3,2,5,1] => [5,4,2,3,1] => [4,5,3,2,1]
[.,[[.,[[.,.],.]],.]] => [3,4,2,5,1] => [5,4,3,2,1] => [5,4,3,2,1]
[.,[[[.,.],[.,.]],.]] => [2,4,3,5,1] => [5,2,4,3,1] => [3,5,4,2,1]
[.,[[[.,[.,.]],.],.]] => [3,2,4,5,1] => [5,3,2,4,1] => [4,3,5,2,1]
[.,[[[[.,.],.],.],.]] => [2,3,4,5,1] => [5,2,3,4,1] => [3,4,5,2,1]
[[.,.],[.,[.,[.,.]]]] => [1,5,4,3,2] => [1,5,2,3,4] => [1,3,4,5,2]
[[.,.],[.,[[.,.],.]]] => [1,4,5,3,2] => [1,5,2,4,3] => [1,3,5,4,2]
[[.,.],[[.,.],[.,.]]] => [1,3,5,4,2] => [1,5,3,2,4] => [1,4,3,5,2]
[[.,.],[[.,[.,.]],.]] => [1,4,3,5,2] => [1,5,4,3,2] => [1,5,4,3,2]
[[.,.],[[[.,.],.],.]] => [1,3,4,5,2] => [1,5,3,4,2] => [1,4,5,3,2]
[[.,[.,.]],[.,[.,.]]] => [2,1,5,4,3] => [2,1,5,3,4] => [2,1,4,5,3]
[[.,[.,.]],[[.,.],.]] => [2,1,4,5,3] => [2,1,5,4,3] => [2,1,5,4,3]
[[[.,.],.],[.,[.,.]]] => [1,2,5,4,3] => [1,2,5,3,4] => [1,2,4,5,3]
[[[.,.],.],[[.,.],.]] => [1,2,4,5,3] => [1,2,5,4,3] => [1,2,5,4,3]
[[.,[.,[.,.]]],[.,.]] => [3,2,1,5,4] => [3,1,2,5,4] => [2,3,1,5,4]
[[.,[[.,.],.]],[.,.]] => [2,3,1,5,4] => [3,2,1,5,4] => [3,2,1,5,4]
[[[.,.],[.,.]],[.,.]] => [1,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4]
[[[.,[.,.]],.],[.,.]] => [2,1,3,5,4] => [2,1,3,5,4] => [2,1,3,5,4]
[[[[.,.],.],.],[.,.]] => [1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,5,4]
[[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => [4,1,2,3,5] => [2,3,4,1,5]
[[.,[.,[[.,.],.]]],.] => [3,4,2,1,5] => [4,1,3,2,5] => [2,4,3,1,5]
[[.,[[.,.],[.,.]]],.] => [2,4,3,1,5] => [4,2,1,3,5] => [3,2,4,1,5]
[[.,[[.,[.,.]],.]],.] => [3,2,4,1,5] => [4,3,2,1,5] => [4,3,2,1,5]
[[.,[[[.,.],.],.]],.] => [2,3,4,1,5] => [4,2,3,1,5] => [3,4,2,1,5]
[[[.,.],[.,[.,.]]],.] => [1,4,3,2,5] => [1,4,2,3,5] => [1,3,4,2,5]
[[[.,.],[[.,.],.]],.] => [1,3,4,2,5] => [1,4,3,2,5] => [1,4,3,2,5]
[[[.,[.,.]],[.,.]],.] => [2,1,4,3,5] => [2,1,4,3,5] => [2,1,4,3,5]
[[[[.,.],.],[.,.]],.] => [1,2,4,3,5] => [1,2,4,3,5] => [1,2,4,3,5]
[[[.,[.,[.,.]]],.],.] => [3,2,1,4,5] => [3,1,2,4,5] => [2,3,1,4,5]
[[[.,[[.,.],.]],.],.] => [2,3,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5]
[[[[.,.],[.,.]],.],.] => [1,3,2,4,5] => [1,3,2,4,5] => [1,3,2,4,5]
[[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => [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]
[.,[.,[.,[.,[.,[.,.]]]]]] => [6,5,4,3,2,1] => [6,1,2,3,4,5] => [2,3,4,5,6,1]
[.,[.,[.,[.,[[.,.],.]]]]] => [5,6,4,3,2,1] => [6,1,2,3,5,4] => [2,3,4,6,5,1]
[.,[.,[.,[[.,.],[.,.]]]]] => [4,6,5,3,2,1] => [6,1,2,4,3,5] => [2,3,5,4,6,1]
[.,[.,[.,[[.,[.,.]],.]]]] => [5,4,6,3,2,1] => [6,1,2,5,4,3] => [2,3,6,5,4,1]
[.,[.,[.,[[[.,.],.],.]]]] => [4,5,6,3,2,1] => [6,1,2,4,5,3] => [2,3,5,6,4,1]
[.,[.,[[.,.],[.,[.,.]]]]] => [3,6,5,4,2,1] => [6,1,3,2,4,5] => [2,4,3,5,6,1]
[.,[.,[[.,.],[[.,.],.]]]] => [3,5,6,4,2,1] => [6,1,3,2,5,4] => [2,4,3,6,5,1]
[.,[.,[[.,[.,.]],[.,.]]]] => [4,3,6,5,2,1] => [6,1,4,3,2,5] => [2,5,4,3,6,1]
[.,[.,[[[.,.],.],[.,.]]]] => [3,4,6,5,2,1] => [6,1,3,4,2,5] => [2,4,5,3,6,1]
[.,[.,[[.,[.,[.,.]]],.]]] => [5,4,3,6,2,1] => [6,1,5,3,4,2] => [2,5,6,4,3,1]
[.,[.,[[.,[[.,.],.]],.]]] => [4,5,3,6,2,1] => [6,1,5,4,3,2] => [2,6,5,4,3,1]
[.,[.,[[[.,.],[.,.]],.]]] => [3,5,4,6,2,1] => [6,1,3,5,4,2] => [2,4,6,5,3,1]
[.,[.,[[[.,[.,.]],.],.]]] => [4,3,5,6,2,1] => [6,1,4,3,5,2] => [2,5,4,6,3,1]
[.,[.,[[[[.,.],.],.],.]]] => [3,4,5,6,2,1] => [6,1,3,4,5,2] => [2,4,5,6,3,1]
[.,[[.,.],[.,[.,[.,.]]]]] => [2,6,5,4,3,1] => [6,2,1,3,4,5] => [3,2,4,5,6,1]
[.,[[.,.],[.,[[.,.],.]]]] => [2,5,6,4,3,1] => [6,2,1,3,5,4] => [3,2,4,6,5,1]
[.,[[.,.],[[.,.],[.,.]]]] => [2,4,6,5,3,1] => [6,2,1,4,3,5] => [3,2,5,4,6,1]
[.,[[.,.],[[.,[.,.]],.]]] => [2,5,4,6,3,1] => [6,2,1,5,4,3] => [3,2,6,5,4,1]
[.,[[.,.],[[[.,.],.],.]]] => [2,4,5,6,3,1] => [6,2,1,4,5,3] => [3,2,5,6,4,1]
[.,[[.,[.,.]],[.,[.,.]]]] => [3,2,6,5,4,1] => [6,3,2,1,4,5] => [4,3,2,5,6,1]
[.,[[.,[.,.]],[[.,.],.]]] => [3,2,5,6,4,1] => [6,3,2,1,5,4] => [4,3,2,6,5,1]
[.,[[[.,.],.],[.,[.,.]]]] => [2,3,6,5,4,1] => [6,2,3,1,4,5] => [3,4,2,5,6,1]
[.,[[[.,.],.],[[.,.],.]]] => [2,3,5,6,4,1] => [6,2,3,1,5,4] => [3,4,2,6,5,1]
[.,[[.,[.,[.,.]]],[.,.]]] => [4,3,2,6,5,1] => [6,4,2,3,1,5] => [4,5,3,2,6,1]
[.,[[.,[[.,.],.]],[.,.]]] => [3,4,2,6,5,1] => [6,4,3,2,1,5] => [5,4,3,2,6,1]
[.,[[[.,.],[.,.]],[.,.]]] => [2,4,3,6,5,1] => [6,2,4,3,1,5] => [3,5,4,2,6,1]
[.,[[[.,[.,.]],.],[.,.]]] => [3,2,4,6,5,1] => [6,3,2,4,1,5] => [4,3,5,2,6,1]
[.,[[[[.,.],.],.],[.,.]]] => [2,3,4,6,5,1] => [6,2,3,4,1,5] => [3,4,5,2,6,1]
[.,[[.,[.,[.,[.,.]]]],.]] => [5,4,3,2,6,1] => [6,5,2,3,4,1] => [4,5,6,3,2,1]
[.,[[.,[.,[[.,.],.]]],.]] => [4,5,3,2,6,1] => [6,5,2,4,3,1] => [4,6,5,3,2,1]
[.,[[.,[[.,.],[.,.]]],.]] => [3,5,4,2,6,1] => [6,5,3,2,4,1] => [5,4,6,3,2,1]
[.,[[.,[[.,[.,.]],.]],.]] => [4,3,5,2,6,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1]
[.,[[.,[[[.,.],.],.]],.]] => [3,4,5,2,6,1] => [6,5,3,4,2,1] => [5,6,4,3,2,1]
[.,[[[.,.],[.,[.,.]]],.]] => [2,5,4,3,6,1] => [6,2,5,3,4,1] => [3,5,6,4,2,1]
[.,[[[.,.],[[.,.],.]],.]] => [2,4,5,3,6,1] => [6,2,5,4,3,1] => [3,6,5,4,2,1]
[.,[[[.,[.,.]],[.,.]],.]] => [3,2,5,4,6,1] => [6,3,2,5,4,1] => [4,3,6,5,2,1]
[.,[[[[.,.],.],[.,.]],.]] => [2,3,5,4,6,1] => [6,2,3,5,4,1] => [3,4,6,5,2,1]
>>> Load all 699 entries. <<<
[.,[[[.,[.,[.,.]]],.],.]] => [4,3,2,5,6,1] => [6,4,2,3,5,1] => [4,5,3,6,2,1]
[.,[[[.,[[.,.],.]],.],.]] => [3,4,2,5,6,1] => [6,4,3,2,5,1] => [5,4,3,6,2,1]
[.,[[[[.,.],[.,.]],.],.]] => [2,4,3,5,6,1] => [6,2,4,3,5,1] => [3,5,4,6,2,1]
[.,[[[[.,[.,.]],.],.],.]] => [3,2,4,5,6,1] => [6,3,2,4,5,1] => [4,3,5,6,2,1]
[.,[[[[[.,.],.],.],.],.]] => [2,3,4,5,6,1] => [6,2,3,4,5,1] => [3,4,5,6,2,1]
[[.,.],[.,[.,[.,[.,.]]]]] => [1,6,5,4,3,2] => [1,6,2,3,4,5] => [1,3,4,5,6,2]
[[.,.],[.,[.,[[.,.],.]]]] => [1,5,6,4,3,2] => [1,6,2,3,5,4] => [1,3,4,6,5,2]
[[.,.],[.,[[.,.],[.,.]]]] => [1,4,6,5,3,2] => [1,6,2,4,3,5] => [1,3,5,4,6,2]
[[.,.],[.,[[.,[.,.]],.]]] => [1,5,4,6,3,2] => [1,6,2,5,4,3] => [1,3,6,5,4,2]
[[.,.],[.,[[[.,.],.],.]]] => [1,4,5,6,3,2] => [1,6,2,4,5,3] => [1,3,5,6,4,2]
[[.,.],[[.,.],[.,[.,.]]]] => [1,3,6,5,4,2] => [1,6,3,2,4,5] => [1,4,3,5,6,2]
[[.,.],[[.,.],[[.,.],.]]] => [1,3,5,6,4,2] => [1,6,3,2,5,4] => [1,4,3,6,5,2]
[[.,.],[[.,[.,.]],[.,.]]] => [1,4,3,6,5,2] => [1,6,4,3,2,5] => [1,5,4,3,6,2]
[[.,.],[[[.,.],.],[.,.]]] => [1,3,4,6,5,2] => [1,6,3,4,2,5] => [1,4,5,3,6,2]
[[.,.],[[.,[.,[.,.]]],.]] => [1,5,4,3,6,2] => [1,6,5,3,4,2] => [1,5,6,4,3,2]
[[.,.],[[.,[[.,.],.]],.]] => [1,4,5,3,6,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2]
[[.,.],[[[.,.],[.,.]],.]] => [1,3,5,4,6,2] => [1,6,3,5,4,2] => [1,4,6,5,3,2]
[[.,.],[[[.,[.,.]],.],.]] => [1,4,3,5,6,2] => [1,6,4,3,5,2] => [1,5,4,6,3,2]
[[.,.],[[[[.,.],.],.],.]] => [1,3,4,5,6,2] => [1,6,3,4,5,2] => [1,4,5,6,3,2]
[[.,[.,.]],[.,[.,[.,.]]]] => [2,1,6,5,4,3] => [2,1,6,3,4,5] => [2,1,4,5,6,3]
[[.,[.,.]],[.,[[.,.],.]]] => [2,1,5,6,4,3] => [2,1,6,3,5,4] => [2,1,4,6,5,3]
[[.,[.,.]],[[.,.],[.,.]]] => [2,1,4,6,5,3] => [2,1,6,4,3,5] => [2,1,5,4,6,3]
[[.,[.,.]],[[.,[.,.]],.]] => [2,1,5,4,6,3] => [2,1,6,5,4,3] => [2,1,6,5,4,3]
[[.,[.,.]],[[[.,.],.],.]] => [2,1,4,5,6,3] => [2,1,6,4,5,3] => [2,1,5,6,4,3]
[[[.,.],.],[.,[.,[.,.]]]] => [1,2,6,5,4,3] => [1,2,6,3,4,5] => [1,2,4,5,6,3]
[[[.,.],.],[.,[[.,.],.]]] => [1,2,5,6,4,3] => [1,2,6,3,5,4] => [1,2,4,6,5,3]
[[[.,.],.],[[.,.],[.,.]]] => [1,2,4,6,5,3] => [1,2,6,4,3,5] => [1,2,5,4,6,3]
[[[.,.],.],[[.,[.,.]],.]] => [1,2,5,4,6,3] => [1,2,6,5,4,3] => [1,2,6,5,4,3]
[[[.,.],.],[[[.,.],.],.]] => [1,2,4,5,6,3] => [1,2,6,4,5,3] => [1,2,5,6,4,3]
[[.,[.,[.,.]]],[.,[.,.]]] => [3,2,1,6,5,4] => [3,1,2,6,4,5] => [2,3,1,5,6,4]
[[.,[.,[.,.]]],[[.,.],.]] => [3,2,1,5,6,4] => [3,1,2,6,5,4] => [2,3,1,6,5,4]
[[.,[[.,.],.]],[.,[.,.]]] => [2,3,1,6,5,4] => [3,2,1,6,4,5] => [3,2,1,5,6,4]
[[.,[[.,.],.]],[[.,.],.]] => [2,3,1,5,6,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4]
[[[.,.],[.,.]],[.,[.,.]]] => [1,3,2,6,5,4] => [1,3,2,6,4,5] => [1,3,2,5,6,4]
[[[.,.],[.,.]],[[.,.],.]] => [1,3,2,5,6,4] => [1,3,2,6,5,4] => [1,3,2,6,5,4]
[[[.,[.,.]],.],[.,[.,.]]] => [2,1,3,6,5,4] => [2,1,3,6,4,5] => [2,1,3,5,6,4]
[[[.,[.,.]],.],[[.,.],.]] => [2,1,3,5,6,4] => [2,1,3,6,5,4] => [2,1,3,6,5,4]
[[[[.,.],.],.],[.,[.,.]]] => [1,2,3,6,5,4] => [1,2,3,6,4,5] => [1,2,3,5,6,4]
[[[[.,.],.],.],[[.,.],.]] => [1,2,3,5,6,4] => [1,2,3,6,5,4] => [1,2,3,6,5,4]
[[.,[.,[.,[.,.]]]],[.,.]] => [4,3,2,1,6,5] => [4,1,2,3,6,5] => [2,3,4,1,6,5]
[[.,[.,[[.,.],.]]],[.,.]] => [3,4,2,1,6,5] => [4,1,3,2,6,5] => [2,4,3,1,6,5]
[[.,[[.,.],[.,.]]],[.,.]] => [2,4,3,1,6,5] => [4,2,1,3,6,5] => [3,2,4,1,6,5]
[[.,[[.,[.,.]],.]],[.,.]] => [3,2,4,1,6,5] => [4,3,2,1,6,5] => [4,3,2,1,6,5]
[[.,[[[.,.],.],.]],[.,.]] => [2,3,4,1,6,5] => [4,2,3,1,6,5] => [3,4,2,1,6,5]
[[[.,.],[.,[.,.]]],[.,.]] => [1,4,3,2,6,5] => [1,4,2,3,6,5] => [1,3,4,2,6,5]
[[[.,.],[[.,.],.]],[.,.]] => [1,3,4,2,6,5] => [1,4,3,2,6,5] => [1,4,3,2,6,5]
[[[.,[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => [2,1,4,3,6,5]
[[[[.,.],.],[.,.]],[.,.]] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => [1,2,4,3,6,5]
[[[.,[.,[.,.]]],.],[.,.]] => [3,2,1,4,6,5] => [3,1,2,4,6,5] => [2,3,1,4,6,5]
[[[.,[[.,.],.]],.],[.,.]] => [2,3,1,4,6,5] => [3,2,1,4,6,5] => [3,2,1,4,6,5]
[[[[.,.],[.,.]],.],[.,.]] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => [1,3,2,4,6,5]
[[[[.,[.,.]],.],.],[.,.]] => [2,1,3,4,6,5] => [2,1,3,4,6,5] => [2,1,3,4,6,5]
[[[[[.,.],.],.],.],[.,.]] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5]
[[.,[.,[.,[.,[.,.]]]]],.] => [5,4,3,2,1,6] => [5,1,2,3,4,6] => [2,3,4,5,1,6]
[[.,[.,[.,[[.,.],.]]]],.] => [4,5,3,2,1,6] => [5,1,2,4,3,6] => [2,3,5,4,1,6]
[[.,[.,[[.,.],[.,.]]]],.] => [3,5,4,2,1,6] => [5,1,3,2,4,6] => [2,4,3,5,1,6]
[[.,[.,[[.,[.,.]],.]]],.] => [4,3,5,2,1,6] => [5,1,4,3,2,6] => [2,5,4,3,1,6]
[[.,[.,[[[.,.],.],.]]],.] => [3,4,5,2,1,6] => [5,1,3,4,2,6] => [2,4,5,3,1,6]
[[.,[[.,.],[.,[.,.]]]],.] => [2,5,4,3,1,6] => [5,2,1,3,4,6] => [3,2,4,5,1,6]
[[.,[[.,.],[[.,.],.]]],.] => [2,4,5,3,1,6] => [5,2,1,4,3,6] => [3,2,5,4,1,6]
[[.,[[.,[.,.]],[.,.]]],.] => [3,2,5,4,1,6] => [5,3,2,1,4,6] => [4,3,2,5,1,6]
[[.,[[[.,.],.],[.,.]]],.] => [2,3,5,4,1,6] => [5,2,3,1,4,6] => [3,4,2,5,1,6]
[[.,[[.,[.,[.,.]]],.]],.] => [4,3,2,5,1,6] => [5,4,2,3,1,6] => [4,5,3,2,1,6]
[[.,[[.,[[.,.],.]],.]],.] => [3,4,2,5,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6]
[[.,[[[.,.],[.,.]],.]],.] => [2,4,3,5,1,6] => [5,2,4,3,1,6] => [3,5,4,2,1,6]
[[.,[[[.,[.,.]],.],.]],.] => [3,2,4,5,1,6] => [5,3,2,4,1,6] => [4,3,5,2,1,6]
[[.,[[[[.,.],.],.],.]],.] => [2,3,4,5,1,6] => [5,2,3,4,1,6] => [3,4,5,2,1,6]
[[[.,.],[.,[.,[.,.]]]],.] => [1,5,4,3,2,6] => [1,5,2,3,4,6] => [1,3,4,5,2,6]
[[[.,.],[.,[[.,.],.]]],.] => [1,4,5,3,2,6] => [1,5,2,4,3,6] => [1,3,5,4,2,6]
[[[.,.],[[.,.],[.,.]]],.] => [1,3,5,4,2,6] => [1,5,3,2,4,6] => [1,4,3,5,2,6]
[[[.,.],[[.,[.,.]],.]],.] => [1,4,3,5,2,6] => [1,5,4,3,2,6] => [1,5,4,3,2,6]
[[[.,.],[[[.,.],.],.]],.] => [1,3,4,5,2,6] => [1,5,3,4,2,6] => [1,4,5,3,2,6]
[[[.,[.,.]],[.,[.,.]]],.] => [2,1,5,4,3,6] => [2,1,5,3,4,6] => [2,1,4,5,3,6]
[[[.,[.,.]],[[.,.],.]],.] => [2,1,4,5,3,6] => [2,1,5,4,3,6] => [2,1,5,4,3,6]
[[[[.,.],.],[.,[.,.]]],.] => [1,2,5,4,3,6] => [1,2,5,3,4,6] => [1,2,4,5,3,6]
[[[[.,.],.],[[.,.],.]],.] => [1,2,4,5,3,6] => [1,2,5,4,3,6] => [1,2,5,4,3,6]
[[[.,[.,[.,.]]],[.,.]],.] => [3,2,1,5,4,6] => [3,1,2,5,4,6] => [2,3,1,5,4,6]
[[[.,[[.,.],.]],[.,.]],.] => [2,3,1,5,4,6] => [3,2,1,5,4,6] => [3,2,1,5,4,6]
[[[[.,.],[.,.]],[.,.]],.] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => [1,3,2,5,4,6]
[[[[.,[.,.]],.],[.,.]],.] => [2,1,3,5,4,6] => [2,1,3,5,4,6] => [2,1,3,5,4,6]
[[[[[.,.],.],.],[.,.]],.] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => [1,2,3,5,4,6]
[[[.,[.,[.,[.,.]]]],.],.] => [4,3,2,1,5,6] => [4,1,2,3,5,6] => [2,3,4,1,5,6]
[[[.,[.,[[.,.],.]]],.],.] => [3,4,2,1,5,6] => [4,1,3,2,5,6] => [2,4,3,1,5,6]
[[[.,[[.,.],[.,.]]],.],.] => [2,4,3,1,5,6] => [4,2,1,3,5,6] => [3,2,4,1,5,6]
[[[.,[[.,[.,.]],.]],.],.] => [3,2,4,1,5,6] => [4,3,2,1,5,6] => [4,3,2,1,5,6]
[[[.,[[[.,.],.],.]],.],.] => [2,3,4,1,5,6] => [4,2,3,1,5,6] => [3,4,2,1,5,6]
[[[[.,.],[.,[.,.]]],.],.] => [1,4,3,2,5,6] => [1,4,2,3,5,6] => [1,3,4,2,5,6]
[[[[.,.],[[.,.],.]],.],.] => [1,3,4,2,5,6] => [1,4,3,2,5,6] => [1,4,3,2,5,6]
[[[[.,[.,.]],[.,.]],.],.] => [2,1,4,3,5,6] => [2,1,4,3,5,6] => [2,1,4,3,5,6]
[[[[[.,.],.],[.,.]],.],.] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => [1,2,4,3,5,6]
[[[[.,[.,[.,.]]],.],.],.] => [3,2,1,4,5,6] => [3,1,2,4,5,6] => [2,3,1,4,5,6]
[[[[.,[[.,.],.]],.],.],.] => [2,3,1,4,5,6] => [3,2,1,4,5,6] => [3,2,1,4,5,6]
[[[[[.,.],[.,.]],.],.],.] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => [1,3,2,4,5,6]
[[[[[.,[.,.]],.],.],.],.] => [2,1,3,4,5,6] => [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]
[.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [7,6,5,4,3,2,1] => [7,1,2,3,4,5,6] => [2,3,4,5,6,7,1]
[.,[.,[.,[.,[.,[[.,.],.]]]]]] => [6,7,5,4,3,2,1] => [7,1,2,3,4,6,5] => [2,3,4,5,7,6,1]
[.,[.,[.,[.,[[.,.],[.,.]]]]]] => [5,7,6,4,3,2,1] => [7,1,2,3,5,4,6] => [2,3,4,6,5,7,1]
[.,[.,[.,[.,[[.,[.,.]],.]]]]] => [6,5,7,4,3,2,1] => [7,1,2,3,6,5,4] => [2,3,4,7,6,5,1]
[.,[.,[.,[.,[[[.,.],.],.]]]]] => [5,6,7,4,3,2,1] => [7,1,2,3,5,6,4] => [2,3,4,6,7,5,1]
[.,[.,[.,[[.,.],[.,[.,.]]]]]] => [4,7,6,5,3,2,1] => [7,1,2,4,3,5,6] => [2,3,5,4,6,7,1]
[.,[.,[.,[[.,.],[[.,.],.]]]]] => [4,6,7,5,3,2,1] => [7,1,2,4,3,6,5] => [2,3,5,4,7,6,1]
[.,[.,[.,[[.,[.,.]],[.,.]]]]] => [5,4,7,6,3,2,1] => [7,1,2,5,4,3,6] => [2,3,6,5,4,7,1]
[.,[.,[.,[[[.,.],.],[.,.]]]]] => [4,5,7,6,3,2,1] => [7,1,2,4,5,3,6] => [2,3,5,6,4,7,1]
[.,[.,[.,[[.,[.,[.,.]]],.]]]] => [6,5,4,7,3,2,1] => [7,1,2,6,4,5,3] => [2,3,6,7,5,4,1]
[.,[.,[.,[[.,[[.,.],.]],.]]]] => [5,6,4,7,3,2,1] => [7,1,2,6,5,4,3] => [2,3,7,6,5,4,1]
[.,[.,[.,[[[.,.],[.,.]],.]]]] => [4,6,5,7,3,2,1] => [7,1,2,4,6,5,3] => [2,3,5,7,6,4,1]
[.,[.,[.,[[[.,[.,.]],.],.]]]] => [5,4,6,7,3,2,1] => [7,1,2,5,4,6,3] => [2,3,6,5,7,4,1]
[.,[.,[.,[[[[.,.],.],.],.]]]] => [4,5,6,7,3,2,1] => [7,1,2,4,5,6,3] => [2,3,5,6,7,4,1]
[.,[.,[[.,.],[.,[.,[.,.]]]]]] => [3,7,6,5,4,2,1] => [7,1,3,2,4,5,6] => [2,4,3,5,6,7,1]
[.,[.,[[.,.],[.,[[.,.],.]]]]] => [3,6,7,5,4,2,1] => [7,1,3,2,4,6,5] => [2,4,3,5,7,6,1]
[.,[.,[[.,.],[[.,.],[.,.]]]]] => [3,5,7,6,4,2,1] => [7,1,3,2,5,4,6] => [2,4,3,6,5,7,1]
[.,[.,[[.,.],[[.,[.,.]],.]]]] => [3,6,5,7,4,2,1] => [7,1,3,2,6,5,4] => [2,4,3,7,6,5,1]
[.,[.,[[.,.],[[[.,.],.],.]]]] => [3,5,6,7,4,2,1] => [7,1,3,2,5,6,4] => [2,4,3,6,7,5,1]
[.,[.,[[.,[.,.]],[.,[.,.]]]]] => [4,3,7,6,5,2,1] => [7,1,4,3,2,5,6] => [2,5,4,3,6,7,1]
[.,[.,[[.,[.,.]],[[.,.],.]]]] => [4,3,6,7,5,2,1] => [7,1,4,3,2,6,5] => [2,5,4,3,7,6,1]
[.,[.,[[[.,.],.],[.,[.,.]]]]] => [3,4,7,6,5,2,1] => [7,1,3,4,2,5,6] => [2,4,5,3,6,7,1]
[.,[.,[[[.,.],.],[[.,.],.]]]] => [3,4,6,7,5,2,1] => [7,1,3,4,2,6,5] => [2,4,5,3,7,6,1]
[.,[.,[[.,[.,[.,.]]],[.,.]]]] => [5,4,3,7,6,2,1] => [7,1,5,3,4,2,6] => [2,5,6,4,3,7,1]
[.,[.,[[.,[[.,.],.]],[.,.]]]] => [4,5,3,7,6,2,1] => [7,1,5,4,3,2,6] => [2,6,5,4,3,7,1]
[.,[.,[[[.,.],[.,.]],[.,.]]]] => [3,5,4,7,6,2,1] => [7,1,3,5,4,2,6] => [2,4,6,5,3,7,1]
[.,[.,[[[.,[.,.]],.],[.,.]]]] => [4,3,5,7,6,2,1] => [7,1,4,3,5,2,6] => [2,5,4,6,3,7,1]
[.,[.,[[[[.,.],.],.],[.,.]]]] => [3,4,5,7,6,2,1] => [7,1,3,4,5,2,6] => [2,4,5,6,3,7,1]
[.,[.,[[.,[.,[.,[.,.]]]],.]]] => [6,5,4,3,7,2,1] => [7,1,6,3,4,5,2] => [2,5,6,7,4,3,1]
[.,[.,[[.,[.,[[.,.],.]]],.]]] => [5,6,4,3,7,2,1] => [7,1,6,3,5,4,2] => [2,5,7,6,4,3,1]
[.,[.,[[.,[[.,.],[.,.]]],.]]] => [4,6,5,3,7,2,1] => [7,1,6,4,3,5,2] => [2,6,5,7,4,3,1]
[.,[.,[[.,[[.,[.,.]],.]],.]]] => [5,4,6,3,7,2,1] => [7,1,6,5,4,3,2] => [2,7,6,5,4,3,1]
[.,[.,[[.,[[[.,.],.],.]],.]]] => [4,5,6,3,7,2,1] => [7,1,6,4,5,3,2] => [2,6,7,5,4,3,1]
[.,[.,[[[.,.],[.,[.,.]]],.]]] => [3,6,5,4,7,2,1] => [7,1,3,6,4,5,2] => [2,4,6,7,5,3,1]
[.,[.,[[[.,.],[[.,.],.]],.]]] => [3,5,6,4,7,2,1] => [7,1,3,6,5,4,2] => [2,4,7,6,5,3,1]
[.,[.,[[[.,[.,.]],[.,.]],.]]] => [4,3,6,5,7,2,1] => [7,1,4,3,6,5,2] => [2,5,4,7,6,3,1]
[.,[.,[[[[.,.],.],[.,.]],.]]] => [3,4,6,5,7,2,1] => [7,1,3,4,6,5,2] => [2,4,5,7,6,3,1]
[.,[.,[[[.,[.,[.,.]]],.],.]]] => [5,4,3,6,7,2,1] => [7,1,5,3,4,6,2] => [2,5,6,4,7,3,1]
[.,[.,[[[.,[[.,.],.]],.],.]]] => [4,5,3,6,7,2,1] => [7,1,5,4,3,6,2] => [2,6,5,4,7,3,1]
[.,[.,[[[[.,.],[.,.]],.],.]]] => [3,5,4,6,7,2,1] => [7,1,3,5,4,6,2] => [2,4,6,5,7,3,1]
[.,[.,[[[[.,[.,.]],.],.],.]]] => [4,3,5,6,7,2,1] => [7,1,4,3,5,6,2] => [2,5,4,6,7,3,1]
[.,[.,[[[[[.,.],.],.],.],.]]] => [3,4,5,6,7,2,1] => [7,1,3,4,5,6,2] => [2,4,5,6,7,3,1]
[.,[[.,.],[.,[.,[.,[.,.]]]]]] => [2,7,6,5,4,3,1] => [7,2,1,3,4,5,6] => [3,2,4,5,6,7,1]
[.,[[.,.],[.,[.,[[.,.],.]]]]] => [2,6,7,5,4,3,1] => [7,2,1,3,4,6,5] => [3,2,4,5,7,6,1]
[.,[[.,.],[.,[[.,.],[.,.]]]]] => [2,5,7,6,4,3,1] => [7,2,1,3,5,4,6] => [3,2,4,6,5,7,1]
[.,[[.,.],[.,[[.,[.,.]],.]]]] => [2,6,5,7,4,3,1] => [7,2,1,3,6,5,4] => [3,2,4,7,6,5,1]
[.,[[.,.],[.,[[[.,.],.],.]]]] => [2,5,6,7,4,3,1] => [7,2,1,3,5,6,4] => [3,2,4,6,7,5,1]
[.,[[.,.],[[.,.],[.,[.,.]]]]] => [2,4,7,6,5,3,1] => [7,2,1,4,3,5,6] => [3,2,5,4,6,7,1]
[.,[[.,.],[[.,.],[[.,.],.]]]] => [2,4,6,7,5,3,1] => [7,2,1,4,3,6,5] => [3,2,5,4,7,6,1]
[.,[[.,.],[[.,[.,.]],[.,.]]]] => [2,5,4,7,6,3,1] => [7,2,1,5,4,3,6] => [3,2,6,5,4,7,1]
[.,[[.,.],[[[.,.],.],[.,.]]]] => [2,4,5,7,6,3,1] => [7,2,1,4,5,3,6] => [3,2,5,6,4,7,1]
[.,[[.,.],[[.,[.,[.,.]]],.]]] => [2,6,5,4,7,3,1] => [7,2,1,6,4,5,3] => [3,2,6,7,5,4,1]
[.,[[.,.],[[.,[[.,.],.]],.]]] => [2,5,6,4,7,3,1] => [7,2,1,6,5,4,3] => [3,2,7,6,5,4,1]
[.,[[.,.],[[[.,.],[.,.]],.]]] => [2,4,6,5,7,3,1] => [7,2,1,4,6,5,3] => [3,2,5,7,6,4,1]
[.,[[.,.],[[[.,[.,.]],.],.]]] => [2,5,4,6,7,3,1] => [7,2,1,5,4,6,3] => [3,2,6,5,7,4,1]
[.,[[.,.],[[[[.,.],.],.],.]]] => [2,4,5,6,7,3,1] => [7,2,1,4,5,6,3] => [3,2,5,6,7,4,1]
[.,[[.,[.,.]],[.,[.,[.,.]]]]] => [3,2,7,6,5,4,1] => [7,3,2,1,4,5,6] => [4,3,2,5,6,7,1]
[.,[[.,[.,.]],[.,[[.,.],.]]]] => [3,2,6,7,5,4,1] => [7,3,2,1,4,6,5] => [4,3,2,5,7,6,1]
[.,[[.,[.,.]],[[.,.],[.,.]]]] => [3,2,5,7,6,4,1] => [7,3,2,1,5,4,6] => [4,3,2,6,5,7,1]
[.,[[.,[.,.]],[[.,[.,.]],.]]] => [3,2,6,5,7,4,1] => [7,3,2,1,6,5,4] => [4,3,2,7,6,5,1]
[.,[[.,[.,.]],[[[.,.],.],.]]] => [3,2,5,6,7,4,1] => [7,3,2,1,5,6,4] => [4,3,2,6,7,5,1]
[.,[[[.,.],.],[.,[.,[.,.]]]]] => [2,3,7,6,5,4,1] => [7,2,3,1,4,5,6] => [3,4,2,5,6,7,1]
[.,[[[.,.],.],[.,[[.,.],.]]]] => [2,3,6,7,5,4,1] => [7,2,3,1,4,6,5] => [3,4,2,5,7,6,1]
[.,[[[.,.],.],[[.,.],[.,.]]]] => [2,3,5,7,6,4,1] => [7,2,3,1,5,4,6] => [3,4,2,6,5,7,1]
[.,[[[.,.],.],[[.,[.,.]],.]]] => [2,3,6,5,7,4,1] => [7,2,3,1,6,5,4] => [3,4,2,7,6,5,1]
[.,[[[.,.],.],[[[.,.],.],.]]] => [2,3,5,6,7,4,1] => [7,2,3,1,5,6,4] => [3,4,2,6,7,5,1]
[.,[[.,[.,[.,.]]],[.,[.,.]]]] => [4,3,2,7,6,5,1] => [7,4,2,3,1,5,6] => [4,5,3,2,6,7,1]
[.,[[.,[.,[.,.]]],[[.,.],.]]] => [4,3,2,6,7,5,1] => [7,4,2,3,1,6,5] => [4,5,3,2,7,6,1]
[.,[[.,[[.,.],.]],[.,[.,.]]]] => [3,4,2,7,6,5,1] => [7,4,3,2,1,5,6] => [5,4,3,2,6,7,1]
[.,[[.,[[.,.],.]],[[.,.],.]]] => [3,4,2,6,7,5,1] => [7,4,3,2,1,6,5] => [5,4,3,2,7,6,1]
[.,[[[.,.],[.,.]],[.,[.,.]]]] => [2,4,3,7,6,5,1] => [7,2,4,3,1,5,6] => [3,5,4,2,6,7,1]
[.,[[[.,.],[.,.]],[[.,.],.]]] => [2,4,3,6,7,5,1] => [7,2,4,3,1,6,5] => [3,5,4,2,7,6,1]
[.,[[[.,[.,.]],.],[.,[.,.]]]] => [3,2,4,7,6,5,1] => [7,3,2,4,1,5,6] => [4,3,5,2,6,7,1]
[.,[[[.,[.,.]],.],[[.,.],.]]] => [3,2,4,6,7,5,1] => [7,3,2,4,1,6,5] => [4,3,5,2,7,6,1]
[.,[[[[.,.],.],.],[.,[.,.]]]] => [2,3,4,7,6,5,1] => [7,2,3,4,1,5,6] => [3,4,5,2,6,7,1]
[.,[[[[.,.],.],.],[[.,.],.]]] => [2,3,4,6,7,5,1] => [7,2,3,4,1,6,5] => [3,4,5,2,7,6,1]
[.,[[.,[.,[.,[.,.]]]],[.,.]]] => [5,4,3,2,7,6,1] => [7,5,2,3,4,1,6] => [4,5,6,3,2,7,1]
[.,[[.,[.,[[.,.],.]]],[.,.]]] => [4,5,3,2,7,6,1] => [7,5,2,4,3,1,6] => [4,6,5,3,2,7,1]
[.,[[.,[[.,.],[.,.]]],[.,.]]] => [3,5,4,2,7,6,1] => [7,5,3,2,4,1,6] => [5,4,6,3,2,7,1]
[.,[[.,[[.,[.,.]],.]],[.,.]]] => [4,3,5,2,7,6,1] => [7,5,4,3,2,1,6] => [6,5,4,3,2,7,1]
[.,[[.,[[[.,.],.],.]],[.,.]]] => [3,4,5,2,7,6,1] => [7,5,3,4,2,1,6] => [5,6,4,3,2,7,1]
[.,[[[.,.],[.,[.,.]]],[.,.]]] => [2,5,4,3,7,6,1] => [7,2,5,3,4,1,6] => [3,5,6,4,2,7,1]
[.,[[[.,.],[[.,.],.]],[.,.]]] => [2,4,5,3,7,6,1] => [7,2,5,4,3,1,6] => [3,6,5,4,2,7,1]
[.,[[[.,[.,.]],[.,.]],[.,.]]] => [3,2,5,4,7,6,1] => [7,3,2,5,4,1,6] => [4,3,6,5,2,7,1]
[.,[[[[.,.],.],[.,.]],[.,.]]] => [2,3,5,4,7,6,1] => [7,2,3,5,4,1,6] => [3,4,6,5,2,7,1]
[.,[[[.,[.,[.,.]]],.],[.,.]]] => [4,3,2,5,7,6,1] => [7,4,2,3,5,1,6] => [4,5,3,6,2,7,1]
[.,[[[.,[[.,.],.]],.],[.,.]]] => [3,4,2,5,7,6,1] => [7,4,3,2,5,1,6] => [5,4,3,6,2,7,1]
[.,[[[[.,.],[.,.]],.],[.,.]]] => [2,4,3,5,7,6,1] => [7,2,4,3,5,1,6] => [3,5,4,6,2,7,1]
[.,[[[[.,[.,.]],.],.],[.,.]]] => [3,2,4,5,7,6,1] => [7,3,2,4,5,1,6] => [4,3,5,6,2,7,1]
[.,[[[[[.,.],.],.],.],[.,.]]] => [2,3,4,5,7,6,1] => [7,2,3,4,5,1,6] => [3,4,5,6,2,7,1]
[.,[[.,[.,[.,[.,[.,.]]]]],.]] => [6,5,4,3,2,7,1] => [7,6,2,3,4,5,1] => [4,5,6,7,3,2,1]
[.,[[.,[.,[.,[[.,.],.]]]],.]] => [5,6,4,3,2,7,1] => [7,6,2,3,5,4,1] => [4,5,7,6,3,2,1]
[.,[[.,[.,[[.,.],[.,.]]]],.]] => [4,6,5,3,2,7,1] => [7,6,2,4,3,5,1] => [4,6,5,7,3,2,1]
[.,[[.,[.,[[.,[.,.]],.]]],.]] => [5,4,6,3,2,7,1] => [7,6,2,5,4,3,1] => [4,7,6,5,3,2,1]
[.,[[.,[.,[[[.,.],.],.]]],.]] => [4,5,6,3,2,7,1] => [7,6,2,4,5,3,1] => [4,6,7,5,3,2,1]
[.,[[.,[[.,.],[.,[.,.]]]],.]] => [3,6,5,4,2,7,1] => [7,6,3,2,4,5,1] => [5,4,6,7,3,2,1]
[.,[[.,[[.,.],[[.,.],.]]],.]] => [3,5,6,4,2,7,1] => [7,6,3,2,5,4,1] => [5,4,7,6,3,2,1]
[.,[[.,[[.,[.,.]],[.,.]]],.]] => [4,3,6,5,2,7,1] => [7,6,4,3,2,5,1] => [6,5,4,7,3,2,1]
[.,[[.,[[[.,.],.],[.,.]]],.]] => [3,4,6,5,2,7,1] => [7,6,3,4,2,5,1] => [5,6,4,7,3,2,1]
[.,[[.,[[.,[.,[.,.]]],.]],.]] => [5,4,3,6,2,7,1] => [7,6,5,3,4,2,1] => [6,7,5,4,3,2,1]
[.,[[.,[[.,[[.,.],.]],.]],.]] => [4,5,3,6,2,7,1] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1]
[.,[[.,[[[.,.],[.,.]],.]],.]] => [3,5,4,6,2,7,1] => [7,6,3,5,4,2,1] => [5,7,6,4,3,2,1]
[.,[[.,[[[.,[.,.]],.],.]],.]] => [4,3,5,6,2,7,1] => [7,6,4,3,5,2,1] => [6,5,7,4,3,2,1]
[.,[[.,[[[[.,.],.],.],.]],.]] => [3,4,5,6,2,7,1] => [7,6,3,4,5,2,1] => [5,6,7,4,3,2,1]
[.,[[[.,.],[.,[.,[.,.]]]],.]] => [2,6,5,4,3,7,1] => [7,2,6,3,4,5,1] => [3,5,6,7,4,2,1]
[.,[[[.,.],[.,[[.,.],.]]],.]] => [2,5,6,4,3,7,1] => [7,2,6,3,5,4,1] => [3,5,7,6,4,2,1]
[.,[[[.,.],[[.,.],[.,.]]],.]] => [2,4,6,5,3,7,1] => [7,2,6,4,3,5,1] => [3,6,5,7,4,2,1]
[.,[[[.,.],[[.,[.,.]],.]],.]] => [2,5,4,6,3,7,1] => [7,2,6,5,4,3,1] => [3,7,6,5,4,2,1]
[.,[[[.,.],[[[.,.],.],.]],.]] => [2,4,5,6,3,7,1] => [7,2,6,4,5,3,1] => [3,6,7,5,4,2,1]
[.,[[[.,[.,.]],[.,[.,.]]],.]] => [3,2,6,5,4,7,1] => [7,3,2,6,4,5,1] => [4,3,6,7,5,2,1]
[.,[[[.,[.,.]],[[.,.],.]],.]] => [3,2,5,6,4,7,1] => [7,3,2,6,5,4,1] => [4,3,7,6,5,2,1]
[.,[[[[.,.],.],[.,[.,.]]],.]] => [2,3,6,5,4,7,1] => [7,2,3,6,4,5,1] => [3,4,6,7,5,2,1]
[.,[[[[.,.],.],[[.,.],.]],.]] => [2,3,5,6,4,7,1] => [7,2,3,6,5,4,1] => [3,4,7,6,5,2,1]
[.,[[[.,[.,[.,.]]],[.,.]],.]] => [4,3,2,6,5,7,1] => [7,4,2,3,6,5,1] => [4,5,3,7,6,2,1]
[.,[[[.,[[.,.],.]],[.,.]],.]] => [3,4,2,6,5,7,1] => [7,4,3,2,6,5,1] => [5,4,3,7,6,2,1]
[.,[[[[.,.],[.,.]],[.,.]],.]] => [2,4,3,6,5,7,1] => [7,2,4,3,6,5,1] => [3,5,4,7,6,2,1]
[.,[[[[.,[.,.]],.],[.,.]],.]] => [3,2,4,6,5,7,1] => [7,3,2,4,6,5,1] => [4,3,5,7,6,2,1]
[.,[[[[[.,.],.],.],[.,.]],.]] => [2,3,4,6,5,7,1] => [7,2,3,4,6,5,1] => [3,4,5,7,6,2,1]
[.,[[[.,[.,[.,[.,.]]]],.],.]] => [5,4,3,2,6,7,1] => [7,5,2,3,4,6,1] => [4,5,6,3,7,2,1]
[.,[[[.,[.,[[.,.],.]]],.],.]] => [4,5,3,2,6,7,1] => [7,5,2,4,3,6,1] => [4,6,5,3,7,2,1]
[.,[[[.,[[.,.],[.,.]]],.],.]] => [3,5,4,2,6,7,1] => [7,5,3,2,4,6,1] => [5,4,6,3,7,2,1]
[.,[[[.,[[.,[.,.]],.]],.],.]] => [4,3,5,2,6,7,1] => [7,5,4,3,2,6,1] => [6,5,4,3,7,2,1]
[.,[[[.,[[[.,.],.],.]],.],.]] => [3,4,5,2,6,7,1] => [7,5,3,4,2,6,1] => [5,6,4,3,7,2,1]
[.,[[[[.,.],[.,[.,.]]],.],.]] => [2,5,4,3,6,7,1] => [7,2,5,3,4,6,1] => [3,5,6,4,7,2,1]
[.,[[[[.,.],[[.,.],.]],.],.]] => [2,4,5,3,6,7,1] => [7,2,5,4,3,6,1] => [3,6,5,4,7,2,1]
[.,[[[[.,[.,.]],[.,.]],.],.]] => [3,2,5,4,6,7,1] => [7,3,2,5,4,6,1] => [4,3,6,5,7,2,1]
[.,[[[[[.,.],.],[.,.]],.],.]] => [2,3,5,4,6,7,1] => [7,2,3,5,4,6,1] => [3,4,6,5,7,2,1]
[.,[[[[.,[.,[.,.]]],.],.],.]] => [4,3,2,5,6,7,1] => [7,4,2,3,5,6,1] => [4,5,3,6,7,2,1]
[.,[[[[.,[[.,.],.]],.],.],.]] => [3,4,2,5,6,7,1] => [7,4,3,2,5,6,1] => [5,4,3,6,7,2,1]
[.,[[[[[.,.],[.,.]],.],.],.]] => [2,4,3,5,6,7,1] => [7,2,4,3,5,6,1] => [3,5,4,6,7,2,1]
[.,[[[[[.,[.,.]],.],.],.],.]] => [3,2,4,5,6,7,1] => [7,3,2,4,5,6,1] => [4,3,5,6,7,2,1]
[.,[[[[[[.,.],.],.],.],.],.]] => [2,3,4,5,6,7,1] => [7,2,3,4,5,6,1] => [3,4,5,6,7,2,1]
[[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,7,6,5,4,3,2] => [1,7,2,3,4,5,6] => [1,3,4,5,6,7,2]
[[.,.],[.,[.,[.,[[.,.],.]]]]] => [1,6,7,5,4,3,2] => [1,7,2,3,4,6,5] => [1,3,4,5,7,6,2]
[[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,5,7,6,4,3,2] => [1,7,2,3,5,4,6] => [1,3,4,6,5,7,2]
[[.,.],[.,[.,[[.,[.,.]],.]]]] => [1,6,5,7,4,3,2] => [1,7,2,3,6,5,4] => [1,3,4,7,6,5,2]
[[.,.],[.,[.,[[[.,.],.],.]]]] => [1,5,6,7,4,3,2] => [1,7,2,3,5,6,4] => [1,3,4,6,7,5,2]
[[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,4,7,6,5,3,2] => [1,7,2,4,3,5,6] => [1,3,5,4,6,7,2]
[[.,.],[.,[[.,.],[[.,.],.]]]] => [1,4,6,7,5,3,2] => [1,7,2,4,3,6,5] => [1,3,5,4,7,6,2]
[[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,5,4,7,6,3,2] => [1,7,2,5,4,3,6] => [1,3,6,5,4,7,2]
[[.,.],[.,[[[.,.],.],[.,.]]]] => [1,4,5,7,6,3,2] => [1,7,2,4,5,3,6] => [1,3,5,6,4,7,2]
[[.,.],[.,[[.,[.,[.,.]]],.]]] => [1,6,5,4,7,3,2] => [1,7,2,6,4,5,3] => [1,3,6,7,5,4,2]
[[.,.],[.,[[.,[[.,.],.]],.]]] => [1,5,6,4,7,3,2] => [1,7,2,6,5,4,3] => [1,3,7,6,5,4,2]
[[.,.],[.,[[[.,.],[.,.]],.]]] => [1,4,6,5,7,3,2] => [1,7,2,4,6,5,3] => [1,3,5,7,6,4,2]
[[.,.],[.,[[[.,[.,.]],.],.]]] => [1,5,4,6,7,3,2] => [1,7,2,5,4,6,3] => [1,3,6,5,7,4,2]
[[.,.],[.,[[[[.,.],.],.],.]]] => [1,4,5,6,7,3,2] => [1,7,2,4,5,6,3] => [1,3,5,6,7,4,2]
[[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,3,7,6,5,4,2] => [1,7,3,2,4,5,6] => [1,4,3,5,6,7,2]
[[.,.],[[.,.],[.,[[.,.],.]]]] => [1,3,6,7,5,4,2] => [1,7,3,2,4,6,5] => [1,4,3,5,7,6,2]
[[.,.],[[.,.],[[.,.],[.,.]]]] => [1,3,5,7,6,4,2] => [1,7,3,2,5,4,6] => [1,4,3,6,5,7,2]
[[.,.],[[.,.],[[.,[.,.]],.]]] => [1,3,6,5,7,4,2] => [1,7,3,2,6,5,4] => [1,4,3,7,6,5,2]
[[.,.],[[.,.],[[[.,.],.],.]]] => [1,3,5,6,7,4,2] => [1,7,3,2,5,6,4] => [1,4,3,6,7,5,2]
[[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,4,3,7,6,5,2] => [1,7,4,3,2,5,6] => [1,5,4,3,6,7,2]
[[.,.],[[.,[.,.]],[[.,.],.]]] => [1,4,3,6,7,5,2] => [1,7,4,3,2,6,5] => [1,5,4,3,7,6,2]
[[.,.],[[[.,.],.],[.,[.,.]]]] => [1,3,4,7,6,5,2] => [1,7,3,4,2,5,6] => [1,4,5,3,6,7,2]
[[.,.],[[[.,.],.],[[.,.],.]]] => [1,3,4,6,7,5,2] => [1,7,3,4,2,6,5] => [1,4,5,3,7,6,2]
[[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,5,4,3,7,6,2] => [1,7,5,3,4,2,6] => [1,5,6,4,3,7,2]
[[.,.],[[.,[[.,.],.]],[.,.]]] => [1,4,5,3,7,6,2] => [1,7,5,4,3,2,6] => [1,6,5,4,3,7,2]
[[.,.],[[[.,.],[.,.]],[.,.]]] => [1,3,5,4,7,6,2] => [1,7,3,5,4,2,6] => [1,4,6,5,3,7,2]
[[.,.],[[[.,[.,.]],.],[.,.]]] => [1,4,3,5,7,6,2] => [1,7,4,3,5,2,6] => [1,5,4,6,3,7,2]
[[.,.],[[[[.,.],.],.],[.,.]]] => [1,3,4,5,7,6,2] => [1,7,3,4,5,2,6] => [1,4,5,6,3,7,2]
[[.,.],[[.,[.,[.,[.,.]]]],.]] => [1,6,5,4,3,7,2] => [1,7,6,3,4,5,2] => [1,5,6,7,4,3,2]
[[.,.],[[.,[.,[[.,.],.]]],.]] => [1,5,6,4,3,7,2] => [1,7,6,3,5,4,2] => [1,5,7,6,4,3,2]
[[.,.],[[.,[[.,.],[.,.]]],.]] => [1,4,6,5,3,7,2] => [1,7,6,4,3,5,2] => [1,6,5,7,4,3,2]
[[.,.],[[.,[[.,[.,.]],.]],.]] => [1,5,4,6,3,7,2] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2]
[[.,.],[[.,[[[.,.],.],.]],.]] => [1,4,5,6,3,7,2] => [1,7,6,4,5,3,2] => [1,6,7,5,4,3,2]
[[.,.],[[[.,.],[.,[.,.]]],.]] => [1,3,6,5,4,7,2] => [1,7,3,6,4,5,2] => [1,4,6,7,5,3,2]
[[.,.],[[[.,.],[[.,.],.]],.]] => [1,3,5,6,4,7,2] => [1,7,3,6,5,4,2] => [1,4,7,6,5,3,2]
[[.,.],[[[.,[.,.]],[.,.]],.]] => [1,4,3,6,5,7,2] => [1,7,4,3,6,5,2] => [1,5,4,7,6,3,2]
[[.,.],[[[[.,.],.],[.,.]],.]] => [1,3,4,6,5,7,2] => [1,7,3,4,6,5,2] => [1,4,5,7,6,3,2]
[[.,.],[[[.,[.,[.,.]]],.],.]] => [1,5,4,3,6,7,2] => [1,7,5,3,4,6,2] => [1,5,6,4,7,3,2]
[[.,.],[[[.,[[.,.],.]],.],.]] => [1,4,5,3,6,7,2] => [1,7,5,4,3,6,2] => [1,6,5,4,7,3,2]
[[.,.],[[[[.,.],[.,.]],.],.]] => [1,3,5,4,6,7,2] => [1,7,3,5,4,6,2] => [1,4,6,5,7,3,2]
[[.,.],[[[[.,[.,.]],.],.],.]] => [1,4,3,5,6,7,2] => [1,7,4,3,5,6,2] => [1,5,4,6,7,3,2]
[[.,.],[[[[[.,.],.],.],.],.]] => [1,3,4,5,6,7,2] => [1,7,3,4,5,6,2] => [1,4,5,6,7,3,2]
[[.,[.,.]],[.,[.,[.,[.,.]]]]] => [2,1,7,6,5,4,3] => [2,1,7,3,4,5,6] => [2,1,4,5,6,7,3]
[[.,[.,.]],[.,[.,[[.,.],.]]]] => [2,1,6,7,5,4,3] => [2,1,7,3,4,6,5] => [2,1,4,5,7,6,3]
[[.,[.,.]],[.,[[.,.],[.,.]]]] => [2,1,5,7,6,4,3] => [2,1,7,3,5,4,6] => [2,1,4,6,5,7,3]
[[.,[.,.]],[.,[[.,[.,.]],.]]] => [2,1,6,5,7,4,3] => [2,1,7,3,6,5,4] => [2,1,4,7,6,5,3]
[[.,[.,.]],[.,[[[.,.],.],.]]] => [2,1,5,6,7,4,3] => [2,1,7,3,5,6,4] => [2,1,4,6,7,5,3]
[[.,[.,.]],[[.,.],[.,[.,.]]]] => [2,1,4,7,6,5,3] => [2,1,7,4,3,5,6] => [2,1,5,4,6,7,3]
[[.,[.,.]],[[.,.],[[.,.],.]]] => [2,1,4,6,7,5,3] => [2,1,7,4,3,6,5] => [2,1,5,4,7,6,3]
[[.,[.,.]],[[.,[.,.]],[.,.]]] => [2,1,5,4,7,6,3] => [2,1,7,5,4,3,6] => [2,1,6,5,4,7,3]
[[.,[.,.]],[[[.,.],.],[.,.]]] => [2,1,4,5,7,6,3] => [2,1,7,4,5,3,6] => [2,1,5,6,4,7,3]
[[.,[.,.]],[[.,[.,[.,.]]],.]] => [2,1,6,5,4,7,3] => [2,1,7,6,4,5,3] => [2,1,6,7,5,4,3]
[[.,[.,.]],[[.,[[.,.],.]],.]] => [2,1,5,6,4,7,3] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3]
[[.,[.,.]],[[[.,.],[.,.]],.]] => [2,1,4,6,5,7,3] => [2,1,7,4,6,5,3] => [2,1,5,7,6,4,3]
[[.,[.,.]],[[[.,[.,.]],.],.]] => [2,1,5,4,6,7,3] => [2,1,7,5,4,6,3] => [2,1,6,5,7,4,3]
[[.,[.,.]],[[[[.,.],.],.],.]] => [2,1,4,5,6,7,3] => [2,1,7,4,5,6,3] => [2,1,5,6,7,4,3]
[[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,2,7,6,5,4,3] => [1,2,7,3,4,5,6] => [1,2,4,5,6,7,3]
[[[.,.],.],[.,[.,[[.,.],.]]]] => [1,2,6,7,5,4,3] => [1,2,7,3,4,6,5] => [1,2,4,5,7,6,3]
[[[.,.],.],[.,[[.,.],[.,.]]]] => [1,2,5,7,6,4,3] => [1,2,7,3,5,4,6] => [1,2,4,6,5,7,3]
[[[.,.],.],[.,[[.,[.,.]],.]]] => [1,2,6,5,7,4,3] => [1,2,7,3,6,5,4] => [1,2,4,7,6,5,3]
[[[.,.],.],[.,[[[.,.],.],.]]] => [1,2,5,6,7,4,3] => [1,2,7,3,5,6,4] => [1,2,4,6,7,5,3]
[[[.,.],.],[[.,.],[.,[.,.]]]] => [1,2,4,7,6,5,3] => [1,2,7,4,3,5,6] => [1,2,5,4,6,7,3]
[[[.,.],.],[[.,.],[[.,.],.]]] => [1,2,4,6,7,5,3] => [1,2,7,4,3,6,5] => [1,2,5,4,7,6,3]
[[[.,.],.],[[.,[.,.]],[.,.]]] => [1,2,5,4,7,6,3] => [1,2,7,5,4,3,6] => [1,2,6,5,4,7,3]
[[[.,.],.],[[[.,.],.],[.,.]]] => [1,2,4,5,7,6,3] => [1,2,7,4,5,3,6] => [1,2,5,6,4,7,3]
[[[.,.],.],[[.,[.,[.,.]]],.]] => [1,2,6,5,4,7,3] => [1,2,7,6,4,5,3] => [1,2,6,7,5,4,3]
[[[.,.],.],[[.,[[.,.],.]],.]] => [1,2,5,6,4,7,3] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3]
[[[.,.],.],[[[.,.],[.,.]],.]] => [1,2,4,6,5,7,3] => [1,2,7,4,6,5,3] => [1,2,5,7,6,4,3]
[[[.,.],.],[[[.,[.,.]],.],.]] => [1,2,5,4,6,7,3] => [1,2,7,5,4,6,3] => [1,2,6,5,7,4,3]
[[[.,.],.],[[[[.,.],.],.],.]] => [1,2,4,5,6,7,3] => [1,2,7,4,5,6,3] => [1,2,5,6,7,4,3]
[[.,[.,[.,.]]],[.,[.,[.,.]]]] => [3,2,1,7,6,5,4] => [3,1,2,7,4,5,6] => [2,3,1,5,6,7,4]
[[.,[.,[.,.]]],[.,[[.,.],.]]] => [3,2,1,6,7,5,4] => [3,1,2,7,4,6,5] => [2,3,1,5,7,6,4]
[[.,[.,[.,.]]],[[.,.],[.,.]]] => [3,2,1,5,7,6,4] => [3,1,2,7,5,4,6] => [2,3,1,6,5,7,4]
[[.,[.,[.,.]]],[[.,[.,.]],.]] => [3,2,1,6,5,7,4] => [3,1,2,7,6,5,4] => [2,3,1,7,6,5,4]
[[.,[.,[.,.]]],[[[.,.],.],.]] => [3,2,1,5,6,7,4] => [3,1,2,7,5,6,4] => [2,3,1,6,7,5,4]
[[.,[[.,.],.]],[.,[.,[.,.]]]] => [2,3,1,7,6,5,4] => [3,2,1,7,4,5,6] => [3,2,1,5,6,7,4]
[[.,[[.,.],.]],[.,[[.,.],.]]] => [2,3,1,6,7,5,4] => [3,2,1,7,4,6,5] => [3,2,1,5,7,6,4]
[[.,[[.,.],.]],[[.,.],[.,.]]] => [2,3,1,5,7,6,4] => [3,2,1,7,5,4,6] => [3,2,1,6,5,7,4]
[[.,[[.,.],.]],[[.,[.,.]],.]] => [2,3,1,6,5,7,4] => [3,2,1,7,6,5,4] => [3,2,1,7,6,5,4]
[[.,[[.,.],.]],[[[.,.],.],.]] => [2,3,1,5,6,7,4] => [3,2,1,7,5,6,4] => [3,2,1,6,7,5,4]
[[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,3,2,7,6,5,4] => [1,3,2,7,4,5,6] => [1,3,2,5,6,7,4]
[[[.,.],[.,.]],[.,[[.,.],.]]] => [1,3,2,6,7,5,4] => [1,3,2,7,4,6,5] => [1,3,2,5,7,6,4]
[[[.,.],[.,.]],[[.,.],[.,.]]] => [1,3,2,5,7,6,4] => [1,3,2,7,5,4,6] => [1,3,2,6,5,7,4]
[[[.,.],[.,.]],[[.,[.,.]],.]] => [1,3,2,6,5,7,4] => [1,3,2,7,6,5,4] => [1,3,2,7,6,5,4]
[[[.,.],[.,.]],[[[.,.],.],.]] => [1,3,2,5,6,7,4] => [1,3,2,7,5,6,4] => [1,3,2,6,7,5,4]
[[[.,[.,.]],.],[.,[.,[.,.]]]] => [2,1,3,7,6,5,4] => [2,1,3,7,4,5,6] => [2,1,3,5,6,7,4]
[[[.,[.,.]],.],[.,[[.,.],.]]] => [2,1,3,6,7,5,4] => [2,1,3,7,4,6,5] => [2,1,3,5,7,6,4]
[[[.,[.,.]],.],[[.,.],[.,.]]] => [2,1,3,5,7,6,4] => [2,1,3,7,5,4,6] => [2,1,3,6,5,7,4]
[[[.,[.,.]],.],[[.,[.,.]],.]] => [2,1,3,6,5,7,4] => [2,1,3,7,6,5,4] => [2,1,3,7,6,5,4]
[[[.,[.,.]],.],[[[.,.],.],.]] => [2,1,3,5,6,7,4] => [2,1,3,7,5,6,4] => [2,1,3,6,7,5,4]
[[[[.,.],.],.],[.,[.,[.,.]]]] => [1,2,3,7,6,5,4] => [1,2,3,7,4,5,6] => [1,2,3,5,6,7,4]
[[[[.,.],.],.],[.,[[.,.],.]]] => [1,2,3,6,7,5,4] => [1,2,3,7,4,6,5] => [1,2,3,5,7,6,4]
[[[[.,.],.],.],[[.,.],[.,.]]] => [1,2,3,5,7,6,4] => [1,2,3,7,5,4,6] => [1,2,3,6,5,7,4]
[[[[.,.],.],.],[[.,[.,.]],.]] => [1,2,3,6,5,7,4] => [1,2,3,7,6,5,4] => [1,2,3,7,6,5,4]
[[[[.,.],.],.],[[[.,.],.],.]] => [1,2,3,5,6,7,4] => [1,2,3,7,5,6,4] => [1,2,3,6,7,5,4]
[[.,[.,[.,[.,.]]]],[.,[.,.]]] => [4,3,2,1,7,6,5] => [4,1,2,3,7,5,6] => [2,3,4,1,6,7,5]
[[.,[.,[.,[.,.]]]],[[.,.],.]] => [4,3,2,1,6,7,5] => [4,1,2,3,7,6,5] => [2,3,4,1,7,6,5]
[[.,[.,[[.,.],.]]],[.,[.,.]]] => [3,4,2,1,7,6,5] => [4,1,3,2,7,5,6] => [2,4,3,1,6,7,5]
[[.,[.,[[.,.],.]]],[[.,.],.]] => [3,4,2,1,6,7,5] => [4,1,3,2,7,6,5] => [2,4,3,1,7,6,5]
[[.,[[.,.],[.,.]]],[.,[.,.]]] => [2,4,3,1,7,6,5] => [4,2,1,3,7,5,6] => [3,2,4,1,6,7,5]
[[.,[[.,.],[.,.]]],[[.,.],.]] => [2,4,3,1,6,7,5] => [4,2,1,3,7,6,5] => [3,2,4,1,7,6,5]
[[.,[[.,[.,.]],.]],[.,[.,.]]] => [3,2,4,1,7,6,5] => [4,3,2,1,7,5,6] => [4,3,2,1,6,7,5]
[[.,[[.,[.,.]],.]],[[.,.],.]] => [3,2,4,1,6,7,5] => [4,3,2,1,7,6,5] => [4,3,2,1,7,6,5]
[[.,[[[.,.],.],.]],[.,[.,.]]] => [2,3,4,1,7,6,5] => [4,2,3,1,7,5,6] => [3,4,2,1,6,7,5]
[[.,[[[.,.],.],.]],[[.,.],.]] => [2,3,4,1,6,7,5] => [4,2,3,1,7,6,5] => [3,4,2,1,7,6,5]
[[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,4,3,2,7,6,5] => [1,4,2,3,7,5,6] => [1,3,4,2,6,7,5]
[[[.,.],[.,[.,.]]],[[.,.],.]] => [1,4,3,2,6,7,5] => [1,4,2,3,7,6,5] => [1,3,4,2,7,6,5]
[[[.,.],[[.,.],.]],[.,[.,.]]] => [1,3,4,2,7,6,5] => [1,4,3,2,7,5,6] => [1,4,3,2,6,7,5]
[[[.,.],[[.,.],.]],[[.,.],.]] => [1,3,4,2,6,7,5] => [1,4,3,2,7,6,5] => [1,4,3,2,7,6,5]
[[[.,[.,.]],[.,.]],[.,[.,.]]] => [2,1,4,3,7,6,5] => [2,1,4,3,7,5,6] => [2,1,4,3,6,7,5]
[[[.,[.,.]],[.,.]],[[.,.],.]] => [2,1,4,3,6,7,5] => [2,1,4,3,7,6,5] => [2,1,4,3,7,6,5]
[[[[.,.],.],[.,.]],[.,[.,.]]] => [1,2,4,3,7,6,5] => [1,2,4,3,7,5,6] => [1,2,4,3,6,7,5]
[[[[.,.],.],[.,.]],[[.,.],.]] => [1,2,4,3,6,7,5] => [1,2,4,3,7,6,5] => [1,2,4,3,7,6,5]
[[[.,[.,[.,.]]],.],[.,[.,.]]] => [3,2,1,4,7,6,5] => [3,1,2,4,7,5,6] => [2,3,1,4,6,7,5]
[[[.,[.,[.,.]]],.],[[.,.],.]] => [3,2,1,4,6,7,5] => [3,1,2,4,7,6,5] => [2,3,1,4,7,6,5]
[[[.,[[.,.],.]],.],[.,[.,.]]] => [2,3,1,4,7,6,5] => [3,2,1,4,7,5,6] => [3,2,1,4,6,7,5]
[[[.,[[.,.],.]],.],[[.,.],.]] => [2,3,1,4,6,7,5] => [3,2,1,4,7,6,5] => [3,2,1,4,7,6,5]
[[[[.,.],[.,.]],.],[.,[.,.]]] => [1,3,2,4,7,6,5] => [1,3,2,4,7,5,6] => [1,3,2,4,6,7,5]
[[[[.,.],[.,.]],.],[[.,.],.]] => [1,3,2,4,6,7,5] => [1,3,2,4,7,6,5] => [1,3,2,4,7,6,5]
[[[[.,[.,.]],.],.],[.,[.,.]]] => [2,1,3,4,7,6,5] => [2,1,3,4,7,5,6] => [2,1,3,4,6,7,5]
[[[[.,[.,.]],.],.],[[.,.],.]] => [2,1,3,4,6,7,5] => [2,1,3,4,7,6,5] => [2,1,3,4,7,6,5]
[[[[[.,.],.],.],.],[.,[.,.]]] => [1,2,3,4,7,6,5] => [1,2,3,4,7,5,6] => [1,2,3,4,6,7,5]
[[[[[.,.],.],.],.],[[.,.],.]] => [1,2,3,4,6,7,5] => [1,2,3,4,7,6,5] => [1,2,3,4,7,6,5]
[[.,[.,[.,[.,[.,.]]]]],[.,.]] => [5,4,3,2,1,7,6] => [5,1,2,3,4,7,6] => [2,3,4,5,1,7,6]
[[.,[.,[.,[[.,.],.]]]],[.,.]] => [4,5,3,2,1,7,6] => [5,1,2,4,3,7,6] => [2,3,5,4,1,7,6]
[[.,[.,[[.,.],[.,.]]]],[.,.]] => [3,5,4,2,1,7,6] => [5,1,3,2,4,7,6] => [2,4,3,5,1,7,6]
[[.,[.,[[.,[.,.]],.]]],[.,.]] => [4,3,5,2,1,7,6] => [5,1,4,3,2,7,6] => [2,5,4,3,1,7,6]
[[.,[.,[[[.,.],.],.]]],[.,.]] => [3,4,5,2,1,7,6] => [5,1,3,4,2,7,6] => [2,4,5,3,1,7,6]
[[.,[[.,.],[.,[.,.]]]],[.,.]] => [2,5,4,3,1,7,6] => [5,2,1,3,4,7,6] => [3,2,4,5,1,7,6]
[[.,[[.,.],[[.,.],.]]],[.,.]] => [2,4,5,3,1,7,6] => [5,2,1,4,3,7,6] => [3,2,5,4,1,7,6]
[[.,[[.,[.,.]],[.,.]]],[.,.]] => [3,2,5,4,1,7,6] => [5,3,2,1,4,7,6] => [4,3,2,5,1,7,6]
[[.,[[[.,.],.],[.,.]]],[.,.]] => [2,3,5,4,1,7,6] => [5,2,3,1,4,7,6] => [3,4,2,5,1,7,6]
[[.,[[.,[.,[.,.]]],.]],[.,.]] => [4,3,2,5,1,7,6] => [5,4,2,3,1,7,6] => [4,5,3,2,1,7,6]
[[.,[[.,[[.,.],.]],.]],[.,.]] => [3,4,2,5,1,7,6] => [5,4,3,2,1,7,6] => [5,4,3,2,1,7,6]
[[.,[[[.,.],[.,.]],.]],[.,.]] => [2,4,3,5,1,7,6] => [5,2,4,3,1,7,6] => [3,5,4,2,1,7,6]
[[.,[[[.,[.,.]],.],.]],[.,.]] => [3,2,4,5,1,7,6] => [5,3,2,4,1,7,6] => [4,3,5,2,1,7,6]
[[.,[[[[.,.],.],.],.]],[.,.]] => [2,3,4,5,1,7,6] => [5,2,3,4,1,7,6] => [3,4,5,2,1,7,6]
[[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,5,4,3,2,7,6] => [1,5,2,3,4,7,6] => [1,3,4,5,2,7,6]
[[[.,.],[.,[[.,.],.]]],[.,.]] => [1,4,5,3,2,7,6] => [1,5,2,4,3,7,6] => [1,3,5,4,2,7,6]
[[[.,.],[[.,.],[.,.]]],[.,.]] => [1,3,5,4,2,7,6] => [1,5,3,2,4,7,6] => [1,4,3,5,2,7,6]
[[[.,.],[[.,[.,.]],.]],[.,.]] => [1,4,3,5,2,7,6] => [1,5,4,3,2,7,6] => [1,5,4,3,2,7,6]
[[[.,.],[[[.,.],.],.]],[.,.]] => [1,3,4,5,2,7,6] => [1,5,3,4,2,7,6] => [1,4,5,3,2,7,6]
[[[.,[.,.]],[.,[.,.]]],[.,.]] => [2,1,5,4,3,7,6] => [2,1,5,3,4,7,6] => [2,1,4,5,3,7,6]
[[[.,[.,.]],[[.,.],.]],[.,.]] => [2,1,4,5,3,7,6] => [2,1,5,4,3,7,6] => [2,1,5,4,3,7,6]
[[[[.,.],.],[.,[.,.]]],[.,.]] => [1,2,5,4,3,7,6] => [1,2,5,3,4,7,6] => [1,2,4,5,3,7,6]
[[[[.,.],.],[[.,.],.]],[.,.]] => [1,2,4,5,3,7,6] => [1,2,5,4,3,7,6] => [1,2,5,4,3,7,6]
[[[.,[.,[.,.]]],[.,.]],[.,.]] => [3,2,1,5,4,7,6] => [3,1,2,5,4,7,6] => [2,3,1,5,4,7,6]
[[[.,[[.,.],.]],[.,.]],[.,.]] => [2,3,1,5,4,7,6] => [3,2,1,5,4,7,6] => [3,2,1,5,4,7,6]
[[[[.,.],[.,.]],[.,.]],[.,.]] => [1,3,2,5,4,7,6] => [1,3,2,5,4,7,6] => [1,3,2,5,4,7,6]
[[[[.,[.,.]],.],[.,.]],[.,.]] => [2,1,3,5,4,7,6] => [2,1,3,5,4,7,6] => [2,1,3,5,4,7,6]
[[[[[.,.],.],.],[.,.]],[.,.]] => [1,2,3,5,4,7,6] => [1,2,3,5,4,7,6] => [1,2,3,5,4,7,6]
[[[.,[.,[.,[.,.]]]],.],[.,.]] => [4,3,2,1,5,7,6] => [4,1,2,3,5,7,6] => [2,3,4,1,5,7,6]
[[[.,[.,[[.,.],.]]],.],[.,.]] => [3,4,2,1,5,7,6] => [4,1,3,2,5,7,6] => [2,4,3,1,5,7,6]
[[[.,[[.,.],[.,.]]],.],[.,.]] => [2,4,3,1,5,7,6] => [4,2,1,3,5,7,6] => [3,2,4,1,5,7,6]
[[[.,[[.,[.,.]],.]],.],[.,.]] => [3,2,4,1,5,7,6] => [4,3,2,1,5,7,6] => [4,3,2,1,5,7,6]
[[[.,[[[.,.],.],.]],.],[.,.]] => [2,3,4,1,5,7,6] => [4,2,3,1,5,7,6] => [3,4,2,1,5,7,6]
[[[[.,.],[.,[.,.]]],.],[.,.]] => [1,4,3,2,5,7,6] => [1,4,2,3,5,7,6] => [1,3,4,2,5,7,6]
[[[[.,.],[[.,.],.]],.],[.,.]] => [1,3,4,2,5,7,6] => [1,4,3,2,5,7,6] => [1,4,3,2,5,7,6]
[[[[.,[.,.]],[.,.]],.],[.,.]] => [2,1,4,3,5,7,6] => [2,1,4,3,5,7,6] => [2,1,4,3,5,7,6]
[[[[[.,.],.],[.,.]],.],[.,.]] => [1,2,4,3,5,7,6] => [1,2,4,3,5,7,6] => [1,2,4,3,5,7,6]
[[[[.,[.,[.,.]]],.],.],[.,.]] => [3,2,1,4,5,7,6] => [3,1,2,4,5,7,6] => [2,3,1,4,5,7,6]
[[[[.,[[.,.],.]],.],.],[.,.]] => [2,3,1,4,5,7,6] => [3,2,1,4,5,7,6] => [3,2,1,4,5,7,6]
[[[[[.,.],[.,.]],.],.],[.,.]] => [1,3,2,4,5,7,6] => [1,3,2,4,5,7,6] => [1,3,2,4,5,7,6]
[[[[[.,[.,.]],.],.],.],[.,.]] => [2,1,3,4,5,7,6] => [2,1,3,4,5,7,6] => [2,1,3,4,5,7,6]
[[[[[[.,.],.],.],.],.],[.,.]] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6]
[[.,[.,[.,[.,[.,[.,.]]]]]],.] => [6,5,4,3,2,1,7] => [6,1,2,3,4,5,7] => [2,3,4,5,6,1,7]
[[.,[.,[.,[.,[[.,.],.]]]]],.] => [5,6,4,3,2,1,7] => [6,1,2,3,5,4,7] => [2,3,4,6,5,1,7]
[[.,[.,[.,[[.,.],[.,.]]]]],.] => [4,6,5,3,2,1,7] => [6,1,2,4,3,5,7] => [2,3,5,4,6,1,7]
[[.,[.,[.,[[.,[.,.]],.]]]],.] => [5,4,6,3,2,1,7] => [6,1,2,5,4,3,7] => [2,3,6,5,4,1,7]
[[.,[.,[.,[[[.,.],.],.]]]],.] => [4,5,6,3,2,1,7] => [6,1,2,4,5,3,7] => [2,3,5,6,4,1,7]
[[.,[.,[[.,.],[.,[.,.]]]]],.] => [3,6,5,4,2,1,7] => [6,1,3,2,4,5,7] => [2,4,3,5,6,1,7]
[[.,[.,[[.,.],[[.,.],.]]]],.] => [3,5,6,4,2,1,7] => [6,1,3,2,5,4,7] => [2,4,3,6,5,1,7]
[[.,[.,[[.,[.,.]],[.,.]]]],.] => [4,3,6,5,2,1,7] => [6,1,4,3,2,5,7] => [2,5,4,3,6,1,7]
[[.,[.,[[[.,.],.],[.,.]]]],.] => [3,4,6,5,2,1,7] => [6,1,3,4,2,5,7] => [2,4,5,3,6,1,7]
[[.,[.,[[.,[.,[.,.]]],.]]],.] => [5,4,3,6,2,1,7] => [6,1,5,3,4,2,7] => [2,5,6,4,3,1,7]
[[.,[.,[[.,[[.,.],.]],.]]],.] => [4,5,3,6,2,1,7] => [6,1,5,4,3,2,7] => [2,6,5,4,3,1,7]
[[.,[.,[[[.,.],[.,.]],.]]],.] => [3,5,4,6,2,1,7] => [6,1,3,5,4,2,7] => [2,4,6,5,3,1,7]
[[.,[.,[[[.,[.,.]],.],.]]],.] => [4,3,5,6,2,1,7] => [6,1,4,3,5,2,7] => [2,5,4,6,3,1,7]
[[.,[.,[[[[.,.],.],.],.]]],.] => [3,4,5,6,2,1,7] => [6,1,3,4,5,2,7] => [2,4,5,6,3,1,7]
[[.,[[.,.],[.,[.,[.,.]]]]],.] => [2,6,5,4,3,1,7] => [6,2,1,3,4,5,7] => [3,2,4,5,6,1,7]
[[.,[[.,.],[.,[[.,.],.]]]],.] => [2,5,6,4,3,1,7] => [6,2,1,3,5,4,7] => [3,2,4,6,5,1,7]
[[.,[[.,.],[[.,.],[.,.]]]],.] => [2,4,6,5,3,1,7] => [6,2,1,4,3,5,7] => [3,2,5,4,6,1,7]
[[.,[[.,.],[[.,[.,.]],.]]],.] => [2,5,4,6,3,1,7] => [6,2,1,5,4,3,7] => [3,2,6,5,4,1,7]
[[.,[[.,.],[[[.,.],.],.]]],.] => [2,4,5,6,3,1,7] => [6,2,1,4,5,3,7] => [3,2,5,6,4,1,7]
[[.,[[.,[.,.]],[.,[.,.]]]],.] => [3,2,6,5,4,1,7] => [6,3,2,1,4,5,7] => [4,3,2,5,6,1,7]
[[.,[[.,[.,.]],[[.,.],.]]],.] => [3,2,5,6,4,1,7] => [6,3,2,1,5,4,7] => [4,3,2,6,5,1,7]
[[.,[[[.,.],.],[.,[.,.]]]],.] => [2,3,6,5,4,1,7] => [6,2,3,1,4,5,7] => [3,4,2,5,6,1,7]
[[.,[[[.,.],.],[[.,.],.]]],.] => [2,3,5,6,4,1,7] => [6,2,3,1,5,4,7] => [3,4,2,6,5,1,7]
[[.,[[.,[.,[.,.]]],[.,.]]],.] => [4,3,2,6,5,1,7] => [6,4,2,3,1,5,7] => [4,5,3,2,6,1,7]
[[.,[[.,[[.,.],.]],[.,.]]],.] => [3,4,2,6,5,1,7] => [6,4,3,2,1,5,7] => [5,4,3,2,6,1,7]
[[.,[[[.,.],[.,.]],[.,.]]],.] => [2,4,3,6,5,1,7] => [6,2,4,3,1,5,7] => [3,5,4,2,6,1,7]
[[.,[[[.,[.,.]],.],[.,.]]],.] => [3,2,4,6,5,1,7] => [6,3,2,4,1,5,7] => [4,3,5,2,6,1,7]
[[.,[[[[.,.],.],.],[.,.]]],.] => [2,3,4,6,5,1,7] => [6,2,3,4,1,5,7] => [3,4,5,2,6,1,7]
[[.,[[.,[.,[.,[.,.]]]],.]],.] => [5,4,3,2,6,1,7] => [6,5,2,3,4,1,7] => [4,5,6,3,2,1,7]
[[.,[[.,[.,[[.,.],.]]],.]],.] => [4,5,3,2,6,1,7] => [6,5,2,4,3,1,7] => [4,6,5,3,2,1,7]
[[.,[[.,[[.,.],[.,.]]],.]],.] => [3,5,4,2,6,1,7] => [6,5,3,2,4,1,7] => [5,4,6,3,2,1,7]
[[.,[[.,[[.,[.,.]],.]],.]],.] => [4,3,5,2,6,1,7] => [6,5,4,3,2,1,7] => [6,5,4,3,2,1,7]
[[.,[[.,[[[.,.],.],.]],.]],.] => [3,4,5,2,6,1,7] => [6,5,3,4,2,1,7] => [5,6,4,3,2,1,7]
[[.,[[[.,.],[.,[.,.]]],.]],.] => [2,5,4,3,6,1,7] => [6,2,5,3,4,1,7] => [3,5,6,4,2,1,7]
[[.,[[[.,.],[[.,.],.]],.]],.] => [2,4,5,3,6,1,7] => [6,2,5,4,3,1,7] => [3,6,5,4,2,1,7]
[[.,[[[.,[.,.]],[.,.]],.]],.] => [3,2,5,4,6,1,7] => [6,3,2,5,4,1,7] => [4,3,6,5,2,1,7]
[[.,[[[[.,.],.],[.,.]],.]],.] => [2,3,5,4,6,1,7] => [6,2,3,5,4,1,7] => [3,4,6,5,2,1,7]
[[.,[[[.,[.,[.,.]]],.],.]],.] => [4,3,2,5,6,1,7] => [6,4,2,3,5,1,7] => [4,5,3,6,2,1,7]
[[.,[[[.,[[.,.],.]],.],.]],.] => [3,4,2,5,6,1,7] => [6,4,3,2,5,1,7] => [5,4,3,6,2,1,7]
[[.,[[[[.,.],[.,.]],.],.]],.] => [2,4,3,5,6,1,7] => [6,2,4,3,5,1,7] => [3,5,4,6,2,1,7]
[[.,[[[[.,[.,.]],.],.],.]],.] => [3,2,4,5,6,1,7] => [6,3,2,4,5,1,7] => [4,3,5,6,2,1,7]
[[.,[[[[[.,.],.],.],.],.]],.] => [2,3,4,5,6,1,7] => [6,2,3,4,5,1,7] => [3,4,5,6,2,1,7]
[[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,6,5,4,3,2,7] => [1,6,2,3,4,5,7] => [1,3,4,5,6,2,7]
[[[.,.],[.,[.,[[.,.],.]]]],.] => [1,5,6,4,3,2,7] => [1,6,2,3,5,4,7] => [1,3,4,6,5,2,7]
[[[.,.],[.,[[.,.],[.,.]]]],.] => [1,4,6,5,3,2,7] => [1,6,2,4,3,5,7] => [1,3,5,4,6,2,7]
[[[.,.],[.,[[.,[.,.]],.]]],.] => [1,5,4,6,3,2,7] => [1,6,2,5,4,3,7] => [1,3,6,5,4,2,7]
[[[.,.],[.,[[[.,.],.],.]]],.] => [1,4,5,6,3,2,7] => [1,6,2,4,5,3,7] => [1,3,5,6,4,2,7]
[[[.,.],[[.,.],[.,[.,.]]]],.] => [1,3,6,5,4,2,7] => [1,6,3,2,4,5,7] => [1,4,3,5,6,2,7]
[[[.,.],[[.,.],[[.,.],.]]],.] => [1,3,5,6,4,2,7] => [1,6,3,2,5,4,7] => [1,4,3,6,5,2,7]
[[[.,.],[[.,[.,.]],[.,.]]],.] => [1,4,3,6,5,2,7] => [1,6,4,3,2,5,7] => [1,5,4,3,6,2,7]
[[[.,.],[[[.,.],.],[.,.]]],.] => [1,3,4,6,5,2,7] => [1,6,3,4,2,5,7] => [1,4,5,3,6,2,7]
[[[.,.],[[.,[.,[.,.]]],.]],.] => [1,5,4,3,6,2,7] => [1,6,5,3,4,2,7] => [1,5,6,4,3,2,7]
[[[.,.],[[.,[[.,.],.]],.]],.] => [1,4,5,3,6,2,7] => [1,6,5,4,3,2,7] => [1,6,5,4,3,2,7]
[[[.,.],[[[.,.],[.,.]],.]],.] => [1,3,5,4,6,2,7] => [1,6,3,5,4,2,7] => [1,4,6,5,3,2,7]
[[[.,.],[[[.,[.,.]],.],.]],.] => [1,4,3,5,6,2,7] => [1,6,4,3,5,2,7] => [1,5,4,6,3,2,7]
[[[.,.],[[[[.,.],.],.],.]],.] => [1,3,4,5,6,2,7] => [1,6,3,4,5,2,7] => [1,4,5,6,3,2,7]
[[[.,[.,.]],[.,[.,[.,.]]]],.] => [2,1,6,5,4,3,7] => [2,1,6,3,4,5,7] => [2,1,4,5,6,3,7]
[[[.,[.,.]],[.,[[.,.],.]]],.] => [2,1,5,6,4,3,7] => [2,1,6,3,5,4,7] => [2,1,4,6,5,3,7]
[[[.,[.,.]],[[.,.],[.,.]]],.] => [2,1,4,6,5,3,7] => [2,1,6,4,3,5,7] => [2,1,5,4,6,3,7]
[[[.,[.,.]],[[.,[.,.]],.]],.] => [2,1,5,4,6,3,7] => [2,1,6,5,4,3,7] => [2,1,6,5,4,3,7]
[[[.,[.,.]],[[[.,.],.],.]],.] => [2,1,4,5,6,3,7] => [2,1,6,4,5,3,7] => [2,1,5,6,4,3,7]
[[[[.,.],.],[.,[.,[.,.]]]],.] => [1,2,6,5,4,3,7] => [1,2,6,3,4,5,7] => [1,2,4,5,6,3,7]
[[[[.,.],.],[.,[[.,.],.]]],.] => [1,2,5,6,4,3,7] => [1,2,6,3,5,4,7] => [1,2,4,6,5,3,7]
[[[[.,.],.],[[.,.],[.,.]]],.] => [1,2,4,6,5,3,7] => [1,2,6,4,3,5,7] => [1,2,5,4,6,3,7]
[[[[.,.],.],[[.,[.,.]],.]],.] => [1,2,5,4,6,3,7] => [1,2,6,5,4,3,7] => [1,2,6,5,4,3,7]
[[[[.,.],.],[[[.,.],.],.]],.] => [1,2,4,5,6,3,7] => [1,2,6,4,5,3,7] => [1,2,5,6,4,3,7]
[[[.,[.,[.,.]]],[.,[.,.]]],.] => [3,2,1,6,5,4,7] => [3,1,2,6,4,5,7] => [2,3,1,5,6,4,7]
[[[.,[.,[.,.]]],[[.,.],.]],.] => [3,2,1,5,6,4,7] => [3,1,2,6,5,4,7] => [2,3,1,6,5,4,7]
[[[.,[[.,.],.]],[.,[.,.]]],.] => [2,3,1,6,5,4,7] => [3,2,1,6,4,5,7] => [3,2,1,5,6,4,7]
[[[.,[[.,.],.]],[[.,.],.]],.] => [2,3,1,5,6,4,7] => [3,2,1,6,5,4,7] => [3,2,1,6,5,4,7]
[[[[.,.],[.,.]],[.,[.,.]]],.] => [1,3,2,6,5,4,7] => [1,3,2,6,4,5,7] => [1,3,2,5,6,4,7]
[[[[.,.],[.,.]],[[.,.],.]],.] => [1,3,2,5,6,4,7] => [1,3,2,6,5,4,7] => [1,3,2,6,5,4,7]
[[[[.,[.,.]],.],[.,[.,.]]],.] => [2,1,3,6,5,4,7] => [2,1,3,6,4,5,7] => [2,1,3,5,6,4,7]
[[[[.,[.,.]],.],[[.,.],.]],.] => [2,1,3,5,6,4,7] => [2,1,3,6,5,4,7] => [2,1,3,6,5,4,7]
[[[[[.,.],.],.],[.,[.,.]]],.] => [1,2,3,6,5,4,7] => [1,2,3,6,4,5,7] => [1,2,3,5,6,4,7]
[[[[[.,.],.],.],[[.,.],.]],.] => [1,2,3,5,6,4,7] => [1,2,3,6,5,4,7] => [1,2,3,6,5,4,7]
[[[.,[.,[.,[.,.]]]],[.,.]],.] => [4,3,2,1,6,5,7] => [4,1,2,3,6,5,7] => [2,3,4,1,6,5,7]
[[[.,[.,[[.,.],.]]],[.,.]],.] => [3,4,2,1,6,5,7] => [4,1,3,2,6,5,7] => [2,4,3,1,6,5,7]
[[[.,[[.,.],[.,.]]],[.,.]],.] => [2,4,3,1,6,5,7] => [4,2,1,3,6,5,7] => [3,2,4,1,6,5,7]
[[[.,[[.,[.,.]],.]],[.,.]],.] => [3,2,4,1,6,5,7] => [4,3,2,1,6,5,7] => [4,3,2,1,6,5,7]
[[[.,[[[.,.],.],.]],[.,.]],.] => [2,3,4,1,6,5,7] => [4,2,3,1,6,5,7] => [3,4,2,1,6,5,7]
[[[[.,.],[.,[.,.]]],[.,.]],.] => [1,4,3,2,6,5,7] => [1,4,2,3,6,5,7] => [1,3,4,2,6,5,7]
[[[[.,.],[[.,.],.]],[.,.]],.] => [1,3,4,2,6,5,7] => [1,4,3,2,6,5,7] => [1,4,3,2,6,5,7]
[[[[.,[.,.]],[.,.]],[.,.]],.] => [2,1,4,3,6,5,7] => [2,1,4,3,6,5,7] => [2,1,4,3,6,5,7]
[[[[[.,.],.],[.,.]],[.,.]],.] => [1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => [1,2,4,3,6,5,7]
[[[[.,[.,[.,.]]],.],[.,.]],.] => [3,2,1,4,6,5,7] => [3,1,2,4,6,5,7] => [2,3,1,4,6,5,7]
[[[[.,[[.,.],.]],.],[.,.]],.] => [2,3,1,4,6,5,7] => [3,2,1,4,6,5,7] => [3,2,1,4,6,5,7]
[[[[[.,.],[.,.]],.],[.,.]],.] => [1,3,2,4,6,5,7] => [1,3,2,4,6,5,7] => [1,3,2,4,6,5,7]
[[[[[.,[.,.]],.],.],[.,.]],.] => [2,1,3,4,6,5,7] => [2,1,3,4,6,5,7] => [2,1,3,4,6,5,7]
[[[[[[.,.],.],.],.],[.,.]],.] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7]
[[[.,[.,[.,[.,[.,.]]]]],.],.] => [5,4,3,2,1,6,7] => [5,1,2,3,4,6,7] => [2,3,4,5,1,6,7]
[[[.,[.,[.,[[.,.],.]]]],.],.] => [4,5,3,2,1,6,7] => [5,1,2,4,3,6,7] => [2,3,5,4,1,6,7]
[[[.,[.,[[.,.],[.,.]]]],.],.] => [3,5,4,2,1,6,7] => [5,1,3,2,4,6,7] => [2,4,3,5,1,6,7]
[[[.,[.,[[.,[.,.]],.]]],.],.] => [4,3,5,2,1,6,7] => [5,1,4,3,2,6,7] => [2,5,4,3,1,6,7]
[[[.,[.,[[[.,.],.],.]]],.],.] => [3,4,5,2,1,6,7] => [5,1,3,4,2,6,7] => [2,4,5,3,1,6,7]
[[[.,[[.,.],[.,[.,.]]]],.],.] => [2,5,4,3,1,6,7] => [5,2,1,3,4,6,7] => [3,2,4,5,1,6,7]
[[[.,[[.,.],[[.,.],.]]],.],.] => [2,4,5,3,1,6,7] => [5,2,1,4,3,6,7] => [3,2,5,4,1,6,7]
[[[.,[[.,[.,.]],[.,.]]],.],.] => [3,2,5,4,1,6,7] => [5,3,2,1,4,6,7] => [4,3,2,5,1,6,7]
[[[.,[[[.,.],.],[.,.]]],.],.] => [2,3,5,4,1,6,7] => [5,2,3,1,4,6,7] => [3,4,2,5,1,6,7]
[[[.,[[.,[.,[.,.]]],.]],.],.] => [4,3,2,5,1,6,7] => [5,4,2,3,1,6,7] => [4,5,3,2,1,6,7]
[[[.,[[.,[[.,.],.]],.]],.],.] => [3,4,2,5,1,6,7] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7]
[[[.,[[[.,.],[.,.]],.]],.],.] => [2,4,3,5,1,6,7] => [5,2,4,3,1,6,7] => [3,5,4,2,1,6,7]
[[[.,[[[.,[.,.]],.],.]],.],.] => [3,2,4,5,1,6,7] => [5,3,2,4,1,6,7] => [4,3,5,2,1,6,7]
[[[.,[[[[.,.],.],.],.]],.],.] => [2,3,4,5,1,6,7] => [5,2,3,4,1,6,7] => [3,4,5,2,1,6,7]
[[[[.,.],[.,[.,[.,.]]]],.],.] => [1,5,4,3,2,6,7] => [1,5,2,3,4,6,7] => [1,3,4,5,2,6,7]
[[[[.,.],[.,[[.,.],.]]],.],.] => [1,4,5,3,2,6,7] => [1,5,2,4,3,6,7] => [1,3,5,4,2,6,7]
[[[[.,.],[[.,.],[.,.]]],.],.] => [1,3,5,4,2,6,7] => [1,5,3,2,4,6,7] => [1,4,3,5,2,6,7]
[[[[.,.],[[.,[.,.]],.]],.],.] => [1,4,3,5,2,6,7] => [1,5,4,3,2,6,7] => [1,5,4,3,2,6,7]
[[[[.,.],[[[.,.],.],.]],.],.] => [1,3,4,5,2,6,7] => [1,5,3,4,2,6,7] => [1,4,5,3,2,6,7]
[[[[.,[.,.]],[.,[.,.]]],.],.] => [2,1,5,4,3,6,7] => [2,1,5,3,4,6,7] => [2,1,4,5,3,6,7]
[[[[.,[.,.]],[[.,.],.]],.],.] => [2,1,4,5,3,6,7] => [2,1,5,4,3,6,7] => [2,1,5,4,3,6,7]
[[[[[.,.],.],[.,[.,.]]],.],.] => [1,2,5,4,3,6,7] => [1,2,5,3,4,6,7] => [1,2,4,5,3,6,7]
[[[[[.,.],.],[[.,.],.]],.],.] => [1,2,4,5,3,6,7] => [1,2,5,4,3,6,7] => [1,2,5,4,3,6,7]
[[[[.,[.,[.,.]]],[.,.]],.],.] => [3,2,1,5,4,6,7] => [3,1,2,5,4,6,7] => [2,3,1,5,4,6,7]
[[[[.,[[.,.],.]],[.,.]],.],.] => [2,3,1,5,4,6,7] => [3,2,1,5,4,6,7] => [3,2,1,5,4,6,7]
[[[[[.,.],[.,.]],[.,.]],.],.] => [1,3,2,5,4,6,7] => [1,3,2,5,4,6,7] => [1,3,2,5,4,6,7]
[[[[[.,[.,.]],.],[.,.]],.],.] => [2,1,3,5,4,6,7] => [2,1,3,5,4,6,7] => [2,1,3,5,4,6,7]
[[[[[[.,.],.],.],[.,.]],.],.] => [1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => [1,2,3,5,4,6,7]
[[[[.,[.,[.,[.,.]]]],.],.],.] => [4,3,2,1,5,6,7] => [4,1,2,3,5,6,7] => [2,3,4,1,5,6,7]
[[[[.,[.,[[.,.],.]]],.],.],.] => [3,4,2,1,5,6,7] => [4,1,3,2,5,6,7] => [2,4,3,1,5,6,7]
[[[[.,[[.,.],[.,.]]],.],.],.] => [2,4,3,1,5,6,7] => [4,2,1,3,5,6,7] => [3,2,4,1,5,6,7]
[[[[.,[[.,[.,.]],.]],.],.],.] => [3,2,4,1,5,6,7] => [4,3,2,1,5,6,7] => [4,3,2,1,5,6,7]
[[[[.,[[[.,.],.],.]],.],.],.] => [2,3,4,1,5,6,7] => [4,2,3,1,5,6,7] => [3,4,2,1,5,6,7]
[[[[[.,.],[.,[.,.]]],.],.],.] => [1,4,3,2,5,6,7] => [1,4,2,3,5,6,7] => [1,3,4,2,5,6,7]
[[[[[.,.],[[.,.],.]],.],.],.] => [1,3,4,2,5,6,7] => [1,4,3,2,5,6,7] => [1,4,3,2,5,6,7]
[[[[[.,[.,.]],[.,.]],.],.],.] => [2,1,4,3,5,6,7] => [2,1,4,3,5,6,7] => [2,1,4,3,5,6,7]
[[[[[[.,.],.],[.,.]],.],.],.] => [1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => [1,2,4,3,5,6,7]
[[[[[.,[.,[.,.]]],.],.],.],.] => [3,2,1,4,5,6,7] => [3,1,2,4,5,6,7] => [2,3,1,4,5,6,7]
[[[[[.,[[.,.],.]],.],.],.],.] => [2,3,1,4,5,6,7] => [3,2,1,4,5,6,7] => [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]
[[[[[[.,[.,.]],.],.],.],.],.] => [2,1,3,4,5,6,7] => [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]
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [8,7,6,5,4,3,2,1] => [8,1,2,3,4,5,6,7] => [2,3,4,5,6,7,8,1]
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]] => [5,6,7,8,4,3,2,1] => [8,1,2,3,5,6,7,4] => [2,3,4,6,7,8,5,1]
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]] => [4,5,6,8,7,3,2,1] => [8,1,2,4,5,6,3,7] => [2,3,5,6,7,4,8,1]
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => [3,5,7,8,6,4,2,1] => [8,1,3,2,5,4,7,6] => [2,4,3,6,5,8,7,1]
[.,[[.,[[.,[[.,.],.]],.]],[.,.]]] => [4,5,3,6,2,8,7,1] => [8,6,5,4,3,2,1,7] => [7,6,5,4,3,2,8,1]
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => [5,4,6,3,7,2,8,1] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1]
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]] => [4,3,6,5,7,2,8,1] => [8,7,4,3,6,5,2,1] => [6,5,8,7,4,3,2,1]
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]] => [3,2,6,5,7,4,8,1] => [8,3,2,7,6,5,4,1] => [4,3,8,7,6,5,2,1]
[.,[[[.,[[.,[.,.]],.]],[.,.]],.]] => [4,3,5,2,7,6,8,1] => [8,5,4,3,2,7,6,1] => [6,5,4,3,8,7,2,1]
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => [3,2,5,4,7,6,8,1] => [8,3,2,5,4,7,6,1] => [4,3,6,5,8,7,2,1]
[[.,.],[[.,[[.,[[.,.],.]],.]],.]] => [1,5,6,4,7,3,8,2] => [1,8,7,6,5,4,3,2] => [1,8,7,6,5,4,3,2]
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [2,1,8,7,6,5,4,3] => [2,1,8,3,4,5,6,7] => [2,1,4,5,6,7,8,3]
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [2,1,6,7,8,5,4,3] => [2,1,8,3,4,6,7,5] => [2,1,4,5,7,8,6,3]
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [2,1,5,7,8,6,4,3] => [2,1,8,3,5,4,7,6] => [2,1,4,6,5,8,7,3]
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]] => [2,1,6,5,7,4,8,3] => [2,1,8,7,6,5,4,3] => [2,1,8,7,6,5,4,3]
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [2,1,5,4,7,6,8,3] => [2,1,8,5,4,7,6,3] => [2,1,6,5,8,7,4,3]
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [3,2,1,7,6,5,8,4] => [3,1,2,8,7,5,6,4] => [2,3,1,7,8,6,5,4]
[[.,[[.,.],.]],[[.,[[.,.],.]],.]] => [2,3,1,6,7,5,8,4] => [3,2,1,8,7,6,5,4] => [3,2,1,8,7,6,5,4]
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [4,3,2,1,8,7,6,5] => [4,1,2,3,8,5,6,7] => [2,3,4,1,6,7,8,5]
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [4,3,2,1,7,6,8,5] => [4,1,2,3,8,7,6,5] => [2,3,4,1,8,7,6,5]
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]] => [3,4,2,1,7,8,6,5] => [4,1,3,2,8,5,7,6] => [2,4,3,1,6,8,7,5]
[[.,[.,[[.,.],.]]],[[.,.],[.,.]]] => [3,4,2,1,6,8,7,5] => [4,1,3,2,8,6,5,7] => [2,4,3,1,7,6,8,5]
[[.,[.,[[.,.],.]]],[[.,[.,.]],.]] => [3,4,2,1,7,6,8,5] => [4,1,3,2,8,7,6,5] => [2,4,3,1,8,7,6,5]
[[.,[[.,.],[.,.]]],[.,[[.,.],.]]] => [2,4,3,1,7,8,6,5] => [4,2,1,3,8,5,7,6] => [3,2,4,1,6,8,7,5]
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]] => [2,4,3,1,7,6,8,5] => [4,2,1,3,8,7,6,5] => [3,2,4,1,8,7,6,5]
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [3,2,4,1,8,7,6,5] => [4,3,2,1,8,5,6,7] => [4,3,2,1,6,7,8,5]
[[.,[[.,[.,.]],.]],[.,[[.,.],.]]] => [3,2,4,1,7,8,6,5] => [4,3,2,1,8,5,7,6] => [4,3,2,1,6,8,7,5]
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [3,2,4,1,6,8,7,5] => [4,3,2,1,8,6,5,7] => [4,3,2,1,7,6,8,5]
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]] => [3,2,4,1,7,6,8,5] => [4,3,2,1,8,7,6,5] => [4,3,2,1,8,7,6,5]
[[.,[[.,[.,.]],.]],[[[.,.],.],.]] => [3,2,4,1,6,7,8,5] => [4,3,2,1,8,6,7,5] => [4,3,2,1,7,8,6,5]
[[.,[[[.,.],.],.]],[[.,[.,.]],.]] => [2,3,4,1,7,6,8,5] => [4,2,3,1,8,7,6,5] => [3,4,2,1,8,7,6,5]
[[.,[[[.,.],.],.]],[[[.,.],.],.]] => [2,3,4,1,6,7,8,5] => [4,2,3,1,8,6,7,5] => [3,4,2,1,7,8,6,5]
[[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [1,4,3,2,7,6,8,5] => [1,4,2,3,8,7,6,5] => [1,3,4,2,8,7,6,5]
[[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [1,3,4,2,7,6,8,5] => [1,4,3,2,8,7,6,5] => [1,4,3,2,8,7,6,5]
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [2,1,4,3,8,7,6,5] => [2,1,4,3,8,5,6,7] => [2,1,4,3,6,7,8,5]
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [2,1,4,3,7,8,6,5] => [2,1,4,3,8,5,7,6] => [2,1,4,3,6,8,7,5]
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [2,1,4,3,7,6,8,5] => [2,1,4,3,8,7,6,5] => [2,1,4,3,8,7,6,5]
[[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [1,2,4,3,7,6,8,5] => [1,2,4,3,8,7,6,5] => [1,2,4,3,8,7,6,5]
[[[.,[.,[.,.]]],.],[[.,[.,.]],.]] => [3,2,1,4,7,6,8,5] => [3,1,2,4,8,7,6,5] => [2,3,1,4,8,7,6,5]
[[[.,[[.,.],.]],.],[[.,[.,.]],.]] => [2,3,1,4,7,6,8,5] => [3,2,1,4,8,7,6,5] => [3,2,1,4,8,7,6,5]
[[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [1,3,2,4,7,6,8,5] => [1,3,2,4,8,7,6,5] => [1,3,2,4,8,7,6,5]
[[[[.,[.,.]],.],.],[[.,[.,.]],.]] => [2,1,3,4,7,6,8,5] => [2,1,3,4,8,7,6,5] => [2,1,3,4,8,7,6,5]
[[[[[.,.],.],.],.],[[.,[.,.]],.]] => [1,2,3,4,7,6,8,5] => [1,2,3,4,8,7,6,5] => [1,2,3,4,8,7,6,5]
[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]] => [4,3,2,5,1,8,7,6] => [5,4,2,3,1,8,6,7] => [4,5,3,2,1,7,8,6]
[[.,[[.,[[.,.],.]],.]],[[.,.],.]] => [3,4,2,5,1,7,8,6] => [5,4,3,2,1,8,7,6] => [5,4,3,2,1,8,7,6]
[[[.,[[.,[.,.]],.]],.],[.,[.,.]]] => [3,2,4,1,5,8,7,6] => [4,3,2,1,5,8,6,7] => [4,3,2,1,5,7,8,6]
[[[.,[[.,[.,.]],.]],.],[[.,.],.]] => [3,2,4,1,5,7,8,6] => [4,3,2,1,5,8,7,6] => [4,3,2,1,5,8,7,6]
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [3,2,1,4,5,8,7,6] => [3,1,2,4,5,8,6,7] => [2,3,1,4,5,7,8,6]
[[[[.,[[.,.],.]],.],.],[[.,.],.]] => [2,3,1,4,5,7,8,6] => [3,2,1,4,5,8,7,6] => [3,2,1,4,5,8,7,6]
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [6,5,4,3,2,1,8,7] => [6,1,2,3,4,5,8,7] => [2,3,4,5,6,1,8,7]
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]] => [4,5,6,3,2,1,8,7] => [6,1,2,4,5,3,8,7] => [2,3,5,6,4,1,8,7]
[[.,[.,[[.,.],[[.,.],.]]]],[.,.]] => [3,5,6,4,2,1,8,7] => [6,1,3,2,5,4,8,7] => [2,4,3,6,5,1,8,7]
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => [4,3,5,2,6,1,8,7] => [6,5,4,3,2,1,8,7] => [6,5,4,3,2,1,8,7]
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]] => [3,2,5,4,6,1,8,7] => [6,3,2,5,4,1,8,7] => [4,3,6,5,2,1,8,7]
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [2,1,6,5,4,3,8,7] => [2,1,6,3,4,5,8,7] => [2,1,4,5,6,3,8,7]
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [2,1,5,6,4,3,8,7] => [2,1,6,3,5,4,8,7] => [2,1,4,6,5,3,8,7]
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [2,1,5,4,6,3,8,7] => [2,1,6,5,4,3,8,7] => [2,1,6,5,4,3,8,7]
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [4,3,2,1,6,5,8,7] => [4,1,2,3,6,5,8,7] => [2,3,4,1,6,5,8,7]
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]] => [3,4,2,1,6,5,8,7] => [4,1,3,2,6,5,8,7] => [2,4,3,1,6,5,8,7]
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => [3,2,4,1,6,5,8,7] => [4,3,2,1,6,5,8,7] => [4,3,2,1,6,5,8,7]
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7]
[[[[.,[[.,[.,.]],.]],.],.],[.,.]] => [3,2,4,1,5,6,8,7] => [4,3,2,1,5,6,8,7] => [4,3,2,1,5,6,8,7]
[[[[[[.,[.,.]],.],.],.],.],[.,.]] => [2,1,3,4,5,6,8,7] => [2,1,3,4,5,6,8,7] => [2,1,3,4,5,6,8,7]
[[.,[[.,[[.,[[.,.],.]],.]],.]],.] => [4,5,3,6,2,7,1,8] => [7,6,5,4,3,2,1,8] => [7,6,5,4,3,2,1,8]
[[[.,[[.,[.,.]],.]],[.,[.,.]]],.] => [3,2,4,1,7,6,5,8] => [4,3,2,1,7,5,6,8] => [4,3,2,1,6,7,5,8]
[[[.,[[.,[.,.]],.]],[[.,.],.]],.] => [3,2,4,1,6,7,5,8] => [4,3,2,1,7,6,5,8] => [4,3,2,1,7,6,5,8]
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,4,3,2,7,6,5,8] => [1,4,2,3,7,5,6,8] => [1,3,4,2,6,7,5,8]
[[[[.,.],[[.,.],.]],[[.,.],.]],.] => [1,3,4,2,6,7,5,8] => [1,4,3,2,7,6,5,8] => [1,4,3,2,7,6,5,8]
[[[[.,[[.,[.,.]],.]],.],[.,.]],.] => [3,2,4,1,5,7,6,8] => [4,3,2,1,5,7,6,8] => [4,3,2,1,5,7,6,8]
[[[[[[.,.],[.,.]],.],.],[.,.]],.] => [1,3,2,4,5,7,6,8] => [1,3,2,4,5,7,6,8] => [1,3,2,4,5,7,6,8]
[[[[.,[[.,[.,.]],.]],[.,.]],.],.] => [3,2,4,1,6,5,7,8] => [4,3,2,1,6,5,7,8] => [4,3,2,1,6,5,7,8]
[[[[[[.,.],.],[.,.]],[.,.]],.],.] => [1,2,4,3,6,5,7,8] => [1,2,4,3,6,5,7,8] => [1,2,4,3,6,5,7,8]
[[[[[.,[[.,[.,.]],.]],.],.],.],.] => [3,2,4,1,5,6,7,8] => [4,3,2,1,5,6,7,8] => [4,3,2,1,5,6,7,8]
[[[[[[[[.,.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8]
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
first fundamental transformation
Description
Return the permutation whose cycles are the subsequences between successive left to right maxima.
Map
catalanization
Description
The catalanization of a permutation.
For a permutation $\sigma$, this is the product of the reflections corresponding to the inversions of $\sigma$ in lex-order.
A permutation is $231$-avoiding if and only if it is a fixpoint of this map. Also, for every permutation there exists an index $k$ such that the $k$-fold application of this map is $231$-avoiding.