Identifier
Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations
Mp00088: Permutations —Kreweras complement⟶ Permutations
Mp00277: Permutations —catalanization⟶ Permutations
Images
[.,.] => [1] => [1] => [1]
[.,[.,.]] => [2,1] => [1,2] => [1,2]
[[.,.],.] => [1,2] => [2,1] => [2,1]
[.,[.,[.,.]]] => [3,2,1] => [1,3,2] => [1,3,2]
[.,[[.,.],.]] => [2,3,1] => [1,2,3] => [1,2,3]
[[.,.],[.,.]] => [1,3,2] => [2,1,3] => [2,1,3]
[[.,[.,.]],.] => [2,1,3] => [3,2,1] => [3,2,1]
[[[.,.],.],.] => [1,2,3] => [2,3,1] => [2,3,1]
[.,[.,[.,[.,.]]]] => [4,3,2,1] => [1,4,3,2] => [1,4,3,2]
[.,[.,[[.,.],.]]] => [3,4,2,1] => [1,4,2,3] => [1,3,4,2]
[.,[[.,.],[.,.]]] => [2,4,3,1] => [1,2,4,3] => [1,2,4,3]
[.,[[.,[.,.]],.]] => [3,2,4,1] => [1,3,2,4] => [1,3,2,4]
[.,[[[.,.],.],.]] => [2,3,4,1] => [1,2,3,4] => [1,2,3,4]
[[.,.],[.,[.,.]]] => [1,4,3,2] => [2,1,4,3] => [2,1,4,3]
[[.,.],[[.,.],.]] => [1,3,4,2] => [2,1,3,4] => [2,1,3,4]
[[.,[.,.]],[.,.]] => [2,1,4,3] => [3,2,1,4] => [3,2,1,4]
[[[.,.],.],[.,.]] => [1,2,4,3] => [2,3,1,4] => [2,3,1,4]
[[.,[.,[.,.]]],.] => [3,2,1,4] => [4,3,2,1] => [4,3,2,1]
[[.,[[.,.],.]],.] => [2,3,1,4] => [4,2,3,1] => [3,4,2,1]
[[[.,.],[.,.]],.] => [1,3,2,4] => [2,4,3,1] => [2,4,3,1]
[[[.,[.,.]],.],.] => [2,1,3,4] => [3,2,4,1] => [3,2,4,1]
[[[[.,.],.],.],.] => [1,2,3,4] => [2,3,4,1] => [2,3,4,1]
[.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => [1,5,4,3,2] => [1,5,4,3,2]
[.,[.,[.,[[.,.],.]]]] => [4,5,3,2,1] => [1,5,4,2,3] => [1,4,5,3,2]
[.,[.,[[.,.],[.,.]]]] => [3,5,4,2,1] => [1,5,2,4,3] => [1,3,5,4,2]
[.,[.,[[.,[.,.]],.]]] => [4,3,5,2,1] => [1,5,3,2,4] => [1,4,3,5,2]
[.,[.,[[[.,.],.],.]]] => [3,4,5,2,1] => [1,5,2,3,4] => [1,3,4,5,2]
[.,[[.,.],[.,[.,.]]]] => [2,5,4,3,1] => [1,2,5,4,3] => [1,2,5,4,3]
[.,[[.,.],[[.,.],.]]] => [2,4,5,3,1] => [1,2,5,3,4] => [1,2,4,5,3]
[.,[[.,[.,.]],[.,.]]] => [3,2,5,4,1] => [1,3,2,5,4] => [1,3,2,5,4]
[.,[[[.,.],.],[.,.]]] => [2,3,5,4,1] => [1,2,3,5,4] => [1,2,3,5,4]
[.,[[.,[.,[.,.]]],.]] => [4,3,2,5,1] => [1,4,3,2,5] => [1,4,3,2,5]
[.,[[.,[[.,.],.]],.]] => [3,4,2,5,1] => [1,4,2,3,5] => [1,3,4,2,5]
[.,[[[.,.],[.,.]],.]] => [2,4,3,5,1] => [1,2,4,3,5] => [1,2,4,3,5]
[.,[[[.,[.,.]],.],.]] => [3,2,4,5,1] => [1,3,2,4,5] => [1,3,2,4,5]
[.,[[[[.,.],.],.],.]] => [2,3,4,5,1] => [1,2,3,4,5] => [1,2,3,4,5]
[[.,.],[.,[.,[.,.]]]] => [1,5,4,3,2] => [2,1,5,4,3] => [2,1,5,4,3]
[[.,.],[.,[[.,.],.]]] => [1,4,5,3,2] => [2,1,5,3,4] => [2,1,4,5,3]
[[.,.],[[.,.],[.,.]]] => [1,3,5,4,2] => [2,1,3,5,4] => [2,1,3,5,4]
[[.,.],[[.,[.,.]],.]] => [1,4,3,5,2] => [2,1,4,3,5] => [2,1,4,3,5]
[[.,.],[[[.,.],.],.]] => [1,3,4,5,2] => [2,1,3,4,5] => [2,1,3,4,5]
[[.,[.,.]],[.,[.,.]]] => [2,1,5,4,3] => [3,2,1,5,4] => [3,2,1,5,4]
[[.,[.,.]],[[.,.],.]] => [2,1,4,5,3] => [3,2,1,4,5] => [3,2,1,4,5]
[[[.,.],.],[.,[.,.]]] => [1,2,5,4,3] => [2,3,1,5,4] => [2,3,1,5,4]
[[[.,.],.],[[.,.],.]] => [1,2,4,5,3] => [2,3,1,4,5] => [2,3,1,4,5]
[[.,[.,[.,.]]],[.,.]] => [3,2,1,5,4] => [4,3,2,1,5] => [4,3,2,1,5]
[[.,[[.,.],.]],[.,.]] => [2,3,1,5,4] => [4,2,3,1,5] => [3,4,2,1,5]
[[[.,.],[.,.]],[.,.]] => [1,3,2,5,4] => [2,4,3,1,5] => [2,4,3,1,5]
[[[.,[.,.]],.],[.,.]] => [2,1,3,5,4] => [3,2,4,1,5] => [3,2,4,1,5]
[[[[.,.],.],.],[.,.]] => [1,2,3,5,4] => [2,3,4,1,5] => [2,3,4,1,5]
[[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => [5,4,3,2,1] => [5,4,3,2,1]
[[.,[.,[[.,.],.]]],.] => [3,4,2,1,5] => [5,4,2,3,1] => [4,5,3,2,1]
[[.,[[.,.],[.,.]]],.] => [2,4,3,1,5] => [5,2,4,3,1] => [3,5,4,2,1]
[[.,[[.,[.,.]],.]],.] => [3,2,4,1,5] => [5,3,2,4,1] => [4,3,5,2,1]
[[.,[[[.,.],.],.]],.] => [2,3,4,1,5] => [5,2,3,4,1] => [3,4,5,2,1]
[[[.,.],[.,[.,.]]],.] => [1,4,3,2,5] => [2,5,4,3,1] => [2,5,4,3,1]
[[[.,.],[[.,.],.]],.] => [1,3,4,2,5] => [2,5,3,4,1] => [2,4,5,3,1]
[[[.,[.,.]],[.,.]],.] => [2,1,4,3,5] => [3,2,5,4,1] => [3,2,5,4,1]
[[[[.,.],.],[.,.]],.] => [1,2,4,3,5] => [2,3,5,4,1] => [2,3,5,4,1]
[[[.,[.,[.,.]]],.],.] => [3,2,1,4,5] => [4,3,2,5,1] => [4,3,2,5,1]
[[[.,[[.,.],.]],.],.] => [2,3,1,4,5] => [4,2,3,5,1] => [3,4,2,5,1]
[[[[.,.],[.,.]],.],.] => [1,3,2,4,5] => [2,4,3,5,1] => [2,4,3,5,1]
[[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => [3,2,4,5,1] => [3,2,4,5,1]
[[[[[.,.],.],.],.],.] => [1,2,3,4,5] => [2,3,4,5,1] => [2,3,4,5,1]
[.,[.,[.,[.,[.,[.,.]]]]]] => [6,5,4,3,2,1] => [1,6,5,4,3,2] => [1,6,5,4,3,2]
[.,[.,[.,[.,[[.,.],.]]]]] => [5,6,4,3,2,1] => [1,6,5,4,2,3] => [1,5,6,4,3,2]
[.,[.,[.,[[.,.],[.,.]]]]] => [4,6,5,3,2,1] => [1,6,5,2,4,3] => [1,4,6,5,3,2]
[.,[.,[.,[[.,[.,.]],.]]]] => [5,4,6,3,2,1] => [1,6,5,3,2,4] => [1,5,4,6,3,2]
[.,[.,[.,[[[.,.],.],.]]]] => [4,5,6,3,2,1] => [1,6,5,2,3,4] => [1,4,5,6,3,2]
[.,[.,[[.,.],[.,[.,.]]]]] => [3,6,5,4,2,1] => [1,6,2,5,4,3] => [1,3,6,5,4,2]
[.,[.,[[.,.],[[.,.],.]]]] => [3,5,6,4,2,1] => [1,6,2,5,3,4] => [1,3,5,6,4,2]
[.,[.,[[.,[.,.]],[.,.]]]] => [4,3,6,5,2,1] => [1,6,3,2,5,4] => [1,4,3,6,5,2]
[.,[.,[[[.,.],.],[.,.]]]] => [3,4,6,5,2,1] => [1,6,2,3,5,4] => [1,3,4,6,5,2]
[.,[.,[[.,[.,[.,.]]],.]]] => [5,4,3,6,2,1] => [1,6,4,3,2,5] => [1,5,4,3,6,2]
[.,[.,[[.,[[.,.],.]],.]]] => [4,5,3,6,2,1] => [1,6,4,2,3,5] => [1,4,5,3,6,2]
[.,[.,[[[.,.],[.,.]],.]]] => [3,5,4,6,2,1] => [1,6,2,4,3,5] => [1,3,5,4,6,2]
[.,[.,[[[.,[.,.]],.],.]]] => [4,3,5,6,2,1] => [1,6,3,2,4,5] => [1,4,3,5,6,2]
[.,[.,[[[[.,.],.],.],.]]] => [3,4,5,6,2,1] => [1,6,2,3,4,5] => [1,3,4,5,6,2]
[.,[[.,.],[.,[.,[.,.]]]]] => [2,6,5,4,3,1] => [1,2,6,5,4,3] => [1,2,6,5,4,3]
[.,[[.,.],[.,[[.,.],.]]]] => [2,5,6,4,3,1] => [1,2,6,5,3,4] => [1,2,5,6,4,3]
[.,[[.,.],[[.,.],[.,.]]]] => [2,4,6,5,3,1] => [1,2,6,3,5,4] => [1,2,4,6,5,3]
[.,[[.,.],[[.,[.,.]],.]]] => [2,5,4,6,3,1] => [1,2,6,4,3,5] => [1,2,5,4,6,3]
[.,[[.,.],[[[.,.],.],.]]] => [2,4,5,6,3,1] => [1,2,6,3,4,5] => [1,2,4,5,6,3]
[.,[[.,[.,.]],[.,[.,.]]]] => [3,2,6,5,4,1] => [1,3,2,6,5,4] => [1,3,2,6,5,4]
[.,[[.,[.,.]],[[.,.],.]]] => [3,2,5,6,4,1] => [1,3,2,6,4,5] => [1,3,2,5,6,4]
[.,[[[.,.],.],[.,[.,.]]]] => [2,3,6,5,4,1] => [1,2,3,6,5,4] => [1,2,3,6,5,4]
[.,[[[.,.],.],[[.,.],.]]] => [2,3,5,6,4,1] => [1,2,3,6,4,5] => [1,2,3,5,6,4]
[.,[[.,[.,[.,.]]],[.,.]]] => [4,3,2,6,5,1] => [1,4,3,2,6,5] => [1,4,3,2,6,5]
[.,[[.,[[.,.],.]],[.,.]]] => [3,4,2,6,5,1] => [1,4,2,3,6,5] => [1,3,4,2,6,5]
[.,[[[.,.],[.,.]],[.,.]]] => [2,4,3,6,5,1] => [1,2,4,3,6,5] => [1,2,4,3,6,5]
[.,[[[.,[.,.]],.],[.,.]]] => [3,2,4,6,5,1] => [1,3,2,4,6,5] => [1,3,2,4,6,5]
[.,[[[[.,.],.],.],[.,.]]] => [2,3,4,6,5,1] => [1,2,3,4,6,5] => [1,2,3,4,6,5]
[.,[[.,[.,[.,[.,.]]]],.]] => [5,4,3,2,6,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6]
[.,[[.,[.,[[.,.],.]]],.]] => [4,5,3,2,6,1] => [1,5,4,2,3,6] => [1,4,5,3,2,6]
[.,[[.,[[.,.],[.,.]]],.]] => [3,5,4,2,6,1] => [1,5,2,4,3,6] => [1,3,5,4,2,6]
[.,[[.,[[.,[.,.]],.]],.]] => [4,3,5,2,6,1] => [1,5,3,2,4,6] => [1,4,3,5,2,6]
[.,[[.,[[[.,.],.],.]],.]] => [3,4,5,2,6,1] => [1,5,2,3,4,6] => [1,3,4,5,2,6]
[.,[[[.,.],[.,[.,.]]],.]] => [2,5,4,3,6,1] => [1,2,5,4,3,6] => [1,2,5,4,3,6]
[.,[[[.,.],[[.,.],.]],.]] => [2,4,5,3,6,1] => [1,2,5,3,4,6] => [1,2,4,5,3,6]
[.,[[[.,[.,.]],[.,.]],.]] => [3,2,5,4,6,1] => [1,3,2,5,4,6] => [1,3,2,5,4,6]
[.,[[[[.,.],.],[.,.]],.]] => [2,3,5,4,6,1] => [1,2,3,5,4,6] => [1,2,3,5,4,6]
>>> Load all 704 entries. <<<
[.,[[[.,[.,[.,.]]],.],.]] => [4,3,2,5,6,1] => [1,4,3,2,5,6] => [1,4,3,2,5,6]
[.,[[[.,[[.,.],.]],.],.]] => [3,4,2,5,6,1] => [1,4,2,3,5,6] => [1,3,4,2,5,6]
[.,[[[[.,.],[.,.]],.],.]] => [2,4,3,5,6,1] => [1,2,4,3,5,6] => [1,2,4,3,5,6]
[.,[[[[.,[.,.]],.],.],.]] => [3,2,4,5,6,1] => [1,3,2,4,5,6] => [1,3,2,4,5,6]
[.,[[[[[.,.],.],.],.],.]] => [2,3,4,5,6,1] => [1,2,3,4,5,6] => [1,2,3,4,5,6]
[[.,.],[.,[.,[.,[.,.]]]]] => [1,6,5,4,3,2] => [2,1,6,5,4,3] => [2,1,6,5,4,3]
[[.,.],[.,[.,[[.,.],.]]]] => [1,5,6,4,3,2] => [2,1,6,5,3,4] => [2,1,5,6,4,3]
[[.,.],[.,[[.,.],[.,.]]]] => [1,4,6,5,3,2] => [2,1,6,3,5,4] => [2,1,4,6,5,3]
[[.,.],[.,[[.,[.,.]],.]]] => [1,5,4,6,3,2] => [2,1,6,4,3,5] => [2,1,5,4,6,3]
[[.,.],[.,[[[.,.],.],.]]] => [1,4,5,6,3,2] => [2,1,6,3,4,5] => [2,1,4,5,6,3]
[[.,.],[[.,.],[.,[.,.]]]] => [1,3,6,5,4,2] => [2,1,3,6,5,4] => [2,1,3,6,5,4]
[[.,.],[[.,.],[[.,.],.]]] => [1,3,5,6,4,2] => [2,1,3,6,4,5] => [2,1,3,5,6,4]
[[.,.],[[.,[.,.]],[.,.]]] => [1,4,3,6,5,2] => [2,1,4,3,6,5] => [2,1,4,3,6,5]
[[.,.],[[[.,.],.],[.,.]]] => [1,3,4,6,5,2] => [2,1,3,4,6,5] => [2,1,3,4,6,5]
[[.,.],[[.,[.,[.,.]]],.]] => [1,5,4,3,6,2] => [2,1,5,4,3,6] => [2,1,5,4,3,6]
[[.,.],[[.,[[.,.],.]],.]] => [1,4,5,3,6,2] => [2,1,5,3,4,6] => [2,1,4,5,3,6]
[[.,.],[[[.,.],[.,.]],.]] => [1,3,5,4,6,2] => [2,1,3,5,4,6] => [2,1,3,5,4,6]
[[.,.],[[[.,[.,.]],.],.]] => [1,4,3,5,6,2] => [2,1,4,3,5,6] => [2,1,4,3,5,6]
[[.,.],[[[[.,.],.],.],.]] => [1,3,4,5,6,2] => [2,1,3,4,5,6] => [2,1,3,4,5,6]
[[.,[.,.]],[.,[.,[.,.]]]] => [2,1,6,5,4,3] => [3,2,1,6,5,4] => [3,2,1,6,5,4]
[[.,[.,.]],[.,[[.,.],.]]] => [2,1,5,6,4,3] => [3,2,1,6,4,5] => [3,2,1,5,6,4]
[[.,[.,.]],[[.,.],[.,.]]] => [2,1,4,6,5,3] => [3,2,1,4,6,5] => [3,2,1,4,6,5]
[[.,[.,.]],[[.,[.,.]],.]] => [2,1,5,4,6,3] => [3,2,1,5,4,6] => [3,2,1,5,4,6]
[[.,[.,.]],[[[.,.],.],.]] => [2,1,4,5,6,3] => [3,2,1,4,5,6] => [3,2,1,4,5,6]
[[[.,.],.],[.,[.,[.,.]]]] => [1,2,6,5,4,3] => [2,3,1,6,5,4] => [2,3,1,6,5,4]
[[[.,.],.],[.,[[.,.],.]]] => [1,2,5,6,4,3] => [2,3,1,6,4,5] => [2,3,1,5,6,4]
[[[.,.],.],[[.,.],[.,.]]] => [1,2,4,6,5,3] => [2,3,1,4,6,5] => [2,3,1,4,6,5]
[[[.,.],.],[[.,[.,.]],.]] => [1,2,5,4,6,3] => [2,3,1,5,4,6] => [2,3,1,5,4,6]
[[[.,.],.],[[[.,.],.],.]] => [1,2,4,5,6,3] => [2,3,1,4,5,6] => [2,3,1,4,5,6]
[[.,[.,[.,.]]],[.,[.,.]]] => [3,2,1,6,5,4] => [4,3,2,1,6,5] => [4,3,2,1,6,5]
[[.,[.,[.,.]]],[[.,.],.]] => [3,2,1,5,6,4] => [4,3,2,1,5,6] => [4,3,2,1,5,6]
[[.,[[.,.],.]],[.,[.,.]]] => [2,3,1,6,5,4] => [4,2,3,1,6,5] => [3,4,2,1,6,5]
[[.,[[.,.],.]],[[.,.],.]] => [2,3,1,5,6,4] => [4,2,3,1,5,6] => [3,4,2,1,5,6]
[[[.,.],[.,.]],[.,[.,.]]] => [1,3,2,6,5,4] => [2,4,3,1,6,5] => [2,4,3,1,6,5]
[[[.,.],[.,.]],[[.,.],.]] => [1,3,2,5,6,4] => [2,4,3,1,5,6] => [2,4,3,1,5,6]
[[[.,[.,.]],.],[.,[.,.]]] => [2,1,3,6,5,4] => [3,2,4,1,6,5] => [3,2,4,1,6,5]
[[[.,[.,.]],.],[[.,.],.]] => [2,1,3,5,6,4] => [3,2,4,1,5,6] => [3,2,4,1,5,6]
[[[[.,.],.],.],[.,[.,.]]] => [1,2,3,6,5,4] => [2,3,4,1,6,5] => [2,3,4,1,6,5]
[[[[.,.],.],.],[[.,.],.]] => [1,2,3,5,6,4] => [2,3,4,1,5,6] => [2,3,4,1,5,6]
[[.,[.,[.,[.,.]]]],[.,.]] => [4,3,2,1,6,5] => [5,4,3,2,1,6] => [5,4,3,2,1,6]
[[.,[.,[[.,.],.]]],[.,.]] => [3,4,2,1,6,5] => [5,4,2,3,1,6] => [4,5,3,2,1,6]
[[.,[[.,.],[.,.]]],[.,.]] => [2,4,3,1,6,5] => [5,2,4,3,1,6] => [3,5,4,2,1,6]
[[.,[[.,[.,.]],.]],[.,.]] => [3,2,4,1,6,5] => [5,3,2,4,1,6] => [4,3,5,2,1,6]
[[.,[[[.,.],.],.]],[.,.]] => [2,3,4,1,6,5] => [5,2,3,4,1,6] => [3,4,5,2,1,6]
[[[.,.],[.,[.,.]]],[.,.]] => [1,4,3,2,6,5] => [2,5,4,3,1,6] => [2,5,4,3,1,6]
[[[.,.],[[.,.],.]],[.,.]] => [1,3,4,2,6,5] => [2,5,3,4,1,6] => [2,4,5,3,1,6]
[[[.,[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5] => [3,2,5,4,1,6] => [3,2,5,4,1,6]
[[[[.,.],.],[.,.]],[.,.]] => [1,2,4,3,6,5] => [2,3,5,4,1,6] => [2,3,5,4,1,6]
[[[.,[.,[.,.]]],.],[.,.]] => [3,2,1,4,6,5] => [4,3,2,5,1,6] => [4,3,2,5,1,6]
[[[.,[[.,.],.]],.],[.,.]] => [2,3,1,4,6,5] => [4,2,3,5,1,6] => [3,4,2,5,1,6]
[[[[.,.],[.,.]],.],[.,.]] => [1,3,2,4,6,5] => [2,4,3,5,1,6] => [2,4,3,5,1,6]
[[[[.,[.,.]],.],.],[.,.]] => [2,1,3,4,6,5] => [3,2,4,5,1,6] => [3,2,4,5,1,6]
[[[[[.,.],.],.],.],[.,.]] => [1,2,3,4,6,5] => [2,3,4,5,1,6] => [2,3,4,5,1,6]
[[.,[.,[.,[.,[.,.]]]]],.] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => [6,5,4,3,2,1]
[[.,[.,[.,[[.,.],.]]]],.] => [4,5,3,2,1,6] => [6,5,4,2,3,1] => [5,6,4,3,2,1]
[[.,[.,[[.,.],[.,.]]]],.] => [3,5,4,2,1,6] => [6,5,2,4,3,1] => [4,6,5,3,2,1]
[[.,[.,[[.,[.,.]],.]]],.] => [4,3,5,2,1,6] => [6,5,3,2,4,1] => [5,4,6,3,2,1]
[[.,[.,[[[.,.],.],.]]],.] => [3,4,5,2,1,6] => [6,5,2,3,4,1] => [4,5,6,3,2,1]
[[.,[[.,.],[.,[.,.]]]],.] => [2,5,4,3,1,6] => [6,2,5,4,3,1] => [3,6,5,4,2,1]
[[.,[[.,.],[[.,.],.]]],.] => [2,4,5,3,1,6] => [6,2,5,3,4,1] => [3,5,6,4,2,1]
[[.,[[.,[.,.]],[.,.]]],.] => [3,2,5,4,1,6] => [6,3,2,5,4,1] => [4,3,6,5,2,1]
[[.,[[[.,.],.],[.,.]]],.] => [2,3,5,4,1,6] => [6,2,3,5,4,1] => [3,4,6,5,2,1]
[[.,[[.,[.,[.,.]]],.]],.] => [4,3,2,5,1,6] => [6,4,3,2,5,1] => [5,4,3,6,2,1]
[[.,[[.,[[.,.],.]],.]],.] => [3,4,2,5,1,6] => [6,4,2,3,5,1] => [4,5,3,6,2,1]
[[.,[[[.,.],[.,.]],.]],.] => [2,4,3,5,1,6] => [6,2,4,3,5,1] => [3,5,4,6,2,1]
[[.,[[[.,[.,.]],.],.]],.] => [3,2,4,5,1,6] => [6,3,2,4,5,1] => [4,3,5,6,2,1]
[[.,[[[[.,.],.],.],.]],.] => [2,3,4,5,1,6] => [6,2,3,4,5,1] => [3,4,5,6,2,1]
[[[.,.],[.,[.,[.,.]]]],.] => [1,5,4,3,2,6] => [2,6,5,4,3,1] => [2,6,5,4,3,1]
[[[.,.],[.,[[.,.],.]]],.] => [1,4,5,3,2,6] => [2,6,5,3,4,1] => [2,5,6,4,3,1]
[[[.,.],[[.,.],[.,.]]],.] => [1,3,5,4,2,6] => [2,6,3,5,4,1] => [2,4,6,5,3,1]
[[[.,.],[[.,[.,.]],.]],.] => [1,4,3,5,2,6] => [2,6,4,3,5,1] => [2,5,4,6,3,1]
[[[.,.],[[[.,.],.],.]],.] => [1,3,4,5,2,6] => [2,6,3,4,5,1] => [2,4,5,6,3,1]
[[[.,[.,.]],[.,[.,.]]],.] => [2,1,5,4,3,6] => [3,2,6,5,4,1] => [3,2,6,5,4,1]
[[[.,[.,.]],[[.,.],.]],.] => [2,1,4,5,3,6] => [3,2,6,4,5,1] => [3,2,5,6,4,1]
[[[[.,.],.],[.,[.,.]]],.] => [1,2,5,4,3,6] => [2,3,6,5,4,1] => [2,3,6,5,4,1]
[[[[.,.],.],[[.,.],.]],.] => [1,2,4,5,3,6] => [2,3,6,4,5,1] => [2,3,5,6,4,1]
[[[.,[.,[.,.]]],[.,.]],.] => [3,2,1,5,4,6] => [4,3,2,6,5,1] => [4,3,2,6,5,1]
[[[.,[[.,.],.]],[.,.]],.] => [2,3,1,5,4,6] => [4,2,3,6,5,1] => [3,4,2,6,5,1]
[[[[.,.],[.,.]],[.,.]],.] => [1,3,2,5,4,6] => [2,4,3,6,5,1] => [2,4,3,6,5,1]
[[[[.,[.,.]],.],[.,.]],.] => [2,1,3,5,4,6] => [3,2,4,6,5,1] => [3,2,4,6,5,1]
[[[[[.,.],.],.],[.,.]],.] => [1,2,3,5,4,6] => [2,3,4,6,5,1] => [2,3,4,6,5,1]
[[[.,[.,[.,[.,.]]]],.],.] => [4,3,2,1,5,6] => [5,4,3,2,6,1] => [5,4,3,2,6,1]
[[[.,[.,[[.,.],.]]],.],.] => [3,4,2,1,5,6] => [5,4,2,3,6,1] => [4,5,3,2,6,1]
[[[.,[[.,.],[.,.]]],.],.] => [2,4,3,1,5,6] => [5,2,4,3,6,1] => [3,5,4,2,6,1]
[[[.,[[.,[.,.]],.]],.],.] => [3,2,4,1,5,6] => [5,3,2,4,6,1] => [4,3,5,2,6,1]
[[[.,[[[.,.],.],.]],.],.] => [2,3,4,1,5,6] => [5,2,3,4,6,1] => [3,4,5,2,6,1]
[[[[.,.],[.,[.,.]]],.],.] => [1,4,3,2,5,6] => [2,5,4,3,6,1] => [2,5,4,3,6,1]
[[[[.,.],[[.,.],.]],.],.] => [1,3,4,2,5,6] => [2,5,3,4,6,1] => [2,4,5,3,6,1]
[[[[.,[.,.]],[.,.]],.],.] => [2,1,4,3,5,6] => [3,2,5,4,6,1] => [3,2,5,4,6,1]
[[[[[.,.],.],[.,.]],.],.] => [1,2,4,3,5,6] => [2,3,5,4,6,1] => [2,3,5,4,6,1]
[[[[.,[.,[.,.]]],.],.],.] => [3,2,1,4,5,6] => [4,3,2,5,6,1] => [4,3,2,5,6,1]
[[[[.,[[.,.],.]],.],.],.] => [2,3,1,4,5,6] => [4,2,3,5,6,1] => [3,4,2,5,6,1]
[[[[[.,.],[.,.]],.],.],.] => [1,3,2,4,5,6] => [2,4,3,5,6,1] => [2,4,3,5,6,1]
[[[[[.,[.,.]],.],.],.],.] => [2,1,3,4,5,6] => [3,2,4,5,6,1] => [3,2,4,5,6,1]
[[[[[[.,.],.],.],.],.],.] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [2,3,4,5,6,1]
[.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [7,6,5,4,3,2,1] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2]
[.,[.,[.,[.,[.,[[.,.],.]]]]]] => [6,7,5,4,3,2,1] => [1,7,6,5,4,2,3] => [1,6,7,5,4,3,2]
[.,[.,[.,[.,[[.,.],[.,.]]]]]] => [5,7,6,4,3,2,1] => [1,7,6,5,2,4,3] => [1,5,7,6,4,3,2]
[.,[.,[.,[.,[[.,[.,.]],.]]]]] => [6,5,7,4,3,2,1] => [1,7,6,5,3,2,4] => [1,6,5,7,4,3,2]
[.,[.,[.,[.,[[[.,.],.],.]]]]] => [5,6,7,4,3,2,1] => [1,7,6,5,2,3,4] => [1,5,6,7,4,3,2]
[.,[.,[.,[[.,.],[.,[.,.]]]]]] => [4,7,6,5,3,2,1] => [1,7,6,2,5,4,3] => [1,4,7,6,5,3,2]
[.,[.,[.,[[.,.],[[.,.],.]]]]] => [4,6,7,5,3,2,1] => [1,7,6,2,5,3,4] => [1,4,6,7,5,3,2]
[.,[.,[.,[[.,[.,.]],[.,.]]]]] => [5,4,7,6,3,2,1] => [1,7,6,3,2,5,4] => [1,5,4,7,6,3,2]
[.,[.,[.,[[[.,.],.],[.,.]]]]] => [4,5,7,6,3,2,1] => [1,7,6,2,3,5,4] => [1,4,5,7,6,3,2]
[.,[.,[.,[[.,[.,[.,.]]],.]]]] => [6,5,4,7,3,2,1] => [1,7,6,4,3,2,5] => [1,6,5,4,7,3,2]
[.,[.,[.,[[.,[[.,.],.]],.]]]] => [5,6,4,7,3,2,1] => [1,7,6,4,2,3,5] => [1,5,6,4,7,3,2]
[.,[.,[.,[[[.,.],[.,.]],.]]]] => [4,6,5,7,3,2,1] => [1,7,6,2,4,3,5] => [1,4,6,5,7,3,2]
[.,[.,[.,[[[.,[.,.]],.],.]]]] => [5,4,6,7,3,2,1] => [1,7,6,3,2,4,5] => [1,5,4,6,7,3,2]
[.,[.,[.,[[[[.,.],.],.],.]]]] => [4,5,6,7,3,2,1] => [1,7,6,2,3,4,5] => [1,4,5,6,7,3,2]
[.,[.,[[.,.],[.,[.,[.,.]]]]]] => [3,7,6,5,4,2,1] => [1,7,2,6,5,4,3] => [1,3,7,6,5,4,2]
[.,[.,[[.,.],[.,[[.,.],.]]]]] => [3,6,7,5,4,2,1] => [1,7,2,6,5,3,4] => [1,3,6,7,5,4,2]
[.,[.,[[.,.],[[.,.],[.,.]]]]] => [3,5,7,6,4,2,1] => [1,7,2,6,3,5,4] => [1,3,5,7,6,4,2]
[.,[.,[[.,.],[[.,[.,.]],.]]]] => [3,6,5,7,4,2,1] => [1,7,2,6,4,3,5] => [1,3,6,5,7,4,2]
[.,[.,[[.,.],[[[.,.],.],.]]]] => [3,5,6,7,4,2,1] => [1,7,2,6,3,4,5] => [1,3,5,6,7,4,2]
[.,[.,[[.,[.,.]],[.,[.,.]]]]] => [4,3,7,6,5,2,1] => [1,7,3,2,6,5,4] => [1,4,3,7,6,5,2]
[.,[.,[[.,[.,.]],[[.,.],.]]]] => [4,3,6,7,5,2,1] => [1,7,3,2,6,4,5] => [1,4,3,6,7,5,2]
[.,[.,[[[.,.],.],[.,[.,.]]]]] => [3,4,7,6,5,2,1] => [1,7,2,3,6,5,4] => [1,3,4,7,6,5,2]
[.,[.,[[[.,.],.],[[.,.],.]]]] => [3,4,6,7,5,2,1] => [1,7,2,3,6,4,5] => [1,3,4,6,7,5,2]
[.,[.,[[.,[.,[.,.]]],[.,.]]]] => [5,4,3,7,6,2,1] => [1,7,4,3,2,6,5] => [1,5,4,3,7,6,2]
[.,[.,[[.,[[.,.],.]],[.,.]]]] => [4,5,3,7,6,2,1] => [1,7,4,2,3,6,5] => [1,4,5,3,7,6,2]
[.,[.,[[[.,.],[.,.]],[.,.]]]] => [3,5,4,7,6,2,1] => [1,7,2,4,3,6,5] => [1,3,5,4,7,6,2]
[.,[.,[[[.,[.,.]],.],[.,.]]]] => [4,3,5,7,6,2,1] => [1,7,3,2,4,6,5] => [1,4,3,5,7,6,2]
[.,[.,[[[[.,.],.],.],[.,.]]]] => [3,4,5,7,6,2,1] => [1,7,2,3,4,6,5] => [1,3,4,5,7,6,2]
[.,[.,[[.,[.,[.,[.,.]]]],.]]] => [6,5,4,3,7,2,1] => [1,7,5,4,3,2,6] => [1,6,5,4,3,7,2]
[.,[.,[[.,[.,[[.,.],.]]],.]]] => [5,6,4,3,7,2,1] => [1,7,5,4,2,3,6] => [1,5,6,4,3,7,2]
[.,[.,[[.,[[.,.],[.,.]]],.]]] => [4,6,5,3,7,2,1] => [1,7,5,2,4,3,6] => [1,4,6,5,3,7,2]
[.,[.,[[.,[[.,[.,.]],.]],.]]] => [5,4,6,3,7,2,1] => [1,7,5,3,2,4,6] => [1,5,4,6,3,7,2]
[.,[.,[[.,[[[.,.],.],.]],.]]] => [4,5,6,3,7,2,1] => [1,7,5,2,3,4,6] => [1,4,5,6,3,7,2]
[.,[.,[[[.,.],[.,[.,.]]],.]]] => [3,6,5,4,7,2,1] => [1,7,2,5,4,3,6] => [1,3,6,5,4,7,2]
[.,[.,[[[.,.],[[.,.],.]],.]]] => [3,5,6,4,7,2,1] => [1,7,2,5,3,4,6] => [1,3,5,6,4,7,2]
[.,[.,[[[.,[.,.]],[.,.]],.]]] => [4,3,6,5,7,2,1] => [1,7,3,2,5,4,6] => [1,4,3,6,5,7,2]
[.,[.,[[[[.,.],.],[.,.]],.]]] => [3,4,6,5,7,2,1] => [1,7,2,3,5,4,6] => [1,3,4,6,5,7,2]
[.,[.,[[[.,[.,[.,.]]],.],.]]] => [5,4,3,6,7,2,1] => [1,7,4,3,2,5,6] => [1,5,4,3,6,7,2]
[.,[.,[[[.,[[.,.],.]],.],.]]] => [4,5,3,6,7,2,1] => [1,7,4,2,3,5,6] => [1,4,5,3,6,7,2]
[.,[.,[[[[.,.],[.,.]],.],.]]] => [3,5,4,6,7,2,1] => [1,7,2,4,3,5,6] => [1,3,5,4,6,7,2]
[.,[.,[[[[.,[.,.]],.],.],.]]] => [4,3,5,6,7,2,1] => [1,7,3,2,4,5,6] => [1,4,3,5,6,7,2]
[.,[.,[[[[[.,.],.],.],.],.]]] => [3,4,5,6,7,2,1] => [1,7,2,3,4,5,6] => [1,3,4,5,6,7,2]
[.,[[.,.],[.,[.,[.,[.,.]]]]]] => [2,7,6,5,4,3,1] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3]
[.,[[.,.],[.,[.,[[.,.],.]]]]] => [2,6,7,5,4,3,1] => [1,2,7,6,5,3,4] => [1,2,6,7,5,4,3]
[.,[[.,.],[.,[[.,.],[.,.]]]]] => [2,5,7,6,4,3,1] => [1,2,7,6,3,5,4] => [1,2,5,7,6,4,3]
[.,[[.,.],[.,[[.,[.,.]],.]]]] => [2,6,5,7,4,3,1] => [1,2,7,6,4,3,5] => [1,2,6,5,7,4,3]
[.,[[.,.],[.,[[[.,.],.],.]]]] => [2,5,6,7,4,3,1] => [1,2,7,6,3,4,5] => [1,2,5,6,7,4,3]
[.,[[.,.],[[.,.],[.,[.,.]]]]] => [2,4,7,6,5,3,1] => [1,2,7,3,6,5,4] => [1,2,4,7,6,5,3]
[.,[[.,.],[[.,.],[[.,.],.]]]] => [2,4,6,7,5,3,1] => [1,2,7,3,6,4,5] => [1,2,4,6,7,5,3]
[.,[[.,.],[[.,[.,.]],[.,.]]]] => [2,5,4,7,6,3,1] => [1,2,7,4,3,6,5] => [1,2,5,4,7,6,3]
[.,[[.,.],[[[.,.],.],[.,.]]]] => [2,4,5,7,6,3,1] => [1,2,7,3,4,6,5] => [1,2,4,5,7,6,3]
[.,[[.,.],[[.,[.,[.,.]]],.]]] => [2,6,5,4,7,3,1] => [1,2,7,5,4,3,6] => [1,2,6,5,4,7,3]
[.,[[.,.],[[.,[[.,.],.]],.]]] => [2,5,6,4,7,3,1] => [1,2,7,5,3,4,6] => [1,2,5,6,4,7,3]
[.,[[.,.],[[[.,.],[.,.]],.]]] => [2,4,6,5,7,3,1] => [1,2,7,3,5,4,6] => [1,2,4,6,5,7,3]
[.,[[.,.],[[[.,[.,.]],.],.]]] => [2,5,4,6,7,3,1] => [1,2,7,4,3,5,6] => [1,2,5,4,6,7,3]
[.,[[.,.],[[[[.,.],.],.],.]]] => [2,4,5,6,7,3,1] => [1,2,7,3,4,5,6] => [1,2,4,5,6,7,3]
[.,[[.,[.,.]],[.,[.,[.,.]]]]] => [3,2,7,6,5,4,1] => [1,3,2,7,6,5,4] => [1,3,2,7,6,5,4]
[.,[[.,[.,.]],[.,[[.,.],.]]]] => [3,2,6,7,5,4,1] => [1,3,2,7,6,4,5] => [1,3,2,6,7,5,4]
[.,[[.,[.,.]],[[.,.],[.,.]]]] => [3,2,5,7,6,4,1] => [1,3,2,7,4,6,5] => [1,3,2,5,7,6,4]
[.,[[.,[.,.]],[[.,[.,.]],.]]] => [3,2,6,5,7,4,1] => [1,3,2,7,5,4,6] => [1,3,2,6,5,7,4]
[.,[[.,[.,.]],[[[.,.],.],.]]] => [3,2,5,6,7,4,1] => [1,3,2,7,4,5,6] => [1,3,2,5,6,7,4]
[.,[[[.,.],.],[.,[.,[.,.]]]]] => [2,3,7,6,5,4,1] => [1,2,3,7,6,5,4] => [1,2,3,7,6,5,4]
[.,[[[.,.],.],[.,[[.,.],.]]]] => [2,3,6,7,5,4,1] => [1,2,3,7,6,4,5] => [1,2,3,6,7,5,4]
[.,[[[.,.],.],[[.,.],[.,.]]]] => [2,3,5,7,6,4,1] => [1,2,3,7,4,6,5] => [1,2,3,5,7,6,4]
[.,[[[.,.],.],[[.,[.,.]],.]]] => [2,3,6,5,7,4,1] => [1,2,3,7,5,4,6] => [1,2,3,6,5,7,4]
[.,[[[.,.],.],[[[.,.],.],.]]] => [2,3,5,6,7,4,1] => [1,2,3,7,4,5,6] => [1,2,3,5,6,7,4]
[.,[[.,[.,[.,.]]],[.,[.,.]]]] => [4,3,2,7,6,5,1] => [1,4,3,2,7,6,5] => [1,4,3,2,7,6,5]
[.,[[.,[.,[.,.]]],[[.,.],.]]] => [4,3,2,6,7,5,1] => [1,4,3,2,7,5,6] => [1,4,3,2,6,7,5]
[.,[[.,[[.,.],.]],[.,[.,.]]]] => [3,4,2,7,6,5,1] => [1,4,2,3,7,6,5] => [1,3,4,2,7,6,5]
[.,[[.,[[.,.],.]],[[.,.],.]]] => [3,4,2,6,7,5,1] => [1,4,2,3,7,5,6] => [1,3,4,2,6,7,5]
[.,[[[.,.],[.,.]],[.,[.,.]]]] => [2,4,3,7,6,5,1] => [1,2,4,3,7,6,5] => [1,2,4,3,7,6,5]
[.,[[[.,.],[.,.]],[[.,.],.]]] => [2,4,3,6,7,5,1] => [1,2,4,3,7,5,6] => [1,2,4,3,6,7,5]
[.,[[[.,[.,.]],.],[.,[.,.]]]] => [3,2,4,7,6,5,1] => [1,3,2,4,7,6,5] => [1,3,2,4,7,6,5]
[.,[[[.,[.,.]],.],[[.,.],.]]] => [3,2,4,6,7,5,1] => [1,3,2,4,7,5,6] => [1,3,2,4,6,7,5]
[.,[[[[.,.],.],.],[.,[.,.]]]] => [2,3,4,7,6,5,1] => [1,2,3,4,7,6,5] => [1,2,3,4,7,6,5]
[.,[[[[.,.],.],.],[[.,.],.]]] => [2,3,4,6,7,5,1] => [1,2,3,4,7,5,6] => [1,2,3,4,6,7,5]
[.,[[.,[.,[.,[.,.]]]],[.,.]]] => [5,4,3,2,7,6,1] => [1,5,4,3,2,7,6] => [1,5,4,3,2,7,6]
[.,[[.,[.,[[.,.],.]]],[.,.]]] => [4,5,3,2,7,6,1] => [1,5,4,2,3,7,6] => [1,4,5,3,2,7,6]
[.,[[.,[[.,.],[.,.]]],[.,.]]] => [3,5,4,2,7,6,1] => [1,5,2,4,3,7,6] => [1,3,5,4,2,7,6]
[.,[[.,[[.,[.,.]],.]],[.,.]]] => [4,3,5,2,7,6,1] => [1,5,3,2,4,7,6] => [1,4,3,5,2,7,6]
[.,[[.,[[[.,.],.],.]],[.,.]]] => [3,4,5,2,7,6,1] => [1,5,2,3,4,7,6] => [1,3,4,5,2,7,6]
[.,[[[.,.],[.,[.,.]]],[.,.]]] => [2,5,4,3,7,6,1] => [1,2,5,4,3,7,6] => [1,2,5,4,3,7,6]
[.,[[[.,.],[[.,.],.]],[.,.]]] => [2,4,5,3,7,6,1] => [1,2,5,3,4,7,6] => [1,2,4,5,3,7,6]
[.,[[[.,[.,.]],[.,.]],[.,.]]] => [3,2,5,4,7,6,1] => [1,3,2,5,4,7,6] => [1,3,2,5,4,7,6]
[.,[[[[.,.],.],[.,.]],[.,.]]] => [2,3,5,4,7,6,1] => [1,2,3,5,4,7,6] => [1,2,3,5,4,7,6]
[.,[[[.,[.,[.,.]]],.],[.,.]]] => [4,3,2,5,7,6,1] => [1,4,3,2,5,7,6] => [1,4,3,2,5,7,6]
[.,[[[.,[[.,.],.]],.],[.,.]]] => [3,4,2,5,7,6,1] => [1,4,2,3,5,7,6] => [1,3,4,2,5,7,6]
[.,[[[[.,.],[.,.]],.],[.,.]]] => [2,4,3,5,7,6,1] => [1,2,4,3,5,7,6] => [1,2,4,3,5,7,6]
[.,[[[[.,[.,.]],.],.],[.,.]]] => [3,2,4,5,7,6,1] => [1,3,2,4,5,7,6] => [1,3,2,4,5,7,6]
[.,[[[[[.,.],.],.],.],[.,.]]] => [2,3,4,5,7,6,1] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6]
[.,[[.,[.,[.,[.,[.,.]]]]],.]] => [6,5,4,3,2,7,1] => [1,6,5,4,3,2,7] => [1,6,5,4,3,2,7]
[.,[[.,[.,[.,[[.,.],.]]]],.]] => [5,6,4,3,2,7,1] => [1,6,5,4,2,3,7] => [1,5,6,4,3,2,7]
[.,[[.,[.,[[.,.],[.,.]]]],.]] => [4,6,5,3,2,7,1] => [1,6,5,2,4,3,7] => [1,4,6,5,3,2,7]
[.,[[.,[.,[[.,[.,.]],.]]],.]] => [5,4,6,3,2,7,1] => [1,6,5,3,2,4,7] => [1,5,4,6,3,2,7]
[.,[[.,[.,[[[.,.],.],.]]],.]] => [4,5,6,3,2,7,1] => [1,6,5,2,3,4,7] => [1,4,5,6,3,2,7]
[.,[[.,[[.,.],[.,[.,.]]]],.]] => [3,6,5,4,2,7,1] => [1,6,2,5,4,3,7] => [1,3,6,5,4,2,7]
[.,[[.,[[.,.],[[.,.],.]]],.]] => [3,5,6,4,2,7,1] => [1,6,2,5,3,4,7] => [1,3,5,6,4,2,7]
[.,[[.,[[.,[.,.]],[.,.]]],.]] => [4,3,6,5,2,7,1] => [1,6,3,2,5,4,7] => [1,4,3,6,5,2,7]
[.,[[.,[[[.,.],.],[.,.]]],.]] => [3,4,6,5,2,7,1] => [1,6,2,3,5,4,7] => [1,3,4,6,5,2,7]
[.,[[.,[[.,[.,[.,.]]],.]],.]] => [5,4,3,6,2,7,1] => [1,6,4,3,2,5,7] => [1,5,4,3,6,2,7]
[.,[[.,[[.,[[.,.],.]],.]],.]] => [4,5,3,6,2,7,1] => [1,6,4,2,3,5,7] => [1,4,5,3,6,2,7]
[.,[[.,[[[.,.],[.,.]],.]],.]] => [3,5,4,6,2,7,1] => [1,6,2,4,3,5,7] => [1,3,5,4,6,2,7]
[.,[[.,[[[.,[.,.]],.],.]],.]] => [4,3,5,6,2,7,1] => [1,6,3,2,4,5,7] => [1,4,3,5,6,2,7]
[.,[[.,[[[[.,.],.],.],.]],.]] => [3,4,5,6,2,7,1] => [1,6,2,3,4,5,7] => [1,3,4,5,6,2,7]
[.,[[[.,.],[.,[.,[.,.]]]],.]] => [2,6,5,4,3,7,1] => [1,2,6,5,4,3,7] => [1,2,6,5,4,3,7]
[.,[[[.,.],[.,[[.,.],.]]],.]] => [2,5,6,4,3,7,1] => [1,2,6,5,3,4,7] => [1,2,5,6,4,3,7]
[.,[[[.,.],[[.,.],[.,.]]],.]] => [2,4,6,5,3,7,1] => [1,2,6,3,5,4,7] => [1,2,4,6,5,3,7]
[.,[[[.,.],[[.,[.,.]],.]],.]] => [2,5,4,6,3,7,1] => [1,2,6,4,3,5,7] => [1,2,5,4,6,3,7]
[.,[[[.,.],[[[.,.],.],.]],.]] => [2,4,5,6,3,7,1] => [1,2,6,3,4,5,7] => [1,2,4,5,6,3,7]
[.,[[[.,[.,.]],[.,[.,.]]],.]] => [3,2,6,5,4,7,1] => [1,3,2,6,5,4,7] => [1,3,2,6,5,4,7]
[.,[[[.,[.,.]],[[.,.],.]],.]] => [3,2,5,6,4,7,1] => [1,3,2,6,4,5,7] => [1,3,2,5,6,4,7]
[.,[[[[.,.],.],[.,[.,.]]],.]] => [2,3,6,5,4,7,1] => [1,2,3,6,5,4,7] => [1,2,3,6,5,4,7]
[.,[[[[.,.],.],[[.,.],.]],.]] => [2,3,5,6,4,7,1] => [1,2,3,6,4,5,7] => [1,2,3,5,6,4,7]
[.,[[[.,[.,[.,.]]],[.,.]],.]] => [4,3,2,6,5,7,1] => [1,4,3,2,6,5,7] => [1,4,3,2,6,5,7]
[.,[[[.,[[.,.],.]],[.,.]],.]] => [3,4,2,6,5,7,1] => [1,4,2,3,6,5,7] => [1,3,4,2,6,5,7]
[.,[[[[.,.],[.,.]],[.,.]],.]] => [2,4,3,6,5,7,1] => [1,2,4,3,6,5,7] => [1,2,4,3,6,5,7]
[.,[[[[.,[.,.]],.],[.,.]],.]] => [3,2,4,6,5,7,1] => [1,3,2,4,6,5,7] => [1,3,2,4,6,5,7]
[.,[[[[[.,.],.],.],[.,.]],.]] => [2,3,4,6,5,7,1] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7]
[.,[[[.,[.,[.,[.,.]]]],.],.]] => [5,4,3,2,6,7,1] => [1,5,4,3,2,6,7] => [1,5,4,3,2,6,7]
[.,[[[.,[.,[[.,.],.]]],.],.]] => [4,5,3,2,6,7,1] => [1,5,4,2,3,6,7] => [1,4,5,3,2,6,7]
[.,[[[.,[[.,.],[.,.]]],.],.]] => [3,5,4,2,6,7,1] => [1,5,2,4,3,6,7] => [1,3,5,4,2,6,7]
[.,[[[.,[[.,[.,.]],.]],.],.]] => [4,3,5,2,6,7,1] => [1,5,3,2,4,6,7] => [1,4,3,5,2,6,7]
[.,[[[.,[[[.,.],.],.]],.],.]] => [3,4,5,2,6,7,1] => [1,5,2,3,4,6,7] => [1,3,4,5,2,6,7]
[.,[[[[.,.],[.,[.,.]]],.],.]] => [2,5,4,3,6,7,1] => [1,2,5,4,3,6,7] => [1,2,5,4,3,6,7]
[.,[[[[.,.],[[.,.],.]],.],.]] => [2,4,5,3,6,7,1] => [1,2,5,3,4,6,7] => [1,2,4,5,3,6,7]
[.,[[[[.,[.,.]],[.,.]],.],.]] => [3,2,5,4,6,7,1] => [1,3,2,5,4,6,7] => [1,3,2,5,4,6,7]
[.,[[[[[.,.],.],[.,.]],.],.]] => [2,3,5,4,6,7,1] => [1,2,3,5,4,6,7] => [1,2,3,5,4,6,7]
[.,[[[[.,[.,[.,.]]],.],.],.]] => [4,3,2,5,6,7,1] => [1,4,3,2,5,6,7] => [1,4,3,2,5,6,7]
[.,[[[[.,[[.,.],.]],.],.],.]] => [3,4,2,5,6,7,1] => [1,4,2,3,5,6,7] => [1,3,4,2,5,6,7]
[.,[[[[[.,.],[.,.]],.],.],.]] => [2,4,3,5,6,7,1] => [1,2,4,3,5,6,7] => [1,2,4,3,5,6,7]
[.,[[[[[.,[.,.]],.],.],.],.]] => [3,2,4,5,6,7,1] => [1,3,2,4,5,6,7] => [1,3,2,4,5,6,7]
[.,[[[[[[.,.],.],.],.],.],.]] => [2,3,4,5,6,7,1] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7]
[[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,7,6,5,4,3,2] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3]
[[.,.],[.,[.,[.,[[.,.],.]]]]] => [1,6,7,5,4,3,2] => [2,1,7,6,5,3,4] => [2,1,6,7,5,4,3]
[[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,5,7,6,4,3,2] => [2,1,7,6,3,5,4] => [2,1,5,7,6,4,3]
[[.,.],[.,[.,[[.,[.,.]],.]]]] => [1,6,5,7,4,3,2] => [2,1,7,6,4,3,5] => [2,1,6,5,7,4,3]
[[.,.],[.,[.,[[[.,.],.],.]]]] => [1,5,6,7,4,3,2] => [2,1,7,6,3,4,5] => [2,1,5,6,7,4,3]
[[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,4,7,6,5,3,2] => [2,1,7,3,6,5,4] => [2,1,4,7,6,5,3]
[[.,.],[.,[[.,.],[[.,.],.]]]] => [1,4,6,7,5,3,2] => [2,1,7,3,6,4,5] => [2,1,4,6,7,5,3]
[[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,5,4,7,6,3,2] => [2,1,7,4,3,6,5] => [2,1,5,4,7,6,3]
[[.,.],[.,[[[.,.],.],[.,.]]]] => [1,4,5,7,6,3,2] => [2,1,7,3,4,6,5] => [2,1,4,5,7,6,3]
[[.,.],[.,[[.,[.,[.,.]]],.]]] => [1,6,5,4,7,3,2] => [2,1,7,5,4,3,6] => [2,1,6,5,4,7,3]
[[.,.],[.,[[.,[[.,.],.]],.]]] => [1,5,6,4,7,3,2] => [2,1,7,5,3,4,6] => [2,1,5,6,4,7,3]
[[.,.],[.,[[[.,.],[.,.]],.]]] => [1,4,6,5,7,3,2] => [2,1,7,3,5,4,6] => [2,1,4,6,5,7,3]
[[.,.],[.,[[[.,[.,.]],.],.]]] => [1,5,4,6,7,3,2] => [2,1,7,4,3,5,6] => [2,1,5,4,6,7,3]
[[.,.],[.,[[[[.,.],.],.],.]]] => [1,4,5,6,7,3,2] => [2,1,7,3,4,5,6] => [2,1,4,5,6,7,3]
[[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,3,7,6,5,4,2] => [2,1,3,7,6,5,4] => [2,1,3,7,6,5,4]
[[.,.],[[.,.],[.,[[.,.],.]]]] => [1,3,6,7,5,4,2] => [2,1,3,7,6,4,5] => [2,1,3,6,7,5,4]
[[.,.],[[.,.],[[.,.],[.,.]]]] => [1,3,5,7,6,4,2] => [2,1,3,7,4,6,5] => [2,1,3,5,7,6,4]
[[.,.],[[.,.],[[.,[.,.]],.]]] => [1,3,6,5,7,4,2] => [2,1,3,7,5,4,6] => [2,1,3,6,5,7,4]
[[.,.],[[.,.],[[[.,.],.],.]]] => [1,3,5,6,7,4,2] => [2,1,3,7,4,5,6] => [2,1,3,5,6,7,4]
[[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,4,3,7,6,5,2] => [2,1,4,3,7,6,5] => [2,1,4,3,7,6,5]
[[.,.],[[.,[.,.]],[[.,.],.]]] => [1,4,3,6,7,5,2] => [2,1,4,3,7,5,6] => [2,1,4,3,6,7,5]
[[.,.],[[[.,.],.],[.,[.,.]]]] => [1,3,4,7,6,5,2] => [2,1,3,4,7,6,5] => [2,1,3,4,7,6,5]
[[.,.],[[[.,.],.],[[.,.],.]]] => [1,3,4,6,7,5,2] => [2,1,3,4,7,5,6] => [2,1,3,4,6,7,5]
[[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,5,4,3,7,6,2] => [2,1,5,4,3,7,6] => [2,1,5,4,3,7,6]
[[.,.],[[.,[[.,.],.]],[.,.]]] => [1,4,5,3,7,6,2] => [2,1,5,3,4,7,6] => [2,1,4,5,3,7,6]
[[.,.],[[[.,.],[.,.]],[.,.]]] => [1,3,5,4,7,6,2] => [2,1,3,5,4,7,6] => [2,1,3,5,4,7,6]
[[.,.],[[[.,[.,.]],.],[.,.]]] => [1,4,3,5,7,6,2] => [2,1,4,3,5,7,6] => [2,1,4,3,5,7,6]
[[.,.],[[[[.,.],.],.],[.,.]]] => [1,3,4,5,7,6,2] => [2,1,3,4,5,7,6] => [2,1,3,4,5,7,6]
[[.,.],[[.,[.,[.,[.,.]]]],.]] => [1,6,5,4,3,7,2] => [2,1,6,5,4,3,7] => [2,1,6,5,4,3,7]
[[.,.],[[.,[.,[[.,.],.]]],.]] => [1,5,6,4,3,7,2] => [2,1,6,5,3,4,7] => [2,1,5,6,4,3,7]
[[.,.],[[.,[[.,.],[.,.]]],.]] => [1,4,6,5,3,7,2] => [2,1,6,3,5,4,7] => [2,1,4,6,5,3,7]
[[.,.],[[.,[[.,[.,.]],.]],.]] => [1,5,4,6,3,7,2] => [2,1,6,4,3,5,7] => [2,1,5,4,6,3,7]
[[.,.],[[.,[[[.,.],.],.]],.]] => [1,4,5,6,3,7,2] => [2,1,6,3,4,5,7] => [2,1,4,5,6,3,7]
[[.,.],[[[.,.],[.,[.,.]]],.]] => [1,3,6,5,4,7,2] => [2,1,3,6,5,4,7] => [2,1,3,6,5,4,7]
[[.,.],[[[.,.],[[.,.],.]],.]] => [1,3,5,6,4,7,2] => [2,1,3,6,4,5,7] => [2,1,3,5,6,4,7]
[[.,.],[[[.,[.,.]],[.,.]],.]] => [1,4,3,6,5,7,2] => [2,1,4,3,6,5,7] => [2,1,4,3,6,5,7]
[[.,.],[[[[.,.],.],[.,.]],.]] => [1,3,4,6,5,7,2] => [2,1,3,4,6,5,7] => [2,1,3,4,6,5,7]
[[.,.],[[[.,[.,[.,.]]],.],.]] => [1,5,4,3,6,7,2] => [2,1,5,4,3,6,7] => [2,1,5,4,3,6,7]
[[.,.],[[[.,[[.,.],.]],.],.]] => [1,4,5,3,6,7,2] => [2,1,5,3,4,6,7] => [2,1,4,5,3,6,7]
[[.,.],[[[[.,.],[.,.]],.],.]] => [1,3,5,4,6,7,2] => [2,1,3,5,4,6,7] => [2,1,3,5,4,6,7]
[[.,.],[[[[.,[.,.]],.],.],.]] => [1,4,3,5,6,7,2] => [2,1,4,3,5,6,7] => [2,1,4,3,5,6,7]
[[.,.],[[[[[.,.],.],.],.],.]] => [1,3,4,5,6,7,2] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7]
[[.,[.,.]],[.,[.,[.,[.,.]]]]] => [2,1,7,6,5,4,3] => [3,2,1,7,6,5,4] => [3,2,1,7,6,5,4]
[[.,[.,.]],[.,[.,[[.,.],.]]]] => [2,1,6,7,5,4,3] => [3,2,1,7,6,4,5] => [3,2,1,6,7,5,4]
[[.,[.,.]],[.,[[.,.],[.,.]]]] => [2,1,5,7,6,4,3] => [3,2,1,7,4,6,5] => [3,2,1,5,7,6,4]
[[.,[.,.]],[.,[[.,[.,.]],.]]] => [2,1,6,5,7,4,3] => [3,2,1,7,5,4,6] => [3,2,1,6,5,7,4]
[[.,[.,.]],[.,[[[.,.],.],.]]] => [2,1,5,6,7,4,3] => [3,2,1,7,4,5,6] => [3,2,1,5,6,7,4]
[[.,[.,.]],[[.,.],[.,[.,.]]]] => [2,1,4,7,6,5,3] => [3,2,1,4,7,6,5] => [3,2,1,4,7,6,5]
[[.,[.,.]],[[.,.],[[.,.],.]]] => [2,1,4,6,7,5,3] => [3,2,1,4,7,5,6] => [3,2,1,4,6,7,5]
[[.,[.,.]],[[.,[.,.]],[.,.]]] => [2,1,5,4,7,6,3] => [3,2,1,5,4,7,6] => [3,2,1,5,4,7,6]
[[.,[.,.]],[[[.,.],.],[.,.]]] => [2,1,4,5,7,6,3] => [3,2,1,4,5,7,6] => [3,2,1,4,5,7,6]
[[.,[.,.]],[[.,[.,[.,.]]],.]] => [2,1,6,5,4,7,3] => [3,2,1,6,5,4,7] => [3,2,1,6,5,4,7]
[[.,[.,.]],[[.,[[.,.],.]],.]] => [2,1,5,6,4,7,3] => [3,2,1,6,4,5,7] => [3,2,1,5,6,4,7]
[[.,[.,.]],[[[.,.],[.,.]],.]] => [2,1,4,6,5,7,3] => [3,2,1,4,6,5,7] => [3,2,1,4,6,5,7]
[[.,[.,.]],[[[.,[.,.]],.],.]] => [2,1,5,4,6,7,3] => [3,2,1,5,4,6,7] => [3,2,1,5,4,6,7]
[[.,[.,.]],[[[[.,.],.],.],.]] => [2,1,4,5,6,7,3] => [3,2,1,4,5,6,7] => [3,2,1,4,5,6,7]
[[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,2,7,6,5,4,3] => [2,3,1,7,6,5,4] => [2,3,1,7,6,5,4]
[[[.,.],.],[.,[.,[[.,.],.]]]] => [1,2,6,7,5,4,3] => [2,3,1,7,6,4,5] => [2,3,1,6,7,5,4]
[[[.,.],.],[.,[[.,.],[.,.]]]] => [1,2,5,7,6,4,3] => [2,3,1,7,4,6,5] => [2,3,1,5,7,6,4]
[[[.,.],.],[.,[[.,[.,.]],.]]] => [1,2,6,5,7,4,3] => [2,3,1,7,5,4,6] => [2,3,1,6,5,7,4]
[[[.,.],.],[.,[[[.,.],.],.]]] => [1,2,5,6,7,4,3] => [2,3,1,7,4,5,6] => [2,3,1,5,6,7,4]
[[[.,.],.],[[.,.],[.,[.,.]]]] => [1,2,4,7,6,5,3] => [2,3,1,4,7,6,5] => [2,3,1,4,7,6,5]
[[[.,.],.],[[.,.],[[.,.],.]]] => [1,2,4,6,7,5,3] => [2,3,1,4,7,5,6] => [2,3,1,4,6,7,5]
[[[.,.],.],[[.,[.,.]],[.,.]]] => [1,2,5,4,7,6,3] => [2,3,1,5,4,7,6] => [2,3,1,5,4,7,6]
[[[.,.],.],[[[.,.],.],[.,.]]] => [1,2,4,5,7,6,3] => [2,3,1,4,5,7,6] => [2,3,1,4,5,7,6]
[[[.,.],.],[[.,[.,[.,.]]],.]] => [1,2,6,5,4,7,3] => [2,3,1,6,5,4,7] => [2,3,1,6,5,4,7]
[[[.,.],.],[[.,[[.,.],.]],.]] => [1,2,5,6,4,7,3] => [2,3,1,6,4,5,7] => [2,3,1,5,6,4,7]
[[[.,.],.],[[[.,.],[.,.]],.]] => [1,2,4,6,5,7,3] => [2,3,1,4,6,5,7] => [2,3,1,4,6,5,7]
[[[.,.],.],[[[.,[.,.]],.],.]] => [1,2,5,4,6,7,3] => [2,3,1,5,4,6,7] => [2,3,1,5,4,6,7]
[[[.,.],.],[[[[.,.],.],.],.]] => [1,2,4,5,6,7,3] => [2,3,1,4,5,6,7] => [2,3,1,4,5,6,7]
[[.,[.,[.,.]]],[.,[.,[.,.]]]] => [3,2,1,7,6,5,4] => [4,3,2,1,7,6,5] => [4,3,2,1,7,6,5]
[[.,[.,[.,.]]],[.,[[.,.],.]]] => [3,2,1,6,7,5,4] => [4,3,2,1,7,5,6] => [4,3,2,1,6,7,5]
[[.,[.,[.,.]]],[[.,.],[.,.]]] => [3,2,1,5,7,6,4] => [4,3,2,1,5,7,6] => [4,3,2,1,5,7,6]
[[.,[.,[.,.]]],[[.,[.,.]],.]] => [3,2,1,6,5,7,4] => [4,3,2,1,6,5,7] => [4,3,2,1,6,5,7]
[[.,[.,[.,.]]],[[[.,.],.],.]] => [3,2,1,5,6,7,4] => [4,3,2,1,5,6,7] => [4,3,2,1,5,6,7]
[[.,[[.,.],.]],[.,[.,[.,.]]]] => [2,3,1,7,6,5,4] => [4,2,3,1,7,6,5] => [3,4,2,1,7,6,5]
[[.,[[.,.],.]],[.,[[.,.],.]]] => [2,3,1,6,7,5,4] => [4,2,3,1,7,5,6] => [3,4,2,1,6,7,5]
[[.,[[.,.],.]],[[.,.],[.,.]]] => [2,3,1,5,7,6,4] => [4,2,3,1,5,7,6] => [3,4,2,1,5,7,6]
[[.,[[.,.],.]],[[.,[.,.]],.]] => [2,3,1,6,5,7,4] => [4,2,3,1,6,5,7] => [3,4,2,1,6,5,7]
[[.,[[.,.],.]],[[[.,.],.],.]] => [2,3,1,5,6,7,4] => [4,2,3,1,5,6,7] => [3,4,2,1,5,6,7]
[[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,3,2,7,6,5,4] => [2,4,3,1,7,6,5] => [2,4,3,1,7,6,5]
[[[.,.],[.,.]],[.,[[.,.],.]]] => [1,3,2,6,7,5,4] => [2,4,3,1,7,5,6] => [2,4,3,1,6,7,5]
[[[.,.],[.,.]],[[.,.],[.,.]]] => [1,3,2,5,7,6,4] => [2,4,3,1,5,7,6] => [2,4,3,1,5,7,6]
[[[.,.],[.,.]],[[.,[.,.]],.]] => [1,3,2,6,5,7,4] => [2,4,3,1,6,5,7] => [2,4,3,1,6,5,7]
[[[.,.],[.,.]],[[[.,.],.],.]] => [1,3,2,5,6,7,4] => [2,4,3,1,5,6,7] => [2,4,3,1,5,6,7]
[[[.,[.,.]],.],[.,[.,[.,.]]]] => [2,1,3,7,6,5,4] => [3,2,4,1,7,6,5] => [3,2,4,1,7,6,5]
[[[.,[.,.]],.],[.,[[.,.],.]]] => [2,1,3,6,7,5,4] => [3,2,4,1,7,5,6] => [3,2,4,1,6,7,5]
[[[.,[.,.]],.],[[.,.],[.,.]]] => [2,1,3,5,7,6,4] => [3,2,4,1,5,7,6] => [3,2,4,1,5,7,6]
[[[.,[.,.]],.],[[.,[.,.]],.]] => [2,1,3,6,5,7,4] => [3,2,4,1,6,5,7] => [3,2,4,1,6,5,7]
[[[.,[.,.]],.],[[[.,.],.],.]] => [2,1,3,5,6,7,4] => [3,2,4,1,5,6,7] => [3,2,4,1,5,6,7]
[[[[.,.],.],.],[.,[.,[.,.]]]] => [1,2,3,7,6,5,4] => [2,3,4,1,7,6,5] => [2,3,4,1,7,6,5]
[[[[.,.],.],.],[.,[[.,.],.]]] => [1,2,3,6,7,5,4] => [2,3,4,1,7,5,6] => [2,3,4,1,6,7,5]
[[[[.,.],.],.],[[.,.],[.,.]]] => [1,2,3,5,7,6,4] => [2,3,4,1,5,7,6] => [2,3,4,1,5,7,6]
[[[[.,.],.],.],[[.,[.,.]],.]] => [1,2,3,6,5,7,4] => [2,3,4,1,6,5,7] => [2,3,4,1,6,5,7]
[[[[.,.],.],.],[[[.,.],.],.]] => [1,2,3,5,6,7,4] => [2,3,4,1,5,6,7] => [2,3,4,1,5,6,7]
[[.,[.,[.,[.,.]]]],[.,[.,.]]] => [4,3,2,1,7,6,5] => [5,4,3,2,1,7,6] => [5,4,3,2,1,7,6]
[[.,[.,[.,[.,.]]]],[[.,.],.]] => [4,3,2,1,6,7,5] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7]
[[.,[.,[[.,.],.]]],[.,[.,.]]] => [3,4,2,1,7,6,5] => [5,4,2,3,1,7,6] => [4,5,3,2,1,7,6]
[[.,[.,[[.,.],.]]],[[.,.],.]] => [3,4,2,1,6,7,5] => [5,4,2,3,1,6,7] => [4,5,3,2,1,6,7]
[[.,[[.,.],[.,.]]],[.,[.,.]]] => [2,4,3,1,7,6,5] => [5,2,4,3,1,7,6] => [3,5,4,2,1,7,6]
[[.,[[.,.],[.,.]]],[[.,.],.]] => [2,4,3,1,6,7,5] => [5,2,4,3,1,6,7] => [3,5,4,2,1,6,7]
[[.,[[.,[.,.]],.]],[.,[.,.]]] => [3,2,4,1,7,6,5] => [5,3,2,4,1,7,6] => [4,3,5,2,1,7,6]
[[.,[[.,[.,.]],.]],[[.,.],.]] => [3,2,4,1,6,7,5] => [5,3,2,4,1,6,7] => [4,3,5,2,1,6,7]
[[.,[[[.,.],.],.]],[.,[.,.]]] => [2,3,4,1,7,6,5] => [5,2,3,4,1,7,6] => [3,4,5,2,1,7,6]
[[.,[[[.,.],.],.]],[[.,.],.]] => [2,3,4,1,6,7,5] => [5,2,3,4,1,6,7] => [3,4,5,2,1,6,7]
[[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,4,3,2,7,6,5] => [2,5,4,3,1,7,6] => [2,5,4,3,1,7,6]
[[[.,.],[.,[.,.]]],[[.,.],.]] => [1,4,3,2,6,7,5] => [2,5,4,3,1,6,7] => [2,5,4,3,1,6,7]
[[[.,.],[[.,.],.]],[.,[.,.]]] => [1,3,4,2,7,6,5] => [2,5,3,4,1,7,6] => [2,4,5,3,1,7,6]
[[[.,.],[[.,.],.]],[[.,.],.]] => [1,3,4,2,6,7,5] => [2,5,3,4,1,6,7] => [2,4,5,3,1,6,7]
[[[.,[.,.]],[.,.]],[.,[.,.]]] => [2,1,4,3,7,6,5] => [3,2,5,4,1,7,6] => [3,2,5,4,1,7,6]
[[[.,[.,.]],[.,.]],[[.,.],.]] => [2,1,4,3,6,7,5] => [3,2,5,4,1,6,7] => [3,2,5,4,1,6,7]
[[[[.,.],.],[.,.]],[.,[.,.]]] => [1,2,4,3,7,6,5] => [2,3,5,4,1,7,6] => [2,3,5,4,1,7,6]
[[[[.,.],.],[.,.]],[[.,.],.]] => [1,2,4,3,6,7,5] => [2,3,5,4,1,6,7] => [2,3,5,4,1,6,7]
[[[.,[.,[.,.]]],.],[.,[.,.]]] => [3,2,1,4,7,6,5] => [4,3,2,5,1,7,6] => [4,3,2,5,1,7,6]
[[[.,[.,[.,.]]],.],[[.,.],.]] => [3,2,1,4,6,7,5] => [4,3,2,5,1,6,7] => [4,3,2,5,1,6,7]
[[[.,[[.,.],.]],.],[.,[.,.]]] => [2,3,1,4,7,6,5] => [4,2,3,5,1,7,6] => [3,4,2,5,1,7,6]
[[[.,[[.,.],.]],.],[[.,.],.]] => [2,3,1,4,6,7,5] => [4,2,3,5,1,6,7] => [3,4,2,5,1,6,7]
[[[[.,.],[.,.]],.],[.,[.,.]]] => [1,3,2,4,7,6,5] => [2,4,3,5,1,7,6] => [2,4,3,5,1,7,6]
[[[[.,.],[.,.]],.],[[.,.],.]] => [1,3,2,4,6,7,5] => [2,4,3,5,1,6,7] => [2,4,3,5,1,6,7]
[[[[.,[.,.]],.],.],[.,[.,.]]] => [2,1,3,4,7,6,5] => [3,2,4,5,1,7,6] => [3,2,4,5,1,7,6]
[[[[.,[.,.]],.],.],[[.,.],.]] => [2,1,3,4,6,7,5] => [3,2,4,5,1,6,7] => [3,2,4,5,1,6,7]
[[[[[.,.],.],.],.],[.,[.,.]]] => [1,2,3,4,7,6,5] => [2,3,4,5,1,7,6] => [2,3,4,5,1,7,6]
[[[[[.,.],.],.],.],[[.,.],.]] => [1,2,3,4,6,7,5] => [2,3,4,5,1,6,7] => [2,3,4,5,1,6,7]
[[.,[.,[.,[.,[.,.]]]]],[.,.]] => [5,4,3,2,1,7,6] => [6,5,4,3,2,1,7] => [6,5,4,3,2,1,7]
[[.,[.,[.,[[.,.],.]]]],[.,.]] => [4,5,3,2,1,7,6] => [6,5,4,2,3,1,7] => [5,6,4,3,2,1,7]
[[.,[.,[[.,.],[.,.]]]],[.,.]] => [3,5,4,2,1,7,6] => [6,5,2,4,3,1,7] => [4,6,5,3,2,1,7]
[[.,[.,[[.,[.,.]],.]]],[.,.]] => [4,3,5,2,1,7,6] => [6,5,3,2,4,1,7] => [5,4,6,3,2,1,7]
[[.,[.,[[[.,.],.],.]]],[.,.]] => [3,4,5,2,1,7,6] => [6,5,2,3,4,1,7] => [4,5,6,3,2,1,7]
[[.,[[.,.],[.,[.,.]]]],[.,.]] => [2,5,4,3,1,7,6] => [6,2,5,4,3,1,7] => [3,6,5,4,2,1,7]
[[.,[[.,.],[[.,.],.]]],[.,.]] => [2,4,5,3,1,7,6] => [6,2,5,3,4,1,7] => [3,5,6,4,2,1,7]
[[.,[[.,[.,.]],[.,.]]],[.,.]] => [3,2,5,4,1,7,6] => [6,3,2,5,4,1,7] => [4,3,6,5,2,1,7]
[[.,[[[.,.],.],[.,.]]],[.,.]] => [2,3,5,4,1,7,6] => [6,2,3,5,4,1,7] => [3,4,6,5,2,1,7]
[[.,[[.,[.,[.,.]]],.]],[.,.]] => [4,3,2,5,1,7,6] => [6,4,3,2,5,1,7] => [5,4,3,6,2,1,7]
[[.,[[.,[[.,.],.]],.]],[.,.]] => [3,4,2,5,1,7,6] => [6,4,2,3,5,1,7] => [4,5,3,6,2,1,7]
[[.,[[[.,.],[.,.]],.]],[.,.]] => [2,4,3,5,1,7,6] => [6,2,4,3,5,1,7] => [3,5,4,6,2,1,7]
[[.,[[[.,[.,.]],.],.]],[.,.]] => [3,2,4,5,1,7,6] => [6,3,2,4,5,1,7] => [4,3,5,6,2,1,7]
[[.,[[[[.,.],.],.],.]],[.,.]] => [2,3,4,5,1,7,6] => [6,2,3,4,5,1,7] => [3,4,5,6,2,1,7]
[[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,5,4,3,2,7,6] => [2,6,5,4,3,1,7] => [2,6,5,4,3,1,7]
[[[.,.],[.,[[.,.],.]]],[.,.]] => [1,4,5,3,2,7,6] => [2,6,5,3,4,1,7] => [2,5,6,4,3,1,7]
[[[.,.],[[.,.],[.,.]]],[.,.]] => [1,3,5,4,2,7,6] => [2,6,3,5,4,1,7] => [2,4,6,5,3,1,7]
[[[.,.],[[.,[.,.]],.]],[.,.]] => [1,4,3,5,2,7,6] => [2,6,4,3,5,1,7] => [2,5,4,6,3,1,7]
[[[.,.],[[[.,.],.],.]],[.,.]] => [1,3,4,5,2,7,6] => [2,6,3,4,5,1,7] => [2,4,5,6,3,1,7]
[[[.,[.,.]],[.,[.,.]]],[.,.]] => [2,1,5,4,3,7,6] => [3,2,6,5,4,1,7] => [3,2,6,5,4,1,7]
[[[.,[.,.]],[[.,.],.]],[.,.]] => [2,1,4,5,3,7,6] => [3,2,6,4,5,1,7] => [3,2,5,6,4,1,7]
[[[[.,.],.],[.,[.,.]]],[.,.]] => [1,2,5,4,3,7,6] => [2,3,6,5,4,1,7] => [2,3,6,5,4,1,7]
[[[[.,.],.],[[.,.],.]],[.,.]] => [1,2,4,5,3,7,6] => [2,3,6,4,5,1,7] => [2,3,5,6,4,1,7]
[[[.,[.,[.,.]]],[.,.]],[.,.]] => [3,2,1,5,4,7,6] => [4,3,2,6,5,1,7] => [4,3,2,6,5,1,7]
[[[.,[[.,.],.]],[.,.]],[.,.]] => [2,3,1,5,4,7,6] => [4,2,3,6,5,1,7] => [3,4,2,6,5,1,7]
[[[[.,.],[.,.]],[.,.]],[.,.]] => [1,3,2,5,4,7,6] => [2,4,3,6,5,1,7] => [2,4,3,6,5,1,7]
[[[[.,[.,.]],.],[.,.]],[.,.]] => [2,1,3,5,4,7,6] => [3,2,4,6,5,1,7] => [3,2,4,6,5,1,7]
[[[[[.,.],.],.],[.,.]],[.,.]] => [1,2,3,5,4,7,6] => [2,3,4,6,5,1,7] => [2,3,4,6,5,1,7]
[[[.,[.,[.,[.,.]]]],.],[.,.]] => [4,3,2,1,5,7,6] => [5,4,3,2,6,1,7] => [5,4,3,2,6,1,7]
[[[.,[.,[[.,.],.]]],.],[.,.]] => [3,4,2,1,5,7,6] => [5,4,2,3,6,1,7] => [4,5,3,2,6,1,7]
[[[.,[[.,.],[.,.]]],.],[.,.]] => [2,4,3,1,5,7,6] => [5,2,4,3,6,1,7] => [3,5,4,2,6,1,7]
[[[.,[[.,[.,.]],.]],.],[.,.]] => [3,2,4,1,5,7,6] => [5,3,2,4,6,1,7] => [4,3,5,2,6,1,7]
[[[.,[[[.,.],.],.]],.],[.,.]] => [2,3,4,1,5,7,6] => [5,2,3,4,6,1,7] => [3,4,5,2,6,1,7]
[[[[.,.],[.,[.,.]]],.],[.,.]] => [1,4,3,2,5,7,6] => [2,5,4,3,6,1,7] => [2,5,4,3,6,1,7]
[[[[.,.],[[.,.],.]],.],[.,.]] => [1,3,4,2,5,7,6] => [2,5,3,4,6,1,7] => [2,4,5,3,6,1,7]
[[[[.,[.,.]],[.,.]],.],[.,.]] => [2,1,4,3,5,7,6] => [3,2,5,4,6,1,7] => [3,2,5,4,6,1,7]
[[[[[.,.],.],[.,.]],.],[.,.]] => [1,2,4,3,5,7,6] => [2,3,5,4,6,1,7] => [2,3,5,4,6,1,7]
[[[[.,[.,[.,.]]],.],.],[.,.]] => [3,2,1,4,5,7,6] => [4,3,2,5,6,1,7] => [4,3,2,5,6,1,7]
[[[[.,[[.,.],.]],.],.],[.,.]] => [2,3,1,4,5,7,6] => [4,2,3,5,6,1,7] => [3,4,2,5,6,1,7]
[[[[[.,.],[.,.]],.],.],[.,.]] => [1,3,2,4,5,7,6] => [2,4,3,5,6,1,7] => [2,4,3,5,6,1,7]
[[[[[.,[.,.]],.],.],.],[.,.]] => [2,1,3,4,5,7,6] => [3,2,4,5,6,1,7] => [3,2,4,5,6,1,7]
[[[[[[.,.],.],.],.],.],[.,.]] => [1,2,3,4,5,7,6] => [2,3,4,5,6,1,7] => [2,3,4,5,6,1,7]
[[.,[.,[.,[.,[.,[.,.]]]]]],.] => [6,5,4,3,2,1,7] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1]
[[.,[.,[.,[.,[[.,.],.]]]]],.] => [5,6,4,3,2,1,7] => [7,6,5,4,2,3,1] => [6,7,5,4,3,2,1]
[[.,[.,[.,[[.,.],[.,.]]]]],.] => [4,6,5,3,2,1,7] => [7,6,5,2,4,3,1] => [5,7,6,4,3,2,1]
[[.,[.,[.,[[.,[.,.]],.]]]],.] => [5,4,6,3,2,1,7] => [7,6,5,3,2,4,1] => [6,5,7,4,3,2,1]
[[.,[.,[.,[[[.,.],.],.]]]],.] => [4,5,6,3,2,1,7] => [7,6,5,2,3,4,1] => [5,6,7,4,3,2,1]
[[.,[.,[[.,.],[.,[.,.]]]]],.] => [3,6,5,4,2,1,7] => [7,6,2,5,4,3,1] => [4,7,6,5,3,2,1]
[[.,[.,[[.,.],[[.,.],.]]]],.] => [3,5,6,4,2,1,7] => [7,6,2,5,3,4,1] => [4,6,7,5,3,2,1]
[[.,[.,[[.,[.,.]],[.,.]]]],.] => [4,3,6,5,2,1,7] => [7,6,3,2,5,4,1] => [5,4,7,6,3,2,1]
[[.,[.,[[[.,.],.],[.,.]]]],.] => [3,4,6,5,2,1,7] => [7,6,2,3,5,4,1] => [4,5,7,6,3,2,1]
[[.,[.,[[.,[.,[.,.]]],.]]],.] => [5,4,3,6,2,1,7] => [7,6,4,3,2,5,1] => [6,5,4,7,3,2,1]
[[.,[.,[[.,[[.,.],.]],.]]],.] => [4,5,3,6,2,1,7] => [7,6,4,2,3,5,1] => [5,6,4,7,3,2,1]
[[.,[.,[[[.,.],[.,.]],.]]],.] => [3,5,4,6,2,1,7] => [7,6,2,4,3,5,1] => [4,6,5,7,3,2,1]
[[.,[.,[[[.,[.,.]],.],.]]],.] => [4,3,5,6,2,1,7] => [7,6,3,2,4,5,1] => [5,4,6,7,3,2,1]
[[.,[.,[[[[.,.],.],.],.]]],.] => [3,4,5,6,2,1,7] => [7,6,2,3,4,5,1] => [4,5,6,7,3,2,1]
[[.,[[.,.],[.,[.,[.,.]]]]],.] => [2,6,5,4,3,1,7] => [7,2,6,5,4,3,1] => [3,7,6,5,4,2,1]
[[.,[[.,.],[.,[[.,.],.]]]],.] => [2,5,6,4,3,1,7] => [7,2,6,5,3,4,1] => [3,6,7,5,4,2,1]
[[.,[[.,.],[[.,.],[.,.]]]],.] => [2,4,6,5,3,1,7] => [7,2,6,3,5,4,1] => [3,5,7,6,4,2,1]
[[.,[[.,.],[[.,[.,.]],.]]],.] => [2,5,4,6,3,1,7] => [7,2,6,4,3,5,1] => [3,6,5,7,4,2,1]
[[.,[[.,.],[[[.,.],.],.]]],.] => [2,4,5,6,3,1,7] => [7,2,6,3,4,5,1] => [3,5,6,7,4,2,1]
[[.,[[.,[.,.]],[.,[.,.]]]],.] => [3,2,6,5,4,1,7] => [7,3,2,6,5,4,1] => [4,3,7,6,5,2,1]
[[.,[[.,[.,.]],[[.,.],.]]],.] => [3,2,5,6,4,1,7] => [7,3,2,6,4,5,1] => [4,3,6,7,5,2,1]
[[.,[[[.,.],.],[.,[.,.]]]],.] => [2,3,6,5,4,1,7] => [7,2,3,6,5,4,1] => [3,4,7,6,5,2,1]
[[.,[[[.,.],.],[[.,.],.]]],.] => [2,3,5,6,4,1,7] => [7,2,3,6,4,5,1] => [3,4,6,7,5,2,1]
[[.,[[.,[.,[.,.]]],[.,.]]],.] => [4,3,2,6,5,1,7] => [7,4,3,2,6,5,1] => [5,4,3,7,6,2,1]
[[.,[[.,[[.,.],.]],[.,.]]],.] => [3,4,2,6,5,1,7] => [7,4,2,3,6,5,1] => [4,5,3,7,6,2,1]
[[.,[[[.,.],[.,.]],[.,.]]],.] => [2,4,3,6,5,1,7] => [7,2,4,3,6,5,1] => [3,5,4,7,6,2,1]
[[.,[[[.,[.,.]],.],[.,.]]],.] => [3,2,4,6,5,1,7] => [7,3,2,4,6,5,1] => [4,3,5,7,6,2,1]
[[.,[[[[.,.],.],.],[.,.]]],.] => [2,3,4,6,5,1,7] => [7,2,3,4,6,5,1] => [3,4,5,7,6,2,1]
[[.,[[.,[.,[.,[.,.]]]],.]],.] => [5,4,3,2,6,1,7] => [7,5,4,3,2,6,1] => [6,5,4,3,7,2,1]
[[.,[[.,[.,[[.,.],.]]],.]],.] => [4,5,3,2,6,1,7] => [7,5,4,2,3,6,1] => [5,6,4,3,7,2,1]
[[.,[[.,[[.,.],[.,.]]],.]],.] => [3,5,4,2,6,1,7] => [7,5,2,4,3,6,1] => [4,6,5,3,7,2,1]
[[.,[[.,[[.,[.,.]],.]],.]],.] => [4,3,5,2,6,1,7] => [7,5,3,2,4,6,1] => [5,4,6,3,7,2,1]
[[.,[[.,[[[.,.],.],.]],.]],.] => [3,4,5,2,6,1,7] => [7,5,2,3,4,6,1] => [4,5,6,3,7,2,1]
[[.,[[[.,.],[.,[.,.]]],.]],.] => [2,5,4,3,6,1,7] => [7,2,5,4,3,6,1] => [3,6,5,4,7,2,1]
[[.,[[[.,.],[[.,.],.]],.]],.] => [2,4,5,3,6,1,7] => [7,2,5,3,4,6,1] => [3,5,6,4,7,2,1]
[[.,[[[.,[.,.]],[.,.]],.]],.] => [3,2,5,4,6,1,7] => [7,3,2,5,4,6,1] => [4,3,6,5,7,2,1]
[[.,[[[[.,.],.],[.,.]],.]],.] => [2,3,5,4,6,1,7] => [7,2,3,5,4,6,1] => [3,4,6,5,7,2,1]
[[.,[[[.,[.,[.,.]]],.],.]],.] => [4,3,2,5,6,1,7] => [7,4,3,2,5,6,1] => [5,4,3,6,7,2,1]
[[.,[[[.,[[.,.],.]],.],.]],.] => [3,4,2,5,6,1,7] => [7,4,2,3,5,6,1] => [4,5,3,6,7,2,1]
[[.,[[[[.,.],[.,.]],.],.]],.] => [2,4,3,5,6,1,7] => [7,2,4,3,5,6,1] => [3,5,4,6,7,2,1]
[[.,[[[[.,[.,.]],.],.],.]],.] => [3,2,4,5,6,1,7] => [7,3,2,4,5,6,1] => [4,3,5,6,7,2,1]
[[.,[[[[[.,.],.],.],.],.]],.] => [2,3,4,5,6,1,7] => [7,2,3,4,5,6,1] => [3,4,5,6,7,2,1]
[[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,6,5,4,3,2,7] => [2,7,6,5,4,3,1] => [2,7,6,5,4,3,1]
[[[.,.],[.,[.,[[.,.],.]]]],.] => [1,5,6,4,3,2,7] => [2,7,6,5,3,4,1] => [2,6,7,5,4,3,1]
[[[.,.],[.,[[.,.],[.,.]]]],.] => [1,4,6,5,3,2,7] => [2,7,6,3,5,4,1] => [2,5,7,6,4,3,1]
[[[.,.],[.,[[.,[.,.]],.]]],.] => [1,5,4,6,3,2,7] => [2,7,6,4,3,5,1] => [2,6,5,7,4,3,1]
[[[.,.],[.,[[[.,.],.],.]]],.] => [1,4,5,6,3,2,7] => [2,7,6,3,4,5,1] => [2,5,6,7,4,3,1]
[[[.,.],[[.,.],[.,[.,.]]]],.] => [1,3,6,5,4,2,7] => [2,7,3,6,5,4,1] => [2,4,7,6,5,3,1]
[[[.,.],[[.,.],[[.,.],.]]],.] => [1,3,5,6,4,2,7] => [2,7,3,6,4,5,1] => [2,4,6,7,5,3,1]
[[[.,.],[[.,[.,.]],[.,.]]],.] => [1,4,3,6,5,2,7] => [2,7,4,3,6,5,1] => [2,5,4,7,6,3,1]
[[[.,.],[[[.,.],.],[.,.]]],.] => [1,3,4,6,5,2,7] => [2,7,3,4,6,5,1] => [2,4,5,7,6,3,1]
[[[.,.],[[.,[.,[.,.]]],.]],.] => [1,5,4,3,6,2,7] => [2,7,5,4,3,6,1] => [2,6,5,4,7,3,1]
[[[.,.],[[.,[[.,.],.]],.]],.] => [1,4,5,3,6,2,7] => [2,7,5,3,4,6,1] => [2,5,6,4,7,3,1]
[[[.,.],[[[.,.],[.,.]],.]],.] => [1,3,5,4,6,2,7] => [2,7,3,5,4,6,1] => [2,4,6,5,7,3,1]
[[[.,.],[[[.,[.,.]],.],.]],.] => [1,4,3,5,6,2,7] => [2,7,4,3,5,6,1] => [2,5,4,6,7,3,1]
[[[.,.],[[[[.,.],.],.],.]],.] => [1,3,4,5,6,2,7] => [2,7,3,4,5,6,1] => [2,4,5,6,7,3,1]
[[[.,[.,.]],[.,[.,[.,.]]]],.] => [2,1,6,5,4,3,7] => [3,2,7,6,5,4,1] => [3,2,7,6,5,4,1]
[[[.,[.,.]],[.,[[.,.],.]]],.] => [2,1,5,6,4,3,7] => [3,2,7,6,4,5,1] => [3,2,6,7,5,4,1]
[[[.,[.,.]],[[.,.],[.,.]]],.] => [2,1,4,6,5,3,7] => [3,2,7,4,6,5,1] => [3,2,5,7,6,4,1]
[[[.,[.,.]],[[.,[.,.]],.]],.] => [2,1,5,4,6,3,7] => [3,2,7,5,4,6,1] => [3,2,6,5,7,4,1]
[[[.,[.,.]],[[[.,.],.],.]],.] => [2,1,4,5,6,3,7] => [3,2,7,4,5,6,1] => [3,2,5,6,7,4,1]
[[[[.,.],.],[.,[.,[.,.]]]],.] => [1,2,6,5,4,3,7] => [2,3,7,6,5,4,1] => [2,3,7,6,5,4,1]
[[[[.,.],.],[.,[[.,.],.]]],.] => [1,2,5,6,4,3,7] => [2,3,7,6,4,5,1] => [2,3,6,7,5,4,1]
[[[[.,.],.],[[.,.],[.,.]]],.] => [1,2,4,6,5,3,7] => [2,3,7,4,6,5,1] => [2,3,5,7,6,4,1]
[[[[.,.],.],[[.,[.,.]],.]],.] => [1,2,5,4,6,3,7] => [2,3,7,5,4,6,1] => [2,3,6,5,7,4,1]
[[[[.,.],.],[[[.,.],.],.]],.] => [1,2,4,5,6,3,7] => [2,3,7,4,5,6,1] => [2,3,5,6,7,4,1]
[[[.,[.,[.,.]]],[.,[.,.]]],.] => [3,2,1,6,5,4,7] => [4,3,2,7,6,5,1] => [4,3,2,7,6,5,1]
[[[.,[.,[.,.]]],[[.,.],.]],.] => [3,2,1,5,6,4,7] => [4,3,2,7,5,6,1] => [4,3,2,6,7,5,1]
[[[.,[[.,.],.]],[.,[.,.]]],.] => [2,3,1,6,5,4,7] => [4,2,3,7,6,5,1] => [3,4,2,7,6,5,1]
[[[.,[[.,.],.]],[[.,.],.]],.] => [2,3,1,5,6,4,7] => [4,2,3,7,5,6,1] => [3,4,2,6,7,5,1]
[[[[.,.],[.,.]],[.,[.,.]]],.] => [1,3,2,6,5,4,7] => [2,4,3,7,6,5,1] => [2,4,3,7,6,5,1]
[[[[.,.],[.,.]],[[.,.],.]],.] => [1,3,2,5,6,4,7] => [2,4,3,7,5,6,1] => [2,4,3,6,7,5,1]
[[[[.,[.,.]],.],[.,[.,.]]],.] => [2,1,3,6,5,4,7] => [3,2,4,7,6,5,1] => [3,2,4,7,6,5,1]
[[[[.,[.,.]],.],[[.,.],.]],.] => [2,1,3,5,6,4,7] => [3,2,4,7,5,6,1] => [3,2,4,6,7,5,1]
[[[[[.,.],.],.],[.,[.,.]]],.] => [1,2,3,6,5,4,7] => [2,3,4,7,6,5,1] => [2,3,4,7,6,5,1]
[[[[[.,.],.],.],[[.,.],.]],.] => [1,2,3,5,6,4,7] => [2,3,4,7,5,6,1] => [2,3,4,6,7,5,1]
[[[.,[.,[.,[.,.]]]],[.,.]],.] => [4,3,2,1,6,5,7] => [5,4,3,2,7,6,1] => [5,4,3,2,7,6,1]
[[[.,[.,[[.,.],.]]],[.,.]],.] => [3,4,2,1,6,5,7] => [5,4,2,3,7,6,1] => [4,5,3,2,7,6,1]
[[[.,[[.,.],[.,.]]],[.,.]],.] => [2,4,3,1,6,5,7] => [5,2,4,3,7,6,1] => [3,5,4,2,7,6,1]
[[[.,[[.,[.,.]],.]],[.,.]],.] => [3,2,4,1,6,5,7] => [5,3,2,4,7,6,1] => [4,3,5,2,7,6,1]
[[[.,[[[.,.],.],.]],[.,.]],.] => [2,3,4,1,6,5,7] => [5,2,3,4,7,6,1] => [3,4,5,2,7,6,1]
[[[[.,.],[.,[.,.]]],[.,.]],.] => [1,4,3,2,6,5,7] => [2,5,4,3,7,6,1] => [2,5,4,3,7,6,1]
[[[[.,.],[[.,.],.]],[.,.]],.] => [1,3,4,2,6,5,7] => [2,5,3,4,7,6,1] => [2,4,5,3,7,6,1]
[[[[.,[.,.]],[.,.]],[.,.]],.] => [2,1,4,3,6,5,7] => [3,2,5,4,7,6,1] => [3,2,5,4,7,6,1]
[[[[[.,.],.],[.,.]],[.,.]],.] => [1,2,4,3,6,5,7] => [2,3,5,4,7,6,1] => [2,3,5,4,7,6,1]
[[[[.,[.,[.,.]]],.],[.,.]],.] => [3,2,1,4,6,5,7] => [4,3,2,5,7,6,1] => [4,3,2,5,7,6,1]
[[[[.,[[.,.],.]],.],[.,.]],.] => [2,3,1,4,6,5,7] => [4,2,3,5,7,6,1] => [3,4,2,5,7,6,1]
[[[[[.,.],[.,.]],.],[.,.]],.] => [1,3,2,4,6,5,7] => [2,4,3,5,7,6,1] => [2,4,3,5,7,6,1]
[[[[[.,[.,.]],.],.],[.,.]],.] => [2,1,3,4,6,5,7] => [3,2,4,5,7,6,1] => [3,2,4,5,7,6,1]
[[[[[[.,.],.],.],.],[.,.]],.] => [1,2,3,4,6,5,7] => [2,3,4,5,7,6,1] => [2,3,4,5,7,6,1]
[[[.,[.,[.,[.,[.,.]]]]],.],.] => [5,4,3,2,1,6,7] => [6,5,4,3,2,7,1] => [6,5,4,3,2,7,1]
[[[.,[.,[.,[[.,.],.]]]],.],.] => [4,5,3,2,1,6,7] => [6,5,4,2,3,7,1] => [5,6,4,3,2,7,1]
[[[.,[.,[[.,.],[.,.]]]],.],.] => [3,5,4,2,1,6,7] => [6,5,2,4,3,7,1] => [4,6,5,3,2,7,1]
[[[.,[.,[[.,[.,.]],.]]],.],.] => [4,3,5,2,1,6,7] => [6,5,3,2,4,7,1] => [5,4,6,3,2,7,1]
[[[.,[.,[[[.,.],.],.]]],.],.] => [3,4,5,2,1,6,7] => [6,5,2,3,4,7,1] => [4,5,6,3,2,7,1]
[[[.,[[.,.],[.,[.,.]]]],.],.] => [2,5,4,3,1,6,7] => [6,2,5,4,3,7,1] => [3,6,5,4,2,7,1]
[[[.,[[.,.],[[.,.],.]]],.],.] => [2,4,5,3,1,6,7] => [6,2,5,3,4,7,1] => [3,5,6,4,2,7,1]
[[[.,[[.,[.,.]],[.,.]]],.],.] => [3,2,5,4,1,6,7] => [6,3,2,5,4,7,1] => [4,3,6,5,2,7,1]
[[[.,[[[.,.],.],[.,.]]],.],.] => [2,3,5,4,1,6,7] => [6,2,3,5,4,7,1] => [3,4,6,5,2,7,1]
[[[.,[[.,[.,[.,.]]],.]],.],.] => [4,3,2,5,1,6,7] => [6,4,3,2,5,7,1] => [5,4,3,6,2,7,1]
[[[.,[[.,[[.,.],.]],.]],.],.] => [3,4,2,5,1,6,7] => [6,4,2,3,5,7,1] => [4,5,3,6,2,7,1]
[[[.,[[[.,.],[.,.]],.]],.],.] => [2,4,3,5,1,6,7] => [6,2,4,3,5,7,1] => [3,5,4,6,2,7,1]
[[[.,[[[.,[.,.]],.],.]],.],.] => [3,2,4,5,1,6,7] => [6,3,2,4,5,7,1] => [4,3,5,6,2,7,1]
[[[.,[[[[.,.],.],.],.]],.],.] => [2,3,4,5,1,6,7] => [6,2,3,4,5,7,1] => [3,4,5,6,2,7,1]
[[[[.,.],[.,[.,[.,.]]]],.],.] => [1,5,4,3,2,6,7] => [2,6,5,4,3,7,1] => [2,6,5,4,3,7,1]
[[[[.,.],[.,[[.,.],.]]],.],.] => [1,4,5,3,2,6,7] => [2,6,5,3,4,7,1] => [2,5,6,4,3,7,1]
[[[[.,.],[[.,.],[.,.]]],.],.] => [1,3,5,4,2,6,7] => [2,6,3,5,4,7,1] => [2,4,6,5,3,7,1]
[[[[.,.],[[.,[.,.]],.]],.],.] => [1,4,3,5,2,6,7] => [2,6,4,3,5,7,1] => [2,5,4,6,3,7,1]
[[[[.,.],[[[.,.],.],.]],.],.] => [1,3,4,5,2,6,7] => [2,6,3,4,5,7,1] => [2,4,5,6,3,7,1]
[[[[.,[.,.]],[.,[.,.]]],.],.] => [2,1,5,4,3,6,7] => [3,2,6,5,4,7,1] => [3,2,6,5,4,7,1]
[[[[.,[.,.]],[[.,.],.]],.],.] => [2,1,4,5,3,6,7] => [3,2,6,4,5,7,1] => [3,2,5,6,4,7,1]
[[[[[.,.],.],[.,[.,.]]],.],.] => [1,2,5,4,3,6,7] => [2,3,6,5,4,7,1] => [2,3,6,5,4,7,1]
[[[[[.,.],.],[[.,.],.]],.],.] => [1,2,4,5,3,6,7] => [2,3,6,4,5,7,1] => [2,3,5,6,4,7,1]
[[[[.,[.,[.,.]]],[.,.]],.],.] => [3,2,1,5,4,6,7] => [4,3,2,6,5,7,1] => [4,3,2,6,5,7,1]
[[[[.,[[.,.],.]],[.,.]],.],.] => [2,3,1,5,4,6,7] => [4,2,3,6,5,7,1] => [3,4,2,6,5,7,1]
[[[[[.,.],[.,.]],[.,.]],.],.] => [1,3,2,5,4,6,7] => [2,4,3,6,5,7,1] => [2,4,3,6,5,7,1]
[[[[[.,[.,.]],.],[.,.]],.],.] => [2,1,3,5,4,6,7] => [3,2,4,6,5,7,1] => [3,2,4,6,5,7,1]
[[[[[[.,.],.],.],[.,.]],.],.] => [1,2,3,5,4,6,7] => [2,3,4,6,5,7,1] => [2,3,4,6,5,7,1]
[[[[.,[.,[.,[.,.]]]],.],.],.] => [4,3,2,1,5,6,7] => [5,4,3,2,6,7,1] => [5,4,3,2,6,7,1]
[[[[.,[.,[[.,.],.]]],.],.],.] => [3,4,2,1,5,6,7] => [5,4,2,3,6,7,1] => [4,5,3,2,6,7,1]
[[[[.,[[.,.],[.,.]]],.],.],.] => [2,4,3,1,5,6,7] => [5,2,4,3,6,7,1] => [3,5,4,2,6,7,1]
[[[[.,[[.,[.,.]],.]],.],.],.] => [3,2,4,1,5,6,7] => [5,3,2,4,6,7,1] => [4,3,5,2,6,7,1]
[[[[.,[[[.,.],.],.]],.],.],.] => [2,3,4,1,5,6,7] => [5,2,3,4,6,7,1] => [3,4,5,2,6,7,1]
[[[[[.,.],[.,[.,.]]],.],.],.] => [1,4,3,2,5,6,7] => [2,5,4,3,6,7,1] => [2,5,4,3,6,7,1]
[[[[[.,.],[[.,.],.]],.],.],.] => [1,3,4,2,5,6,7] => [2,5,3,4,6,7,1] => [2,4,5,3,6,7,1]
[[[[[.,[.,.]],[.,.]],.],.],.] => [2,1,4,3,5,6,7] => [3,2,5,4,6,7,1] => [3,2,5,4,6,7,1]
[[[[[[.,.],.],[.,.]],.],.],.] => [1,2,4,3,5,6,7] => [2,3,5,4,6,7,1] => [2,3,5,4,6,7,1]
[[[[[.,[.,[.,.]]],.],.],.],.] => [3,2,1,4,5,6,7] => [4,3,2,5,6,7,1] => [4,3,2,5,6,7,1]
[[[[[.,[[.,.],.]],.],.],.],.] => [2,3,1,4,5,6,7] => [4,2,3,5,6,7,1] => [3,4,2,5,6,7,1]
[[[[[[.,.],[.,.]],.],.],.],.] => [1,3,2,4,5,6,7] => [2,4,3,5,6,7,1] => [2,4,3,5,6,7,1]
[[[[[[.,[.,.]],.],.],.],.],.] => [2,1,3,4,5,6,7] => [3,2,4,5,6,7,1] => [3,2,4,5,6,7,1]
[[[[[[[.,.],.],.],.],.],.],.] => [1,2,3,4,5,6,7] => [2,3,4,5,6,7,1] => [2,3,4,5,6,7,1]
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [8,7,6,5,4,3,2,1] => [1,8,7,6,5,4,3,2] => [1,8,7,6,5,4,3,2]
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]] => [5,6,7,8,4,3,2,1] => [1,8,7,6,2,3,4,5] => [1,5,6,7,8,4,3,2]
[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [4,3,2,8,7,6,5,1] => [1,4,3,2,8,7,6,5] => [1,4,3,2,8,7,6,5]
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]] => [3,4,2,8,7,6,5,1] => [1,4,2,3,8,7,6,5] => [1,3,4,2,8,7,6,5]
[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => [2,4,3,8,7,6,5,1] => [1,2,4,3,8,7,6,5] => [1,2,4,3,8,7,6,5]
[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]] => [3,2,4,8,7,6,5,1] => [1,3,2,4,8,7,6,5] => [1,3,2,4,8,7,6,5]
[.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [2,3,4,8,7,6,5,1] => [1,2,3,4,8,7,6,5] => [1,2,3,4,8,7,6,5]
[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]] => [4,3,2,7,6,5,8,1] => [1,4,3,2,7,6,5,8] => [1,4,3,2,7,6,5,8]
[.,[[[.,[[.,.],.]],[[.,.],.]],.]] => [3,4,2,6,7,5,8,1] => [1,4,2,3,7,5,6,8] => [1,3,4,2,6,7,5,8]
[.,[[[[[.,[.,.]],.],.],[.,.]],.]] => [3,2,4,5,7,6,8,1] => [1,3,2,4,5,7,6,8] => [1,3,2,4,5,7,6,8]
[.,[[[[[.,.],[.,.]],[.,.]],.],.]] => [2,4,3,6,5,7,8,1] => [1,2,4,3,6,5,7,8] => [1,2,4,3,6,5,7,8]
[.,[[[[[[[.,.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,1] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8]
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,8,7,6,5,4,3,2] => [2,1,8,7,6,5,4,3] => [2,1,8,7,6,5,4,3]
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => [1,6,7,8,5,4,3,2] => [2,1,8,7,6,3,4,5] => [2,1,6,7,8,5,4,3]
[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [1,6,5,8,7,4,3,2] => [2,1,8,7,4,3,6,5] => [2,1,6,5,8,7,4,3]
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]] => [1,6,7,5,8,4,3,2] => [2,1,8,7,5,3,4,6] => [2,1,6,7,5,8,4,3]
[[.,.],[.,[[[[[.,.],.],.],.],.]]] => [1,4,5,6,7,8,3,2] => [2,1,8,3,4,5,6,7] => [2,1,4,5,6,7,8,3]
[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,4,3,8,7,6,5,2] => [2,1,4,3,8,7,6,5] => [2,1,4,3,8,7,6,5]
[[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,4,3,7,8,6,5,2] => [2,1,4,3,8,7,5,6] => [2,1,4,3,7,8,6,5]
[[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,4,3,6,8,7,5,2] => [2,1,4,3,8,5,7,6] => [2,1,4,3,6,8,7,5]
[[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [1,4,3,6,7,8,5,2] => [2,1,4,3,8,5,6,7] => [2,1,4,3,6,7,8,5]
[[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,3,4,8,7,6,5,2] => [2,1,3,4,8,7,6,5] => [2,1,3,4,8,7,6,5]
[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,6,5,4,3,8,7,2] => [2,1,6,5,4,3,8,7] => [2,1,6,5,4,3,8,7]
[[.,.],[[.,[.,[[.,.],.]]],[.,.]]] => [1,5,6,4,3,8,7,2] => [2,1,6,5,3,4,8,7] => [2,1,5,6,4,3,8,7]
[[.,.],[[.,[[[.,.],.],.]],[.,.]]] => [1,4,5,6,3,8,7,2] => [2,1,6,3,4,5,8,7] => [2,1,4,5,6,3,8,7]
[[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,4,3,6,5,8,7,2] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7]
[[.,.],[[[[[.,.],.],.],.],[.,.]]] => [1,3,4,5,6,8,7,2] => [2,1,3,4,5,6,8,7] => [2,1,3,4,5,6,8,7]
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [2,1,8,7,6,5,4,3] => [3,2,1,8,7,6,5,4] => [3,2,1,8,7,6,5,4]
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [2,1,6,7,8,5,4,3] => [3,2,1,8,7,4,5,6] => [3,2,1,6,7,8,5,4]
[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [2,1,4,8,7,6,5,3] => [3,2,1,4,8,7,6,5] => [3,2,1,4,8,7,6,5]
[[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [2,1,4,5,8,7,6,3] => [3,2,1,4,5,8,7,6] => [3,2,1,4,5,8,7,6]
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,2,4,8,7,6,5,3] => [2,3,1,4,8,7,6,5] => [2,3,1,4,8,7,6,5]
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [3,2,1,8,7,6,5,4] => [4,3,2,1,8,7,6,5] => [4,3,2,1,8,7,6,5]
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [3,2,1,7,8,6,5,4] => [4,3,2,1,8,7,5,6] => [4,3,2,1,7,8,6,5]
[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [3,2,1,6,8,7,5,4] => [4,3,2,1,8,5,7,6] => [4,3,2,1,6,8,7,5]
[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [3,2,1,7,6,8,5,4] => [4,3,2,1,8,6,5,7] => [4,3,2,1,7,6,8,5]
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => [3,2,1,6,7,8,5,4] => [4,3,2,1,8,5,6,7] => [4,3,2,1,6,7,8,5]
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [3,2,1,5,8,7,6,4] => [4,3,2,1,5,8,7,6] => [4,3,2,1,5,8,7,6]
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [3,2,1,5,7,8,6,4] => [4,3,2,1,5,8,6,7] => [4,3,2,1,5,7,8,6]
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [3,2,1,6,5,8,7,4] => [4,3,2,1,6,5,8,7] => [4,3,2,1,6,5,8,7]
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [3,2,1,5,6,8,7,4] => [4,3,2,1,5,6,8,7] => [4,3,2,1,5,6,8,7]
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [3,2,1,7,6,5,8,4] => [4,3,2,1,7,6,5,8] => [4,3,2,1,7,6,5,8]
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]] => [3,2,1,6,7,5,8,4] => [4,3,2,1,7,5,6,8] => [4,3,2,1,6,7,5,8]
[[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [3,2,1,5,7,6,8,4] => [4,3,2,1,5,7,6,8] => [4,3,2,1,5,7,6,8]
[[.,[.,[.,.]]],[[[.,[.,.]],.],.]] => [3,2,1,6,5,7,8,4] => [4,3,2,1,6,5,7,8] => [4,3,2,1,6,5,7,8]
[[.,[.,[.,.]]],[[[[.,.],.],.],.]] => [3,2,1,5,6,7,8,4] => [4,3,2,1,5,6,7,8] => [4,3,2,1,5,6,7,8]
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]] => [2,3,1,8,7,6,5,4] => [4,2,3,1,8,7,6,5] => [3,4,2,1,8,7,6,5]
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,3,2,8,7,6,5,4] => [2,4,3,1,8,7,6,5] => [2,4,3,1,8,7,6,5]
[[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [1,3,2,6,8,7,5,4] => [2,4,3,1,8,5,7,6] => [2,4,3,1,6,8,7,5]
[[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [1,3,2,6,7,8,5,4] => [2,4,3,1,8,5,6,7] => [2,4,3,1,6,7,8,5]
[[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [1,3,2,6,5,8,7,4] => [2,4,3,1,6,5,8,7] => [2,4,3,1,6,5,8,7]
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [2,1,3,8,7,6,5,4] => [3,2,4,1,8,7,6,5] => [3,2,4,1,8,7,6,5]
[[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [2,1,3,6,5,8,7,4] => [3,2,4,1,6,5,8,7] => [3,2,4,1,6,5,8,7]
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,2,3,8,7,6,5,4] => [2,3,4,1,8,7,6,5] => [2,3,4,1,8,7,6,5]
[[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [1,2,3,6,8,7,5,4] => [2,3,4,1,8,5,7,6] => [2,3,4,1,6,8,7,5]
[[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [1,2,3,6,5,8,7,4] => [2,3,4,1,6,5,8,7] => [2,3,4,1,6,5,8,7]
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [4,3,2,1,8,7,6,5] => [5,4,3,2,1,8,7,6] => [5,4,3,2,1,8,7,6]
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]] => [3,4,2,1,7,8,6,5] => [5,4,2,3,1,8,6,7] => [4,5,3,2,1,7,8,6]
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [2,1,4,3,8,7,6,5] => [3,2,5,4,1,8,7,6] => [3,2,5,4,1,8,7,6]
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [2,1,4,3,7,8,6,5] => [3,2,5,4,1,8,6,7] => [3,2,5,4,1,7,8,6]
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [5,4,3,2,1,8,7,6] => [6,5,4,3,2,1,8,7] => [6,5,4,3,2,1,8,7]
[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [3,2,5,4,1,8,7,6] => [6,3,2,5,4,1,8,7] => [4,3,6,5,2,1,8,7]
[[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [1,2,4,5,3,8,7,6] => [2,3,6,4,5,1,8,7] => [2,3,5,6,4,1,8,7]
[[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [2,1,4,3,5,8,7,6] => [3,2,5,4,6,1,8,7] => [3,2,5,4,6,1,8,7]
[[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,2,3,4,5,8,7,6] => [2,3,4,5,6,1,8,7] => [2,3,4,5,6,1,8,7]
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [6,5,4,3,2,1,8,7] => [7,6,5,4,3,2,1,8] => [7,6,5,4,3,2,1,8]
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]] => [4,5,6,3,2,1,8,7] => [7,6,5,2,3,4,1,8] => [5,6,7,4,3,2,1,8]
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [2,1,6,5,4,3,8,7] => [3,2,7,6,5,4,1,8] => [3,2,7,6,5,4,1,8]
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [2,1,5,6,4,3,8,7] => [3,2,7,6,4,5,1,8] => [3,2,6,7,5,4,1,8]
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [4,3,2,1,6,5,8,7] => [5,4,3,2,7,6,1,8] => [5,4,3,2,7,6,1,8]
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]] => [3,4,2,1,6,5,8,7] => [5,4,2,3,7,6,1,8] => [4,5,3,2,7,6,1,8]
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5,8,7] => [3,2,5,4,7,6,1,8] => [3,2,5,4,7,6,1,8]
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [7,6,5,4,3,2,1,8] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1]
[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.] => [3,2,7,6,5,4,1,8] => [8,3,2,7,6,5,4,1] => [4,3,8,7,6,5,2,1]
[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.] => [5,4,3,2,7,6,1,8] => [8,5,4,3,2,7,6,1] => [6,5,4,3,8,7,2,1]
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.] => [3,2,5,4,7,6,1,8] => [8,3,2,5,4,7,6,1] => [4,3,6,5,8,7,2,1]
[[[[[.,.],.],.],[[[.,.],.],.]],.] => [1,2,3,5,6,7,4,8] => [2,3,4,8,5,6,7,1] => [2,3,4,6,7,8,5,1]
[[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [2,1,4,3,6,5,7,8] => [3,2,5,4,7,6,8,1] => [3,2,5,4,7,6,8,1]
[[[[[[[[.,.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8] => [2,3,4,5,6,7,8,1] => [2,3,4,5,6,7,8,1]
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
Kreweras complement
Description
Sends the permutation $\pi \in \mathfrak{S}_n$ to the permutation $\pi^{-1}c$ where $c = (1,\ldots,n)$ is the long cycle.
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.