Identifier
-
Mp00014:
Binary trees
—to 132-avoiding permutation⟶
Permutations
Mp00223: Permutations —runsort⟶ Permutations
Mp00066: Permutations —inverse⟶ Permutations
St000696: Permutations ⟶ ℤ
Values
[.,.] => [1] => [1] => [1] => 2
[.,[.,.]] => [2,1] => [1,2] => [1,2] => 3
[[.,.],.] => [1,2] => [1,2] => [1,2] => 3
[.,[.,[.,.]]] => [3,2,1] => [1,2,3] => [1,2,3] => 4
[.,[[.,.],.]] => [2,3,1] => [1,2,3] => [1,2,3] => 4
[[.,.],[.,.]] => [3,1,2] => [1,2,3] => [1,2,3] => 4
[[.,[.,.]],.] => [2,1,3] => [1,3,2] => [1,3,2] => 2
[[[.,.],.],.] => [1,2,3] => [1,2,3] => [1,2,3] => 4
[.,[.,[.,[.,.]]]] => [4,3,2,1] => [1,2,3,4] => [1,2,3,4] => 5
[.,[.,[[.,.],.]]] => [3,4,2,1] => [1,2,3,4] => [1,2,3,4] => 5
[.,[[.,.],[.,.]]] => [4,2,3,1] => [1,2,3,4] => [1,2,3,4] => 5
[.,[[.,[.,.]],.]] => [3,2,4,1] => [1,2,4,3] => [1,2,4,3] => 3
[.,[[[.,.],.],.]] => [2,3,4,1] => [1,2,3,4] => [1,2,3,4] => 5
[[.,.],[.,[.,.]]] => [4,3,1,2] => [1,2,3,4] => [1,2,3,4] => 5
[[.,.],[[.,.],.]] => [3,4,1,2] => [1,2,3,4] => [1,2,3,4] => 5
[[.,[.,.]],[.,.]] => [4,2,1,3] => [1,3,2,4] => [1,3,2,4] => 3
[[[.,.],.],[.,.]] => [4,1,2,3] => [1,2,3,4] => [1,2,3,4] => 5
[[.,[.,[.,.]]],.] => [3,2,1,4] => [1,4,2,3] => [1,3,4,2] => 3
[[.,[[.,.],.]],.] => [2,3,1,4] => [1,4,2,3] => [1,3,4,2] => 3
[[[.,.],[.,.]],.] => [3,1,2,4] => [1,2,4,3] => [1,2,4,3] => 3
[[[.,[.,.]],.],.] => [2,1,3,4] => [1,3,4,2] => [1,4,2,3] => 3
[[[[.,.],.],.],.] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 5
[.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => [1,2,3,4,5] => [1,2,3,4,5] => 6
[.,[.,[.,[[.,.],.]]]] => [4,5,3,2,1] => [1,2,3,4,5] => [1,2,3,4,5] => 6
[.,[.,[[.,.],[.,.]]]] => [5,3,4,2,1] => [1,2,3,4,5] => [1,2,3,4,5] => 6
[.,[.,[[.,[.,.]],.]]] => [4,3,5,2,1] => [1,2,3,5,4] => [1,2,3,5,4] => 4
[.,[.,[[[.,.],.],.]]] => [3,4,5,2,1] => [1,2,3,4,5] => [1,2,3,4,5] => 6
[.,[[.,.],[.,[.,.]]]] => [5,4,2,3,1] => [1,2,3,4,5] => [1,2,3,4,5] => 6
[.,[[.,.],[[.,.],.]]] => [4,5,2,3,1] => [1,2,3,4,5] => [1,2,3,4,5] => 6
[.,[[.,[.,.]],[.,.]]] => [5,3,2,4,1] => [1,2,4,3,5] => [1,2,4,3,5] => 4
[.,[[[.,.],.],[.,.]]] => [5,2,3,4,1] => [1,2,3,4,5] => [1,2,3,4,5] => 6
[.,[[.,[.,[.,.]]],.]] => [4,3,2,5,1] => [1,2,5,3,4] => [1,2,4,5,3] => 4
[.,[[.,[[.,.],.]],.]] => [3,4,2,5,1] => [1,2,5,3,4] => [1,2,4,5,3] => 4
[.,[[[.,.],[.,.]],.]] => [4,2,3,5,1] => [1,2,3,5,4] => [1,2,3,5,4] => 4
[.,[[[.,[.,.]],.],.]] => [3,2,4,5,1] => [1,2,4,5,3] => [1,2,5,3,4] => 4
[.,[[[[.,.],.],.],.]] => [2,3,4,5,1] => [1,2,3,4,5] => [1,2,3,4,5] => 6
[[.,.],[.,[.,[.,.]]]] => [5,4,3,1,2] => [1,2,3,4,5] => [1,2,3,4,5] => 6
[[.,.],[.,[[.,.],.]]] => [4,5,3,1,2] => [1,2,3,4,5] => [1,2,3,4,5] => 6
[[.,.],[[.,.],[.,.]]] => [5,3,4,1,2] => [1,2,3,4,5] => [1,2,3,4,5] => 6
[[.,.],[[.,[.,.]],.]] => [4,3,5,1,2] => [1,2,3,5,4] => [1,2,3,5,4] => 4
[[.,.],[[[.,.],.],.]] => [3,4,5,1,2] => [1,2,3,4,5] => [1,2,3,4,5] => 6
[[.,[.,.]],[.,[.,.]]] => [5,4,2,1,3] => [1,3,2,4,5] => [1,3,2,4,5] => 4
[[.,[.,.]],[[.,.],.]] => [4,5,2,1,3] => [1,3,2,4,5] => [1,3,2,4,5] => 4
[[[.,.],.],[.,[.,.]]] => [5,4,1,2,3] => [1,2,3,4,5] => [1,2,3,4,5] => 6
[[[.,.],.],[[.,.],.]] => [4,5,1,2,3] => [1,2,3,4,5] => [1,2,3,4,5] => 6
[[.,[.,[.,.]]],[.,.]] => [5,3,2,1,4] => [1,4,2,3,5] => [1,3,4,2,5] => 4
[[.,[[.,.],.]],[.,.]] => [5,2,3,1,4] => [1,4,2,3,5] => [1,3,4,2,5] => 4
[[[.,.],[.,.]],[.,.]] => [5,3,1,2,4] => [1,2,4,3,5] => [1,2,4,3,5] => 4
[[[.,[.,.]],.],[.,.]] => [5,2,1,3,4] => [1,3,4,2,5] => [1,4,2,3,5] => 4
[[[[.,.],.],.],[.,.]] => [5,1,2,3,4] => [1,2,3,4,5] => [1,2,3,4,5] => 6
[[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => [1,5,2,3,4] => [1,3,4,5,2] => 4
[[.,[.,[[.,.],.]]],.] => [3,4,2,1,5] => [1,5,2,3,4] => [1,3,4,5,2] => 4
[[.,[[.,.],[.,.]]],.] => [4,2,3,1,5] => [1,5,2,3,4] => [1,3,4,5,2] => 4
[[.,[[.,[.,.]],.]],.] => [3,2,4,1,5] => [1,5,2,4,3] => [1,3,5,4,2] => 2
[[.,[[[.,.],.],.]],.] => [2,3,4,1,5] => [1,5,2,3,4] => [1,3,4,5,2] => 4
[[[.,.],[.,[.,.]]],.] => [4,3,1,2,5] => [1,2,5,3,4] => [1,2,4,5,3] => 4
[[[.,.],[[.,.],.]],.] => [3,4,1,2,5] => [1,2,5,3,4] => [1,2,4,5,3] => 4
[[[.,[.,.]],[.,.]],.] => [4,2,1,3,5] => [1,3,5,2,4] => [1,4,2,5,3] => 2
[[[[.,.],.],[.,.]],.] => [4,1,2,3,5] => [1,2,3,5,4] => [1,2,3,5,4] => 4
[[[.,[.,[.,.]]],.],.] => [3,2,1,4,5] => [1,4,5,2,3] => [1,4,5,2,3] => 4
[[[.,[[.,.],.]],.],.] => [2,3,1,4,5] => [1,4,5,2,3] => [1,4,5,2,3] => 4
[[[[.,.],[.,.]],.],.] => [3,1,2,4,5] => [1,2,4,5,3] => [1,2,5,3,4] => 4
[[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => [1,3,4,5,2] => [1,5,2,3,4] => 4
[[[[[.,.],.],.],.],.] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 6
[.,[.,[.,[.,[.,[.,.]]]]]] => [6,5,4,3,2,1] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 7
[.,[.,[.,[.,[[.,.],.]]]]] => [5,6,4,3,2,1] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 7
[.,[.,[.,[[.,.],[.,.]]]]] => [6,4,5,3,2,1] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 7
[.,[.,[.,[[.,[.,.]],.]]]] => [5,4,6,3,2,1] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => 5
[.,[.,[.,[[[.,.],.],.]]]] => [4,5,6,3,2,1] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 7
[.,[.,[[.,.],[.,[.,.]]]]] => [6,5,3,4,2,1] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 7
[.,[.,[[.,.],[[.,.],.]]]] => [5,6,3,4,2,1] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 7
[.,[.,[[.,[.,.]],[.,.]]]] => [6,4,3,5,2,1] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => 5
[.,[.,[[[.,.],.],[.,.]]]] => [6,3,4,5,2,1] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 7
[.,[.,[[.,[.,[.,.]]],.]]] => [5,4,3,6,2,1] => [1,2,3,6,4,5] => [1,2,3,5,6,4] => 5
[.,[.,[[.,[[.,.],.]],.]]] => [4,5,3,6,2,1] => [1,2,3,6,4,5] => [1,2,3,5,6,4] => 5
[.,[.,[[[.,.],[.,.]],.]]] => [5,3,4,6,2,1] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => 5
[.,[.,[[[.,[.,.]],.],.]]] => [4,3,5,6,2,1] => [1,2,3,5,6,4] => [1,2,3,6,4,5] => 5
[.,[.,[[[[.,.],.],.],.]]] => [3,4,5,6,2,1] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 7
[.,[[.,.],[.,[.,[.,.]]]]] => [6,5,4,2,3,1] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 7
[.,[[.,.],[.,[[.,.],.]]]] => [5,6,4,2,3,1] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 7
[.,[[.,.],[[.,.],[.,.]]]] => [6,4,5,2,3,1] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 7
[.,[[.,.],[[.,[.,.]],.]]] => [5,4,6,2,3,1] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => 5
[.,[[.,.],[[[.,.],.],.]]] => [4,5,6,2,3,1] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 7
[.,[[.,[.,.]],[.,[.,.]]]] => [6,5,3,2,4,1] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => 5
[.,[[.,[.,.]],[[.,.],.]]] => [5,6,3,2,4,1] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => 5
[.,[[[.,.],.],[.,[.,.]]]] => [6,5,2,3,4,1] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 7
[.,[[[.,.],.],[[.,.],.]]] => [5,6,2,3,4,1] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 7
[.,[[.,[.,[.,.]]],[.,.]]] => [6,4,3,2,5,1] => [1,2,5,3,4,6] => [1,2,4,5,3,6] => 5
[.,[[.,[[.,.],.]],[.,.]]] => [6,3,4,2,5,1] => [1,2,5,3,4,6] => [1,2,4,5,3,6] => 5
[.,[[[.,.],[.,.]],[.,.]]] => [6,4,2,3,5,1] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => 5
[.,[[[.,[.,.]],.],[.,.]]] => [6,3,2,4,5,1] => [1,2,4,5,3,6] => [1,2,5,3,4,6] => 5
[.,[[[[.,.],.],.],[.,.]]] => [6,2,3,4,5,1] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 7
[.,[[.,[.,[.,[.,.]]]],.]] => [5,4,3,2,6,1] => [1,2,6,3,4,5] => [1,2,4,5,6,3] => 5
[.,[[.,[.,[[.,.],.]]],.]] => [4,5,3,2,6,1] => [1,2,6,3,4,5] => [1,2,4,5,6,3] => 5
[.,[[.,[[.,.],[.,.]]],.]] => [5,3,4,2,6,1] => [1,2,6,3,4,5] => [1,2,4,5,6,3] => 5
[.,[[.,[[.,[.,.]],.]],.]] => [4,3,5,2,6,1] => [1,2,6,3,5,4] => [1,2,4,6,5,3] => 3
[.,[[.,[[[.,.],.],.]],.]] => [3,4,5,2,6,1] => [1,2,6,3,4,5] => [1,2,4,5,6,3] => 5
[.,[[[.,.],[.,[.,.]]],.]] => [5,4,2,3,6,1] => [1,2,3,6,4,5] => [1,2,3,5,6,4] => 5
[.,[[[.,.],[[.,.],.]],.]] => [4,5,2,3,6,1] => [1,2,3,6,4,5] => [1,2,3,5,6,4] => 5
[.,[[[.,[.,.]],[.,.]],.]] => [5,3,2,4,6,1] => [1,2,4,6,3,5] => [1,2,5,3,6,4] => 3
[.,[[[[.,.],.],[.,.]],.]] => [5,2,3,4,6,1] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => 5
>>> Load all 788 entries. <<<[.,[[[.,[.,[.,.]]],.],.]] => [4,3,2,5,6,1] => [1,2,5,6,3,4] => [1,2,5,6,3,4] => 5
[.,[[[.,[[.,.],.]],.],.]] => [3,4,2,5,6,1] => [1,2,5,6,3,4] => [1,2,5,6,3,4] => 5
[.,[[[[.,.],[.,.]],.],.]] => [4,2,3,5,6,1] => [1,2,3,5,6,4] => [1,2,3,6,4,5] => 5
[.,[[[[.,[.,.]],.],.],.]] => [3,2,4,5,6,1] => [1,2,4,5,6,3] => [1,2,6,3,4,5] => 5
[.,[[[[[.,.],.],.],.],.]] => [2,3,4,5,6,1] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 7
[[.,.],[.,[.,[.,[.,.]]]]] => [6,5,4,3,1,2] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 7
[[.,.],[.,[.,[[.,.],.]]]] => [5,6,4,3,1,2] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 7
[[.,.],[.,[[.,.],[.,.]]]] => [6,4,5,3,1,2] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 7
[[.,.],[.,[[.,[.,.]],.]]] => [5,4,6,3,1,2] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => 5
[[.,.],[.,[[[.,.],.],.]]] => [4,5,6,3,1,2] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 7
[[.,.],[[.,.],[.,[.,.]]]] => [6,5,3,4,1,2] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 7
[[.,.],[[.,.],[[.,.],.]]] => [5,6,3,4,1,2] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 7
[[.,.],[[.,[.,.]],[.,.]]] => [6,4,3,5,1,2] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => 5
[[.,.],[[[.,.],.],[.,.]]] => [6,3,4,5,1,2] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 7
[[.,.],[[.,[.,[.,.]]],.]] => [5,4,3,6,1,2] => [1,2,3,6,4,5] => [1,2,3,5,6,4] => 5
[[.,.],[[.,[[.,.],.]],.]] => [4,5,3,6,1,2] => [1,2,3,6,4,5] => [1,2,3,5,6,4] => 5
[[.,.],[[[.,.],[.,.]],.]] => [5,3,4,6,1,2] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => 5
[[.,.],[[[.,[.,.]],.],.]] => [4,3,5,6,1,2] => [1,2,3,5,6,4] => [1,2,3,6,4,5] => 5
[[.,.],[[[[.,.],.],.],.]] => [3,4,5,6,1,2] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 7
[[.,[.,.]],[.,[.,[.,.]]]] => [6,5,4,2,1,3] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => 5
[[.,[.,.]],[.,[[.,.],.]]] => [5,6,4,2,1,3] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => 5
[[.,[.,.]],[[.,.],[.,.]]] => [6,4,5,2,1,3] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => 5
[[.,[.,.]],[[.,[.,.]],.]] => [5,4,6,2,1,3] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => 3
[[.,[.,.]],[[[.,.],.],.]] => [4,5,6,2,1,3] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => 5
[[[.,.],.],[.,[.,[.,.]]]] => [6,5,4,1,2,3] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 7
[[[.,.],.],[.,[[.,.],.]]] => [5,6,4,1,2,3] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 7
[[[.,.],.],[[.,.],[.,.]]] => [6,4,5,1,2,3] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 7
[[[.,.],.],[[.,[.,.]],.]] => [5,4,6,1,2,3] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => 5
[[[.,.],.],[[[.,.],.],.]] => [4,5,6,1,2,3] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 7
[[.,[.,[.,.]]],[.,[.,.]]] => [6,5,3,2,1,4] => [1,4,2,3,5,6] => [1,3,4,2,5,6] => 5
[[.,[.,[.,.]]],[[.,.],.]] => [5,6,3,2,1,4] => [1,4,2,3,5,6] => [1,3,4,2,5,6] => 5
[[.,[[.,.],.]],[.,[.,.]]] => [6,5,2,3,1,4] => [1,4,2,3,5,6] => [1,3,4,2,5,6] => 5
[[.,[[.,.],.]],[[.,.],.]] => [5,6,2,3,1,4] => [1,4,2,3,5,6] => [1,3,4,2,5,6] => 5
[[[.,.],[.,.]],[.,[.,.]]] => [6,5,3,1,2,4] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => 5
[[[.,.],[.,.]],[[.,.],.]] => [5,6,3,1,2,4] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => 5
[[[.,[.,.]],.],[.,[.,.]]] => [6,5,2,1,3,4] => [1,3,4,2,5,6] => [1,4,2,3,5,6] => 5
[[[.,[.,.]],.],[[.,.],.]] => [5,6,2,1,3,4] => [1,3,4,2,5,6] => [1,4,2,3,5,6] => 5
[[[[.,.],.],.],[.,[.,.]]] => [6,5,1,2,3,4] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 7
[[[[.,.],.],.],[[.,.],.]] => [5,6,1,2,3,4] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 7
[[.,[.,[.,[.,.]]]],[.,.]] => [6,4,3,2,1,5] => [1,5,2,3,4,6] => [1,3,4,5,2,6] => 5
[[.,[.,[[.,.],.]]],[.,.]] => [6,3,4,2,1,5] => [1,5,2,3,4,6] => [1,3,4,5,2,6] => 5
[[.,[[.,.],[.,.]]],[.,.]] => [6,4,2,3,1,5] => [1,5,2,3,4,6] => [1,3,4,5,2,6] => 5
[[.,[[.,[.,.]],.]],[.,.]] => [6,3,2,4,1,5] => [1,5,2,4,3,6] => [1,3,5,4,2,6] => 3
[[.,[[[.,.],.],.]],[.,.]] => [6,2,3,4,1,5] => [1,5,2,3,4,6] => [1,3,4,5,2,6] => 5
[[[.,.],[.,[.,.]]],[.,.]] => [6,4,3,1,2,5] => [1,2,5,3,4,6] => [1,2,4,5,3,6] => 5
[[[.,.],[[.,.],.]],[.,.]] => [6,3,4,1,2,5] => [1,2,5,3,4,6] => [1,2,4,5,3,6] => 5
[[[.,[.,.]],[.,.]],[.,.]] => [6,4,2,1,3,5] => [1,3,5,2,4,6] => [1,4,2,5,3,6] => 3
[[[[.,.],.],[.,.]],[.,.]] => [6,4,1,2,3,5] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => 5
[[[.,[.,[.,.]]],.],[.,.]] => [6,3,2,1,4,5] => [1,4,5,2,3,6] => [1,4,5,2,3,6] => 5
[[[.,[[.,.],.]],.],[.,.]] => [6,2,3,1,4,5] => [1,4,5,2,3,6] => [1,4,5,2,3,6] => 5
[[[[.,.],[.,.]],.],[.,.]] => [6,3,1,2,4,5] => [1,2,4,5,3,6] => [1,2,5,3,4,6] => 5
[[[[.,[.,.]],.],.],[.,.]] => [6,2,1,3,4,5] => [1,3,4,5,2,6] => [1,5,2,3,4,6] => 5
[[[[[.,.],.],.],.],[.,.]] => [6,1,2,3,4,5] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 7
[[.,[.,[.,[.,[.,.]]]]],.] => [5,4,3,2,1,6] => [1,6,2,3,4,5] => [1,3,4,5,6,2] => 5
[[.,[.,[.,[[.,.],.]]]],.] => [4,5,3,2,1,6] => [1,6,2,3,4,5] => [1,3,4,5,6,2] => 5
[[.,[.,[[.,.],[.,.]]]],.] => [5,3,4,2,1,6] => [1,6,2,3,4,5] => [1,3,4,5,6,2] => 5
[[.,[.,[[.,[.,.]],.]]],.] => [4,3,5,2,1,6] => [1,6,2,3,5,4] => [1,3,4,6,5,2] => 3
[[.,[.,[[[.,.],.],.]]],.] => [3,4,5,2,1,6] => [1,6,2,3,4,5] => [1,3,4,5,6,2] => 5
[[.,[[.,.],[.,[.,.]]]],.] => [5,4,2,3,1,6] => [1,6,2,3,4,5] => [1,3,4,5,6,2] => 5
[[.,[[.,.],[[.,.],.]]],.] => [4,5,2,3,1,6] => [1,6,2,3,4,5] => [1,3,4,5,6,2] => 5
[[.,[[.,[.,.]],[.,.]]],.] => [5,3,2,4,1,6] => [1,6,2,4,3,5] => [1,3,5,4,6,2] => 3
[[.,[[[.,.],.],[.,.]]],.] => [5,2,3,4,1,6] => [1,6,2,3,4,5] => [1,3,4,5,6,2] => 5
[[.,[[.,[.,[.,.]]],.]],.] => [4,3,2,5,1,6] => [1,6,2,5,3,4] => [1,3,5,6,4,2] => 3
[[.,[[.,[[.,.],.]],.]],.] => [3,4,2,5,1,6] => [1,6,2,5,3,4] => [1,3,5,6,4,2] => 3
[[.,[[[.,.],[.,.]],.]],.] => [4,2,3,5,1,6] => [1,6,2,3,5,4] => [1,3,4,6,5,2] => 3
[[.,[[[.,[.,.]],.],.]],.] => [3,2,4,5,1,6] => [1,6,2,4,5,3] => [1,3,6,4,5,2] => 3
[[.,[[[[.,.],.],.],.]],.] => [2,3,4,5,1,6] => [1,6,2,3,4,5] => [1,3,4,5,6,2] => 5
[[[.,.],[.,[.,[.,.]]]],.] => [5,4,3,1,2,6] => [1,2,6,3,4,5] => [1,2,4,5,6,3] => 5
[[[.,.],[.,[[.,.],.]]],.] => [4,5,3,1,2,6] => [1,2,6,3,4,5] => [1,2,4,5,6,3] => 5
[[[.,.],[[.,.],[.,.]]],.] => [5,3,4,1,2,6] => [1,2,6,3,4,5] => [1,2,4,5,6,3] => 5
[[[.,.],[[.,[.,.]],.]],.] => [4,3,5,1,2,6] => [1,2,6,3,5,4] => [1,2,4,6,5,3] => 3
[[[.,.],[[[.,.],.],.]],.] => [3,4,5,1,2,6] => [1,2,6,3,4,5] => [1,2,4,5,6,3] => 5
[[[.,[.,.]],[.,[.,.]]],.] => [5,4,2,1,3,6] => [1,3,6,2,4,5] => [1,4,2,5,6,3] => 3
[[[.,[.,.]],[[.,.],.]],.] => [4,5,2,1,3,6] => [1,3,6,2,4,5] => [1,4,2,5,6,3] => 3
[[[[.,.],.],[.,[.,.]]],.] => [5,4,1,2,3,6] => [1,2,3,6,4,5] => [1,2,3,5,6,4] => 5
[[[[.,.],.],[[.,.],.]],.] => [4,5,1,2,3,6] => [1,2,3,6,4,5] => [1,2,3,5,6,4] => 5
[[[.,[.,[.,.]]],[.,.]],.] => [5,3,2,1,4,6] => [1,4,6,2,3,5] => [1,4,5,2,6,3] => 3
[[[.,[[.,.],.]],[.,.]],.] => [5,2,3,1,4,6] => [1,4,6,2,3,5] => [1,4,5,2,6,3] => 3
[[[[.,.],[.,.]],[.,.]],.] => [5,3,1,2,4,6] => [1,2,4,6,3,5] => [1,2,5,3,6,4] => 3
[[[[.,[.,.]],.],[.,.]],.] => [5,2,1,3,4,6] => [1,3,4,6,2,5] => [1,5,2,3,6,4] => 3
[[[[[.,.],.],.],[.,.]],.] => [5,1,2,3,4,6] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => 5
[[[.,[.,[.,[.,.]]]],.],.] => [4,3,2,1,5,6] => [1,5,6,2,3,4] => [1,4,5,6,2,3] => 5
[[[.,[.,[[.,.],.]]],.],.] => [3,4,2,1,5,6] => [1,5,6,2,3,4] => [1,4,5,6,2,3] => 5
[[[.,[[.,.],[.,.]]],.],.] => [4,2,3,1,5,6] => [1,5,6,2,3,4] => [1,4,5,6,2,3] => 5
[[[.,[[.,[.,.]],.]],.],.] => [3,2,4,1,5,6] => [1,5,6,2,4,3] => [1,4,6,5,2,3] => 3
[[[.,[[[.,.],.],.]],.],.] => [2,3,4,1,5,6] => [1,5,6,2,3,4] => [1,4,5,6,2,3] => 5
[[[[.,.],[.,[.,.]]],.],.] => [4,3,1,2,5,6] => [1,2,5,6,3,4] => [1,2,5,6,3,4] => 5
[[[[.,.],[[.,.],.]],.],.] => [3,4,1,2,5,6] => [1,2,5,6,3,4] => [1,2,5,6,3,4] => 5
[[[[.,[.,.]],[.,.]],.],.] => [4,2,1,3,5,6] => [1,3,5,6,2,4] => [1,5,2,6,3,4] => 3
[[[[[.,.],.],[.,.]],.],.] => [4,1,2,3,5,6] => [1,2,3,5,6,4] => [1,2,3,6,4,5] => 5
[[[[.,[.,[.,.]]],.],.],.] => [3,2,1,4,5,6] => [1,4,5,6,2,3] => [1,5,6,2,3,4] => 5
[[[[.,[[.,.],.]],.],.],.] => [2,3,1,4,5,6] => [1,4,5,6,2,3] => [1,5,6,2,3,4] => 5
[[[[[.,.],[.,.]],.],.],.] => [3,1,2,4,5,6] => [1,2,4,5,6,3] => [1,2,6,3,4,5] => 5
[[[[[.,[.,.]],.],.],.],.] => [2,1,3,4,5,6] => [1,3,4,5,6,2] => [1,6,2,3,4,5] => 5
[[[[[[.,.],.],.],.],.],.] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 7
[.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [7,6,5,4,3,2,1] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 8
[.,[.,[.,[.,[.,[[.,.],.]]]]]] => [6,7,5,4,3,2,1] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 8
[.,[.,[.,[.,[[.,.],[.,.]]]]]] => [7,5,6,4,3,2,1] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 8
[.,[.,[.,[.,[[.,[.,.]],.]]]]] => [6,5,7,4,3,2,1] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => 6
[.,[.,[.,[.,[[[.,.],.],.]]]]] => [5,6,7,4,3,2,1] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 8
[.,[.,[.,[[.,.],[.,[.,.]]]]]] => [7,6,4,5,3,2,1] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 8
[.,[.,[.,[[.,.],[[.,.],.]]]]] => [6,7,4,5,3,2,1] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 8
[.,[.,[.,[[.,[.,.]],[.,.]]]]] => [7,5,4,6,3,2,1] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => 6
[.,[.,[.,[[[.,.],.],[.,.]]]]] => [7,4,5,6,3,2,1] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 8
[.,[.,[.,[[.,[.,[.,.]]],.]]]] => [6,5,4,7,3,2,1] => [1,2,3,4,7,5,6] => [1,2,3,4,6,7,5] => 6
[.,[.,[.,[[.,[[.,.],.]],.]]]] => [5,6,4,7,3,2,1] => [1,2,3,4,7,5,6] => [1,2,3,4,6,7,5] => 6
[.,[.,[.,[[[.,.],[.,.]],.]]]] => [6,4,5,7,3,2,1] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => 6
[.,[.,[.,[[[.,[.,.]],.],.]]]] => [5,4,6,7,3,2,1] => [1,2,3,4,6,7,5] => [1,2,3,4,7,5,6] => 6
[.,[.,[.,[[[[.,.],.],.],.]]]] => [4,5,6,7,3,2,1] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 8
[.,[.,[[.,.],[.,[.,[.,.]]]]]] => [7,6,5,3,4,2,1] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 8
[.,[.,[[.,.],[.,[[.,.],.]]]]] => [6,7,5,3,4,2,1] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 8
[.,[.,[[.,.],[[.,.],[.,.]]]]] => [7,5,6,3,4,2,1] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 8
[.,[.,[[.,.],[[.,[.,.]],.]]]] => [6,5,7,3,4,2,1] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => 6
[.,[.,[[.,.],[[[.,.],.],.]]]] => [5,6,7,3,4,2,1] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 8
[.,[.,[[.,[.,.]],[.,[.,.]]]]] => [7,6,4,3,5,2,1] => [1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => 6
[.,[.,[[.,[.,.]],[[.,.],.]]]] => [6,7,4,3,5,2,1] => [1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => 6
[.,[.,[[[.,.],.],[.,[.,.]]]]] => [7,6,3,4,5,2,1] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 8
[.,[.,[[[.,.],.],[[.,.],.]]]] => [6,7,3,4,5,2,1] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 8
[.,[.,[[.,[.,[.,.]]],[.,.]]]] => [7,5,4,3,6,2,1] => [1,2,3,6,4,5,7] => [1,2,3,5,6,4,7] => 6
[.,[.,[[.,[[.,.],.]],[.,.]]]] => [7,4,5,3,6,2,1] => [1,2,3,6,4,5,7] => [1,2,3,5,6,4,7] => 6
[.,[.,[[[.,.],[.,.]],[.,.]]]] => [7,5,3,4,6,2,1] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => 6
[.,[.,[[[.,[.,.]],.],[.,.]]]] => [7,4,3,5,6,2,1] => [1,2,3,5,6,4,7] => [1,2,3,6,4,5,7] => 6
[.,[.,[[[[.,.],.],.],[.,.]]]] => [7,3,4,5,6,2,1] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 8
[.,[.,[[.,[.,[.,[.,.]]]],.]]] => [6,5,4,3,7,2,1] => [1,2,3,7,4,5,6] => [1,2,3,5,6,7,4] => 6
[.,[.,[[.,[.,[[.,.],.]]],.]]] => [5,6,4,3,7,2,1] => [1,2,3,7,4,5,6] => [1,2,3,5,6,7,4] => 6
[.,[.,[[.,[[.,.],[.,.]]],.]]] => [6,4,5,3,7,2,1] => [1,2,3,7,4,5,6] => [1,2,3,5,6,7,4] => 6
[.,[.,[[.,[[.,[.,.]],.]],.]]] => [5,4,6,3,7,2,1] => [1,2,3,7,4,6,5] => [1,2,3,5,7,6,4] => 4
[.,[.,[[.,[[[.,.],.],.]],.]]] => [4,5,6,3,7,2,1] => [1,2,3,7,4,5,6] => [1,2,3,5,6,7,4] => 6
[.,[.,[[[.,.],[.,[.,.]]],.]]] => [6,5,3,4,7,2,1] => [1,2,3,4,7,5,6] => [1,2,3,4,6,7,5] => 6
[.,[.,[[[.,.],[[.,.],.]],.]]] => [5,6,3,4,7,2,1] => [1,2,3,4,7,5,6] => [1,2,3,4,6,7,5] => 6
[.,[.,[[[.,[.,.]],[.,.]],.]]] => [6,4,3,5,7,2,1] => [1,2,3,5,7,4,6] => [1,2,3,6,4,7,5] => 4
[.,[.,[[[[.,.],.],[.,.]],.]]] => [6,3,4,5,7,2,1] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => 6
[.,[.,[[[.,[.,[.,.]]],.],.]]] => [5,4,3,6,7,2,1] => [1,2,3,6,7,4,5] => [1,2,3,6,7,4,5] => 6
[.,[.,[[[.,[[.,.],.]],.],.]]] => [4,5,3,6,7,2,1] => [1,2,3,6,7,4,5] => [1,2,3,6,7,4,5] => 6
[.,[.,[[[[.,.],[.,.]],.],.]]] => [5,3,4,6,7,2,1] => [1,2,3,4,6,7,5] => [1,2,3,4,7,5,6] => 6
[.,[.,[[[[.,[.,.]],.],.],.]]] => [4,3,5,6,7,2,1] => [1,2,3,5,6,7,4] => [1,2,3,7,4,5,6] => 6
[.,[.,[[[[[.,.],.],.],.],.]]] => [3,4,5,6,7,2,1] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 8
[.,[[.,.],[.,[.,[.,[.,.]]]]]] => [7,6,5,4,2,3,1] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 8
[.,[[.,.],[.,[.,[[.,.],.]]]]] => [6,7,5,4,2,3,1] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 8
[.,[[.,.],[.,[[.,.],[.,.]]]]] => [7,5,6,4,2,3,1] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 8
[.,[[.,.],[.,[[.,[.,.]],.]]]] => [6,5,7,4,2,3,1] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => 6
[.,[[.,.],[.,[[[.,.],.],.]]]] => [5,6,7,4,2,3,1] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 8
[.,[[.,.],[[.,.],[.,[.,.]]]]] => [7,6,4,5,2,3,1] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 8
[.,[[.,.],[[.,.],[[.,.],.]]]] => [6,7,4,5,2,3,1] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 8
[.,[[.,.],[[.,[.,.]],[.,.]]]] => [7,5,4,6,2,3,1] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => 6
[.,[[.,.],[[[.,.],.],[.,.]]]] => [7,4,5,6,2,3,1] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 8
[.,[[.,.],[[.,[.,[.,.]]],.]]] => [6,5,4,7,2,3,1] => [1,2,3,4,7,5,6] => [1,2,3,4,6,7,5] => 6
[.,[[.,.],[[.,[[.,.],.]],.]]] => [5,6,4,7,2,3,1] => [1,2,3,4,7,5,6] => [1,2,3,4,6,7,5] => 6
[.,[[.,.],[[[.,.],[.,.]],.]]] => [6,4,5,7,2,3,1] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => 6
[.,[[.,.],[[[.,[.,.]],.],.]]] => [5,4,6,7,2,3,1] => [1,2,3,4,6,7,5] => [1,2,3,4,7,5,6] => 6
[.,[[.,.],[[[[.,.],.],.],.]]] => [4,5,6,7,2,3,1] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 8
[.,[[.,[.,.]],[.,[.,[.,.]]]]] => [7,6,5,3,2,4,1] => [1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => 6
[.,[[.,[.,.]],[.,[[.,.],.]]]] => [6,7,5,3,2,4,1] => [1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => 6
[.,[[.,[.,.]],[[.,.],[.,.]]]] => [7,5,6,3,2,4,1] => [1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => 6
[.,[[.,[.,.]],[[.,[.,.]],.]]] => [6,5,7,3,2,4,1] => [1,2,4,3,5,7,6] => [1,2,4,3,5,7,6] => 4
[.,[[.,[.,.]],[[[.,.],.],.]]] => [5,6,7,3,2,4,1] => [1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => 6
[.,[[[.,.],.],[.,[.,[.,.]]]]] => [7,6,5,2,3,4,1] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 8
[.,[[[.,.],.],[.,[[.,.],.]]]] => [6,7,5,2,3,4,1] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 8
[.,[[[.,.],.],[[.,.],[.,.]]]] => [7,5,6,2,3,4,1] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 8
[.,[[[.,.],.],[[.,[.,.]],.]]] => [6,5,7,2,3,4,1] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => 6
[.,[[[.,.],.],[[[.,.],.],.]]] => [5,6,7,2,3,4,1] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 8
[.,[[.,[.,[.,.]]],[.,[.,.]]]] => [7,6,4,3,2,5,1] => [1,2,5,3,4,6,7] => [1,2,4,5,3,6,7] => 6
[.,[[.,[.,[.,.]]],[[.,.],.]]] => [6,7,4,3,2,5,1] => [1,2,5,3,4,6,7] => [1,2,4,5,3,6,7] => 6
[.,[[.,[[.,.],.]],[.,[.,.]]]] => [7,6,3,4,2,5,1] => [1,2,5,3,4,6,7] => [1,2,4,5,3,6,7] => 6
[.,[[.,[[.,.],.]],[[.,.],.]]] => [6,7,3,4,2,5,1] => [1,2,5,3,4,6,7] => [1,2,4,5,3,6,7] => 6
[.,[[[.,.],[.,.]],[.,[.,.]]]] => [7,6,4,2,3,5,1] => [1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => 6
[.,[[[.,.],[.,.]],[[.,.],.]]] => [6,7,4,2,3,5,1] => [1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => 6
[.,[[[.,[.,.]],.],[.,[.,.]]]] => [7,6,3,2,4,5,1] => [1,2,4,5,3,6,7] => [1,2,5,3,4,6,7] => 6
[.,[[[.,[.,.]],.],[[.,.],.]]] => [6,7,3,2,4,5,1] => [1,2,4,5,3,6,7] => [1,2,5,3,4,6,7] => 6
[.,[[[[.,.],.],.],[.,[.,.]]]] => [7,6,2,3,4,5,1] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 8
[.,[[[[.,.],.],.],[[.,.],.]]] => [6,7,2,3,4,5,1] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 8
[.,[[.,[.,[.,[.,.]]]],[.,.]]] => [7,5,4,3,2,6,1] => [1,2,6,3,4,5,7] => [1,2,4,5,6,3,7] => 6
[.,[[.,[.,[[.,.],.]]],[.,.]]] => [7,4,5,3,2,6,1] => [1,2,6,3,4,5,7] => [1,2,4,5,6,3,7] => 6
[.,[[.,[[.,.],[.,.]]],[.,.]]] => [7,5,3,4,2,6,1] => [1,2,6,3,4,5,7] => [1,2,4,5,6,3,7] => 6
[.,[[.,[[.,[.,.]],.]],[.,.]]] => [7,4,3,5,2,6,1] => [1,2,6,3,5,4,7] => [1,2,4,6,5,3,7] => 4
[.,[[.,[[[.,.],.],.]],[.,.]]] => [7,3,4,5,2,6,1] => [1,2,6,3,4,5,7] => [1,2,4,5,6,3,7] => 6
[.,[[[.,.],[.,[.,.]]],[.,.]]] => [7,5,4,2,3,6,1] => [1,2,3,6,4,5,7] => [1,2,3,5,6,4,7] => 6
[.,[[[.,.],[[.,.],.]],[.,.]]] => [7,4,5,2,3,6,1] => [1,2,3,6,4,5,7] => [1,2,3,5,6,4,7] => 6
[.,[[[.,[.,.]],[.,.]],[.,.]]] => [7,5,3,2,4,6,1] => [1,2,4,6,3,5,7] => [1,2,5,3,6,4,7] => 4
[.,[[[[.,.],.],[.,.]],[.,.]]] => [7,5,2,3,4,6,1] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => 6
[.,[[[.,[.,[.,.]]],.],[.,.]]] => [7,4,3,2,5,6,1] => [1,2,5,6,3,4,7] => [1,2,5,6,3,4,7] => 6
[.,[[[.,[[.,.],.]],.],[.,.]]] => [7,3,4,2,5,6,1] => [1,2,5,6,3,4,7] => [1,2,5,6,3,4,7] => 6
[.,[[[[.,.],[.,.]],.],[.,.]]] => [7,4,2,3,5,6,1] => [1,2,3,5,6,4,7] => [1,2,3,6,4,5,7] => 6
[.,[[[[.,[.,.]],.],.],[.,.]]] => [7,3,2,4,5,6,1] => [1,2,4,5,6,3,7] => [1,2,6,3,4,5,7] => 6
[.,[[[[[.,.],.],.],.],[.,.]]] => [7,2,3,4,5,6,1] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 8
[.,[[.,[.,[.,[.,[.,.]]]]],.]] => [6,5,4,3,2,7,1] => [1,2,7,3,4,5,6] => [1,2,4,5,6,7,3] => 6
[.,[[.,[.,[.,[[.,.],.]]]],.]] => [5,6,4,3,2,7,1] => [1,2,7,3,4,5,6] => [1,2,4,5,6,7,3] => 6
[.,[[.,[.,[[.,.],[.,.]]]],.]] => [6,4,5,3,2,7,1] => [1,2,7,3,4,5,6] => [1,2,4,5,6,7,3] => 6
[.,[[.,[.,[[.,[.,.]],.]]],.]] => [5,4,6,3,2,7,1] => [1,2,7,3,4,6,5] => [1,2,4,5,7,6,3] => 4
[.,[[.,[.,[[[.,.],.],.]]],.]] => [4,5,6,3,2,7,1] => [1,2,7,3,4,5,6] => [1,2,4,5,6,7,3] => 6
[.,[[.,[[.,.],[.,[.,.]]]],.]] => [6,5,3,4,2,7,1] => [1,2,7,3,4,5,6] => [1,2,4,5,6,7,3] => 6
[.,[[.,[[.,.],[[.,.],.]]],.]] => [5,6,3,4,2,7,1] => [1,2,7,3,4,5,6] => [1,2,4,5,6,7,3] => 6
[.,[[.,[[.,[.,.]],[.,.]]],.]] => [6,4,3,5,2,7,1] => [1,2,7,3,5,4,6] => [1,2,4,6,5,7,3] => 4
[.,[[.,[[[.,.],.],[.,.]]],.]] => [6,3,4,5,2,7,1] => [1,2,7,3,4,5,6] => [1,2,4,5,6,7,3] => 6
[.,[[.,[[.,[.,[.,.]]],.]],.]] => [5,4,3,6,2,7,1] => [1,2,7,3,6,4,5] => [1,2,4,6,7,5,3] => 4
[.,[[.,[[.,[[.,.],.]],.]],.]] => [4,5,3,6,2,7,1] => [1,2,7,3,6,4,5] => [1,2,4,6,7,5,3] => 4
[.,[[.,[[[.,.],[.,.]],.]],.]] => [5,3,4,6,2,7,1] => [1,2,7,3,4,6,5] => [1,2,4,5,7,6,3] => 4
[.,[[.,[[[.,[.,.]],.],.]],.]] => [4,3,5,6,2,7,1] => [1,2,7,3,5,6,4] => [1,2,4,7,5,6,3] => 4
[.,[[.,[[[[.,.],.],.],.]],.]] => [3,4,5,6,2,7,1] => [1,2,7,3,4,5,6] => [1,2,4,5,6,7,3] => 6
[.,[[[.,.],[.,[.,[.,.]]]],.]] => [6,5,4,2,3,7,1] => [1,2,3,7,4,5,6] => [1,2,3,5,6,7,4] => 6
[.,[[[.,.],[.,[[.,.],.]]],.]] => [5,6,4,2,3,7,1] => [1,2,3,7,4,5,6] => [1,2,3,5,6,7,4] => 6
[.,[[[.,.],[[.,.],[.,.]]],.]] => [6,4,5,2,3,7,1] => [1,2,3,7,4,5,6] => [1,2,3,5,6,7,4] => 6
[.,[[[.,.],[[.,[.,.]],.]],.]] => [5,4,6,2,3,7,1] => [1,2,3,7,4,6,5] => [1,2,3,5,7,6,4] => 4
[.,[[[.,.],[[[.,.],.],.]],.]] => [4,5,6,2,3,7,1] => [1,2,3,7,4,5,6] => [1,2,3,5,6,7,4] => 6
[.,[[[.,[.,.]],[.,[.,.]]],.]] => [6,5,3,2,4,7,1] => [1,2,4,7,3,5,6] => [1,2,5,3,6,7,4] => 4
[.,[[[.,[.,.]],[[.,.],.]],.]] => [5,6,3,2,4,7,1] => [1,2,4,7,3,5,6] => [1,2,5,3,6,7,4] => 4
[.,[[[[.,.],.],[.,[.,.]]],.]] => [6,5,2,3,4,7,1] => [1,2,3,4,7,5,6] => [1,2,3,4,6,7,5] => 6
[.,[[[[.,.],.],[[.,.],.]],.]] => [5,6,2,3,4,7,1] => [1,2,3,4,7,5,6] => [1,2,3,4,6,7,5] => 6
[.,[[[.,[.,[.,.]]],[.,.]],.]] => [6,4,3,2,5,7,1] => [1,2,5,7,3,4,6] => [1,2,5,6,3,7,4] => 4
[.,[[[.,[[.,.],.]],[.,.]],.]] => [6,3,4,2,5,7,1] => [1,2,5,7,3,4,6] => [1,2,5,6,3,7,4] => 4
[.,[[[[.,.],[.,.]],[.,.]],.]] => [6,4,2,3,5,7,1] => [1,2,3,5,7,4,6] => [1,2,3,6,4,7,5] => 4
[.,[[[[.,[.,.]],.],[.,.]],.]] => [6,3,2,4,5,7,1] => [1,2,4,5,7,3,6] => [1,2,6,3,4,7,5] => 4
[.,[[[[[.,.],.],.],[.,.]],.]] => [6,2,3,4,5,7,1] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => 6
[.,[[[.,[.,[.,[.,.]]]],.],.]] => [5,4,3,2,6,7,1] => [1,2,6,7,3,4,5] => [1,2,5,6,7,3,4] => 6
[.,[[[.,[.,[[.,.],.]]],.],.]] => [4,5,3,2,6,7,1] => [1,2,6,7,3,4,5] => [1,2,5,6,7,3,4] => 6
[.,[[[.,[[.,.],[.,.]]],.],.]] => [5,3,4,2,6,7,1] => [1,2,6,7,3,4,5] => [1,2,5,6,7,3,4] => 6
[.,[[[.,[[.,[.,.]],.]],.],.]] => [4,3,5,2,6,7,1] => [1,2,6,7,3,5,4] => [1,2,5,7,6,3,4] => 4
[.,[[[.,[[[.,.],.],.]],.],.]] => [3,4,5,2,6,7,1] => [1,2,6,7,3,4,5] => [1,2,5,6,7,3,4] => 6
[.,[[[[.,.],[.,[.,.]]],.],.]] => [5,4,2,3,6,7,1] => [1,2,3,6,7,4,5] => [1,2,3,6,7,4,5] => 6
[.,[[[[.,.],[[.,.],.]],.],.]] => [4,5,2,3,6,7,1] => [1,2,3,6,7,4,5] => [1,2,3,6,7,4,5] => 6
[.,[[[[.,[.,.]],[.,.]],.],.]] => [5,3,2,4,6,7,1] => [1,2,4,6,7,3,5] => [1,2,6,3,7,4,5] => 4
[.,[[[[[.,.],.],[.,.]],.],.]] => [5,2,3,4,6,7,1] => [1,2,3,4,6,7,5] => [1,2,3,4,7,5,6] => 6
[.,[[[[.,[.,[.,.]]],.],.],.]] => [4,3,2,5,6,7,1] => [1,2,5,6,7,3,4] => [1,2,6,7,3,4,5] => 6
[.,[[[[.,[[.,.],.]],.],.],.]] => [3,4,2,5,6,7,1] => [1,2,5,6,7,3,4] => [1,2,6,7,3,4,5] => 6
[.,[[[[[.,.],[.,.]],.],.],.]] => [4,2,3,5,6,7,1] => [1,2,3,5,6,7,4] => [1,2,3,7,4,5,6] => 6
[.,[[[[[.,[.,.]],.],.],.],.]] => [3,2,4,5,6,7,1] => [1,2,4,5,6,7,3] => [1,2,7,3,4,5,6] => 6
[.,[[[[[[.,.],.],.],.],.],.]] => [2,3,4,5,6,7,1] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 8
[[.,.],[.,[.,[.,[.,[.,.]]]]]] => [7,6,5,4,3,1,2] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 8
[[.,.],[.,[.,[.,[[.,.],.]]]]] => [6,7,5,4,3,1,2] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 8
[[.,.],[.,[.,[[.,.],[.,.]]]]] => [7,5,6,4,3,1,2] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 8
[[.,.],[.,[.,[[.,[.,.]],.]]]] => [6,5,7,4,3,1,2] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => 6
[[.,.],[.,[.,[[[.,.],.],.]]]] => [5,6,7,4,3,1,2] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 8
[[.,.],[.,[[.,.],[.,[.,.]]]]] => [7,6,4,5,3,1,2] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 8
[[.,.],[.,[[.,.],[[.,.],.]]]] => [6,7,4,5,3,1,2] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 8
[[.,.],[.,[[.,[.,.]],[.,.]]]] => [7,5,4,6,3,1,2] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => 6
[[.,.],[.,[[[.,.],.],[.,.]]]] => [7,4,5,6,3,1,2] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 8
[[.,.],[.,[[.,[.,[.,.]]],.]]] => [6,5,4,7,3,1,2] => [1,2,3,4,7,5,6] => [1,2,3,4,6,7,5] => 6
[[.,.],[.,[[.,[[.,.],.]],.]]] => [5,6,4,7,3,1,2] => [1,2,3,4,7,5,6] => [1,2,3,4,6,7,5] => 6
[[.,.],[.,[[[.,.],[.,.]],.]]] => [6,4,5,7,3,1,2] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => 6
[[.,.],[.,[[[.,[.,.]],.],.]]] => [5,4,6,7,3,1,2] => [1,2,3,4,6,7,5] => [1,2,3,4,7,5,6] => 6
[[.,.],[.,[[[[.,.],.],.],.]]] => [4,5,6,7,3,1,2] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 8
[[.,.],[[.,.],[.,[.,[.,.]]]]] => [7,6,5,3,4,1,2] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 8
[[.,.],[[.,.],[.,[[.,.],.]]]] => [6,7,5,3,4,1,2] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 8
[[.,.],[[.,.],[[.,.],[.,.]]]] => [7,5,6,3,4,1,2] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 8
[[.,.],[[.,.],[[.,[.,.]],.]]] => [6,5,7,3,4,1,2] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => 6
[[.,.],[[.,.],[[[.,.],.],.]]] => [5,6,7,3,4,1,2] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 8
[[.,.],[[.,[.,.]],[.,[.,.]]]] => [7,6,4,3,5,1,2] => [1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => 6
[[.,.],[[.,[.,.]],[[.,.],.]]] => [6,7,4,3,5,1,2] => [1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => 6
[[.,.],[[[.,.],.],[.,[.,.]]]] => [7,6,3,4,5,1,2] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 8
[[.,.],[[[.,.],.],[[.,.],.]]] => [6,7,3,4,5,1,2] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 8
[[.,.],[[.,[.,[.,.]]],[.,.]]] => [7,5,4,3,6,1,2] => [1,2,3,6,4,5,7] => [1,2,3,5,6,4,7] => 6
[[.,.],[[.,[[.,.],.]],[.,.]]] => [7,4,5,3,6,1,2] => [1,2,3,6,4,5,7] => [1,2,3,5,6,4,7] => 6
[[.,.],[[[.,.],[.,.]],[.,.]]] => [7,5,3,4,6,1,2] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => 6
[[.,.],[[[.,[.,.]],.],[.,.]]] => [7,4,3,5,6,1,2] => [1,2,3,5,6,4,7] => [1,2,3,6,4,5,7] => 6
[[.,.],[[[[.,.],.],.],[.,.]]] => [7,3,4,5,6,1,2] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 8
[[.,.],[[.,[.,[.,[.,.]]]],.]] => [6,5,4,3,7,1,2] => [1,2,3,7,4,5,6] => [1,2,3,5,6,7,4] => 6
[[.,.],[[.,[.,[[.,.],.]]],.]] => [5,6,4,3,7,1,2] => [1,2,3,7,4,5,6] => [1,2,3,5,6,7,4] => 6
[[.,.],[[.,[[.,.],[.,.]]],.]] => [6,4,5,3,7,1,2] => [1,2,3,7,4,5,6] => [1,2,3,5,6,7,4] => 6
[[.,.],[[.,[[.,[.,.]],.]],.]] => [5,4,6,3,7,1,2] => [1,2,3,7,4,6,5] => [1,2,3,5,7,6,4] => 4
[[.,.],[[.,[[[.,.],.],.]],.]] => [4,5,6,3,7,1,2] => [1,2,3,7,4,5,6] => [1,2,3,5,6,7,4] => 6
[[.,.],[[[.,.],[.,[.,.]]],.]] => [6,5,3,4,7,1,2] => [1,2,3,4,7,5,6] => [1,2,3,4,6,7,5] => 6
[[.,.],[[[.,.],[[.,.],.]],.]] => [5,6,3,4,7,1,2] => [1,2,3,4,7,5,6] => [1,2,3,4,6,7,5] => 6
[[.,.],[[[.,[.,.]],[.,.]],.]] => [6,4,3,5,7,1,2] => [1,2,3,5,7,4,6] => [1,2,3,6,4,7,5] => 4
[[.,.],[[[[.,.],.],[.,.]],.]] => [6,3,4,5,7,1,2] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => 6
[[.,.],[[[.,[.,[.,.]]],.],.]] => [5,4,3,6,7,1,2] => [1,2,3,6,7,4,5] => [1,2,3,6,7,4,5] => 6
[[.,.],[[[.,[[.,.],.]],.],.]] => [4,5,3,6,7,1,2] => [1,2,3,6,7,4,5] => [1,2,3,6,7,4,5] => 6
[[.,.],[[[[.,.],[.,.]],.],.]] => [5,3,4,6,7,1,2] => [1,2,3,4,6,7,5] => [1,2,3,4,7,5,6] => 6
[[.,.],[[[[.,[.,.]],.],.],.]] => [4,3,5,6,7,1,2] => [1,2,3,5,6,7,4] => [1,2,3,7,4,5,6] => 6
[[.,.],[[[[[.,.],.],.],.],.]] => [3,4,5,6,7,1,2] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 8
[[.,[.,.]],[.,[.,[.,[.,.]]]]] => [7,6,5,4,2,1,3] => [1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => 6
[[.,[.,.]],[.,[.,[[.,.],.]]]] => [6,7,5,4,2,1,3] => [1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => 6
[[.,[.,.]],[.,[[.,.],[.,.]]]] => [7,5,6,4,2,1,3] => [1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => 6
[[.,[.,.]],[.,[[.,[.,.]],.]]] => [6,5,7,4,2,1,3] => [1,3,2,4,5,7,6] => [1,3,2,4,5,7,6] => 4
[[.,[.,.]],[.,[[[.,.],.],.]]] => [5,6,7,4,2,1,3] => [1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => 6
[[.,[.,.]],[[.,.],[.,[.,.]]]] => [7,6,4,5,2,1,3] => [1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => 6
[[.,[.,.]],[[.,.],[[.,.],.]]] => [6,7,4,5,2,1,3] => [1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => 6
[[.,[.,.]],[[.,[.,.]],[.,.]]] => [7,5,4,6,2,1,3] => [1,3,2,4,6,5,7] => [1,3,2,4,6,5,7] => 4
[[.,[.,.]],[[[.,.],.],[.,.]]] => [7,4,5,6,2,1,3] => [1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => 6
[[.,[.,.]],[[.,[.,[.,.]]],.]] => [6,5,4,7,2,1,3] => [1,3,2,4,7,5,6] => [1,3,2,4,6,7,5] => 4
[[.,[.,.]],[[.,[[.,.],.]],.]] => [5,6,4,7,2,1,3] => [1,3,2,4,7,5,6] => [1,3,2,4,6,7,5] => 4
[[.,[.,.]],[[[.,.],[.,.]],.]] => [6,4,5,7,2,1,3] => [1,3,2,4,5,7,6] => [1,3,2,4,5,7,6] => 4
[[.,[.,.]],[[[.,[.,.]],.],.]] => [5,4,6,7,2,1,3] => [1,3,2,4,6,7,5] => [1,3,2,4,7,5,6] => 4
[[.,[.,.]],[[[[.,.],.],.],.]] => [4,5,6,7,2,1,3] => [1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => 6
[[[.,.],.],[.,[.,[.,[.,.]]]]] => [7,6,5,4,1,2,3] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 8
[[[.,.],.],[.,[.,[[.,.],.]]]] => [6,7,5,4,1,2,3] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 8
[[[.,.],.],[.,[[.,.],[.,.]]]] => [7,5,6,4,1,2,3] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 8
[[[.,.],.],[.,[[.,[.,.]],.]]] => [6,5,7,4,1,2,3] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => 6
[[[.,.],.],[.,[[[.,.],.],.]]] => [5,6,7,4,1,2,3] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 8
[[[.,.],.],[[.,.],[.,[.,.]]]] => [7,6,4,5,1,2,3] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 8
[[[.,.],.],[[.,.],[[.,.],.]]] => [6,7,4,5,1,2,3] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 8
[[[.,.],.],[[.,[.,.]],[.,.]]] => [7,5,4,6,1,2,3] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => 6
[[[.,.],.],[[[.,.],.],[.,.]]] => [7,4,5,6,1,2,3] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 8
[[[.,.],.],[[.,[.,[.,.]]],.]] => [6,5,4,7,1,2,3] => [1,2,3,4,7,5,6] => [1,2,3,4,6,7,5] => 6
[[[.,.],.],[[.,[[.,.],.]],.]] => [5,6,4,7,1,2,3] => [1,2,3,4,7,5,6] => [1,2,3,4,6,7,5] => 6
[[[.,.],.],[[[.,.],[.,.]],.]] => [6,4,5,7,1,2,3] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => 6
[[[.,.],.],[[[.,[.,.]],.],.]] => [5,4,6,7,1,2,3] => [1,2,3,4,6,7,5] => [1,2,3,4,7,5,6] => 6
[[[.,.],.],[[[[.,.],.],.],.]] => [4,5,6,7,1,2,3] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 8
[[.,[.,[.,.]]],[.,[.,[.,.]]]] => [7,6,5,3,2,1,4] => [1,4,2,3,5,6,7] => [1,3,4,2,5,6,7] => 6
[[.,[.,[.,.]]],[.,[[.,.],.]]] => [6,7,5,3,2,1,4] => [1,4,2,3,5,6,7] => [1,3,4,2,5,6,7] => 6
[[.,[.,[.,.]]],[[.,.],[.,.]]] => [7,5,6,3,2,1,4] => [1,4,2,3,5,6,7] => [1,3,4,2,5,6,7] => 6
[[.,[.,[.,.]]],[[.,[.,.]],.]] => [6,5,7,3,2,1,4] => [1,4,2,3,5,7,6] => [1,3,4,2,5,7,6] => 4
[[.,[.,[.,.]]],[[[.,.],.],.]] => [5,6,7,3,2,1,4] => [1,4,2,3,5,6,7] => [1,3,4,2,5,6,7] => 6
[[.,[[.,.],.]],[.,[.,[.,.]]]] => [7,6,5,2,3,1,4] => [1,4,2,3,5,6,7] => [1,3,4,2,5,6,7] => 6
[[.,[[.,.],.]],[.,[[.,.],.]]] => [6,7,5,2,3,1,4] => [1,4,2,3,5,6,7] => [1,3,4,2,5,6,7] => 6
[[.,[[.,.],.]],[[.,.],[.,.]]] => [7,5,6,2,3,1,4] => [1,4,2,3,5,6,7] => [1,3,4,2,5,6,7] => 6
[[.,[[.,.],.]],[[.,[.,.]],.]] => [6,5,7,2,3,1,4] => [1,4,2,3,5,7,6] => [1,3,4,2,5,7,6] => 4
[[.,[[.,.],.]],[[[.,.],.],.]] => [5,6,7,2,3,1,4] => [1,4,2,3,5,6,7] => [1,3,4,2,5,6,7] => 6
[[[.,.],[.,.]],[.,[.,[.,.]]]] => [7,6,5,3,1,2,4] => [1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => 6
[[[.,.],[.,.]],[.,[[.,.],.]]] => [6,7,5,3,1,2,4] => [1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => 6
[[[.,.],[.,.]],[[.,.],[.,.]]] => [7,5,6,3,1,2,4] => [1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => 6
[[[.,.],[.,.]],[[.,[.,.]],.]] => [6,5,7,3,1,2,4] => [1,2,4,3,5,7,6] => [1,2,4,3,5,7,6] => 4
[[[.,.],[.,.]],[[[.,.],.],.]] => [5,6,7,3,1,2,4] => [1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => 6
[[[.,[.,.]],.],[.,[.,[.,.]]]] => [7,6,5,2,1,3,4] => [1,3,4,2,5,6,7] => [1,4,2,3,5,6,7] => 6
[[[.,[.,.]],.],[.,[[.,.],.]]] => [6,7,5,2,1,3,4] => [1,3,4,2,5,6,7] => [1,4,2,3,5,6,7] => 6
[[[.,[.,.]],.],[[.,.],[.,.]]] => [7,5,6,2,1,3,4] => [1,3,4,2,5,6,7] => [1,4,2,3,5,6,7] => 6
[[[.,[.,.]],.],[[.,[.,.]],.]] => [6,5,7,2,1,3,4] => [1,3,4,2,5,7,6] => [1,4,2,3,5,7,6] => 4
[[[.,[.,.]],.],[[[.,.],.],.]] => [5,6,7,2,1,3,4] => [1,3,4,2,5,6,7] => [1,4,2,3,5,6,7] => 6
[[[[.,.],.],.],[.,[.,[.,.]]]] => [7,6,5,1,2,3,4] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 8
[[[[.,.],.],.],[.,[[.,.],.]]] => [6,7,5,1,2,3,4] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 8
[[[[.,.],.],.],[[.,.],[.,.]]] => [7,5,6,1,2,3,4] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 8
[[[[.,.],.],.],[[.,[.,.]],.]] => [6,5,7,1,2,3,4] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => 6
[[[[.,.],.],.],[[[.,.],.],.]] => [5,6,7,1,2,3,4] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 8
[[.,[.,[.,[.,.]]]],[.,[.,.]]] => [7,6,4,3,2,1,5] => [1,5,2,3,4,6,7] => [1,3,4,5,2,6,7] => 6
[[.,[.,[.,[.,.]]]],[[.,.],.]] => [6,7,4,3,2,1,5] => [1,5,2,3,4,6,7] => [1,3,4,5,2,6,7] => 6
[[.,[.,[[.,.],.]]],[.,[.,.]]] => [7,6,3,4,2,1,5] => [1,5,2,3,4,6,7] => [1,3,4,5,2,6,7] => 6
[[.,[.,[[.,.],.]]],[[.,.],.]] => [6,7,3,4,2,1,5] => [1,5,2,3,4,6,7] => [1,3,4,5,2,6,7] => 6
[[.,[[.,.],[.,.]]],[.,[.,.]]] => [7,6,4,2,3,1,5] => [1,5,2,3,4,6,7] => [1,3,4,5,2,6,7] => 6
[[.,[[.,.],[.,.]]],[[.,.],.]] => [6,7,4,2,3,1,5] => [1,5,2,3,4,6,7] => [1,3,4,5,2,6,7] => 6
[[.,[[.,[.,.]],.]],[.,[.,.]]] => [7,6,3,2,4,1,5] => [1,5,2,4,3,6,7] => [1,3,5,4,2,6,7] => 4
[[.,[[.,[.,.]],.]],[[.,.],.]] => [6,7,3,2,4,1,5] => [1,5,2,4,3,6,7] => [1,3,5,4,2,6,7] => 4
[[.,[[[.,.],.],.]],[.,[.,.]]] => [7,6,2,3,4,1,5] => [1,5,2,3,4,6,7] => [1,3,4,5,2,6,7] => 6
[[.,[[[.,.],.],.]],[[.,.],.]] => [6,7,2,3,4,1,5] => [1,5,2,3,4,6,7] => [1,3,4,5,2,6,7] => 6
[[[.,.],[.,[.,.]]],[.,[.,.]]] => [7,6,4,3,1,2,5] => [1,2,5,3,4,6,7] => [1,2,4,5,3,6,7] => 6
[[[.,.],[.,[.,.]]],[[.,.],.]] => [6,7,4,3,1,2,5] => [1,2,5,3,4,6,7] => [1,2,4,5,3,6,7] => 6
[[[.,.],[[.,.],.]],[.,[.,.]]] => [7,6,3,4,1,2,5] => [1,2,5,3,4,6,7] => [1,2,4,5,3,6,7] => 6
[[[.,.],[[.,.],.]],[[.,.],.]] => [6,7,3,4,1,2,5] => [1,2,5,3,4,6,7] => [1,2,4,5,3,6,7] => 6
[[[.,[.,.]],[.,.]],[.,[.,.]]] => [7,6,4,2,1,3,5] => [1,3,5,2,4,6,7] => [1,4,2,5,3,6,7] => 4
[[[.,[.,.]],[.,.]],[[.,.],.]] => [6,7,4,2,1,3,5] => [1,3,5,2,4,6,7] => [1,4,2,5,3,6,7] => 4
[[[[.,.],.],[.,.]],[.,[.,.]]] => [7,6,4,1,2,3,5] => [1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => 6
[[[[.,.],.],[.,.]],[[.,.],.]] => [6,7,4,1,2,3,5] => [1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => 6
[[[.,[.,[.,.]]],.],[.,[.,.]]] => [7,6,3,2,1,4,5] => [1,4,5,2,3,6,7] => [1,4,5,2,3,6,7] => 6
[[[.,[.,[.,.]]],.],[[.,.],.]] => [6,7,3,2,1,4,5] => [1,4,5,2,3,6,7] => [1,4,5,2,3,6,7] => 6
[[[.,[[.,.],.]],.],[.,[.,.]]] => [7,6,2,3,1,4,5] => [1,4,5,2,3,6,7] => [1,4,5,2,3,6,7] => 6
[[[.,[[.,.],.]],.],[[.,.],.]] => [6,7,2,3,1,4,5] => [1,4,5,2,3,6,7] => [1,4,5,2,3,6,7] => 6
[[[[.,.],[.,.]],.],[.,[.,.]]] => [7,6,3,1,2,4,5] => [1,2,4,5,3,6,7] => [1,2,5,3,4,6,7] => 6
[[[[.,.],[.,.]],.],[[.,.],.]] => [6,7,3,1,2,4,5] => [1,2,4,5,3,6,7] => [1,2,5,3,4,6,7] => 6
[[[[[.,.],.],.],.],[.,[.,.]]] => [7,6,1,2,3,4,5] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 8
[[[[[.,.],.],.],.],[[.,.],.]] => [6,7,1,2,3,4,5] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 8
[[.,[.,[.,[.,[.,.]]]]],[.,.]] => [7,5,4,3,2,1,6] => [1,6,2,3,4,5,7] => [1,3,4,5,6,2,7] => 6
[[.,[.,[.,[[.,.],.]]]],[.,.]] => [7,4,5,3,2,1,6] => [1,6,2,3,4,5,7] => [1,3,4,5,6,2,7] => 6
[[.,[.,[[.,.],[.,.]]]],[.,.]] => [7,5,3,4,2,1,6] => [1,6,2,3,4,5,7] => [1,3,4,5,6,2,7] => 6
[[.,[.,[[.,[.,.]],.]]],[.,.]] => [7,4,3,5,2,1,6] => [1,6,2,3,5,4,7] => [1,3,4,6,5,2,7] => 4
[[.,[.,[[[.,.],.],.]]],[.,.]] => [7,3,4,5,2,1,6] => [1,6,2,3,4,5,7] => [1,3,4,5,6,2,7] => 6
[[.,[[.,.],[.,[.,.]]]],[.,.]] => [7,5,4,2,3,1,6] => [1,6,2,3,4,5,7] => [1,3,4,5,6,2,7] => 6
[[.,[[.,.],[[.,.],.]]],[.,.]] => [7,4,5,2,3,1,6] => [1,6,2,3,4,5,7] => [1,3,4,5,6,2,7] => 6
[[.,[[.,[.,.]],[.,.]]],[.,.]] => [7,5,3,2,4,1,6] => [1,6,2,4,3,5,7] => [1,3,5,4,6,2,7] => 4
[[.,[[[.,.],.],[.,.]]],[.,.]] => [7,5,2,3,4,1,6] => [1,6,2,3,4,5,7] => [1,3,4,5,6,2,7] => 6
[[.,[[.,[.,[.,.]]],.]],[.,.]] => [7,4,3,2,5,1,6] => [1,6,2,5,3,4,7] => [1,3,5,6,4,2,7] => 4
[[.,[[.,[[.,.],.]],.]],[.,.]] => [7,3,4,2,5,1,6] => [1,6,2,5,3,4,7] => [1,3,5,6,4,2,7] => 4
[[.,[[[.,.],[.,.]],.]],[.,.]] => [7,4,2,3,5,1,6] => [1,6,2,3,5,4,7] => [1,3,4,6,5,2,7] => 4
[[.,[[[.,[.,.]],.],.]],[.,.]] => [7,3,2,4,5,1,6] => [1,6,2,4,5,3,7] => [1,3,6,4,5,2,7] => 4
[[.,[[[[.,.],.],.],.]],[.,.]] => [7,2,3,4,5,1,6] => [1,6,2,3,4,5,7] => [1,3,4,5,6,2,7] => 6
[[[.,.],[.,[.,[.,.]]]],[.,.]] => [7,5,4,3,1,2,6] => [1,2,6,3,4,5,7] => [1,2,4,5,6,3,7] => 6
[[[.,.],[.,[[.,.],.]]],[.,.]] => [7,4,5,3,1,2,6] => [1,2,6,3,4,5,7] => [1,2,4,5,6,3,7] => 6
[[[.,.],[[.,.],[.,.]]],[.,.]] => [7,5,3,4,1,2,6] => [1,2,6,3,4,5,7] => [1,2,4,5,6,3,7] => 6
[[[.,.],[[.,[.,.]],.]],[.,.]] => [7,4,3,5,1,2,6] => [1,2,6,3,5,4,7] => [1,2,4,6,5,3,7] => 4
[[[.,.],[[[.,.],.],.]],[.,.]] => [7,3,4,5,1,2,6] => [1,2,6,3,4,5,7] => [1,2,4,5,6,3,7] => 6
[[[.,[.,.]],[.,[.,.]]],[.,.]] => [7,5,4,2,1,3,6] => [1,3,6,2,4,5,7] => [1,4,2,5,6,3,7] => 4
[[[.,[.,.]],[[.,.],.]],[.,.]] => [7,4,5,2,1,3,6] => [1,3,6,2,4,5,7] => [1,4,2,5,6,3,7] => 4
[[[[.,.],.],[.,[.,.]]],[.,.]] => [7,5,4,1,2,3,6] => [1,2,3,6,4,5,7] => [1,2,3,5,6,4,7] => 6
[[[[.,.],.],[[.,.],.]],[.,.]] => [7,4,5,1,2,3,6] => [1,2,3,6,4,5,7] => [1,2,3,5,6,4,7] => 6
[[[.,[.,[.,.]]],[.,.]],[.,.]] => [7,5,3,2,1,4,6] => [1,4,6,2,3,5,7] => [1,4,5,2,6,3,7] => 4
[[[.,[[.,.],.]],[.,.]],[.,.]] => [7,5,2,3,1,4,6] => [1,4,6,2,3,5,7] => [1,4,5,2,6,3,7] => 4
[[[[.,.],[.,.]],[.,.]],[.,.]] => [7,5,3,1,2,4,6] => [1,2,4,6,3,5,7] => [1,2,5,3,6,4,7] => 4
[[[[[.,.],.],.],[.,.]],[.,.]] => [7,5,1,2,3,4,6] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => 6
[[[.,[.,[.,[.,.]]]],.],[.,.]] => [7,4,3,2,1,5,6] => [1,5,6,2,3,4,7] => [1,4,5,6,2,3,7] => 6
[[[.,[.,[[.,.],.]]],.],[.,.]] => [7,3,4,2,1,5,6] => [1,5,6,2,3,4,7] => [1,4,5,6,2,3,7] => 6
[[[.,[[.,.],[.,.]]],.],[.,.]] => [7,4,2,3,1,5,6] => [1,5,6,2,3,4,7] => [1,4,5,6,2,3,7] => 6
[[[.,[[.,[.,.]],.]],.],[.,.]] => [7,3,2,4,1,5,6] => [1,5,6,2,4,3,7] => [1,4,6,5,2,3,7] => 4
[[[.,[[[.,.],.],.]],.],[.,.]] => [7,2,3,4,1,5,6] => [1,5,6,2,3,4,7] => [1,4,5,6,2,3,7] => 6
[[[[.,.],[.,[.,.]]],.],[.,.]] => [7,4,3,1,2,5,6] => [1,2,5,6,3,4,7] => [1,2,5,6,3,4,7] => 6
[[[[.,.],[[.,.],.]],.],[.,.]] => [7,3,4,1,2,5,6] => [1,2,5,6,3,4,7] => [1,2,5,6,3,4,7] => 6
[[[[[.,.],.],[.,.]],.],[.,.]] => [7,4,1,2,3,5,6] => [1,2,3,5,6,4,7] => [1,2,3,6,4,5,7] => 6
[[[[[.,.],[.,.]],.],.],[.,.]] => [7,3,1,2,4,5,6] => [1,2,4,5,6,3,7] => [1,2,6,3,4,5,7] => 6
[[[[[[.,.],.],.],.],.],[.,.]] => [7,1,2,3,4,5,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 8
[[.,[.,[.,[.,[.,[.,.]]]]]],.] => [6,5,4,3,2,1,7] => [1,7,2,3,4,5,6] => [1,3,4,5,6,7,2] => 6
[[.,[.,[.,[.,[[.,.],.]]]]],.] => [5,6,4,3,2,1,7] => [1,7,2,3,4,5,6] => [1,3,4,5,6,7,2] => 6
[[.,[.,[.,[[.,.],[.,.]]]]],.] => [6,4,5,3,2,1,7] => [1,7,2,3,4,5,6] => [1,3,4,5,6,7,2] => 6
[[.,[.,[.,[[.,[.,.]],.]]]],.] => [5,4,6,3,2,1,7] => [1,7,2,3,4,6,5] => [1,3,4,5,7,6,2] => 4
[[.,[.,[.,[[[.,.],.],.]]]],.] => [4,5,6,3,2,1,7] => [1,7,2,3,4,5,6] => [1,3,4,5,6,7,2] => 6
[[.,[.,[[.,.],[.,[.,.]]]]],.] => [6,5,3,4,2,1,7] => [1,7,2,3,4,5,6] => [1,3,4,5,6,7,2] => 6
[[.,[.,[[.,.],[[.,.],.]]]],.] => [5,6,3,4,2,1,7] => [1,7,2,3,4,5,6] => [1,3,4,5,6,7,2] => 6
[[.,[.,[[.,[.,.]],[.,.]]]],.] => [6,4,3,5,2,1,7] => [1,7,2,3,5,4,6] => [1,3,4,6,5,7,2] => 4
[[.,[.,[[[.,.],.],[.,.]]]],.] => [6,3,4,5,2,1,7] => [1,7,2,3,4,5,6] => [1,3,4,5,6,7,2] => 6
[[.,[.,[[.,[.,[.,.]]],.]]],.] => [5,4,3,6,2,1,7] => [1,7,2,3,6,4,5] => [1,3,4,6,7,5,2] => 4
[[.,[.,[[.,[[.,.],.]],.]]],.] => [4,5,3,6,2,1,7] => [1,7,2,3,6,4,5] => [1,3,4,6,7,5,2] => 4
[[.,[.,[[[.,.],[.,.]],.]]],.] => [5,3,4,6,2,1,7] => [1,7,2,3,4,6,5] => [1,3,4,5,7,6,2] => 4
[[.,[.,[[[.,[.,.]],.],.]]],.] => [4,3,5,6,2,1,7] => [1,7,2,3,5,6,4] => [1,3,4,7,5,6,2] => 4
[[.,[.,[[[[.,.],.],.],.]]],.] => [3,4,5,6,2,1,7] => [1,7,2,3,4,5,6] => [1,3,4,5,6,7,2] => 6
[[.,[[.,.],[.,[.,[.,.]]]]],.] => [6,5,4,2,3,1,7] => [1,7,2,3,4,5,6] => [1,3,4,5,6,7,2] => 6
[[.,[[.,.],[.,[[.,.],.]]]],.] => [5,6,4,2,3,1,7] => [1,7,2,3,4,5,6] => [1,3,4,5,6,7,2] => 6
[[.,[[.,.],[[.,.],[.,.]]]],.] => [6,4,5,2,3,1,7] => [1,7,2,3,4,5,6] => [1,3,4,5,6,7,2] => 6
[[.,[[.,.],[[.,[.,.]],.]]],.] => [5,4,6,2,3,1,7] => [1,7,2,3,4,6,5] => [1,3,4,5,7,6,2] => 4
[[.,[[.,.],[[[.,.],.],.]]],.] => [4,5,6,2,3,1,7] => [1,7,2,3,4,5,6] => [1,3,4,5,6,7,2] => 6
[[.,[[.,[.,.]],[.,[.,.]]]],.] => [6,5,3,2,4,1,7] => [1,7,2,4,3,5,6] => [1,3,5,4,6,7,2] => 4
[[.,[[.,[.,.]],[[.,.],.]]],.] => [5,6,3,2,4,1,7] => [1,7,2,4,3,5,6] => [1,3,5,4,6,7,2] => 4
[[.,[[[.,.],.],[.,[.,.]]]],.] => [6,5,2,3,4,1,7] => [1,7,2,3,4,5,6] => [1,3,4,5,6,7,2] => 6
[[.,[[[.,.],.],[[.,.],.]]],.] => [5,6,2,3,4,1,7] => [1,7,2,3,4,5,6] => [1,3,4,5,6,7,2] => 6
[[.,[[.,[.,[.,.]]],[.,.]]],.] => [6,4,3,2,5,1,7] => [1,7,2,5,3,4,6] => [1,3,5,6,4,7,2] => 4
[[.,[[.,[[.,.],.]],[.,.]]],.] => [6,3,4,2,5,1,7] => [1,7,2,5,3,4,6] => [1,3,5,6,4,7,2] => 4
[[.,[[[.,.],[.,.]],[.,.]]],.] => [6,4,2,3,5,1,7] => [1,7,2,3,5,4,6] => [1,3,4,6,5,7,2] => 4
[[.,[[[.,[.,.]],.],[.,.]]],.] => [6,3,2,4,5,1,7] => [1,7,2,4,5,3,6] => [1,3,6,4,5,7,2] => 4
[[.,[[[[.,.],.],.],[.,.]]],.] => [6,2,3,4,5,1,7] => [1,7,2,3,4,5,6] => [1,3,4,5,6,7,2] => 6
[[.,[[.,[.,[.,[.,.]]]],.]],.] => [5,4,3,2,6,1,7] => [1,7,2,6,3,4,5] => [1,3,5,6,7,4,2] => 4
[[.,[[.,[.,[[.,.],.]]],.]],.] => [4,5,3,2,6,1,7] => [1,7,2,6,3,4,5] => [1,3,5,6,7,4,2] => 4
[[.,[[.,[[.,.],[.,.]]],.]],.] => [5,3,4,2,6,1,7] => [1,7,2,6,3,4,5] => [1,3,5,6,7,4,2] => 4
[[.,[[.,[[.,[.,.]],.]],.]],.] => [4,3,5,2,6,1,7] => [1,7,2,6,3,5,4] => [1,3,5,7,6,4,2] => 2
[[.,[[.,[[[.,.],.],.]],.]],.] => [3,4,5,2,6,1,7] => [1,7,2,6,3,4,5] => [1,3,5,6,7,4,2] => 4
[[.,[[[.,.],[.,[.,.]]],.]],.] => [5,4,2,3,6,1,7] => [1,7,2,3,6,4,5] => [1,3,4,6,7,5,2] => 4
[[.,[[[.,.],[[.,.],.]],.]],.] => [4,5,2,3,6,1,7] => [1,7,2,3,6,4,5] => [1,3,4,6,7,5,2] => 4
[[.,[[[.,[.,.]],[.,.]],.]],.] => [5,3,2,4,6,1,7] => [1,7,2,4,6,3,5] => [1,3,6,4,7,5,2] => 2
[[.,[[[[.,.],.],[.,.]],.]],.] => [5,2,3,4,6,1,7] => [1,7,2,3,4,6,5] => [1,3,4,5,7,6,2] => 4
[[.,[[[.,[.,[.,.]]],.],.]],.] => [4,3,2,5,6,1,7] => [1,7,2,5,6,3,4] => [1,3,6,7,4,5,2] => 4
[[.,[[[.,[[.,.],.]],.],.]],.] => [3,4,2,5,6,1,7] => [1,7,2,5,6,3,4] => [1,3,6,7,4,5,2] => 4
[[.,[[[[.,.],[.,.]],.],.]],.] => [4,2,3,5,6,1,7] => [1,7,2,3,5,6,4] => [1,3,4,7,5,6,2] => 4
[[.,[[[[.,[.,.]],.],.],.]],.] => [3,2,4,5,6,1,7] => [1,7,2,4,5,6,3] => [1,3,7,4,5,6,2] => 4
[[.,[[[[[.,.],.],.],.],.]],.] => [2,3,4,5,6,1,7] => [1,7,2,3,4,5,6] => [1,3,4,5,6,7,2] => 6
[[[.,.],[.,[.,[.,[.,.]]]]],.] => [6,5,4,3,1,2,7] => [1,2,7,3,4,5,6] => [1,2,4,5,6,7,3] => 6
[[[.,.],[.,[.,[[.,.],.]]]],.] => [5,6,4,3,1,2,7] => [1,2,7,3,4,5,6] => [1,2,4,5,6,7,3] => 6
[[[.,.],[.,[[.,.],[.,.]]]],.] => [6,4,5,3,1,2,7] => [1,2,7,3,4,5,6] => [1,2,4,5,6,7,3] => 6
[[[.,.],[.,[[.,[.,.]],.]]],.] => [5,4,6,3,1,2,7] => [1,2,7,3,4,6,5] => [1,2,4,5,7,6,3] => 4
[[[.,.],[.,[[[.,.],.],.]]],.] => [4,5,6,3,1,2,7] => [1,2,7,3,4,5,6] => [1,2,4,5,6,7,3] => 6
[[[.,.],[[.,.],[.,[.,.]]]],.] => [6,5,3,4,1,2,7] => [1,2,7,3,4,5,6] => [1,2,4,5,6,7,3] => 6
[[[.,.],[[.,.],[[.,.],.]]],.] => [5,6,3,4,1,2,7] => [1,2,7,3,4,5,6] => [1,2,4,5,6,7,3] => 6
[[[.,.],[[.,[.,.]],[.,.]]],.] => [6,4,3,5,1,2,7] => [1,2,7,3,5,4,6] => [1,2,4,6,5,7,3] => 4
[[[.,.],[[[.,.],.],[.,.]]],.] => [6,3,4,5,1,2,7] => [1,2,7,3,4,5,6] => [1,2,4,5,6,7,3] => 6
[[[.,.],[[.,[.,[.,.]]],.]],.] => [5,4,3,6,1,2,7] => [1,2,7,3,6,4,5] => [1,2,4,6,7,5,3] => 4
[[[.,.],[[.,[[.,.],.]],.]],.] => [4,5,3,6,1,2,7] => [1,2,7,3,6,4,5] => [1,2,4,6,7,5,3] => 4
[[[.,.],[[[.,.],[.,.]],.]],.] => [5,3,4,6,1,2,7] => [1,2,7,3,4,6,5] => [1,2,4,5,7,6,3] => 4
[[[.,.],[[[.,[.,.]],.],.]],.] => [4,3,5,6,1,2,7] => [1,2,7,3,5,6,4] => [1,2,4,7,5,6,3] => 4
[[[.,.],[[[[.,.],.],.],.]],.] => [3,4,5,6,1,2,7] => [1,2,7,3,4,5,6] => [1,2,4,5,6,7,3] => 6
[[[.,[.,.]],[.,[.,[.,.]]]],.] => [6,5,4,2,1,3,7] => [1,3,7,2,4,5,6] => [1,4,2,5,6,7,3] => 4
[[[.,[.,.]],[.,[[.,.],.]]],.] => [5,6,4,2,1,3,7] => [1,3,7,2,4,5,6] => [1,4,2,5,6,7,3] => 4
[[[.,[.,.]],[[.,.],[.,.]]],.] => [6,4,5,2,1,3,7] => [1,3,7,2,4,5,6] => [1,4,2,5,6,7,3] => 4
[[[.,[.,.]],[[.,[.,.]],.]],.] => [5,4,6,2,1,3,7] => [1,3,7,2,4,6,5] => [1,4,2,5,7,6,3] => 2
[[[.,[.,.]],[[[.,.],.],.]],.] => [4,5,6,2,1,3,7] => [1,3,7,2,4,5,6] => [1,4,2,5,6,7,3] => 4
[[[[.,.],.],[.,[.,[.,.]]]],.] => [6,5,4,1,2,3,7] => [1,2,3,7,4,5,6] => [1,2,3,5,6,7,4] => 6
[[[[.,.],.],[.,[[.,.],.]]],.] => [5,6,4,1,2,3,7] => [1,2,3,7,4,5,6] => [1,2,3,5,6,7,4] => 6
[[[[.,.],.],[[.,.],[.,.]]],.] => [6,4,5,1,2,3,7] => [1,2,3,7,4,5,6] => [1,2,3,5,6,7,4] => 6
[[[[.,.],.],[[.,[.,.]],.]],.] => [5,4,6,1,2,3,7] => [1,2,3,7,4,6,5] => [1,2,3,5,7,6,4] => 4
[[[[.,.],.],[[[.,.],.],.]],.] => [4,5,6,1,2,3,7] => [1,2,3,7,4,5,6] => [1,2,3,5,6,7,4] => 6
[[[.,[.,[.,.]]],[.,[.,.]]],.] => [6,5,3,2,1,4,7] => [1,4,7,2,3,5,6] => [1,4,5,2,6,7,3] => 4
[[[.,[.,[.,.]]],[[.,.],.]],.] => [5,6,3,2,1,4,7] => [1,4,7,2,3,5,6] => [1,4,5,2,6,7,3] => 4
[[[.,[[.,.],.]],[.,[.,.]]],.] => [6,5,2,3,1,4,7] => [1,4,7,2,3,5,6] => [1,4,5,2,6,7,3] => 4
[[[.,[[.,.],.]],[[.,.],.]],.] => [5,6,2,3,1,4,7] => [1,4,7,2,3,5,6] => [1,4,5,2,6,7,3] => 4
[[[[.,.],[.,.]],[.,[.,.]]],.] => [6,5,3,1,2,4,7] => [1,2,4,7,3,5,6] => [1,2,5,3,6,7,4] => 4
[[[[.,.],[.,.]],[[.,.],.]],.] => [5,6,3,1,2,4,7] => [1,2,4,7,3,5,6] => [1,2,5,3,6,7,4] => 4
[[[[[.,.],.],.],[.,[.,.]]],.] => [6,5,1,2,3,4,7] => [1,2,3,4,7,5,6] => [1,2,3,4,6,7,5] => 6
[[[[[.,.],.],.],[[.,.],.]],.] => [5,6,1,2,3,4,7] => [1,2,3,4,7,5,6] => [1,2,3,4,6,7,5] => 6
[[[.,[.,[.,[.,.]]]],[.,.]],.] => [6,4,3,2,1,5,7] => [1,5,7,2,3,4,6] => [1,4,5,6,2,7,3] => 4
[[[.,[.,[[.,.],.]]],[.,.]],.] => [6,3,4,2,1,5,7] => [1,5,7,2,3,4,6] => [1,4,5,6,2,7,3] => 4
[[[.,[[.,.],[.,.]]],[.,.]],.] => [6,4,2,3,1,5,7] => [1,5,7,2,3,4,6] => [1,4,5,6,2,7,3] => 4
[[[.,[[.,[.,.]],.]],[.,.]],.] => [6,3,2,4,1,5,7] => [1,5,7,2,4,3,6] => [1,4,6,5,2,7,3] => 2
[[[.,[[[.,.],.],.]],[.,.]],.] => [6,2,3,4,1,5,7] => [1,5,7,2,3,4,6] => [1,4,5,6,2,7,3] => 4
[[[[.,.],[.,[.,.]]],[.,.]],.] => [6,4,3,1,2,5,7] => [1,2,5,7,3,4,6] => [1,2,5,6,3,7,4] => 4
[[[[.,.],[[.,.],.]],[.,.]],.] => [6,3,4,1,2,5,7] => [1,2,5,7,3,4,6] => [1,2,5,6,3,7,4] => 4
[[[[[.,.],.],[.,.]],[.,.]],.] => [6,4,1,2,3,5,7] => [1,2,3,5,7,4,6] => [1,2,3,6,4,7,5] => 4
[[[[[.,.],[.,.]],.],[.,.]],.] => [6,3,1,2,4,5,7] => [1,2,4,5,7,3,6] => [1,2,6,3,4,7,5] => 4
[[[[[.,[.,.]],.],.],[.,.]],.] => [6,2,1,3,4,5,7] => [1,3,4,5,7,2,6] => [1,6,2,3,4,7,5] => 4
[[[[[[.,.],.],.],.],[.,.]],.] => [6,1,2,3,4,5,7] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => 6
[[[.,[.,[.,[.,[.,.]]]]],.],.] => [5,4,3,2,1,6,7] => [1,6,7,2,3,4,5] => [1,4,5,6,7,2,3] => 6
[[[.,[.,[.,[[.,.],.]]]],.],.] => [4,5,3,2,1,6,7] => [1,6,7,2,3,4,5] => [1,4,5,6,7,2,3] => 6
[[[.,[.,[[.,.],[.,.]]]],.],.] => [5,3,4,2,1,6,7] => [1,6,7,2,3,4,5] => [1,4,5,6,7,2,3] => 6
[[[.,[.,[[.,[.,.]],.]]],.],.] => [4,3,5,2,1,6,7] => [1,6,7,2,3,5,4] => [1,4,5,7,6,2,3] => 4
[[[.,[.,[[[.,.],.],.]]],.],.] => [3,4,5,2,1,6,7] => [1,6,7,2,3,4,5] => [1,4,5,6,7,2,3] => 6
[[[.,[[.,.],[.,[.,.]]]],.],.] => [5,4,2,3,1,6,7] => [1,6,7,2,3,4,5] => [1,4,5,6,7,2,3] => 6
[[[.,[[.,.],[[.,.],.]]],.],.] => [4,5,2,3,1,6,7] => [1,6,7,2,3,4,5] => [1,4,5,6,7,2,3] => 6
[[[.,[[[.,.],.],[.,.]]],.],.] => [5,2,3,4,1,6,7] => [1,6,7,2,3,4,5] => [1,4,5,6,7,2,3] => 6
[[[.,[[[.,.],[.,.]],.]],.],.] => [4,2,3,5,1,6,7] => [1,6,7,2,3,5,4] => [1,4,5,7,6,2,3] => 4
[[[.,[[[[.,.],.],.],.]],.],.] => [2,3,4,5,1,6,7] => [1,6,7,2,3,4,5] => [1,4,5,6,7,2,3] => 6
[[[[.,.],[.,[.,[.,.]]]],.],.] => [5,4,3,1,2,6,7] => [1,2,6,7,3,4,5] => [1,2,5,6,7,3,4] => 6
[[[[.,.],[.,[[.,.],.]]],.],.] => [4,5,3,1,2,6,7] => [1,2,6,7,3,4,5] => [1,2,5,6,7,3,4] => 6
[[[[.,.],[[.,.],[.,.]]],.],.] => [5,3,4,1,2,6,7] => [1,2,6,7,3,4,5] => [1,2,5,6,7,3,4] => 6
[[[[.,.],[[.,[.,.]],.]],.],.] => [4,3,5,1,2,6,7] => [1,2,6,7,3,5,4] => [1,2,5,7,6,3,4] => 4
[[[[.,.],[[[.,.],.],.]],.],.] => [3,4,5,1,2,6,7] => [1,2,6,7,3,4,5] => [1,2,5,6,7,3,4] => 6
[[[[[.,.],.],[.,[.,.]]],.],.] => [5,4,1,2,3,6,7] => [1,2,3,6,7,4,5] => [1,2,3,6,7,4,5] => 6
[[[[[.,.],.],[[.,.],.]],.],.] => [4,5,1,2,3,6,7] => [1,2,3,6,7,4,5] => [1,2,3,6,7,4,5] => 6
[[[[.,[.,[.,.]]],[.,.]],.],.] => [5,3,2,1,4,6,7] => [1,4,6,7,2,3,5] => [1,5,6,2,7,3,4] => 4
[[[[.,[[.,.],.]],[.,.]],.],.] => [5,2,3,1,4,6,7] => [1,4,6,7,2,3,5] => [1,5,6,2,7,3,4] => 4
[[[[[.,.],[.,.]],[.,.]],.],.] => [5,3,1,2,4,6,7] => [1,2,4,6,7,3,5] => [1,2,6,3,7,4,5] => 4
[[[[[.,[.,.]],.],[.,.]],.],.] => [5,2,1,3,4,6,7] => [1,3,4,6,7,2,5] => [1,6,2,3,7,4,5] => 4
[[[[[[.,.],.],.],[.,.]],.],.] => [5,1,2,3,4,6,7] => [1,2,3,4,6,7,5] => [1,2,3,4,7,5,6] => 6
[[[[.,[.,[.,[.,.]]]],.],.],.] => [4,3,2,1,5,6,7] => [1,5,6,7,2,3,4] => [1,5,6,7,2,3,4] => 6
[[[[.,[.,[[.,.],.]]],.],.],.] => [3,4,2,1,5,6,7] => [1,5,6,7,2,3,4] => [1,5,6,7,2,3,4] => 6
[[[[.,[[.,.],[.,.]]],.],.],.] => [4,2,3,1,5,6,7] => [1,5,6,7,2,3,4] => [1,5,6,7,2,3,4] => 6
[[[[.,[[[.,.],.],.]],.],.],.] => [2,3,4,1,5,6,7] => [1,5,6,7,2,3,4] => [1,5,6,7,2,3,4] => 6
[[[[[.,.],[.,[.,.]]],.],.],.] => [4,3,1,2,5,6,7] => [1,2,5,6,7,3,4] => [1,2,6,7,3,4,5] => 6
[[[[[.,.],[[.,.],.]],.],.],.] => [3,4,1,2,5,6,7] => [1,2,5,6,7,3,4] => [1,2,6,7,3,4,5] => 6
[[[[[.,[.,.]],[.,.]],.],.],.] => [4,2,1,3,5,6,7] => [1,3,5,6,7,2,4] => [1,6,2,7,3,4,5] => 4
[[[[[[.,.],.],[.,.]],.],.],.] => [4,1,2,3,5,6,7] => [1,2,3,5,6,7,4] => [1,2,3,7,4,5,6] => 6
[[[[[.,[.,[.,.]]],.],.],.],.] => [3,2,1,4,5,6,7] => [1,4,5,6,7,2,3] => [1,6,7,2,3,4,5] => 6
[[[[[.,[[.,.],.]],.],.],.],.] => [2,3,1,4,5,6,7] => [1,4,5,6,7,2,3] => [1,6,7,2,3,4,5] => 6
[[[[[[.,.],[.,.]],.],.],.],.] => [3,1,2,4,5,6,7] => [1,2,4,5,6,7,3] => [1,2,7,3,4,5,6] => 6
[[[[[[.,[.,.]],.],.],.],.],.] => [2,1,3,4,5,6,7] => [1,3,4,5,6,7,2] => [1,7,2,3,4,5,6] => 6
[[[[[[[.,.],.],.],.],.],.],.] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 8
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [7,8,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [7,6,8,5,4,3,2,1] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => 7
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]] => [6,7,8,5,4,3,2,1] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]] => [7,8,5,6,4,3,2,1] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]] => [7,5,6,8,4,3,2,1] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => 7
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]] => [6,5,7,8,4,3,2,1] => [1,2,3,4,5,7,8,6] => [1,2,3,4,5,8,6,7] => 7
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]] => [5,6,7,8,4,3,2,1] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => [8,7,6,4,5,3,2,1] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] => [7,8,6,4,5,3,2,1] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => [8,6,7,4,5,3,2,1] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]] => [7,4,5,6,8,3,2,1] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => 7
[.,[.,[.,[[[[[.,.],.],.],.],.]]]] => [4,5,6,7,8,3,2,1] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => [8,7,6,5,3,4,2,1] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => [7,8,6,5,3,4,2,1] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => [8,6,7,5,3,4,2,1] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [8,7,5,6,3,4,2,1] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[.,[.,[[.,.],[[[[.,.],.],.],.]]]] => [5,6,7,8,3,4,2,1] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[.,[.,[[[.,.],.],[[[.,.],.],.]]]] => [6,7,8,3,4,5,2,1] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]] => [7,6,5,4,3,8,2,1] => [1,2,3,8,4,5,6,7] => [1,2,3,5,6,7,8,4] => 7
[.,[.,[[.,[[[[.,.],.],.],.]],.]]] => [4,5,6,7,3,8,2,1] => [1,2,3,8,4,5,6,7] => [1,2,3,5,6,7,8,4] => 7
[.,[.,[[[[[.,.],.],[.,.]],.],.]]] => [6,3,4,5,7,8,2,1] => [1,2,3,4,5,7,8,6] => [1,2,3,4,5,8,6,7] => 7
[.,[.,[[[[[.,[.,.]],.],.],.],.]]] => [4,3,5,6,7,8,2,1] => [1,2,3,5,6,7,8,4] => [1,2,3,8,4,5,6,7] => 7
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [8,7,6,5,4,2,3,1] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => [7,8,6,5,4,2,3,1] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [8,6,7,5,4,2,3,1] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [8,7,5,6,4,2,3,1] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[.,[[.,.],[.,[[[[.,.],.],.],.]]]] => [5,6,7,8,4,2,3,1] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [8,7,6,4,5,2,3,1] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [8,6,7,4,5,2,3,1] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[.,[[.,.],[[[[[.,.],.],.],.],.]]] => [4,5,6,7,8,2,3,1] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [8,7,6,5,2,3,4,1] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[.,[[[.,.],.],[.,[[[.,.],.],.]]]] => [6,7,8,5,2,3,4,1] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [8,5,6,7,2,3,4,1] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[.,[[[.,.],.],[[[[.,.],.],.],.]]] => [5,6,7,8,2,3,4,1] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]] => [7,6,5,4,2,3,8,1] => [1,2,3,8,4,5,6,7] => [1,2,3,5,6,7,8,4] => 7
[.,[[[.,.],[[.,.],[[.,.],.]]],.]] => [6,7,4,5,2,3,8,1] => [1,2,3,8,4,5,6,7] => [1,2,3,5,6,7,8,4] => 7
[.,[[[.,.],[[[[.,.],.],.],.]],.]] => [4,5,6,7,2,3,8,1] => [1,2,3,8,4,5,6,7] => [1,2,3,5,6,7,8,4] => 7
[.,[[[[[[.,.],[.,.]],.],.],.],.]] => [4,2,3,5,6,7,8,1] => [1,2,3,5,6,7,8,4] => [1,2,3,8,4,5,6,7] => 7
[.,[[[[[[[.,.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,1] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [8,7,6,5,4,3,1,2] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [7,8,6,5,4,3,1,2] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [8,6,7,5,4,3,1,2] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [8,7,5,6,4,3,1,2] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]] => [6,5,7,8,4,3,1,2] => [1,2,3,4,5,7,8,6] => [1,2,3,4,5,8,6,7] => 7
[[.,.],[.,[.,[[[[.,.],.],.],.]]]] => [5,6,7,8,4,3,1,2] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [8,7,6,4,5,3,1,2] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [7,8,6,4,5,3,1,2] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[[.,.],[.,[[[[[.,.],.],.],.],.]]] => [4,5,6,7,8,3,1,2] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [8,7,6,5,3,4,1,2] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [8,7,5,6,3,4,1,2] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [7,8,5,6,3,4,1,2] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [7,5,6,8,3,4,1,2] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => 7
[[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [6,5,7,8,3,4,1,2] => [1,2,3,4,5,7,8,6] => [1,2,3,4,5,8,6,7] => 7
[[.,.],[[.,.],[[[[.,.],.],.],.]]] => [5,6,7,8,3,4,1,2] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [7,8,4,3,5,6,1,2] => [1,2,3,5,6,4,7,8] => [1,2,3,6,4,5,7,8] => 7
[[.,.],[[[[.,.],.],.],[[.,.],.]]] => [7,8,3,4,5,6,1,2] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[[.,.],[[[[.,[.,.]],.],.],[.,.]]] => [8,4,3,5,6,7,1,2] => [1,2,3,5,6,7,4,8] => [1,2,3,7,4,5,6,8] => 7
[[.,.],[[[[[.,.],.],.],.],[.,.]]] => [8,3,4,5,6,7,1,2] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => [7,6,5,4,3,8,1,2] => [1,2,3,8,4,5,6,7] => [1,2,3,5,6,7,8,4] => 7
[[.,.],[[.,[.,[[[.,.],.],.]]],.]] => [5,6,7,4,3,8,1,2] => [1,2,3,8,4,5,6,7] => [1,2,3,5,6,7,8,4] => 7
[[.,.],[[.,[[.,.],[[.,.],.]]],.]] => [6,7,4,5,3,8,1,2] => [1,2,3,8,4,5,6,7] => [1,2,3,5,6,7,8,4] => 7
[[.,.],[[.,[[[[.,.],.],.],.]],.]] => [4,5,6,7,3,8,1,2] => [1,2,3,8,4,5,6,7] => [1,2,3,5,6,7,8,4] => 7
[[.,.],[[[[.,[.,.]],[.,.]],.],.]] => [6,4,3,5,7,8,1,2] => [1,2,3,5,7,8,4,6] => [1,2,3,7,4,8,5,6] => 5
[[.,.],[[[[[.,.],.],[.,.]],.],.]] => [6,3,4,5,7,8,1,2] => [1,2,3,4,5,7,8,6] => [1,2,3,4,5,8,6,7] => 7
[[.,.],[[[[[.,[.,.]],.],.],.],.]] => [4,3,5,6,7,8,1,2] => [1,2,3,5,6,7,8,4] => [1,2,3,8,4,5,6,7] => 7
[[.,.],[[[[[[.,.],.],.],.],.],.]] => [3,4,5,6,7,8,1,2] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [8,7,6,5,4,2,1,3] => [1,3,2,4,5,6,7,8] => [1,3,2,4,5,6,7,8] => 7
[[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [5,6,7,8,4,2,1,3] => [1,3,2,4,5,6,7,8] => [1,3,2,4,5,6,7,8] => 7
[[.,[.,.]],[[[[[.,.],.],.],.],.]] => [4,5,6,7,8,2,1,3] => [1,3,2,4,5,6,7,8] => [1,3,2,4,5,6,7,8] => 7
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [8,7,6,5,4,1,2,3] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [6,7,8,5,4,1,2,3] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [8,5,6,7,4,1,2,3] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[[[.,.],.],[.,[[[.,[.,.]],.],.]]] => [6,5,7,8,4,1,2,3] => [1,2,3,4,5,7,8,6] => [1,2,3,4,5,8,6,7] => 7
[[[.,.],.],[.,[[[[.,.],.],.],.]]] => [5,6,7,8,4,1,2,3] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [8,7,6,4,5,1,2,3] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [8,6,7,4,5,1,2,3] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [8,7,4,5,6,1,2,3] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[[[.,.],.],[[[.,.],.],[[.,.],.]]] => [7,8,4,5,6,1,2,3] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[[[.,.],.],[[[[[.,.],.],.],.],.]] => [4,5,6,7,8,1,2,3] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [8,7,6,5,2,1,3,4] => [1,3,4,2,5,6,7,8] => [1,4,2,3,5,6,7,8] => 7
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]] => [7,8,6,5,2,1,3,4] => [1,3,4,2,5,6,7,8] => [1,4,2,3,5,6,7,8] => 7
[[[.,[.,.]],.],[.,[[[.,.],.],.]]] => [6,7,8,5,2,1,3,4] => [1,3,4,2,5,6,7,8] => [1,4,2,3,5,6,7,8] => 7
[[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [7,8,5,6,2,1,3,4] => [1,3,4,2,5,6,7,8] => [1,4,2,3,5,6,7,8] => 7
[[[.,[.,.]],.],[[[.,[.,.]],.],.]] => [6,5,7,8,2,1,3,4] => [1,3,4,2,5,7,8,6] => [1,4,2,3,5,8,6,7] => 5
[[[.,[.,.]],.],[[[[.,.],.],.],.]] => [5,6,7,8,2,1,3,4] => [1,3,4,2,5,6,7,8] => [1,4,2,3,5,6,7,8] => 7
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [8,7,6,5,1,2,3,4] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [7,8,6,5,1,2,3,4] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [8,6,7,5,1,2,3,4] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[[[[.,.],.],.],[.,[[.,[.,.]],.]]] => [7,6,8,5,1,2,3,4] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => 7
[[[[.,.],.],.],[.,[[[.,.],.],.]]] => [6,7,8,5,1,2,3,4] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [8,7,5,6,1,2,3,4] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[[[[.,.],.],.],[[.,.],[[.,.],.]]] => [7,8,5,6,1,2,3,4] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [8,6,5,7,1,2,3,4] => [1,2,3,4,5,7,6,8] => [1,2,3,4,5,7,6,8] => 7
[[[[.,.],.],.],[[[.,.],.],[.,.]]] => [8,5,6,7,1,2,3,4] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[[[[.,.],.],.],[[[.,.],[.,.]],.]] => [7,5,6,8,1,2,3,4] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => 7
[[[[.,.],.],.],[[[.,[.,.]],.],.]] => [6,5,7,8,1,2,3,4] => [1,2,3,4,5,7,8,6] => [1,2,3,4,5,8,6,7] => 7
[[[[.,.],.],.],[[[[.,.],.],.],.]] => [5,6,7,8,1,2,3,4] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [8,7,6,4,2,1,3,5] => [1,3,5,2,4,6,7,8] => [1,4,2,5,3,6,7,8] => 5
[[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [6,7,8,4,2,1,3,5] => [1,3,5,2,4,6,7,8] => [1,4,2,5,3,6,7,8] => 5
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [8,7,6,4,1,2,3,5] => [1,2,3,5,4,6,7,8] => [1,2,3,5,4,6,7,8] => 7
[[[[.,.],.],[.,.]],[[[.,.],.],.]] => [6,7,8,4,1,2,3,5] => [1,2,3,5,4,6,7,8] => [1,2,3,5,4,6,7,8] => 7
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [8,7,6,2,1,3,4,5] => [1,3,4,5,2,6,7,8] => [1,5,2,3,4,6,7,8] => 7
[[[[.,[.,.]],.],.],[[[.,.],.],.]] => [6,7,8,2,1,3,4,5] => [1,3,4,5,2,6,7,8] => [1,5,2,3,4,6,7,8] => 7
[[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [8,7,6,1,2,3,4,5] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[[[[[.,.],.],.],.],[.,[[.,.],.]]] => [7,8,6,1,2,3,4,5] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[[[[[.,.],.],.],.],[[.,.],[.,.]]] => [8,6,7,1,2,3,4,5] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[[[[[.,.],.],.],.],[[.,[.,.]],.]] => [7,6,8,1,2,3,4,5] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => 7
[[[[[.,.],.],.],.],[[[.,.],.],.]] => [6,7,8,1,2,3,4,5] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[[[[.,.],[[.,.],.]],.],[[.,.],.]] => [7,8,3,4,1,2,5,6] => [1,2,5,6,3,4,7,8] => [1,2,5,6,3,4,7,8] => 7
[[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [7,8,4,2,1,3,5,6] => [1,3,5,6,2,4,7,8] => [1,5,2,6,3,4,7,8] => 5
[[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [8,7,4,1,2,3,5,6] => [1,2,3,5,6,4,7,8] => [1,2,3,6,4,5,7,8] => 7
[[[[[.,[.,.]],.],.],.],[[.,.],.]] => [7,8,2,1,3,4,5,6] => [1,3,4,5,6,2,7,8] => [1,6,2,3,4,5,7,8] => 7
[[[[[[.,.],.],.],.],.],[.,[.,.]]] => [8,7,1,2,3,4,5,6] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[[[[[[.,.],.],.],.],.],[[.,.],.]] => [7,8,1,2,3,4,5,6] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [8,6,4,2,1,3,5,7] => [1,3,5,7,2,4,6,8] => [1,5,2,6,3,7,4,8] => 3
[[[[[[.,.],.],[.,.]],.],.],[.,.]] => [8,4,1,2,3,5,6,7] => [1,2,3,5,6,7,4,8] => [1,2,3,7,4,5,6,8] => 7
[[[[[.,[.,[.,.]]],.],.],.],[.,.]] => [8,3,2,1,4,5,6,7] => [1,4,5,6,7,2,3,8] => [1,6,7,2,3,4,5,8] => 7
[[[[[.,[[.,.],.]],.],.],.],[.,.]] => [8,2,3,1,4,5,6,7] => [1,4,5,6,7,2,3,8] => [1,6,7,2,3,4,5,8] => 7
[[[[[[.,[.,.]],.],.],.],.],[.,.]] => [8,2,1,3,4,5,6,7] => [1,3,4,5,6,7,2,8] => [1,7,2,3,4,5,6,8] => 7
[[[[[[[.,.],.],.],.],.],.],[.,.]] => [8,1,2,3,4,5,6,7] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[[.,[[.,[[.,[[.,.],.]],.]],.]],.] => [4,5,3,6,2,7,1,8] => [1,8,2,7,3,6,4,5] => [1,3,5,7,8,6,4,2] => 3
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [7,6,5,4,1,2,3,8] => [1,2,3,8,4,5,6,7] => [1,2,3,5,6,7,8,4] => 7
[[[[.,.],.],[.,[[[.,.],.],.]]],.] => [5,6,7,4,1,2,3,8] => [1,2,3,8,4,5,6,7] => [1,2,3,5,6,7,8,4] => 7
[[[[.,.],.],[[[.,.],.],[.,.]]],.] => [7,4,5,6,1,2,3,8] => [1,2,3,8,4,5,6,7] => [1,2,3,5,6,7,8,4] => 7
[[[[.,.],.],[[[[.,.],.],.],.]],.] => [4,5,6,7,1,2,3,8] => [1,2,3,8,4,5,6,7] => [1,2,3,5,6,7,8,4] => 7
[[[[[[.,.],[.,.]],.],.],[.,.]],.] => [7,3,1,2,4,5,6,8] => [1,2,4,5,6,8,3,7] => [1,2,7,3,4,5,8,6] => 5
[[[[[[.,[.,.]],.],.],.],[.,.]],.] => [7,2,1,3,4,5,6,8] => [1,3,4,5,6,8,2,7] => [1,7,2,3,4,5,8,6] => 5
[[[[[[[.,.],.],.],.],.],[.,.]],.] => [7,1,2,3,4,5,6,8] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => 7
[[[[[[.,.],.],[.,.]],[.,.]],.],.] => [6,4,1,2,3,5,7,8] => [1,2,3,5,7,8,4,6] => [1,2,3,7,4,8,5,6] => 5
[[[[[[[.,.],.],.],.],[.,.]],.],.] => [6,1,2,3,4,5,7,8] => [1,2,3,4,5,7,8,6] => [1,2,3,4,5,8,6,7] => 7
[[[[[.,[.,[.,[.,.]]]],.],.],.],.] => [4,3,2,1,5,6,7,8] => [1,5,6,7,8,2,3,4] => [1,6,7,8,2,3,4,5] => 7
[[[[[.,[[[.,.],.],.]],.],.],.],.] => [2,3,4,1,5,6,7,8] => [1,5,6,7,8,2,3,4] => [1,6,7,8,2,3,4,5] => 7
[[[[[[[.,.],.],[.,.]],.],.],.],.] => [4,1,2,3,5,6,7,8] => [1,2,3,5,6,7,8,4] => [1,2,3,8,4,5,6,7] => 7
[[[[[[.,[.,[.,.]]],.],.],.],.],.] => [3,2,1,4,5,6,7,8] => [1,4,5,6,7,8,2,3] => [1,7,8,2,3,4,5,6] => 7
[[[[[[[.,[.,.]],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8] => [1,3,4,5,6,7,8,2] => [1,8,2,3,4,5,6,7] => 7
[[[[[[[[.,.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 9
[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [9,8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 10
[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [8,9,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 10
[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]] => [7,8,9,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 10
[.,[[[[[[[[.,.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,1] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 10
[[[[[[[[[.,.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 10
[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [10,9,8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 11
[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]] => [9,10,8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 11
[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]] => [6,7,8,9,10,5,4,3,2,1] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 11
[[.,.],[[[[[[[.,.],.],.],.],.],.],.]] => [3,4,5,6,7,8,9,1,2] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 10
[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,10,1] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 11
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 11
[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]] => [8,7,9,6,5,4,3,2,1] => [1,2,3,4,5,6,7,9,8] => [1,2,3,4,5,6,7,9,8] => 8
[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]] => [9,8,10,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,10,9] => [1,2,3,4,5,6,7,8,10,9] => 9
[.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]] => [8,6,7,9,5,4,3,2,1] => [1,2,3,4,5,6,7,9,8] => [1,2,3,4,5,6,7,9,8] => 8
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [9,10,7,8,5,6,3,4,1,2] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 11
[[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [9,1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 10
[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [10,1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 11
[[[[[[[.,.],.],.],.],.],.],[[.,.],.]] => [8,9,1,2,3,4,5,6,7] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 10
[[[[[[.,.],.],.],.],.],[[[.,.],.],.]] => [7,8,9,1,2,3,4,5,6] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 10
[[[[[.,.],.],.],.],[[[[.,.],.],.],.]] => [6,7,8,9,1,2,3,4,5] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 10
[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => [9,8,1,2,3,4,5,6,7] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 10
[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]] => [9,10,1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 11
[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]] => [8,9,10,1,2,3,4,5,6,7] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 11
[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]] => [7,8,9,10,1,2,3,4,5,6] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 11
[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]] => [6,7,8,9,10,1,2,3,4,5] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 11
[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]] => [3,4,5,6,7,8,9,10,1,2] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 11
[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [9,8,7,6,5,4,3,1,2] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 10
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [10,9,8,7,6,5,4,3,1,2] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 11
[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [9,8,7,6,5,4,1,2,3] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 10
[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.] => [3,2,1,4,5,6,7,8,9] => [1,4,5,6,7,8,9,2,3] => [1,8,9,2,3,4,5,6,7] => 8
[[[[[[[[.,[.,.]],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9] => [1,3,4,5,6,7,8,9,2] => [1,9,2,3,4,5,6,7,8] => 8
[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.] => [3,2,1,4,5,6,7,8,9,10] => [1,4,5,6,7,8,9,10,2,3] => [1,9,10,2,3,4,5,6,7,8] => 9
[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9,10] => [1,3,4,5,6,7,8,9,10,2] => [1,10,2,3,4,5,6,7,8,9] => 9
[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9,10,11] => [1,3,4,5,6,7,8,9,10,11,2] => [1,11,2,3,4,5,6,7,8,9,10] => 10
[[[[[[[[.,.],.],.],.],.],.],[.,.]],.] => [8,1,2,3,4,5,6,7,9] => [1,2,3,4,5,6,7,9,8] => [1,2,3,4,5,6,7,9,8] => 8
[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.] => [9,1,2,3,4,5,6,7,8,10] => [1,2,3,4,5,6,7,8,10,9] => [1,2,3,4,5,6,7,8,10,9] => 9
[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [10,9,8,7,6,5,4,1,2,3] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 11
[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => [10,9,1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 11
[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] => [9,8,7,1,2,3,4,5,6] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 10
[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => [9,8,7,6,1,2,3,4,5] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 10
[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [9,8,7,6,5,1,2,3,4] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 10
[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]] => [10,9,8,1,2,3,4,5,6,7] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 11
[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]] => [10,9,8,7,1,2,3,4,5,6] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 11
[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [10,9,8,7,6,1,2,3,4,5] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 11
[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [10,9,8,7,6,5,1,2,3,4] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 11
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,0,4 6,0,8 2,0,24,0,16 20,0,80,0,32
$F_{1} = q^{2}$
$F_{2} = 2\ q^{3}$
$F_{3} = q^{2} + 4\ q^{4}$
$F_{4} = 6\ q^{3} + 8\ q^{5}$
$F_{5} = 2\ q^{2} + 24\ q^{4} + 16\ q^{6}$
$F_{6} = 20\ q^{3} + 80\ q^{5} + 32\ q^{7}$
Description
The number of cycles in the breakpoint graph of a permutation.
The breakpoint graph of a permutation $\pi_1,\dots,\pi_n$ is the directed, bicoloured graph with vertices $0,\dots,n$, a grey edge from $i$ to $i+1$ and a black edge from $\pi_i$ to $\pi_{i-1}$ for $0\leq i\leq n$, all indices taken modulo $n+1$.
This graph decomposes into alternating cycles, which this statistic counts.
The distribution of this statistic on permutations of $n-1$ is, according to [cor.1, 5] and [eq.6, 6], given by
$$ \frac{1}{n(n+1)}((q+n)_{n+1}-(q)_{n+1}), $$
where $(x)_n=x(x-1)\dots(x-n+1)$.
The breakpoint graph of a permutation $\pi_1,\dots,\pi_n$ is the directed, bicoloured graph with vertices $0,\dots,n$, a grey edge from $i$ to $i+1$ and a black edge from $\pi_i$ to $\pi_{i-1}$ for $0\leq i\leq n$, all indices taken modulo $n+1$.
This graph decomposes into alternating cycles, which this statistic counts.
The distribution of this statistic on permutations of $n-1$ is, according to [cor.1, 5] and [eq.6, 6], given by
$$ \frac{1}{n(n+1)}((q+n)_{n+1}-(q)_{n+1}), $$
where $(x)_n=x(x-1)\dots(x-n+1)$.
Map
runsort
Description
The permutation obtained by sorting the increasing runs lexicographically.
Map
inverse
Description
Sends a permutation to its inverse.
Map
to 132-avoiding permutation
Description
Return a 132-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the maximal element of the Sylvester class.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the maximal element of the Sylvester class.
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