Identifier
-
Mp00014:
Binary trees
—to 132-avoiding permutation⟶
Permutations
Mp00064: Permutations —reverse⟶ Permutations
Mp00151: Permutations —to cycle type⟶ Set partitions
St000505: Set partitions ⟶ ℤ
Values
[.,.] => [1] => [1] => {{1}} => 1
[.,[.,.]] => [2,1] => [1,2] => {{1},{2}} => 1
[[.,.],.] => [1,2] => [2,1] => {{1,2}} => 2
[.,[.,[.,.]]] => [3,2,1] => [1,2,3] => {{1},{2},{3}} => 1
[.,[[.,.],.]] => [2,3,1] => [1,3,2] => {{1},{2,3}} => 1
[[.,.],[.,.]] => [3,1,2] => [2,1,3] => {{1,2},{3}} => 2
[[.,[.,.]],.] => [2,1,3] => [3,1,2] => {{1,2,3}} => 3
[[[.,.],.],.] => [1,2,3] => [3,2,1] => {{1,3},{2}} => 3
[.,[.,[.,[.,.]]]] => [4,3,2,1] => [1,2,3,4] => {{1},{2},{3},{4}} => 1
[.,[.,[[.,.],.]]] => [3,4,2,1] => [1,2,4,3] => {{1},{2},{3,4}} => 1
[.,[[.,.],[.,.]]] => [4,2,3,1] => [1,3,2,4] => {{1},{2,3},{4}} => 1
[.,[[.,[.,.]],.]] => [3,2,4,1] => [1,4,2,3] => {{1},{2,3,4}} => 1
[.,[[[.,.],.],.]] => [2,3,4,1] => [1,4,3,2] => {{1},{2,4},{3}} => 1
[[.,.],[.,[.,.]]] => [4,3,1,2] => [2,1,3,4] => {{1,2},{3},{4}} => 2
[[.,.],[[.,.],.]] => [3,4,1,2] => [2,1,4,3] => {{1,2},{3,4}} => 2
[[.,[.,.]],[.,.]] => [4,2,1,3] => [3,1,2,4] => {{1,2,3},{4}} => 3
[[[.,.],.],[.,.]] => [4,1,2,3] => [3,2,1,4] => {{1,3},{2},{4}} => 3
[[.,[.,[.,.]]],.] => [3,2,1,4] => [4,1,2,3] => {{1,2,3,4}} => 4
[[.,[[.,.],.]],.] => [2,3,1,4] => [4,1,3,2] => {{1,2,4},{3}} => 4
[[[.,.],[.,.]],.] => [3,1,2,4] => [4,2,1,3] => {{1,3,4},{2}} => 4
[[[.,[.,.]],.],.] => [2,1,3,4] => [4,3,1,2] => {{1,2,3,4}} => 4
[[[[.,.],.],.],.] => [1,2,3,4] => [4,3,2,1] => {{1,4},{2,3}} => 4
[.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => [1,2,3,4,5] => {{1},{2},{3},{4},{5}} => 1
[.,[.,[.,[[.,.],.]]]] => [4,5,3,2,1] => [1,2,3,5,4] => {{1},{2},{3},{4,5}} => 1
[.,[.,[[.,.],[.,.]]]] => [5,3,4,2,1] => [1,2,4,3,5] => {{1},{2},{3,4},{5}} => 1
[.,[.,[[.,[.,.]],.]]] => [4,3,5,2,1] => [1,2,5,3,4] => {{1},{2},{3,4,5}} => 1
[.,[.,[[[.,.],.],.]]] => [3,4,5,2,1] => [1,2,5,4,3] => {{1},{2},{3,5},{4}} => 1
[.,[[.,.],[.,[.,.]]]] => [5,4,2,3,1] => [1,3,2,4,5] => {{1},{2,3},{4},{5}} => 1
[.,[[.,.],[[.,.],.]]] => [4,5,2,3,1] => [1,3,2,5,4] => {{1},{2,3},{4,5}} => 1
[.,[[.,[.,.]],[.,.]]] => [5,3,2,4,1] => [1,4,2,3,5] => {{1},{2,3,4},{5}} => 1
[.,[[[.,.],.],[.,.]]] => [5,2,3,4,1] => [1,4,3,2,5] => {{1},{2,4},{3},{5}} => 1
[.,[[.,[.,[.,.]]],.]] => [4,3,2,5,1] => [1,5,2,3,4] => {{1},{2,3,4,5}} => 1
[.,[[.,[[.,.],.]],.]] => [3,4,2,5,1] => [1,5,2,4,3] => {{1},{2,3,5},{4}} => 1
[.,[[[.,.],[.,.]],.]] => [4,2,3,5,1] => [1,5,3,2,4] => {{1},{2,4,5},{3}} => 1
[.,[[[.,[.,.]],.],.]] => [3,2,4,5,1] => [1,5,4,2,3] => {{1},{2,3,4,5}} => 1
[.,[[[[.,.],.],.],.]] => [2,3,4,5,1] => [1,5,4,3,2] => {{1},{2,5},{3,4}} => 1
[[.,.],[.,[.,[.,.]]]] => [5,4,3,1,2] => [2,1,3,4,5] => {{1,2},{3},{4},{5}} => 2
[[.,.],[.,[[.,.],.]]] => [4,5,3,1,2] => [2,1,3,5,4] => {{1,2},{3},{4,5}} => 2
[[.,.],[[.,.],[.,.]]] => [5,3,4,1,2] => [2,1,4,3,5] => {{1,2},{3,4},{5}} => 2
[[.,.],[[.,[.,.]],.]] => [4,3,5,1,2] => [2,1,5,3,4] => {{1,2},{3,4,5}} => 2
[[.,.],[[[.,.],.],.]] => [3,4,5,1,2] => [2,1,5,4,3] => {{1,2},{3,5},{4}} => 2
[[.,[.,.]],[.,[.,.]]] => [5,4,2,1,3] => [3,1,2,4,5] => {{1,2,3},{4},{5}} => 3
[[.,[.,.]],[[.,.],.]] => [4,5,2,1,3] => [3,1,2,5,4] => {{1,2,3},{4,5}} => 3
[[[.,.],.],[.,[.,.]]] => [5,4,1,2,3] => [3,2,1,4,5] => {{1,3},{2},{4},{5}} => 3
[[[.,.],.],[[.,.],.]] => [4,5,1,2,3] => [3,2,1,5,4] => {{1,3},{2},{4,5}} => 3
[[.,[.,[.,.]]],[.,.]] => [5,3,2,1,4] => [4,1,2,3,5] => {{1,2,3,4},{5}} => 4
[[.,[[.,.],.]],[.,.]] => [5,2,3,1,4] => [4,1,3,2,5] => {{1,2,4},{3},{5}} => 4
[[[.,.],[.,.]],[.,.]] => [5,3,1,2,4] => [4,2,1,3,5] => {{1,3,4},{2},{5}} => 4
[[[.,[.,.]],.],[.,.]] => [5,2,1,3,4] => [4,3,1,2,5] => {{1,2,3,4},{5}} => 4
[[[[.,.],.],.],[.,.]] => [5,1,2,3,4] => [4,3,2,1,5] => {{1,4},{2,3},{5}} => 4
[[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => [5,1,2,3,4] => {{1,2,3,4,5}} => 5
[[.,[.,[[.,.],.]]],.] => [3,4,2,1,5] => [5,1,2,4,3] => {{1,2,3,5},{4}} => 5
[[.,[[.,.],[.,.]]],.] => [4,2,3,1,5] => [5,1,3,2,4] => {{1,2,4,5},{3}} => 5
[[.,[[.,[.,.]],.]],.] => [3,2,4,1,5] => [5,1,4,2,3] => {{1,2,3,4,5}} => 5
[[.,[[[.,.],.],.]],.] => [2,3,4,1,5] => [5,1,4,3,2] => {{1,2,5},{3,4}} => 5
[[[.,.],[.,[.,.]]],.] => [4,3,1,2,5] => [5,2,1,3,4] => {{1,3,4,5},{2}} => 5
[[[.,.],[[.,.],.]],.] => [3,4,1,2,5] => [5,2,1,4,3] => {{1,3,5},{2},{4}} => 5
[[[.,[.,.]],[.,.]],.] => [4,2,1,3,5] => [5,3,1,2,4] => {{1,2,3,4,5}} => 5
[[[[.,.],.],[.,.]],.] => [4,1,2,3,5] => [5,3,2,1,4] => {{1,4,5},{2,3}} => 5
[[[.,[.,[.,.]]],.],.] => [3,2,1,4,5] => [5,4,1,2,3] => {{1,3,5},{2,4}} => 5
[[[.,[[.,.],.]],.],.] => [2,3,1,4,5] => [5,4,1,3,2] => {{1,2,3,4,5}} => 5
[[[[.,.],[.,.]],.],.] => [3,1,2,4,5] => [5,4,2,1,3] => {{1,2,3,4,5}} => 5
[[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => [5,4,3,1,2] => {{1,2,4,5},{3}} => 5
[[[[[.,.],.],.],.],.] => [1,2,3,4,5] => [5,4,3,2,1] => {{1,5},{2,4},{3}} => 5
[.,[.,[.,[.,[.,[.,.]]]]]] => [6,5,4,3,2,1] => [1,2,3,4,5,6] => {{1},{2},{3},{4},{5},{6}} => 1
[.,[.,[.,[.,[[.,.],.]]]]] => [5,6,4,3,2,1] => [1,2,3,4,6,5] => {{1},{2},{3},{4},{5,6}} => 1
[.,[.,[.,[[.,.],[.,.]]]]] => [6,4,5,3,2,1] => [1,2,3,5,4,6] => {{1},{2},{3},{4,5},{6}} => 1
[.,[.,[.,[[.,[.,.]],.]]]] => [5,4,6,3,2,1] => [1,2,3,6,4,5] => {{1},{2},{3},{4,5,6}} => 1
[.,[.,[.,[[[.,.],.],.]]]] => [4,5,6,3,2,1] => [1,2,3,6,5,4] => {{1},{2},{3},{4,6},{5}} => 1
[.,[.,[[.,.],[.,[.,.]]]]] => [6,5,3,4,2,1] => [1,2,4,3,5,6] => {{1},{2},{3,4},{5},{6}} => 1
[.,[.,[[.,.],[[.,.],.]]]] => [5,6,3,4,2,1] => [1,2,4,3,6,5] => {{1},{2},{3,4},{5,6}} => 1
[.,[.,[[.,[.,.]],[.,.]]]] => [6,4,3,5,2,1] => [1,2,5,3,4,6] => {{1},{2},{3,4,5},{6}} => 1
[.,[.,[[[.,.],.],[.,.]]]] => [6,3,4,5,2,1] => [1,2,5,4,3,6] => {{1},{2},{3,5},{4},{6}} => 1
[.,[.,[[.,[.,[.,.]]],.]]] => [5,4,3,6,2,1] => [1,2,6,3,4,5] => {{1},{2},{3,4,5,6}} => 1
[.,[.,[[.,[[.,.],.]],.]]] => [4,5,3,6,2,1] => [1,2,6,3,5,4] => {{1},{2},{3,4,6},{5}} => 1
[.,[.,[[[.,.],[.,.]],.]]] => [5,3,4,6,2,1] => [1,2,6,4,3,5] => {{1},{2},{3,5,6},{4}} => 1
[.,[.,[[[.,[.,.]],.],.]]] => [4,3,5,6,2,1] => [1,2,6,5,3,4] => {{1},{2},{3,4,5,6}} => 1
[.,[.,[[[[.,.],.],.],.]]] => [3,4,5,6,2,1] => [1,2,6,5,4,3] => {{1},{2},{3,6},{4,5}} => 1
[.,[[.,.],[.,[.,[.,.]]]]] => [6,5,4,2,3,1] => [1,3,2,4,5,6] => {{1},{2,3},{4},{5},{6}} => 1
[.,[[.,.],[.,[[.,.],.]]]] => [5,6,4,2,3,1] => [1,3,2,4,6,5] => {{1},{2,3},{4},{5,6}} => 1
[.,[[.,.],[[.,.],[.,.]]]] => [6,4,5,2,3,1] => [1,3,2,5,4,6] => {{1},{2,3},{4,5},{6}} => 1
[.,[[.,.],[[.,[.,.]],.]]] => [5,4,6,2,3,1] => [1,3,2,6,4,5] => {{1},{2,3},{4,5,6}} => 1
[.,[[.,.],[[[.,.],.],.]]] => [4,5,6,2,3,1] => [1,3,2,6,5,4] => {{1},{2,3},{4,6},{5}} => 1
[.,[[.,[.,.]],[.,[.,.]]]] => [6,5,3,2,4,1] => [1,4,2,3,5,6] => {{1},{2,3,4},{5},{6}} => 1
[.,[[.,[.,.]],[[.,.],.]]] => [5,6,3,2,4,1] => [1,4,2,3,6,5] => {{1},{2,3,4},{5,6}} => 1
[.,[[[.,.],.],[.,[.,.]]]] => [6,5,2,3,4,1] => [1,4,3,2,5,6] => {{1},{2,4},{3},{5},{6}} => 1
[.,[[[.,.],.],[[.,.],.]]] => [5,6,2,3,4,1] => [1,4,3,2,6,5] => {{1},{2,4},{3},{5,6}} => 1
[.,[[.,[.,[.,.]]],[.,.]]] => [6,4,3,2,5,1] => [1,5,2,3,4,6] => {{1},{2,3,4,5},{6}} => 1
[.,[[.,[[.,.],.]],[.,.]]] => [6,3,4,2,5,1] => [1,5,2,4,3,6] => {{1},{2,3,5},{4},{6}} => 1
[.,[[[.,.],[.,.]],[.,.]]] => [6,4,2,3,5,1] => [1,5,3,2,4,6] => {{1},{2,4,5},{3},{6}} => 1
[.,[[[.,[.,.]],.],[.,.]]] => [6,3,2,4,5,1] => [1,5,4,2,3,6] => {{1},{2,3,4,5},{6}} => 1
[.,[[[[.,.],.],.],[.,.]]] => [6,2,3,4,5,1] => [1,5,4,3,2,6] => {{1},{2,5},{3,4},{6}} => 1
[.,[[.,[.,[.,[.,.]]]],.]] => [5,4,3,2,6,1] => [1,6,2,3,4,5] => {{1},{2,3,4,5,6}} => 1
[.,[[.,[.,[[.,.],.]]],.]] => [4,5,3,2,6,1] => [1,6,2,3,5,4] => {{1},{2,3,4,6},{5}} => 1
[.,[[.,[[.,.],[.,.]]],.]] => [5,3,4,2,6,1] => [1,6,2,4,3,5] => {{1},{2,3,5,6},{4}} => 1
[.,[[.,[[.,[.,.]],.]],.]] => [4,3,5,2,6,1] => [1,6,2,5,3,4] => {{1},{2,3,4,5,6}} => 1
[.,[[.,[[[.,.],.],.]],.]] => [3,4,5,2,6,1] => [1,6,2,5,4,3] => {{1},{2,3,6},{4,5}} => 1
[.,[[[.,.],[.,[.,.]]],.]] => [5,4,2,3,6,1] => [1,6,3,2,4,5] => {{1},{2,4,5,6},{3}} => 1
[.,[[[.,.],[[.,.],.]],.]] => [4,5,2,3,6,1] => [1,6,3,2,5,4] => {{1},{2,4,6},{3},{5}} => 1
[.,[[[.,[.,.]],[.,.]],.]] => [5,3,2,4,6,1] => [1,6,4,2,3,5] => {{1},{2,3,4,5,6}} => 1
[.,[[[[.,.],.],[.,.]],.]] => [5,2,3,4,6,1] => [1,6,4,3,2,5] => {{1},{2,5,6},{3,4}} => 1
>>> Load all 948 entries. <<<[.,[[[.,[.,[.,.]]],.],.]] => [4,3,2,5,6,1] => [1,6,5,2,3,4] => {{1},{2,4,6},{3,5}} => 1
[.,[[[.,[[.,.],.]],.],.]] => [3,4,2,5,6,1] => [1,6,5,2,4,3] => {{1},{2,3,4,5,6}} => 1
[.,[[[[.,.],[.,.]],.],.]] => [4,2,3,5,6,1] => [1,6,5,3,2,4] => {{1},{2,3,4,5,6}} => 1
[.,[[[[.,[.,.]],.],.],.]] => [3,2,4,5,6,1] => [1,6,5,4,2,3] => {{1},{2,3,5,6},{4}} => 1
[.,[[[[[.,.],.],.],.],.]] => [2,3,4,5,6,1] => [1,6,5,4,3,2] => {{1},{2,6},{3,5},{4}} => 1
[[.,.],[.,[.,[.,[.,.]]]]] => [6,5,4,3,1,2] => [2,1,3,4,5,6] => {{1,2},{3},{4},{5},{6}} => 2
[[.,.],[.,[.,[[.,.],.]]]] => [5,6,4,3,1,2] => [2,1,3,4,6,5] => {{1,2},{3},{4},{5,6}} => 2
[[.,.],[.,[[.,.],[.,.]]]] => [6,4,5,3,1,2] => [2,1,3,5,4,6] => {{1,2},{3},{4,5},{6}} => 2
[[.,.],[.,[[.,[.,.]],.]]] => [5,4,6,3,1,2] => [2,1,3,6,4,5] => {{1,2},{3},{4,5,6}} => 2
[[.,.],[.,[[[.,.],.],.]]] => [4,5,6,3,1,2] => [2,1,3,6,5,4] => {{1,2},{3},{4,6},{5}} => 2
[[.,.],[[.,.],[.,[.,.]]]] => [6,5,3,4,1,2] => [2,1,4,3,5,6] => {{1,2},{3,4},{5},{6}} => 2
[[.,.],[[.,.],[[.,.],.]]] => [5,6,3,4,1,2] => [2,1,4,3,6,5] => {{1,2},{3,4},{5,6}} => 2
[[.,.],[[.,[.,.]],[.,.]]] => [6,4,3,5,1,2] => [2,1,5,3,4,6] => {{1,2},{3,4,5},{6}} => 2
[[.,.],[[[.,.],.],[.,.]]] => [6,3,4,5,1,2] => [2,1,5,4,3,6] => {{1,2},{3,5},{4},{6}} => 2
[[.,.],[[.,[.,[.,.]]],.]] => [5,4,3,6,1,2] => [2,1,6,3,4,5] => {{1,2},{3,4,5,6}} => 2
[[.,.],[[.,[[.,.],.]],.]] => [4,5,3,6,1,2] => [2,1,6,3,5,4] => {{1,2},{3,4,6},{5}} => 2
[[.,.],[[[.,.],[.,.]],.]] => [5,3,4,6,1,2] => [2,1,6,4,3,5] => {{1,2},{3,5,6},{4}} => 2
[[.,.],[[[.,[.,.]],.],.]] => [4,3,5,6,1,2] => [2,1,6,5,3,4] => {{1,2},{3,4,5,6}} => 2
[[.,.],[[[[.,.],.],.],.]] => [3,4,5,6,1,2] => [2,1,6,5,4,3] => {{1,2},{3,6},{4,5}} => 2
[[.,[.,.]],[.,[.,[.,.]]]] => [6,5,4,2,1,3] => [3,1,2,4,5,6] => {{1,2,3},{4},{5},{6}} => 3
[[.,[.,.]],[.,[[.,.],.]]] => [5,6,4,2,1,3] => [3,1,2,4,6,5] => {{1,2,3},{4},{5,6}} => 3
[[.,[.,.]],[[.,.],[.,.]]] => [6,4,5,2,1,3] => [3,1,2,5,4,6] => {{1,2,3},{4,5},{6}} => 3
[[.,[.,.]],[[.,[.,.]],.]] => [5,4,6,2,1,3] => [3,1,2,6,4,5] => {{1,2,3},{4,5,6}} => 3
[[.,[.,.]],[[[.,.],.],.]] => [4,5,6,2,1,3] => [3,1,2,6,5,4] => {{1,2,3},{4,6},{5}} => 3
[[[.,.],.],[.,[.,[.,.]]]] => [6,5,4,1,2,3] => [3,2,1,4,5,6] => {{1,3},{2},{4},{5},{6}} => 3
[[[.,.],.],[.,[[.,.],.]]] => [5,6,4,1,2,3] => [3,2,1,4,6,5] => {{1,3},{2},{4},{5,6}} => 3
[[[.,.],.],[[.,.],[.,.]]] => [6,4,5,1,2,3] => [3,2,1,5,4,6] => {{1,3},{2},{4,5},{6}} => 3
[[[.,.],.],[[.,[.,.]],.]] => [5,4,6,1,2,3] => [3,2,1,6,4,5] => {{1,3},{2},{4,5,6}} => 3
[[[.,.],.],[[[.,.],.],.]] => [4,5,6,1,2,3] => [3,2,1,6,5,4] => {{1,3},{2},{4,6},{5}} => 3
[[.,[.,[.,.]]],[.,[.,.]]] => [6,5,3,2,1,4] => [4,1,2,3,5,6] => {{1,2,3,4},{5},{6}} => 4
[[.,[.,[.,.]]],[[.,.],.]] => [5,6,3,2,1,4] => [4,1,2,3,6,5] => {{1,2,3,4},{5,6}} => 4
[[.,[[.,.],.]],[.,[.,.]]] => [6,5,2,3,1,4] => [4,1,3,2,5,6] => {{1,2,4},{3},{5},{6}} => 4
[[.,[[.,.],.]],[[.,.],.]] => [5,6,2,3,1,4] => [4,1,3,2,6,5] => {{1,2,4},{3},{5,6}} => 4
[[[.,.],[.,.]],[.,[.,.]]] => [6,5,3,1,2,4] => [4,2,1,3,5,6] => {{1,3,4},{2},{5},{6}} => 4
[[[.,.],[.,.]],[[.,.],.]] => [5,6,3,1,2,4] => [4,2,1,3,6,5] => {{1,3,4},{2},{5,6}} => 4
[[[.,[.,.]],.],[.,[.,.]]] => [6,5,2,1,3,4] => [4,3,1,2,5,6] => {{1,2,3,4},{5},{6}} => 4
[[[.,[.,.]],.],[[.,.],.]] => [5,6,2,1,3,4] => [4,3,1,2,6,5] => {{1,2,3,4},{5,6}} => 4
[[[[.,.],.],.],[.,[.,.]]] => [6,5,1,2,3,4] => [4,3,2,1,5,6] => {{1,4},{2,3},{5},{6}} => 4
[[[[.,.],.],.],[[.,.],.]] => [5,6,1,2,3,4] => [4,3,2,1,6,5] => {{1,4},{2,3},{5,6}} => 4
[[.,[.,[.,[.,.]]]],[.,.]] => [6,4,3,2,1,5] => [5,1,2,3,4,6] => {{1,2,3,4,5},{6}} => 5
[[.,[.,[[.,.],.]]],[.,.]] => [6,3,4,2,1,5] => [5,1,2,4,3,6] => {{1,2,3,5},{4},{6}} => 5
[[.,[[.,.],[.,.]]],[.,.]] => [6,4,2,3,1,5] => [5,1,3,2,4,6] => {{1,2,4,5},{3},{6}} => 5
[[.,[[.,[.,.]],.]],[.,.]] => [6,3,2,4,1,5] => [5,1,4,2,3,6] => {{1,2,3,4,5},{6}} => 5
[[.,[[[.,.],.],.]],[.,.]] => [6,2,3,4,1,5] => [5,1,4,3,2,6] => {{1,2,5},{3,4},{6}} => 5
[[[.,.],[.,[.,.]]],[.,.]] => [6,4,3,1,2,5] => [5,2,1,3,4,6] => {{1,3,4,5},{2},{6}} => 5
[[[.,.],[[.,.],.]],[.,.]] => [6,3,4,1,2,5] => [5,2,1,4,3,6] => {{1,3,5},{2},{4},{6}} => 5
[[[.,[.,.]],[.,.]],[.,.]] => [6,4,2,1,3,5] => [5,3,1,2,4,6] => {{1,2,3,4,5},{6}} => 5
[[[[.,.],.],[.,.]],[.,.]] => [6,4,1,2,3,5] => [5,3,2,1,4,6] => {{1,4,5},{2,3},{6}} => 5
[[[.,[.,[.,.]]],.],[.,.]] => [6,3,2,1,4,5] => [5,4,1,2,3,6] => {{1,3,5},{2,4},{6}} => 5
[[[.,[[.,.],.]],.],[.,.]] => [6,2,3,1,4,5] => [5,4,1,3,2,6] => {{1,2,3,4,5},{6}} => 5
[[[[.,.],[.,.]],.],[.,.]] => [6,3,1,2,4,5] => [5,4,2,1,3,6] => {{1,2,3,4,5},{6}} => 5
[[[[.,[.,.]],.],.],[.,.]] => [6,2,1,3,4,5] => [5,4,3,1,2,6] => {{1,2,4,5},{3},{6}} => 5
[[[[[.,.],.],.],.],[.,.]] => [6,1,2,3,4,5] => [5,4,3,2,1,6] => {{1,5},{2,4},{3},{6}} => 5
[[.,[.,[.,[.,[.,.]]]]],.] => [5,4,3,2,1,6] => [6,1,2,3,4,5] => {{1,2,3,4,5,6}} => 6
[[.,[.,[.,[[.,.],.]]]],.] => [4,5,3,2,1,6] => [6,1,2,3,5,4] => {{1,2,3,4,6},{5}} => 6
[[.,[.,[[.,.],[.,.]]]],.] => [5,3,4,2,1,6] => [6,1,2,4,3,5] => {{1,2,3,5,6},{4}} => 6
[[.,[.,[[.,[.,.]],.]]],.] => [4,3,5,2,1,6] => [6,1,2,5,3,4] => {{1,2,3,4,5,6}} => 6
[[.,[.,[[[.,.],.],.]]],.] => [3,4,5,2,1,6] => [6,1,2,5,4,3] => {{1,2,3,6},{4,5}} => 6
[[.,[[.,.],[.,[.,.]]]],.] => [5,4,2,3,1,6] => [6,1,3,2,4,5] => {{1,2,4,5,6},{3}} => 6
[[.,[[.,.],[[.,.],.]]],.] => [4,5,2,3,1,6] => [6,1,3,2,5,4] => {{1,2,4,6},{3},{5}} => 6
[[.,[[.,[.,.]],[.,.]]],.] => [5,3,2,4,1,6] => [6,1,4,2,3,5] => {{1,2,3,4,5,6}} => 6
[[.,[[[.,.],.],[.,.]]],.] => [5,2,3,4,1,6] => [6,1,4,3,2,5] => {{1,2,5,6},{3,4}} => 6
[[.,[[.,[.,[.,.]]],.]],.] => [4,3,2,5,1,6] => [6,1,5,2,3,4] => {{1,2,4,6},{3,5}} => 6
[[.,[[.,[[.,.],.]],.]],.] => [3,4,2,5,1,6] => [6,1,5,2,4,3] => {{1,2,3,4,5,6}} => 6
[[.,[[[.,.],[.,.]],.]],.] => [4,2,3,5,1,6] => [6,1,5,3,2,4] => {{1,2,3,4,5,6}} => 6
[[.,[[[.,[.,.]],.],.]],.] => [3,2,4,5,1,6] => [6,1,5,4,2,3] => {{1,2,3,5,6},{4}} => 6
[[.,[[[[.,.],.],.],.]],.] => [2,3,4,5,1,6] => [6,1,5,4,3,2] => {{1,2,6},{3,5},{4}} => 6
[[[.,.],[.,[.,[.,.]]]],.] => [5,4,3,1,2,6] => [6,2,1,3,4,5] => {{1,3,4,5,6},{2}} => 6
[[[.,.],[.,[[.,.],.]]],.] => [4,5,3,1,2,6] => [6,2,1,3,5,4] => {{1,3,4,6},{2},{5}} => 6
[[[.,.],[[.,.],[.,.]]],.] => [5,3,4,1,2,6] => [6,2,1,4,3,5] => {{1,3,5,6},{2},{4}} => 6
[[[.,.],[[.,[.,.]],.]],.] => [4,3,5,1,2,6] => [6,2,1,5,3,4] => {{1,3,4,5,6},{2}} => 6
[[[.,.],[[[.,.],.],.]],.] => [3,4,5,1,2,6] => [6,2,1,5,4,3] => {{1,3,6},{2},{4,5}} => 6
[[[.,[.,.]],[.,[.,.]]],.] => [5,4,2,1,3,6] => [6,3,1,2,4,5] => {{1,2,3,4,5,6}} => 6
[[[.,[.,.]],[[.,.],.]],.] => [4,5,2,1,3,6] => [6,3,1,2,5,4] => {{1,2,3,4,6},{5}} => 6
[[[[.,.],.],[.,[.,.]]],.] => [5,4,1,2,3,6] => [6,3,2,1,4,5] => {{1,4,5,6},{2,3}} => 6
[[[[.,.],.],[[.,.],.]],.] => [4,5,1,2,3,6] => [6,3,2,1,5,4] => {{1,4,6},{2,3},{5}} => 6
[[[.,[.,[.,.]]],[.,.]],.] => [5,3,2,1,4,6] => [6,4,1,2,3,5] => {{1,3,5,6},{2,4}} => 6
[[[.,[[.,.],.]],[.,.]],.] => [5,2,3,1,4,6] => [6,4,1,3,2,5] => {{1,2,3,4,5,6}} => 6
[[[[.,.],[.,.]],[.,.]],.] => [5,3,1,2,4,6] => [6,4,2,1,3,5] => {{1,2,3,4,5,6}} => 6
[[[[.,[.,.]],.],[.,.]],.] => [5,2,1,3,4,6] => [6,4,3,1,2,5] => {{1,2,4,5,6},{3}} => 6
[[[[[.,.],.],.],[.,.]],.] => [5,1,2,3,4,6] => [6,4,3,2,1,5] => {{1,5,6},{2,4},{3}} => 6
[[[.,[.,[.,[.,.]]]],.],.] => [4,3,2,1,5,6] => [6,5,1,2,3,4] => {{1,2,3,4,5,6}} => 6
[[[.,[.,[[.,.],.]]],.],.] => [3,4,2,1,5,6] => [6,5,1,2,4,3] => {{1,3,6},{2,4,5}} => 6
[[[.,[[.,.],[.,.]]],.],.] => [4,2,3,1,5,6] => [6,5,1,3,2,4] => {{1,3,4,6},{2,5}} => 6
[[[.,[[.,[.,.]],.]],.],.] => [3,2,4,1,5,6] => [6,5,1,4,2,3] => {{1,3,6},{2,5},{4}} => 6
[[[.,[[[.,.],.],.]],.],.] => [2,3,4,1,5,6] => [6,5,1,4,3,2] => {{1,2,3,5,6},{4}} => 6
[[[[.,.],[.,[.,.]]],.],.] => [4,3,1,2,5,6] => [6,5,2,1,3,4] => {{1,4,6},{2,3,5}} => 6
[[[[.,.],[[.,.],.]],.],.] => [3,4,1,2,5,6] => [6,5,2,1,4,3] => {{1,2,3,4,5,6}} => 6
[[[[.,[.,.]],[.,.]],.],.] => [4,2,1,3,5,6] => [6,5,3,1,2,4] => {{1,4,6},{2,5},{3}} => 6
[[[[[.,.],.],[.,.]],.],.] => [4,1,2,3,5,6] => [6,5,3,2,1,4] => {{1,2,4,5,6},{3}} => 6
[[[[.,[.,[.,.]]],.],.],.] => [3,2,1,4,5,6] => [6,5,4,1,2,3] => {{1,3,4,6},{2,5}} => 6
[[[[.,[[.,.],.]],.],.],.] => [2,3,1,4,5,6] => [6,5,4,1,3,2] => {{1,2,3,4,5,6}} => 6
[[[[[.,.],[.,.]],.],.],.] => [3,1,2,4,5,6] => [6,5,4,2,1,3] => {{1,2,3,4,5,6}} => 6
[[[[[.,[.,.]],.],.],.],.] => [2,1,3,4,5,6] => [6,5,4,3,1,2] => {{1,2,5,6},{3,4}} => 6
[[[[[[.,.],.],.],.],.],.] => [1,2,3,4,5,6] => [6,5,4,3,2,1] => {{1,6},{2,5},{3,4}} => 6
[.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [7,6,5,4,3,2,1] => [1,2,3,4,5,6,7] => {{1},{2},{3},{4},{5},{6},{7}} => 1
[.,[.,[.,[.,[.,[[.,.],.]]]]]] => [6,7,5,4,3,2,1] => [1,2,3,4,5,7,6] => {{1},{2},{3},{4},{5},{6,7}} => 1
[.,[.,[.,[.,[[.,.],[.,.]]]]]] => [7,5,6,4,3,2,1] => [1,2,3,4,6,5,7] => {{1},{2},{3},{4},{5,6},{7}} => 1
[.,[.,[.,[.,[[.,[.,.]],.]]]]] => [6,5,7,4,3,2,1] => [1,2,3,4,7,5,6] => {{1},{2},{3},{4},{5,6,7}} => 1
[.,[.,[.,[.,[[[.,.],.],.]]]]] => [5,6,7,4,3,2,1] => [1,2,3,4,7,6,5] => {{1},{2},{3},{4},{5,7},{6}} => 1
[.,[.,[.,[[.,.],[.,[.,.]]]]]] => [7,6,4,5,3,2,1] => [1,2,3,5,4,6,7] => {{1},{2},{3},{4,5},{6},{7}} => 1
[.,[.,[.,[[.,.],[[.,.],.]]]]] => [6,7,4,5,3,2,1] => [1,2,3,5,4,7,6] => {{1},{2},{3},{4,5},{6,7}} => 1
[.,[.,[.,[[.,[.,.]],[.,.]]]]] => [7,5,4,6,3,2,1] => [1,2,3,6,4,5,7] => {{1},{2},{3},{4,5,6},{7}} => 1
[.,[.,[.,[[[.,.],.],[.,.]]]]] => [7,4,5,6,3,2,1] => [1,2,3,6,5,4,7] => {{1},{2},{3},{4,6},{5},{7}} => 1
[.,[.,[.,[[.,[.,[.,.]]],.]]]] => [6,5,4,7,3,2,1] => [1,2,3,7,4,5,6] => {{1},{2},{3},{4,5,6,7}} => 1
[.,[.,[.,[[.,[[.,.],.]],.]]]] => [5,6,4,7,3,2,1] => [1,2,3,7,4,6,5] => {{1},{2},{3},{4,5,7},{6}} => 1
[.,[.,[.,[[[.,.],[.,.]],.]]]] => [6,4,5,7,3,2,1] => [1,2,3,7,5,4,6] => {{1},{2},{3},{4,6,7},{5}} => 1
[.,[.,[.,[[[.,[.,.]],.],.]]]] => [5,4,6,7,3,2,1] => [1,2,3,7,6,4,5] => {{1},{2},{3},{4,5,6,7}} => 1
[.,[.,[.,[[[[.,.],.],.],.]]]] => [4,5,6,7,3,2,1] => [1,2,3,7,6,5,4] => {{1},{2},{3},{4,7},{5,6}} => 1
[.,[.,[[.,.],[.,[.,[.,.]]]]]] => [7,6,5,3,4,2,1] => [1,2,4,3,5,6,7] => {{1},{2},{3,4},{5},{6},{7}} => 1
[.,[.,[[.,.],[.,[[.,.],.]]]]] => [6,7,5,3,4,2,1] => [1,2,4,3,5,7,6] => {{1},{2},{3,4},{5},{6,7}} => 1
[.,[.,[[.,.],[[.,.],[.,.]]]]] => [7,5,6,3,4,2,1] => [1,2,4,3,6,5,7] => {{1},{2},{3,4},{5,6},{7}} => 1
[.,[.,[[.,.],[[.,[.,.]],.]]]] => [6,5,7,3,4,2,1] => [1,2,4,3,7,5,6] => {{1},{2},{3,4},{5,6,7}} => 1
[.,[.,[[.,.],[[[.,.],.],.]]]] => [5,6,7,3,4,2,1] => [1,2,4,3,7,6,5] => {{1},{2},{3,4},{5,7},{6}} => 1
[.,[.,[[.,[.,.]],[.,[.,.]]]]] => [7,6,4,3,5,2,1] => [1,2,5,3,4,6,7] => {{1},{2},{3,4,5},{6},{7}} => 1
[.,[.,[[.,[.,.]],[[.,.],.]]]] => [6,7,4,3,5,2,1] => [1,2,5,3,4,7,6] => {{1},{2},{3,4,5},{6,7}} => 1
[.,[.,[[[.,.],.],[.,[.,.]]]]] => [7,6,3,4,5,2,1] => [1,2,5,4,3,6,7] => {{1},{2},{3,5},{4},{6},{7}} => 1
[.,[.,[[[.,.],.],[[.,.],.]]]] => [6,7,3,4,5,2,1] => [1,2,5,4,3,7,6] => {{1},{2},{3,5},{4},{6,7}} => 1
[.,[.,[[.,[.,[.,.]]],[.,.]]]] => [7,5,4,3,6,2,1] => [1,2,6,3,4,5,7] => {{1},{2},{3,4,5,6},{7}} => 1
[.,[.,[[.,[[.,.],.]],[.,.]]]] => [7,4,5,3,6,2,1] => [1,2,6,3,5,4,7] => {{1},{2},{3,4,6},{5},{7}} => 1
[.,[.,[[[.,.],[.,.]],[.,.]]]] => [7,5,3,4,6,2,1] => [1,2,6,4,3,5,7] => {{1},{2},{3,5,6},{4},{7}} => 1
[.,[.,[[[.,[.,.]],.],[.,.]]]] => [7,4,3,5,6,2,1] => [1,2,6,5,3,4,7] => {{1},{2},{3,4,5,6},{7}} => 1
[.,[.,[[[[.,.],.],.],[.,.]]]] => [7,3,4,5,6,2,1] => [1,2,6,5,4,3,7] => {{1},{2},{3,6},{4,5},{7}} => 1
[.,[.,[[.,[.,[.,[.,.]]]],.]]] => [6,5,4,3,7,2,1] => [1,2,7,3,4,5,6] => {{1},{2},{3,4,5,6,7}} => 1
[.,[.,[[.,[.,[[.,.],.]]],.]]] => [5,6,4,3,7,2,1] => [1,2,7,3,4,6,5] => {{1},{2},{3,4,5,7},{6}} => 1
[.,[.,[[.,[[.,.],[.,.]]],.]]] => [6,4,5,3,7,2,1] => [1,2,7,3,5,4,6] => {{1},{2},{3,4,6,7},{5}} => 1
[.,[.,[[.,[[.,[.,.]],.]],.]]] => [5,4,6,3,7,2,1] => [1,2,7,3,6,4,5] => {{1},{2},{3,4,5,6,7}} => 1
[.,[.,[[.,[[[.,.],.],.]],.]]] => [4,5,6,3,7,2,1] => [1,2,7,3,6,5,4] => {{1},{2},{3,4,7},{5,6}} => 1
[.,[.,[[[.,.],[.,[.,.]]],.]]] => [6,5,3,4,7,2,1] => [1,2,7,4,3,5,6] => {{1},{2},{3,5,6,7},{4}} => 1
[.,[.,[[[.,.],[[.,.],.]],.]]] => [5,6,3,4,7,2,1] => [1,2,7,4,3,6,5] => {{1},{2},{3,5,7},{4},{6}} => 1
[.,[.,[[[.,[.,.]],[.,.]],.]]] => [6,4,3,5,7,2,1] => [1,2,7,5,3,4,6] => {{1},{2},{3,4,5,6,7}} => 1
[.,[.,[[[[.,.],.],[.,.]],.]]] => [6,3,4,5,7,2,1] => [1,2,7,5,4,3,6] => {{1},{2},{3,6,7},{4,5}} => 1
[.,[.,[[[.,[.,[.,.]]],.],.]]] => [5,4,3,6,7,2,1] => [1,2,7,6,3,4,5] => {{1},{2},{3,5,7},{4,6}} => 1
[.,[.,[[[.,[[.,.],.]],.],.]]] => [4,5,3,6,7,2,1] => [1,2,7,6,3,5,4] => {{1},{2},{3,4,5,6,7}} => 1
[.,[.,[[[[.,.],[.,.]],.],.]]] => [5,3,4,6,7,2,1] => [1,2,7,6,4,3,5] => {{1},{2},{3,4,5,6,7}} => 1
[.,[.,[[[[.,[.,.]],.],.],.]]] => [4,3,5,6,7,2,1] => [1,2,7,6,5,3,4] => {{1},{2},{3,4,6,7},{5}} => 1
[.,[.,[[[[[.,.],.],.],.],.]]] => [3,4,5,6,7,2,1] => [1,2,7,6,5,4,3] => {{1},{2},{3,7},{4,6},{5}} => 1
[.,[[.,.],[.,[.,[.,[.,.]]]]]] => [7,6,5,4,2,3,1] => [1,3,2,4,5,6,7] => {{1},{2,3},{4},{5},{6},{7}} => 1
[.,[[.,.],[.,[.,[[.,.],.]]]]] => [6,7,5,4,2,3,1] => [1,3,2,4,5,7,6] => {{1},{2,3},{4},{5},{6,7}} => 1
[.,[[.,.],[.,[[.,.],[.,.]]]]] => [7,5,6,4,2,3,1] => [1,3,2,4,6,5,7] => {{1},{2,3},{4},{5,6},{7}} => 1
[.,[[.,.],[.,[[.,[.,.]],.]]]] => [6,5,7,4,2,3,1] => [1,3,2,4,7,5,6] => {{1},{2,3},{4},{5,6,7}} => 1
[.,[[.,.],[.,[[[.,.],.],.]]]] => [5,6,7,4,2,3,1] => [1,3,2,4,7,6,5] => {{1},{2,3},{4},{5,7},{6}} => 1
[.,[[.,.],[[.,.],[.,[.,.]]]]] => [7,6,4,5,2,3,1] => [1,3,2,5,4,6,7] => {{1},{2,3},{4,5},{6},{7}} => 1
[.,[[.,.],[[.,.],[[.,.],.]]]] => [6,7,4,5,2,3,1] => [1,3,2,5,4,7,6] => {{1},{2,3},{4,5},{6,7}} => 1
[.,[[.,.],[[.,[.,.]],[.,.]]]] => [7,5,4,6,2,3,1] => [1,3,2,6,4,5,7] => {{1},{2,3},{4,5,6},{7}} => 1
[.,[[.,.],[[[.,.],.],[.,.]]]] => [7,4,5,6,2,3,1] => [1,3,2,6,5,4,7] => {{1},{2,3},{4,6},{5},{7}} => 1
[.,[[.,.],[[.,[.,[.,.]]],.]]] => [6,5,4,7,2,3,1] => [1,3,2,7,4,5,6] => {{1},{2,3},{4,5,6,7}} => 1
[.,[[.,.],[[.,[[.,.],.]],.]]] => [5,6,4,7,2,3,1] => [1,3,2,7,4,6,5] => {{1},{2,3},{4,5,7},{6}} => 1
[.,[[.,.],[[[.,.],[.,.]],.]]] => [6,4,5,7,2,3,1] => [1,3,2,7,5,4,6] => {{1},{2,3},{4,6,7},{5}} => 1
[.,[[.,.],[[[.,[.,.]],.],.]]] => [5,4,6,7,2,3,1] => [1,3,2,7,6,4,5] => {{1},{2,3},{4,5,6,7}} => 1
[.,[[.,.],[[[[.,.],.],.],.]]] => [4,5,6,7,2,3,1] => [1,3,2,7,6,5,4] => {{1},{2,3},{4,7},{5,6}} => 1
[.,[[.,[.,.]],[.,[.,[.,.]]]]] => [7,6,5,3,2,4,1] => [1,4,2,3,5,6,7] => {{1},{2,3,4},{5},{6},{7}} => 1
[.,[[.,[.,.]],[.,[[.,.],.]]]] => [6,7,5,3,2,4,1] => [1,4,2,3,5,7,6] => {{1},{2,3,4},{5},{6,7}} => 1
[.,[[.,[.,.]],[[.,.],[.,.]]]] => [7,5,6,3,2,4,1] => [1,4,2,3,6,5,7] => {{1},{2,3,4},{5,6},{7}} => 1
[.,[[.,[.,.]],[[.,[.,.]],.]]] => [6,5,7,3,2,4,1] => [1,4,2,3,7,5,6] => {{1},{2,3,4},{5,6,7}} => 1
[.,[[.,[.,.]],[[[.,.],.],.]]] => [5,6,7,3,2,4,1] => [1,4,2,3,7,6,5] => {{1},{2,3,4},{5,7},{6}} => 1
[.,[[[.,.],.],[.,[.,[.,.]]]]] => [7,6,5,2,3,4,1] => [1,4,3,2,5,6,7] => {{1},{2,4},{3},{5},{6},{7}} => 1
[.,[[[.,.],.],[.,[[.,.],.]]]] => [6,7,5,2,3,4,1] => [1,4,3,2,5,7,6] => {{1},{2,4},{3},{5},{6,7}} => 1
[.,[[[.,.],.],[[.,.],[.,.]]]] => [7,5,6,2,3,4,1] => [1,4,3,2,6,5,7] => {{1},{2,4},{3},{5,6},{7}} => 1
[.,[[[.,.],.],[[.,[.,.]],.]]] => [6,5,7,2,3,4,1] => [1,4,3,2,7,5,6] => {{1},{2,4},{3},{5,6,7}} => 1
[.,[[[.,.],.],[[[.,.],.],.]]] => [5,6,7,2,3,4,1] => [1,4,3,2,7,6,5] => {{1},{2,4},{3},{5,7},{6}} => 1
[.,[[.,[.,[.,.]]],[.,[.,.]]]] => [7,6,4,3,2,5,1] => [1,5,2,3,4,6,7] => {{1},{2,3,4,5},{6},{7}} => 1
[.,[[.,[.,[.,.]]],[[.,.],.]]] => [6,7,4,3,2,5,1] => [1,5,2,3,4,7,6] => {{1},{2,3,4,5},{6,7}} => 1
[.,[[.,[[.,.],.]],[.,[.,.]]]] => [7,6,3,4,2,5,1] => [1,5,2,4,3,6,7] => {{1},{2,3,5},{4},{6},{7}} => 1
[.,[[.,[[.,.],.]],[[.,.],.]]] => [6,7,3,4,2,5,1] => [1,5,2,4,3,7,6] => {{1},{2,3,5},{4},{6,7}} => 1
[.,[[[.,.],[.,.]],[.,[.,.]]]] => [7,6,4,2,3,5,1] => [1,5,3,2,4,6,7] => {{1},{2,4,5},{3},{6},{7}} => 1
[.,[[[.,.],[.,.]],[[.,.],.]]] => [6,7,4,2,3,5,1] => [1,5,3,2,4,7,6] => {{1},{2,4,5},{3},{6,7}} => 1
[.,[[[.,[.,.]],.],[.,[.,.]]]] => [7,6,3,2,4,5,1] => [1,5,4,2,3,6,7] => {{1},{2,3,4,5},{6},{7}} => 1
[.,[[[.,[.,.]],.],[[.,.],.]]] => [6,7,3,2,4,5,1] => [1,5,4,2,3,7,6] => {{1},{2,3,4,5},{6,7}} => 1
[.,[[[[.,.],.],.],[.,[.,.]]]] => [7,6,2,3,4,5,1] => [1,5,4,3,2,6,7] => {{1},{2,5},{3,4},{6},{7}} => 1
[.,[[[[.,.],.],.],[[.,.],.]]] => [6,7,2,3,4,5,1] => [1,5,4,3,2,7,6] => {{1},{2,5},{3,4},{6,7}} => 1
[.,[[.,[.,[.,[.,.]]]],[.,.]]] => [7,5,4,3,2,6,1] => [1,6,2,3,4,5,7] => {{1},{2,3,4,5,6},{7}} => 1
[.,[[.,[.,[[.,.],.]]],[.,.]]] => [7,4,5,3,2,6,1] => [1,6,2,3,5,4,7] => {{1},{2,3,4,6},{5},{7}} => 1
[.,[[.,[[.,.],[.,.]]],[.,.]]] => [7,5,3,4,2,6,1] => [1,6,2,4,3,5,7] => {{1},{2,3,5,6},{4},{7}} => 1
[.,[[.,[[.,[.,.]],.]],[.,.]]] => [7,4,3,5,2,6,1] => [1,6,2,5,3,4,7] => {{1},{2,3,4,5,6},{7}} => 1
[.,[[.,[[[.,.],.],.]],[.,.]]] => [7,3,4,5,2,6,1] => [1,6,2,5,4,3,7] => {{1},{2,3,6},{4,5},{7}} => 1
[.,[[[.,.],[.,[.,.]]],[.,.]]] => [7,5,4,2,3,6,1] => [1,6,3,2,4,5,7] => {{1},{2,4,5,6},{3},{7}} => 1
[.,[[[.,.],[[.,.],.]],[.,.]]] => [7,4,5,2,3,6,1] => [1,6,3,2,5,4,7] => {{1},{2,4,6},{3},{5},{7}} => 1
[.,[[[.,[.,.]],[.,.]],[.,.]]] => [7,5,3,2,4,6,1] => [1,6,4,2,3,5,7] => {{1},{2,3,4,5,6},{7}} => 1
[.,[[[[.,.],.],[.,.]],[.,.]]] => [7,5,2,3,4,6,1] => [1,6,4,3,2,5,7] => {{1},{2,5,6},{3,4},{7}} => 1
[.,[[[.,[.,[.,.]]],.],[.,.]]] => [7,4,3,2,5,6,1] => [1,6,5,2,3,4,7] => {{1},{2,4,6},{3,5},{7}} => 1
[.,[[[.,[[.,.],.]],.],[.,.]]] => [7,3,4,2,5,6,1] => [1,6,5,2,4,3,7] => {{1},{2,3,4,5,6},{7}} => 1
[.,[[[[.,.],[.,.]],.],[.,.]]] => [7,4,2,3,5,6,1] => [1,6,5,3,2,4,7] => {{1},{2,3,4,5,6},{7}} => 1
[.,[[[[.,[.,.]],.],.],[.,.]]] => [7,3,2,4,5,6,1] => [1,6,5,4,2,3,7] => {{1},{2,3,5,6},{4},{7}} => 1
[.,[[[[[.,.],.],.],.],[.,.]]] => [7,2,3,4,5,6,1] => [1,6,5,4,3,2,7] => {{1},{2,6},{3,5},{4},{7}} => 1
[.,[[.,[.,[.,[.,[.,.]]]]],.]] => [6,5,4,3,2,7,1] => [1,7,2,3,4,5,6] => {{1},{2,3,4,5,6,7}} => 1
[.,[[.,[.,[.,[[.,.],.]]]],.]] => [5,6,4,3,2,7,1] => [1,7,2,3,4,6,5] => {{1},{2,3,4,5,7},{6}} => 1
[.,[[.,[.,[[.,.],[.,.]]]],.]] => [6,4,5,3,2,7,1] => [1,7,2,3,5,4,6] => {{1},{2,3,4,6,7},{5}} => 1
[.,[[.,[.,[[.,[.,.]],.]]],.]] => [5,4,6,3,2,7,1] => [1,7,2,3,6,4,5] => {{1},{2,3,4,5,6,7}} => 1
[.,[[.,[.,[[[.,.],.],.]]],.]] => [4,5,6,3,2,7,1] => [1,7,2,3,6,5,4] => {{1},{2,3,4,7},{5,6}} => 1
[.,[[.,[[.,.],[.,[.,.]]]],.]] => [6,5,3,4,2,7,1] => [1,7,2,4,3,5,6] => {{1},{2,3,5,6,7},{4}} => 1
[.,[[.,[[.,.],[[.,.],.]]],.]] => [5,6,3,4,2,7,1] => [1,7,2,4,3,6,5] => {{1},{2,3,5,7},{4},{6}} => 1
[.,[[.,[[.,[.,.]],[.,.]]],.]] => [6,4,3,5,2,7,1] => [1,7,2,5,3,4,6] => {{1},{2,3,4,5,6,7}} => 1
[.,[[.,[[[.,.],.],[.,.]]],.]] => [6,3,4,5,2,7,1] => [1,7,2,5,4,3,6] => {{1},{2,3,6,7},{4,5}} => 1
[.,[[.,[[.,[.,[.,.]]],.]],.]] => [5,4,3,6,2,7,1] => [1,7,2,6,3,4,5] => {{1},{2,3,5,7},{4,6}} => 1
[.,[[.,[[.,[[.,.],.]],.]],.]] => [4,5,3,6,2,7,1] => [1,7,2,6,3,5,4] => {{1},{2,3,4,5,6,7}} => 1
[.,[[.,[[[.,.],[.,.]],.]],.]] => [5,3,4,6,2,7,1] => [1,7,2,6,4,3,5] => {{1},{2,3,4,5,6,7}} => 1
[.,[[.,[[[.,[.,.]],.],.]],.]] => [4,3,5,6,2,7,1] => [1,7,2,6,5,3,4] => {{1},{2,3,4,6,7},{5}} => 1
[.,[[.,[[[[.,.],.],.],.]],.]] => [3,4,5,6,2,7,1] => [1,7,2,6,5,4,3] => {{1},{2,3,7},{4,6},{5}} => 1
[.,[[[.,.],[.,[.,[.,.]]]],.]] => [6,5,4,2,3,7,1] => [1,7,3,2,4,5,6] => {{1},{2,4,5,6,7},{3}} => 1
[.,[[[.,.],[.,[[.,.],.]]],.]] => [5,6,4,2,3,7,1] => [1,7,3,2,4,6,5] => {{1},{2,4,5,7},{3},{6}} => 1
[.,[[[.,.],[[.,.],[.,.]]],.]] => [6,4,5,2,3,7,1] => [1,7,3,2,5,4,6] => {{1},{2,4,6,7},{3},{5}} => 1
[.,[[[.,.],[[.,[.,.]],.]],.]] => [5,4,6,2,3,7,1] => [1,7,3,2,6,4,5] => {{1},{2,4,5,6,7},{3}} => 1
[.,[[[.,.],[[[.,.],.],.]],.]] => [4,5,6,2,3,7,1] => [1,7,3,2,6,5,4] => {{1},{2,4,7},{3},{5,6}} => 1
[.,[[[.,[.,.]],[.,[.,.]]],.]] => [6,5,3,2,4,7,1] => [1,7,4,2,3,5,6] => {{1},{2,3,4,5,6,7}} => 1
[.,[[[.,[.,.]],[[.,.],.]],.]] => [5,6,3,2,4,7,1] => [1,7,4,2,3,6,5] => {{1},{2,3,4,5,7},{6}} => 1
[.,[[[[.,.],.],[.,[.,.]]],.]] => [6,5,2,3,4,7,1] => [1,7,4,3,2,5,6] => {{1},{2,5,6,7},{3,4}} => 1
[.,[[[[.,.],.],[[.,.],.]],.]] => [5,6,2,3,4,7,1] => [1,7,4,3,2,6,5] => {{1},{2,5,7},{3,4},{6}} => 1
[.,[[[.,[.,[.,.]]],[.,.]],.]] => [6,4,3,2,5,7,1] => [1,7,5,2,3,4,6] => {{1},{2,4,6,7},{3,5}} => 1
[.,[[[.,[[.,.],.]],[.,.]],.]] => [6,3,4,2,5,7,1] => [1,7,5,2,4,3,6] => {{1},{2,3,4,5,6,7}} => 1
[.,[[[[.,.],[.,.]],[.,.]],.]] => [6,4,2,3,5,7,1] => [1,7,5,3,2,4,6] => {{1},{2,3,4,5,6,7}} => 1
[.,[[[[.,[.,.]],.],[.,.]],.]] => [6,3,2,4,5,7,1] => [1,7,5,4,2,3,6] => {{1},{2,3,5,6,7},{4}} => 1
[.,[[[[[.,.],.],.],[.,.]],.]] => [6,2,3,4,5,7,1] => [1,7,5,4,3,2,6] => {{1},{2,6,7},{3,5},{4}} => 1
[.,[[[.,[.,[.,[.,.]]]],.],.]] => [5,4,3,2,6,7,1] => [1,7,6,2,3,4,5] => {{1},{2,3,4,5,6,7}} => 1
[.,[[[.,[.,[[.,.],.]]],.],.]] => [4,5,3,2,6,7,1] => [1,7,6,2,3,5,4] => {{1},{2,4,7},{3,5,6}} => 1
[.,[[[.,[[.,.],[.,.]]],.],.]] => [5,3,4,2,6,7,1] => [1,7,6,2,4,3,5] => {{1},{2,4,5,7},{3,6}} => 1
[.,[[[.,[[.,[.,.]],.]],.],.]] => [4,3,5,2,6,7,1] => [1,7,6,2,5,3,4] => {{1},{2,4,7},{3,6},{5}} => 1
[.,[[[.,[[[.,.],.],.]],.],.]] => [3,4,5,2,6,7,1] => [1,7,6,2,5,4,3] => {{1},{2,3,4,6,7},{5}} => 1
[.,[[[[.,.],[.,[.,.]]],.],.]] => [5,4,2,3,6,7,1] => [1,7,6,3,2,4,5] => {{1},{2,5,7},{3,4,6}} => 1
[.,[[[[.,.],[[.,.],.]],.],.]] => [4,5,2,3,6,7,1] => [1,7,6,3,2,5,4] => {{1},{2,3,4,5,6,7}} => 1
[.,[[[[.,[.,.]],[.,.]],.],.]] => [5,3,2,4,6,7,1] => [1,7,6,4,2,3,5] => {{1},{2,5,7},{3,6},{4}} => 1
[.,[[[[[.,.],.],[.,.]],.],.]] => [5,2,3,4,6,7,1] => [1,7,6,4,3,2,5] => {{1},{2,3,5,6,7},{4}} => 1
[.,[[[[.,[.,[.,.]]],.],.],.]] => [4,3,2,5,6,7,1] => [1,7,6,5,2,3,4] => {{1},{2,4,5,7},{3,6}} => 1
[.,[[[[.,[[.,.],.]],.],.],.]] => [3,4,2,5,6,7,1] => [1,7,6,5,2,4,3] => {{1},{2,3,4,5,6,7}} => 1
[.,[[[[[.,.],[.,.]],.],.],.]] => [4,2,3,5,6,7,1] => [1,7,6,5,3,2,4] => {{1},{2,3,4,5,6,7}} => 1
[.,[[[[[.,[.,.]],.],.],.],.]] => [3,2,4,5,6,7,1] => [1,7,6,5,4,2,3] => {{1},{2,3,6,7},{4,5}} => 1
[.,[[[[[[.,.],.],.],.],.],.]] => [2,3,4,5,6,7,1] => [1,7,6,5,4,3,2] => {{1},{2,7},{3,6},{4,5}} => 1
[[.,.],[.,[.,[.,[.,[.,.]]]]]] => [7,6,5,4,3,1,2] => [2,1,3,4,5,6,7] => {{1,2},{3},{4},{5},{6},{7}} => 2
[[.,.],[.,[.,[.,[[.,.],.]]]]] => [6,7,5,4,3,1,2] => [2,1,3,4,5,7,6] => {{1,2},{3},{4},{5},{6,7}} => 2
[[.,.],[.,[.,[[.,.],[.,.]]]]] => [7,5,6,4,3,1,2] => [2,1,3,4,6,5,7] => {{1,2},{3},{4},{5,6},{7}} => 2
[[.,.],[.,[.,[[.,[.,.]],.]]]] => [6,5,7,4,3,1,2] => [2,1,3,4,7,5,6] => {{1,2},{3},{4},{5,6,7}} => 2
[[.,.],[.,[.,[[[.,.],.],.]]]] => [5,6,7,4,3,1,2] => [2,1,3,4,7,6,5] => {{1,2},{3},{4},{5,7},{6}} => 2
[[.,.],[.,[[.,.],[.,[.,.]]]]] => [7,6,4,5,3,1,2] => [2,1,3,5,4,6,7] => {{1,2},{3},{4,5},{6},{7}} => 2
[[.,.],[.,[[.,.],[[.,.],.]]]] => [6,7,4,5,3,1,2] => [2,1,3,5,4,7,6] => {{1,2},{3},{4,5},{6,7}} => 2
[[.,.],[.,[[.,[.,.]],[.,.]]]] => [7,5,4,6,3,1,2] => [2,1,3,6,4,5,7] => {{1,2},{3},{4,5,6},{7}} => 2
[[.,.],[.,[[[.,.],.],[.,.]]]] => [7,4,5,6,3,1,2] => [2,1,3,6,5,4,7] => {{1,2},{3},{4,6},{5},{7}} => 2
[[.,.],[.,[[.,[.,[.,.]]],.]]] => [6,5,4,7,3,1,2] => [2,1,3,7,4,5,6] => {{1,2},{3},{4,5,6,7}} => 2
[[.,.],[.,[[.,[[.,.],.]],.]]] => [5,6,4,7,3,1,2] => [2,1,3,7,4,6,5] => {{1,2},{3},{4,5,7},{6}} => 2
[[.,.],[.,[[[.,.],[.,.]],.]]] => [6,4,5,7,3,1,2] => [2,1,3,7,5,4,6] => {{1,2},{3},{4,6,7},{5}} => 2
[[.,.],[.,[[[.,[.,.]],.],.]]] => [5,4,6,7,3,1,2] => [2,1,3,7,6,4,5] => {{1,2},{3},{4,5,6,7}} => 2
[[.,.],[.,[[[[.,.],.],.],.]]] => [4,5,6,7,3,1,2] => [2,1,3,7,6,5,4] => {{1,2},{3},{4,7},{5,6}} => 2
[[.,.],[[.,.],[.,[.,[.,.]]]]] => [7,6,5,3,4,1,2] => [2,1,4,3,5,6,7] => {{1,2},{3,4},{5},{6},{7}} => 2
[[.,.],[[.,.],[.,[[.,.],.]]]] => [6,7,5,3,4,1,2] => [2,1,4,3,5,7,6] => {{1,2},{3,4},{5},{6,7}} => 2
[[.,.],[[.,.],[[.,.],[.,.]]]] => [7,5,6,3,4,1,2] => [2,1,4,3,6,5,7] => {{1,2},{3,4},{5,6},{7}} => 2
[[.,.],[[.,.],[[.,[.,.]],.]]] => [6,5,7,3,4,1,2] => [2,1,4,3,7,5,6] => {{1,2},{3,4},{5,6,7}} => 2
[[.,.],[[.,.],[[[.,.],.],.]]] => [5,6,7,3,4,1,2] => [2,1,4,3,7,6,5] => {{1,2},{3,4},{5,7},{6}} => 2
[[.,.],[[.,[.,.]],[.,[.,.]]]] => [7,6,4,3,5,1,2] => [2,1,5,3,4,6,7] => {{1,2},{3,4,5},{6},{7}} => 2
[[.,.],[[.,[.,.]],[[.,.],.]]] => [6,7,4,3,5,1,2] => [2,1,5,3,4,7,6] => {{1,2},{3,4,5},{6,7}} => 2
[[.,.],[[[.,.],.],[.,[.,.]]]] => [7,6,3,4,5,1,2] => [2,1,5,4,3,6,7] => {{1,2},{3,5},{4},{6},{7}} => 2
[[.,.],[[[.,.],.],[[.,.],.]]] => [6,7,3,4,5,1,2] => [2,1,5,4,3,7,6] => {{1,2},{3,5},{4},{6,7}} => 2
[[.,.],[[.,[.,[.,.]]],[.,.]]] => [7,5,4,3,6,1,2] => [2,1,6,3,4,5,7] => {{1,2},{3,4,5,6},{7}} => 2
[[.,.],[[.,[[.,.],.]],[.,.]]] => [7,4,5,3,6,1,2] => [2,1,6,3,5,4,7] => {{1,2},{3,4,6},{5},{7}} => 2
[[.,.],[[[.,.],[.,.]],[.,.]]] => [7,5,3,4,6,1,2] => [2,1,6,4,3,5,7] => {{1,2},{3,5,6},{4},{7}} => 2
[[.,.],[[[.,[.,.]],.],[.,.]]] => [7,4,3,5,6,1,2] => [2,1,6,5,3,4,7] => {{1,2},{3,4,5,6},{7}} => 2
[[.,.],[[[[.,.],.],.],[.,.]]] => [7,3,4,5,6,1,2] => [2,1,6,5,4,3,7] => {{1,2},{3,6},{4,5},{7}} => 2
[[.,.],[[.,[.,[.,[.,.]]]],.]] => [6,5,4,3,7,1,2] => [2,1,7,3,4,5,6] => {{1,2},{3,4,5,6,7}} => 2
[[.,.],[[.,[.,[[.,.],.]]],.]] => [5,6,4,3,7,1,2] => [2,1,7,3,4,6,5] => {{1,2},{3,4,5,7},{6}} => 2
[[.,.],[[.,[[.,.],[.,.]]],.]] => [6,4,5,3,7,1,2] => [2,1,7,3,5,4,6] => {{1,2},{3,4,6,7},{5}} => 2
[[.,.],[[.,[[.,[.,.]],.]],.]] => [5,4,6,3,7,1,2] => [2,1,7,3,6,4,5] => {{1,2},{3,4,5,6,7}} => 2
[[.,.],[[.,[[[.,.],.],.]],.]] => [4,5,6,3,7,1,2] => [2,1,7,3,6,5,4] => {{1,2},{3,4,7},{5,6}} => 2
[[.,.],[[[.,.],[.,[.,.]]],.]] => [6,5,3,4,7,1,2] => [2,1,7,4,3,5,6] => {{1,2},{3,5,6,7},{4}} => 2
[[.,.],[[[.,.],[[.,.],.]],.]] => [5,6,3,4,7,1,2] => [2,1,7,4,3,6,5] => {{1,2},{3,5,7},{4},{6}} => 2
[[.,.],[[[.,[.,.]],[.,.]],.]] => [6,4,3,5,7,1,2] => [2,1,7,5,3,4,6] => {{1,2},{3,4,5,6,7}} => 2
[[.,.],[[[[.,.],.],[.,.]],.]] => [6,3,4,5,7,1,2] => [2,1,7,5,4,3,6] => {{1,2},{3,6,7},{4,5}} => 2
[[.,.],[[[.,[.,[.,.]]],.],.]] => [5,4,3,6,7,1,2] => [2,1,7,6,3,4,5] => {{1,2},{3,5,7},{4,6}} => 2
[[.,.],[[[.,[[.,.],.]],.],.]] => [4,5,3,6,7,1,2] => [2,1,7,6,3,5,4] => {{1,2},{3,4,5,6,7}} => 2
[[.,.],[[[[.,.],[.,.]],.],.]] => [5,3,4,6,7,1,2] => [2,1,7,6,4,3,5] => {{1,2},{3,4,5,6,7}} => 2
[[.,.],[[[[.,[.,.]],.],.],.]] => [4,3,5,6,7,1,2] => [2,1,7,6,5,3,4] => {{1,2},{3,4,6,7},{5}} => 2
[[.,.],[[[[[.,.],.],.],.],.]] => [3,4,5,6,7,1,2] => [2,1,7,6,5,4,3] => {{1,2},{3,7},{4,6},{5}} => 2
[[.,[.,.]],[.,[.,[.,[.,.]]]]] => [7,6,5,4,2,1,3] => [3,1,2,4,5,6,7] => {{1,2,3},{4},{5},{6},{7}} => 3
[[.,[.,.]],[.,[.,[[.,.],.]]]] => [6,7,5,4,2,1,3] => [3,1,2,4,5,7,6] => {{1,2,3},{4},{5},{6,7}} => 3
[[.,[.,.]],[.,[[.,.],[.,.]]]] => [7,5,6,4,2,1,3] => [3,1,2,4,6,5,7] => {{1,2,3},{4},{5,6},{7}} => 3
[[.,[.,.]],[.,[[.,[.,.]],.]]] => [6,5,7,4,2,1,3] => [3,1,2,4,7,5,6] => {{1,2,3},{4},{5,6,7}} => 3
[[.,[.,.]],[.,[[[.,.],.],.]]] => [5,6,7,4,2,1,3] => [3,1,2,4,7,6,5] => {{1,2,3},{4},{5,7},{6}} => 3
[[.,[.,.]],[[.,.],[.,[.,.]]]] => [7,6,4,5,2,1,3] => [3,1,2,5,4,6,7] => {{1,2,3},{4,5},{6},{7}} => 3
[[.,[.,.]],[[.,.],[[.,.],.]]] => [6,7,4,5,2,1,3] => [3,1,2,5,4,7,6] => {{1,2,3},{4,5},{6,7}} => 3
[[.,[.,.]],[[.,[.,.]],[.,.]]] => [7,5,4,6,2,1,3] => [3,1,2,6,4,5,7] => {{1,2,3},{4,5,6},{7}} => 3
[[.,[.,.]],[[[.,.],.],[.,.]]] => [7,4,5,6,2,1,3] => [3,1,2,6,5,4,7] => {{1,2,3},{4,6},{5},{7}} => 3
[[.,[.,.]],[[.,[.,[.,.]]],.]] => [6,5,4,7,2,1,3] => [3,1,2,7,4,5,6] => {{1,2,3},{4,5,6,7}} => 3
[[.,[.,.]],[[.,[[.,.],.]],.]] => [5,6,4,7,2,1,3] => [3,1,2,7,4,6,5] => {{1,2,3},{4,5,7},{6}} => 3
[[.,[.,.]],[[[.,.],[.,.]],.]] => [6,4,5,7,2,1,3] => [3,1,2,7,5,4,6] => {{1,2,3},{4,6,7},{5}} => 3
[[.,[.,.]],[[[.,[.,.]],.],.]] => [5,4,6,7,2,1,3] => [3,1,2,7,6,4,5] => {{1,2,3},{4,5,6,7}} => 3
[[.,[.,.]],[[[[.,.],.],.],.]] => [4,5,6,7,2,1,3] => [3,1,2,7,6,5,4] => {{1,2,3},{4,7},{5,6}} => 3
[[[.,.],.],[.,[.,[.,[.,.]]]]] => [7,6,5,4,1,2,3] => [3,2,1,4,5,6,7] => {{1,3},{2},{4},{5},{6},{7}} => 3
[[[.,.],.],[.,[.,[[.,.],.]]]] => [6,7,5,4,1,2,3] => [3,2,1,4,5,7,6] => {{1,3},{2},{4},{5},{6,7}} => 3
[[[.,.],.],[.,[[.,.],[.,.]]]] => [7,5,6,4,1,2,3] => [3,2,1,4,6,5,7] => {{1,3},{2},{4},{5,6},{7}} => 3
[[[.,.],.],[.,[[.,[.,.]],.]]] => [6,5,7,4,1,2,3] => [3,2,1,4,7,5,6] => {{1,3},{2},{4},{5,6,7}} => 3
[[[.,.],.],[.,[[[.,.],.],.]]] => [5,6,7,4,1,2,3] => [3,2,1,4,7,6,5] => {{1,3},{2},{4},{5,7},{6}} => 3
[[[.,.],.],[[.,.],[.,[.,.]]]] => [7,6,4,5,1,2,3] => [3,2,1,5,4,6,7] => {{1,3},{2},{4,5},{6},{7}} => 3
[[[.,.],.],[[.,.],[[.,.],.]]] => [6,7,4,5,1,2,3] => [3,2,1,5,4,7,6] => {{1,3},{2},{4,5},{6,7}} => 3
[[[.,.],.],[[.,[.,.]],[.,.]]] => [7,5,4,6,1,2,3] => [3,2,1,6,4,5,7] => {{1,3},{2},{4,5,6},{7}} => 3
[[[.,.],.],[[[.,.],.],[.,.]]] => [7,4,5,6,1,2,3] => [3,2,1,6,5,4,7] => {{1,3},{2},{4,6},{5},{7}} => 3
[[[.,.],.],[[.,[.,[.,.]]],.]] => [6,5,4,7,1,2,3] => [3,2,1,7,4,5,6] => {{1,3},{2},{4,5,6,7}} => 3
[[[.,.],.],[[.,[[.,.],.]],.]] => [5,6,4,7,1,2,3] => [3,2,1,7,4,6,5] => {{1,3},{2},{4,5,7},{6}} => 3
[[[.,.],.],[[[.,.],[.,.]],.]] => [6,4,5,7,1,2,3] => [3,2,1,7,5,4,6] => {{1,3},{2},{4,6,7},{5}} => 3
[[[.,.],.],[[[.,[.,.]],.],.]] => [5,4,6,7,1,2,3] => [3,2,1,7,6,4,5] => {{1,3},{2},{4,5,6,7}} => 3
[[[.,.],.],[[[[.,.],.],.],.]] => [4,5,6,7,1,2,3] => [3,2,1,7,6,5,4] => {{1,3},{2},{4,7},{5,6}} => 3
[[.,[.,[.,.]]],[.,[.,[.,.]]]] => [7,6,5,3,2,1,4] => [4,1,2,3,5,6,7] => {{1,2,3,4},{5},{6},{7}} => 4
[[.,[.,[.,.]]],[.,[[.,.],.]]] => [6,7,5,3,2,1,4] => [4,1,2,3,5,7,6] => {{1,2,3,4},{5},{6,7}} => 4
[[.,[.,[.,.]]],[[.,.],[.,.]]] => [7,5,6,3,2,1,4] => [4,1,2,3,6,5,7] => {{1,2,3,4},{5,6},{7}} => 4
[[.,[.,[.,.]]],[[.,[.,.]],.]] => [6,5,7,3,2,1,4] => [4,1,2,3,7,5,6] => {{1,2,3,4},{5,6,7}} => 4
[[.,[.,[.,.]]],[[[.,.],.],.]] => [5,6,7,3,2,1,4] => [4,1,2,3,7,6,5] => {{1,2,3,4},{5,7},{6}} => 4
[[.,[[.,.],.]],[.,[.,[.,.]]]] => [7,6,5,2,3,1,4] => [4,1,3,2,5,6,7] => {{1,2,4},{3},{5},{6},{7}} => 4
[[.,[[.,.],.]],[.,[[.,.],.]]] => [6,7,5,2,3,1,4] => [4,1,3,2,5,7,6] => {{1,2,4},{3},{5},{6,7}} => 4
[[.,[[.,.],.]],[[.,.],[.,.]]] => [7,5,6,2,3,1,4] => [4,1,3,2,6,5,7] => {{1,2,4},{3},{5,6},{7}} => 4
[[.,[[.,.],.]],[[.,[.,.]],.]] => [6,5,7,2,3,1,4] => [4,1,3,2,7,5,6] => {{1,2,4},{3},{5,6,7}} => 4
[[.,[[.,.],.]],[[[.,.],.],.]] => [5,6,7,2,3,1,4] => [4,1,3,2,7,6,5] => {{1,2,4},{3},{5,7},{6}} => 4
[[[.,.],[.,.]],[.,[.,[.,.]]]] => [7,6,5,3,1,2,4] => [4,2,1,3,5,6,7] => {{1,3,4},{2},{5},{6},{7}} => 4
[[[.,.],[.,.]],[.,[[.,.],.]]] => [6,7,5,3,1,2,4] => [4,2,1,3,5,7,6] => {{1,3,4},{2},{5},{6,7}} => 4
[[[.,.],[.,.]],[[.,.],[.,.]]] => [7,5,6,3,1,2,4] => [4,2,1,3,6,5,7] => {{1,3,4},{2},{5,6},{7}} => 4
[[[.,.],[.,.]],[[.,[.,.]],.]] => [6,5,7,3,1,2,4] => [4,2,1,3,7,5,6] => {{1,3,4},{2},{5,6,7}} => 4
[[[.,.],[.,.]],[[[.,.],.],.]] => [5,6,7,3,1,2,4] => [4,2,1,3,7,6,5] => {{1,3,4},{2},{5,7},{6}} => 4
[[[.,[.,.]],.],[.,[.,[.,.]]]] => [7,6,5,2,1,3,4] => [4,3,1,2,5,6,7] => {{1,2,3,4},{5},{6},{7}} => 4
[[[.,[.,.]],.],[.,[[.,.],.]]] => [6,7,5,2,1,3,4] => [4,3,1,2,5,7,6] => {{1,2,3,4},{5},{6,7}} => 4
[[[.,[.,.]],.],[[.,.],[.,.]]] => [7,5,6,2,1,3,4] => [4,3,1,2,6,5,7] => {{1,2,3,4},{5,6},{7}} => 4
[[[.,[.,.]],.],[[.,[.,.]],.]] => [6,5,7,2,1,3,4] => [4,3,1,2,7,5,6] => {{1,2,3,4},{5,6,7}} => 4
[[[.,[.,.]],.],[[[.,.],.],.]] => [5,6,7,2,1,3,4] => [4,3,1,2,7,6,5] => {{1,2,3,4},{5,7},{6}} => 4
[[[[.,.],.],.],[.,[.,[.,.]]]] => [7,6,5,1,2,3,4] => [4,3,2,1,5,6,7] => {{1,4},{2,3},{5},{6},{7}} => 4
[[[[.,.],.],.],[.,[[.,.],.]]] => [6,7,5,1,2,3,4] => [4,3,2,1,5,7,6] => {{1,4},{2,3},{5},{6,7}} => 4
[[[[.,.],.],.],[[.,.],[.,.]]] => [7,5,6,1,2,3,4] => [4,3,2,1,6,5,7] => {{1,4},{2,3},{5,6},{7}} => 4
[[[[.,.],.],.],[[.,[.,.]],.]] => [6,5,7,1,2,3,4] => [4,3,2,1,7,5,6] => {{1,4},{2,3},{5,6,7}} => 4
[[[[.,.],.],.],[[[.,.],.],.]] => [5,6,7,1,2,3,4] => [4,3,2,1,7,6,5] => {{1,4},{2,3},{5,7},{6}} => 4
[[.,[.,[.,[.,.]]]],[.,[.,.]]] => [7,6,4,3,2,1,5] => [5,1,2,3,4,6,7] => {{1,2,3,4,5},{6},{7}} => 5
[[.,[.,[.,[.,.]]]],[[.,.],.]] => [6,7,4,3,2,1,5] => [5,1,2,3,4,7,6] => {{1,2,3,4,5},{6,7}} => 5
[[.,[.,[[.,.],.]]],[.,[.,.]]] => [7,6,3,4,2,1,5] => [5,1,2,4,3,6,7] => {{1,2,3,5},{4},{6},{7}} => 5
[[.,[.,[[.,.],.]]],[[.,.],.]] => [6,7,3,4,2,1,5] => [5,1,2,4,3,7,6] => {{1,2,3,5},{4},{6,7}} => 5
[[.,[[.,.],[.,.]]],[.,[.,.]]] => [7,6,4,2,3,1,5] => [5,1,3,2,4,6,7] => {{1,2,4,5},{3},{6},{7}} => 5
[[.,[[.,.],[.,.]]],[[.,.],.]] => [6,7,4,2,3,1,5] => [5,1,3,2,4,7,6] => {{1,2,4,5},{3},{6,7}} => 5
[[.,[[.,[.,.]],.]],[.,[.,.]]] => [7,6,3,2,4,1,5] => [5,1,4,2,3,6,7] => {{1,2,3,4,5},{6},{7}} => 5
[[.,[[.,[.,.]],.]],[[.,.],.]] => [6,7,3,2,4,1,5] => [5,1,4,2,3,7,6] => {{1,2,3,4,5},{6,7}} => 5
[[.,[[[.,.],.],.]],[.,[.,.]]] => [7,6,2,3,4,1,5] => [5,1,4,3,2,6,7] => {{1,2,5},{3,4},{6},{7}} => 5
[[.,[[[.,.],.],.]],[[.,.],.]] => [6,7,2,3,4,1,5] => [5,1,4,3,2,7,6] => {{1,2,5},{3,4},{6,7}} => 5
[[[.,.],[.,[.,.]]],[.,[.,.]]] => [7,6,4,3,1,2,5] => [5,2,1,3,4,6,7] => {{1,3,4,5},{2},{6},{7}} => 5
[[[.,.],[.,[.,.]]],[[.,.],.]] => [6,7,4,3,1,2,5] => [5,2,1,3,4,7,6] => {{1,3,4,5},{2},{6,7}} => 5
[[[.,.],[[.,.],.]],[.,[.,.]]] => [7,6,3,4,1,2,5] => [5,2,1,4,3,6,7] => {{1,3,5},{2},{4},{6},{7}} => 5
[[[.,.],[[.,.],.]],[[.,.],.]] => [6,7,3,4,1,2,5] => [5,2,1,4,3,7,6] => {{1,3,5},{2},{4},{6,7}} => 5
[[[.,[.,.]],[.,.]],[.,[.,.]]] => [7,6,4,2,1,3,5] => [5,3,1,2,4,6,7] => {{1,2,3,4,5},{6},{7}} => 5
[[[.,[.,.]],[.,.]],[[.,.],.]] => [6,7,4,2,1,3,5] => [5,3,1,2,4,7,6] => {{1,2,3,4,5},{6,7}} => 5
[[[[.,.],.],[.,.]],[.,[.,.]]] => [7,6,4,1,2,3,5] => [5,3,2,1,4,6,7] => {{1,4,5},{2,3},{6},{7}} => 5
[[[[.,.],.],[.,.]],[[.,.],.]] => [6,7,4,1,2,3,5] => [5,3,2,1,4,7,6] => {{1,4,5},{2,3},{6,7}} => 5
[[[.,[.,[.,.]]],.],[.,[.,.]]] => [7,6,3,2,1,4,5] => [5,4,1,2,3,6,7] => {{1,3,5},{2,4},{6},{7}} => 5
[[[.,[.,[.,.]]],.],[[.,.],.]] => [6,7,3,2,1,4,5] => [5,4,1,2,3,7,6] => {{1,3,5},{2,4},{6,7}} => 5
[[[.,[[.,.],.]],.],[.,[.,.]]] => [7,6,2,3,1,4,5] => [5,4,1,3,2,6,7] => {{1,2,3,4,5},{6},{7}} => 5
[[[.,[[.,.],.]],.],[[.,.],.]] => [6,7,2,3,1,4,5] => [5,4,1,3,2,7,6] => {{1,2,3,4,5},{6,7}} => 5
[[[[.,.],[.,.]],.],[.,[.,.]]] => [7,6,3,1,2,4,5] => [5,4,2,1,3,6,7] => {{1,2,3,4,5},{6},{7}} => 5
[[[[.,.],[.,.]],.],[[.,.],.]] => [6,7,3,1,2,4,5] => [5,4,2,1,3,7,6] => {{1,2,3,4,5},{6,7}} => 5
[[[[.,[.,.]],.],.],[.,[.,.]]] => [7,6,2,1,3,4,5] => [5,4,3,1,2,6,7] => {{1,2,4,5},{3},{6},{7}} => 5
[[[[.,[.,.]],.],.],[[.,.],.]] => [6,7,2,1,3,4,5] => [5,4,3,1,2,7,6] => {{1,2,4,5},{3},{6,7}} => 5
[[[[[.,.],.],.],.],[.,[.,.]]] => [7,6,1,2,3,4,5] => [5,4,3,2,1,6,7] => {{1,5},{2,4},{3},{6},{7}} => 5
[[[[[.,.],.],.],.],[[.,.],.]] => [6,7,1,2,3,4,5] => [5,4,3,2,1,7,6] => {{1,5},{2,4},{3},{6,7}} => 5
[[.,[.,[.,[.,[.,.]]]]],[.,.]] => [7,5,4,3,2,1,6] => [6,1,2,3,4,5,7] => {{1,2,3,4,5,6},{7}} => 6
[[.,[.,[.,[[.,.],.]]]],[.,.]] => [7,4,5,3,2,1,6] => [6,1,2,3,5,4,7] => {{1,2,3,4,6},{5},{7}} => 6
[[.,[.,[[.,.],[.,.]]]],[.,.]] => [7,5,3,4,2,1,6] => [6,1,2,4,3,5,7] => {{1,2,3,5,6},{4},{7}} => 6
[[.,[.,[[.,[.,.]],.]]],[.,.]] => [7,4,3,5,2,1,6] => [6,1,2,5,3,4,7] => {{1,2,3,4,5,6},{7}} => 6
[[.,[.,[[[.,.],.],.]]],[.,.]] => [7,3,4,5,2,1,6] => [6,1,2,5,4,3,7] => {{1,2,3,6},{4,5},{7}} => 6
[[.,[[.,.],[.,[.,.]]]],[.,.]] => [7,5,4,2,3,1,6] => [6,1,3,2,4,5,7] => {{1,2,4,5,6},{3},{7}} => 6
[[.,[[.,.],[[.,.],.]]],[.,.]] => [7,4,5,2,3,1,6] => [6,1,3,2,5,4,7] => {{1,2,4,6},{3},{5},{7}} => 6
[[.,[[.,[.,.]],[.,.]]],[.,.]] => [7,5,3,2,4,1,6] => [6,1,4,2,3,5,7] => {{1,2,3,4,5,6},{7}} => 6
[[.,[[[.,.],.],[.,.]]],[.,.]] => [7,5,2,3,4,1,6] => [6,1,4,3,2,5,7] => {{1,2,5,6},{3,4},{7}} => 6
[[.,[[.,[.,[.,.]]],.]],[.,.]] => [7,4,3,2,5,1,6] => [6,1,5,2,3,4,7] => {{1,2,4,6},{3,5},{7}} => 6
[[.,[[.,[[.,.],.]],.]],[.,.]] => [7,3,4,2,5,1,6] => [6,1,5,2,4,3,7] => {{1,2,3,4,5,6},{7}} => 6
[[.,[[[.,.],[.,.]],.]],[.,.]] => [7,4,2,3,5,1,6] => [6,1,5,3,2,4,7] => {{1,2,3,4,5,6},{7}} => 6
[[.,[[[.,[.,.]],.],.]],[.,.]] => [7,3,2,4,5,1,6] => [6,1,5,4,2,3,7] => {{1,2,3,5,6},{4},{7}} => 6
[[.,[[[[.,.],.],.],.]],[.,.]] => [7,2,3,4,5,1,6] => [6,1,5,4,3,2,7] => {{1,2,6},{3,5},{4},{7}} => 6
[[[.,.],[.,[.,[.,.]]]],[.,.]] => [7,5,4,3,1,2,6] => [6,2,1,3,4,5,7] => {{1,3,4,5,6},{2},{7}} => 6
[[[.,.],[.,[[.,.],.]]],[.,.]] => [7,4,5,3,1,2,6] => [6,2,1,3,5,4,7] => {{1,3,4,6},{2},{5},{7}} => 6
[[[.,.],[[.,.],[.,.]]],[.,.]] => [7,5,3,4,1,2,6] => [6,2,1,4,3,5,7] => {{1,3,5,6},{2},{4},{7}} => 6
[[[.,.],[[.,[.,.]],.]],[.,.]] => [7,4,3,5,1,2,6] => [6,2,1,5,3,4,7] => {{1,3,4,5,6},{2},{7}} => 6
[[[.,.],[[[.,.],.],.]],[.,.]] => [7,3,4,5,1,2,6] => [6,2,1,5,4,3,7] => {{1,3,6},{2},{4,5},{7}} => 6
[[[.,[.,.]],[.,[.,.]]],[.,.]] => [7,5,4,2,1,3,6] => [6,3,1,2,4,5,7] => {{1,2,3,4,5,6},{7}} => 6
[[[.,[.,.]],[[.,.],.]],[.,.]] => [7,4,5,2,1,3,6] => [6,3,1,2,5,4,7] => {{1,2,3,4,6},{5},{7}} => 6
[[[[.,.],.],[.,[.,.]]],[.,.]] => [7,5,4,1,2,3,6] => [6,3,2,1,4,5,7] => {{1,4,5,6},{2,3},{7}} => 6
[[[[.,.],.],[[.,.],.]],[.,.]] => [7,4,5,1,2,3,6] => [6,3,2,1,5,4,7] => {{1,4,6},{2,3},{5},{7}} => 6
[[[.,[.,[.,.]]],[.,.]],[.,.]] => [7,5,3,2,1,4,6] => [6,4,1,2,3,5,7] => {{1,3,5,6},{2,4},{7}} => 6
[[[.,[[.,.],.]],[.,.]],[.,.]] => [7,5,2,3,1,4,6] => [6,4,1,3,2,5,7] => {{1,2,3,4,5,6},{7}} => 6
[[[[.,.],[.,.]],[.,.]],[.,.]] => [7,5,3,1,2,4,6] => [6,4,2,1,3,5,7] => {{1,2,3,4,5,6},{7}} => 6
[[[[.,[.,.]],.],[.,.]],[.,.]] => [7,5,2,1,3,4,6] => [6,4,3,1,2,5,7] => {{1,2,4,5,6},{3},{7}} => 6
[[[[[.,.],.],.],[.,.]],[.,.]] => [7,5,1,2,3,4,6] => [6,4,3,2,1,5,7] => {{1,5,6},{2,4},{3},{7}} => 6
[[[.,[.,[.,[.,.]]]],.],[.,.]] => [7,4,3,2,1,5,6] => [6,5,1,2,3,4,7] => {{1,2,3,4,5,6},{7}} => 6
[[[.,[.,[[.,.],.]]],.],[.,.]] => [7,3,4,2,1,5,6] => [6,5,1,2,4,3,7] => {{1,3,6},{2,4,5},{7}} => 6
[[[.,[[.,.],[.,.]]],.],[.,.]] => [7,4,2,3,1,5,6] => [6,5,1,3,2,4,7] => {{1,3,4,6},{2,5},{7}} => 6
[[[.,[[.,[.,.]],.]],.],[.,.]] => [7,3,2,4,1,5,6] => [6,5,1,4,2,3,7] => {{1,3,6},{2,5},{4},{7}} => 6
[[[.,[[[.,.],.],.]],.],[.,.]] => [7,2,3,4,1,5,6] => [6,5,1,4,3,2,7] => {{1,2,3,5,6},{4},{7}} => 6
[[[[.,.],[.,[.,.]]],.],[.,.]] => [7,4,3,1,2,5,6] => [6,5,2,1,3,4,7] => {{1,4,6},{2,3,5},{7}} => 6
[[[[.,.],[[.,.],.]],.],[.,.]] => [7,3,4,1,2,5,6] => [6,5,2,1,4,3,7] => {{1,2,3,4,5,6},{7}} => 6
[[[[.,[.,.]],[.,.]],.],[.,.]] => [7,4,2,1,3,5,6] => [6,5,3,1,2,4,7] => {{1,4,6},{2,5},{3},{7}} => 6
[[[[[.,.],.],[.,.]],.],[.,.]] => [7,4,1,2,3,5,6] => [6,5,3,2,1,4,7] => {{1,2,4,5,6},{3},{7}} => 6
[[[[.,[.,[.,.]]],.],.],[.,.]] => [7,3,2,1,4,5,6] => [6,5,4,1,2,3,7] => {{1,3,4,6},{2,5},{7}} => 6
[[[[.,[[.,.],.]],.],.],[.,.]] => [7,2,3,1,4,5,6] => [6,5,4,1,3,2,7] => {{1,2,3,4,5,6},{7}} => 6
[[[[[.,.],[.,.]],.],.],[.,.]] => [7,3,1,2,4,5,6] => [6,5,4,2,1,3,7] => {{1,2,3,4,5,6},{7}} => 6
[[[[[.,[.,.]],.],.],.],[.,.]] => [7,2,1,3,4,5,6] => [6,5,4,3,1,2,7] => {{1,2,5,6},{3,4},{7}} => 6
[[[[[[.,.],.],.],.],.],[.,.]] => [7,1,2,3,4,5,6] => [6,5,4,3,2,1,7] => {{1,6},{2,5},{3,4},{7}} => 6
[[.,[.,[.,[.,[.,[.,.]]]]]],.] => [6,5,4,3,2,1,7] => [7,1,2,3,4,5,6] => {{1,2,3,4,5,6,7}} => 7
[[.,[.,[.,[.,[[.,.],.]]]]],.] => [5,6,4,3,2,1,7] => [7,1,2,3,4,6,5] => {{1,2,3,4,5,7},{6}} => 7
[[.,[.,[.,[[.,.],[.,.]]]]],.] => [6,4,5,3,2,1,7] => [7,1,2,3,5,4,6] => {{1,2,3,4,6,7},{5}} => 7
[[.,[.,[.,[[.,[.,.]],.]]]],.] => [5,4,6,3,2,1,7] => [7,1,2,3,6,4,5] => {{1,2,3,4,5,6,7}} => 7
[[.,[.,[.,[[[.,.],.],.]]]],.] => [4,5,6,3,2,1,7] => [7,1,2,3,6,5,4] => {{1,2,3,4,7},{5,6}} => 7
[[.,[.,[[.,.],[.,[.,.]]]]],.] => [6,5,3,4,2,1,7] => [7,1,2,4,3,5,6] => {{1,2,3,5,6,7},{4}} => 7
[[.,[.,[[.,.],[[.,.],.]]]],.] => [5,6,3,4,2,1,7] => [7,1,2,4,3,6,5] => {{1,2,3,5,7},{4},{6}} => 7
[[.,[.,[[.,[.,.]],[.,.]]]],.] => [6,4,3,5,2,1,7] => [7,1,2,5,3,4,6] => {{1,2,3,4,5,6,7}} => 7
[[.,[.,[[[.,.],.],[.,.]]]],.] => [6,3,4,5,2,1,7] => [7,1,2,5,4,3,6] => {{1,2,3,6,7},{4,5}} => 7
[[.,[.,[[.,[.,[.,.]]],.]]],.] => [5,4,3,6,2,1,7] => [7,1,2,6,3,4,5] => {{1,2,3,5,7},{4,6}} => 7
[[.,[.,[[.,[[.,.],.]],.]]],.] => [4,5,3,6,2,1,7] => [7,1,2,6,3,5,4] => {{1,2,3,4,5,6,7}} => 7
[[.,[.,[[[.,.],[.,.]],.]]],.] => [5,3,4,6,2,1,7] => [7,1,2,6,4,3,5] => {{1,2,3,4,5,6,7}} => 7
[[.,[.,[[[.,[.,.]],.],.]]],.] => [4,3,5,6,2,1,7] => [7,1,2,6,5,3,4] => {{1,2,3,4,6,7},{5}} => 7
[[.,[.,[[[[.,.],.],.],.]]],.] => [3,4,5,6,2,1,7] => [7,1,2,6,5,4,3] => {{1,2,3,7},{4,6},{5}} => 7
[[.,[[.,.],[.,[.,[.,.]]]]],.] => [6,5,4,2,3,1,7] => [7,1,3,2,4,5,6] => {{1,2,4,5,6,7},{3}} => 7
[[.,[[.,.],[.,[[.,.],.]]]],.] => [5,6,4,2,3,1,7] => [7,1,3,2,4,6,5] => {{1,2,4,5,7},{3},{6}} => 7
[[.,[[.,.],[[.,.],[.,.]]]],.] => [6,4,5,2,3,1,7] => [7,1,3,2,5,4,6] => {{1,2,4,6,7},{3},{5}} => 7
[[.,[[.,.],[[.,[.,.]],.]]],.] => [5,4,6,2,3,1,7] => [7,1,3,2,6,4,5] => {{1,2,4,5,6,7},{3}} => 7
[[.,[[.,.],[[[.,.],.],.]]],.] => [4,5,6,2,3,1,7] => [7,1,3,2,6,5,4] => {{1,2,4,7},{3},{5,6}} => 7
[[.,[[.,[.,.]],[.,[.,.]]]],.] => [6,5,3,2,4,1,7] => [7,1,4,2,3,5,6] => {{1,2,3,4,5,6,7}} => 7
[[.,[[.,[.,.]],[[.,.],.]]],.] => [5,6,3,2,4,1,7] => [7,1,4,2,3,6,5] => {{1,2,3,4,5,7},{6}} => 7
[[.,[[[.,.],.],[.,[.,.]]]],.] => [6,5,2,3,4,1,7] => [7,1,4,3,2,5,6] => {{1,2,5,6,7},{3,4}} => 7
[[.,[[[.,.],.],[[.,.],.]]],.] => [5,6,2,3,4,1,7] => [7,1,4,3,2,6,5] => {{1,2,5,7},{3,4},{6}} => 7
[[.,[[.,[.,[.,.]]],[.,.]]],.] => [6,4,3,2,5,1,7] => [7,1,5,2,3,4,6] => {{1,2,4,6,7},{3,5}} => 7
[[.,[[.,[[.,.],.]],[.,.]]],.] => [6,3,4,2,5,1,7] => [7,1,5,2,4,3,6] => {{1,2,3,4,5,6,7}} => 7
[[.,[[[.,.],[.,.]],[.,.]]],.] => [6,4,2,3,5,1,7] => [7,1,5,3,2,4,6] => {{1,2,3,4,5,6,7}} => 7
[[.,[[[.,[.,.]],.],[.,.]]],.] => [6,3,2,4,5,1,7] => [7,1,5,4,2,3,6] => {{1,2,3,5,6,7},{4}} => 7
[[.,[[[[.,.],.],.],[.,.]]],.] => [6,2,3,4,5,1,7] => [7,1,5,4,3,2,6] => {{1,2,6,7},{3,5},{4}} => 7
[[.,[[.,[.,[.,[.,.]]]],.]],.] => [5,4,3,2,6,1,7] => [7,1,6,2,3,4,5] => {{1,2,3,4,5,6,7}} => 7
[[.,[[.,[.,[[.,.],.]]],.]],.] => [4,5,3,2,6,1,7] => [7,1,6,2,3,5,4] => {{1,2,4,7},{3,5,6}} => 7
[[.,[[.,[[.,.],[.,.]]],.]],.] => [5,3,4,2,6,1,7] => [7,1,6,2,4,3,5] => {{1,2,4,5,7},{3,6}} => 7
[[.,[[.,[[.,[.,.]],.]],.]],.] => [4,3,5,2,6,1,7] => [7,1,6,2,5,3,4] => {{1,2,4,7},{3,6},{5}} => 7
[[.,[[.,[[[.,.],.],.]],.]],.] => [3,4,5,2,6,1,7] => [7,1,6,2,5,4,3] => {{1,2,3,4,6,7},{5}} => 7
[[.,[[[.,.],[.,[.,.]]],.]],.] => [5,4,2,3,6,1,7] => [7,1,6,3,2,4,5] => {{1,2,5,7},{3,4,6}} => 7
[[.,[[[.,.],[[.,.],.]],.]],.] => [4,5,2,3,6,1,7] => [7,1,6,3,2,5,4] => {{1,2,3,4,5,6,7}} => 7
[[.,[[[.,[.,.]],[.,.]],.]],.] => [5,3,2,4,6,1,7] => [7,1,6,4,2,3,5] => {{1,2,5,7},{3,6},{4}} => 7
[[.,[[[[.,.],.],[.,.]],.]],.] => [5,2,3,4,6,1,7] => [7,1,6,4,3,2,5] => {{1,2,3,5,6,7},{4}} => 7
[[.,[[[.,[.,[.,.]]],.],.]],.] => [4,3,2,5,6,1,7] => [7,1,6,5,2,3,4] => {{1,2,4,5,7},{3,6}} => 7
[[.,[[[.,[[.,.],.]],.],.]],.] => [3,4,2,5,6,1,7] => [7,1,6,5,2,4,3] => {{1,2,3,4,5,6,7}} => 7
[[.,[[[[.,.],[.,.]],.],.]],.] => [4,2,3,5,6,1,7] => [7,1,6,5,3,2,4] => {{1,2,3,4,5,6,7}} => 7
[[.,[[[[.,[.,.]],.],.],.]],.] => [3,2,4,5,6,1,7] => [7,1,6,5,4,2,3] => {{1,2,3,6,7},{4,5}} => 7
[[.,[[[[[.,.],.],.],.],.]],.] => [2,3,4,5,6,1,7] => [7,1,6,5,4,3,2] => {{1,2,7},{3,6},{4,5}} => 7
[[[.,.],[.,[.,[.,[.,.]]]]],.] => [6,5,4,3,1,2,7] => [7,2,1,3,4,5,6] => {{1,3,4,5,6,7},{2}} => 7
[[[.,.],[.,[.,[[.,.],.]]]],.] => [5,6,4,3,1,2,7] => [7,2,1,3,4,6,5] => {{1,3,4,5,7},{2},{6}} => 7
[[[.,.],[.,[[.,.],[.,.]]]],.] => [6,4,5,3,1,2,7] => [7,2,1,3,5,4,6] => {{1,3,4,6,7},{2},{5}} => 7
[[[.,.],[.,[[.,[.,.]],.]]],.] => [5,4,6,3,1,2,7] => [7,2,1,3,6,4,5] => {{1,3,4,5,6,7},{2}} => 7
[[[.,.],[.,[[[.,.],.],.]]],.] => [4,5,6,3,1,2,7] => [7,2,1,3,6,5,4] => {{1,3,4,7},{2},{5,6}} => 7
[[[.,.],[[.,.],[.,[.,.]]]],.] => [6,5,3,4,1,2,7] => [7,2,1,4,3,5,6] => {{1,3,5,6,7},{2},{4}} => 7
[[[.,.],[[.,.],[[.,.],.]]],.] => [5,6,3,4,1,2,7] => [7,2,1,4,3,6,5] => {{1,3,5,7},{2},{4},{6}} => 7
[[[.,.],[[.,[.,.]],[.,.]]],.] => [6,4,3,5,1,2,7] => [7,2,1,5,3,4,6] => {{1,3,4,5,6,7},{2}} => 7
[[[.,.],[[[.,.],.],[.,.]]],.] => [6,3,4,5,1,2,7] => [7,2,1,5,4,3,6] => {{1,3,6,7},{2},{4,5}} => 7
[[[.,.],[[.,[.,[.,.]]],.]],.] => [5,4,3,6,1,2,7] => [7,2,1,6,3,4,5] => {{1,3,5,7},{2},{4,6}} => 7
[[[.,.],[[.,[[.,.],.]],.]],.] => [4,5,3,6,1,2,7] => [7,2,1,6,3,5,4] => {{1,3,4,5,6,7},{2}} => 7
[[[.,.],[[[.,.],[.,.]],.]],.] => [5,3,4,6,1,2,7] => [7,2,1,6,4,3,5] => {{1,3,4,5,6,7},{2}} => 7
[[[.,.],[[[.,[.,.]],.],.]],.] => [4,3,5,6,1,2,7] => [7,2,1,6,5,3,4] => {{1,3,4,6,7},{2},{5}} => 7
[[[.,.],[[[[.,.],.],.],.]],.] => [3,4,5,6,1,2,7] => [7,2,1,6,5,4,3] => {{1,3,7},{2},{4,6},{5}} => 7
[[[.,[.,.]],[.,[.,[.,.]]]],.] => [6,5,4,2,1,3,7] => [7,3,1,2,4,5,6] => {{1,2,3,4,5,6,7}} => 7
[[[.,[.,.]],[.,[[.,.],.]]],.] => [5,6,4,2,1,3,7] => [7,3,1,2,4,6,5] => {{1,2,3,4,5,7},{6}} => 7
[[[.,[.,.]],[[.,.],[.,.]]],.] => [6,4,5,2,1,3,7] => [7,3,1,2,5,4,6] => {{1,2,3,4,6,7},{5}} => 7
[[[.,[.,.]],[[.,[.,.]],.]],.] => [5,4,6,2,1,3,7] => [7,3,1,2,6,4,5] => {{1,2,3,4,5,6,7}} => 7
[[[.,[.,.]],[[[.,.],.],.]],.] => [4,5,6,2,1,3,7] => [7,3,1,2,6,5,4] => {{1,2,3,4,7},{5,6}} => 7
[[[[.,.],.],[.,[.,[.,.]]]],.] => [6,5,4,1,2,3,7] => [7,3,2,1,4,5,6] => {{1,4,5,6,7},{2,3}} => 7
[[[[.,.],.],[.,[[.,.],.]]],.] => [5,6,4,1,2,3,7] => [7,3,2,1,4,6,5] => {{1,4,5,7},{2,3},{6}} => 7
[[[[.,.],.],[[.,.],[.,.]]],.] => [6,4,5,1,2,3,7] => [7,3,2,1,5,4,6] => {{1,4,6,7},{2,3},{5}} => 7
[[[[.,.],.],[[.,[.,.]],.]],.] => [5,4,6,1,2,3,7] => [7,3,2,1,6,4,5] => {{1,4,5,6,7},{2,3}} => 7
[[[[.,.],.],[[[.,.],.],.]],.] => [4,5,6,1,2,3,7] => [7,3,2,1,6,5,4] => {{1,4,7},{2,3},{5,6}} => 7
[[[.,[.,[.,.]]],[.,[.,.]]],.] => [6,5,3,2,1,4,7] => [7,4,1,2,3,5,6] => {{1,3,5,6,7},{2,4}} => 7
[[[.,[.,[.,.]]],[[.,.],.]],.] => [5,6,3,2,1,4,7] => [7,4,1,2,3,6,5] => {{1,3,5,7},{2,4},{6}} => 7
[[[.,[[.,.],.]],[.,[.,.]]],.] => [6,5,2,3,1,4,7] => [7,4,1,3,2,5,6] => {{1,2,3,4,5,6,7}} => 7
[[[.,[[.,.],.]],[[.,.],.]],.] => [5,6,2,3,1,4,7] => [7,4,1,3,2,6,5] => {{1,2,3,4,5,7},{6}} => 7
[[[[.,.],[.,.]],[.,[.,.]]],.] => [6,5,3,1,2,4,7] => [7,4,2,1,3,5,6] => {{1,2,3,4,5,6,7}} => 7
[[[[.,.],[.,.]],[[.,.],.]],.] => [5,6,3,1,2,4,7] => [7,4,2,1,3,6,5] => {{1,2,3,4,5,7},{6}} => 7
[[[[.,[.,.]],.],[.,[.,.]]],.] => [6,5,2,1,3,4,7] => [7,4,3,1,2,5,6] => {{1,2,4,5,6,7},{3}} => 7
[[[[.,[.,.]],.],[[.,.],.]],.] => [5,6,2,1,3,4,7] => [7,4,3,1,2,6,5] => {{1,2,4,5,7},{3},{6}} => 7
[[[[[.,.],.],.],[.,[.,.]]],.] => [6,5,1,2,3,4,7] => [7,4,3,2,1,5,6] => {{1,5,6,7},{2,4},{3}} => 7
[[[[[.,.],.],.],[[.,.],.]],.] => [5,6,1,2,3,4,7] => [7,4,3,2,1,6,5] => {{1,5,7},{2,4},{3},{6}} => 7
[[[.,[.,[.,[.,.]]]],[.,.]],.] => [6,4,3,2,1,5,7] => [7,5,1,2,3,4,6] => {{1,2,3,4,5,6,7}} => 7
[[[.,[.,[[.,.],.]]],[.,.]],.] => [6,3,4,2,1,5,7] => [7,5,1,2,4,3,6] => {{1,3,6,7},{2,4,5}} => 7
[[[.,[[.,.],[.,.]]],[.,.]],.] => [6,4,2,3,1,5,7] => [7,5,1,3,2,4,6] => {{1,3,4,6,7},{2,5}} => 7
[[[.,[[.,[.,.]],.]],[.,.]],.] => [6,3,2,4,1,5,7] => [7,5,1,4,2,3,6] => {{1,3,6,7},{2,5},{4}} => 7
[[[.,[[[.,.],.],.]],[.,.]],.] => [6,2,3,4,1,5,7] => [7,5,1,4,3,2,6] => {{1,2,3,5,6,7},{4}} => 7
[[[[.,.],[.,[.,.]]],[.,.]],.] => [6,4,3,1,2,5,7] => [7,5,2,1,3,4,6] => {{1,4,6,7},{2,3,5}} => 7
[[[[.,.],[[.,.],.]],[.,.]],.] => [6,3,4,1,2,5,7] => [7,5,2,1,4,3,6] => {{1,2,3,4,5,6,7}} => 7
[[[[.,[.,.]],[.,.]],[.,.]],.] => [6,4,2,1,3,5,7] => [7,5,3,1,2,4,6] => {{1,4,6,7},{2,5},{3}} => 7
[[[[[.,.],.],[.,.]],[.,.]],.] => [6,4,1,2,3,5,7] => [7,5,3,2,1,4,6] => {{1,2,4,5,6,7},{3}} => 7
[[[[.,[.,[.,.]]],.],[.,.]],.] => [6,3,2,1,4,5,7] => [7,5,4,1,2,3,6] => {{1,3,4,6,7},{2,5}} => 7
[[[[.,[[.,.],.]],.],[.,.]],.] => [6,2,3,1,4,5,7] => [7,5,4,1,3,2,6] => {{1,2,3,4,5,6,7}} => 7
[[[[[.,.],[.,.]],.],[.,.]],.] => [6,3,1,2,4,5,7] => [7,5,4,2,1,3,6] => {{1,2,3,4,5,6,7}} => 7
[[[[[.,[.,.]],.],.],[.,.]],.] => [6,2,1,3,4,5,7] => [7,5,4,3,1,2,6] => {{1,2,5,6,7},{3,4}} => 7
[[[[[[.,.],.],.],.],[.,.]],.] => [6,1,2,3,4,5,7] => [7,5,4,3,2,1,6] => {{1,6,7},{2,5},{3,4}} => 7
[[[.,[.,[.,[.,[.,.]]]]],.],.] => [5,4,3,2,1,6,7] => [7,6,1,2,3,4,5] => {{1,3,5,7},{2,4,6}} => 7
[[[.,[.,[.,[[.,.],.]]]],.],.] => [4,5,3,2,1,6,7] => [7,6,1,2,3,5,4] => {{1,2,3,4,5,6,7}} => 7
[[[.,[.,[[.,.],[.,.]]]],.],.] => [5,3,4,2,1,6,7] => [7,6,1,2,4,3,5] => {{1,2,3,4,5,6,7}} => 7
[[[.,[.,[[.,[.,.]],.]]],.],.] => [4,3,5,2,1,6,7] => [7,6,1,2,5,3,4] => {{1,2,3,4,6,7},{5}} => 7
[[[.,[.,[[[.,.],.],.]]],.],.] => [3,4,5,2,1,6,7] => [7,6,1,2,5,4,3] => {{1,3,7},{2,4,6},{5}} => 7
[[[.,[[.,.],[.,[.,.]]]],.],.] => [5,4,2,3,1,6,7] => [7,6,1,3,2,4,5] => {{1,2,3,4,5,6,7}} => 7
[[[.,[[.,.],[[.,.],.]]],.],.] => [4,5,2,3,1,6,7] => [7,6,1,3,2,5,4] => {{1,3,4,7},{2,5,6}} => 7
[[[.,[[.,[.,.]],[.,.]]],.],.] => [5,3,2,4,1,6,7] => [7,6,1,4,2,3,5] => {{1,2,3,5,6,7},{4}} => 7
[[[.,[[[.,.],.],[.,.]]],.],.] => [5,2,3,4,1,6,7] => [7,6,1,4,3,2,5] => {{1,3,5,7},{2,6},{4}} => 7
[[[.,[[.,[.,[.,.]]],.]],.],.] => [4,3,2,5,1,6,7] => [7,6,1,5,2,3,4] => {{1,2,3,4,5,6,7}} => 7
[[[.,[[.,[[.,.],.]],.]],.],.] => [3,4,2,5,1,6,7] => [7,6,1,5,2,4,3] => {{1,3,7},{2,4,5,6}} => 7
[[[.,[[[.,.],[.,.]],.]],.],.] => [4,2,3,5,1,6,7] => [7,6,1,5,3,2,4] => {{1,3,4,5,7},{2,6}} => 7
[[[.,[[[.,[.,.]],.],.]],.],.] => [3,2,4,5,1,6,7] => [7,6,1,5,4,2,3] => {{1,3,7},{2,6},{4,5}} => 7
[[[.,[[[[.,.],.],.],.]],.],.] => [2,3,4,5,1,6,7] => [7,6,1,5,4,3,2] => {{1,2,3,6,7},{4,5}} => 7
[[[[.,.],[.,[.,[.,.]]]],.],.] => [5,4,3,1,2,6,7] => [7,6,2,1,3,4,5] => {{1,2,3,4,5,6,7}} => 7
[[[[.,.],[.,[[.,.],.]]],.],.] => [4,5,3,1,2,6,7] => [7,6,2,1,3,5,4] => {{1,4,7},{2,3,5,6}} => 7
[[[[.,.],[[.,.],[.,.]]],.],.] => [5,3,4,1,2,6,7] => [7,6,2,1,4,3,5] => {{1,4,5,7},{2,3,6}} => 7
[[[[.,.],[[.,[.,.]],.]],.],.] => [4,3,5,1,2,6,7] => [7,6,2,1,5,3,4] => {{1,4,7},{2,3,6},{5}} => 7
[[[[.,.],[[[.,.],.],.]],.],.] => [3,4,5,1,2,6,7] => [7,6,2,1,5,4,3] => {{1,2,3,4,6,7},{5}} => 7
[[[[.,[.,.]],[.,[.,.]]],.],.] => [5,4,2,1,3,6,7] => [7,6,3,1,2,4,5] => {{1,2,4,5,6,7},{3}} => 7
[[[[.,[.,.]],[[.,.],.]],.],.] => [4,5,2,1,3,6,7] => [7,6,3,1,2,5,4] => {{1,4,7},{2,5,6},{3}} => 7
[[[[[.,.],.],[.,[.,.]]],.],.] => [5,4,1,2,3,6,7] => [7,6,3,2,1,4,5] => {{1,5,7},{2,4,6},{3}} => 7
[[[[[.,.],.],[[.,.],.]],.],.] => [4,5,1,2,3,6,7] => [7,6,3,2,1,5,4] => {{1,2,4,5,6,7},{3}} => 7
[[[[.,[.,[.,.]]],[.,.]],.],.] => [5,3,2,1,4,6,7] => [7,6,4,1,2,3,5] => {{1,2,3,4,5,6,7}} => 7
[[[[.,[[.,.],.]],[.,.]],.],.] => [5,2,3,1,4,6,7] => [7,6,4,1,3,2,5] => {{1,3,4,5,7},{2,6}} => 7
[[[[[.,.],[.,.]],[.,.]],.],.] => [5,3,1,2,4,6,7] => [7,6,4,2,1,3,5] => {{1,5,7},{2,3,4,6}} => 7
[[[[[.,[.,.]],.],[.,.]],.],.] => [5,2,1,3,4,6,7] => [7,6,4,3,1,2,5] => {{1,5,7},{2,6},{3,4}} => 7
[[[[[[.,.],.],.],[.,.]],.],.] => [5,1,2,3,4,6,7] => [7,6,4,3,2,1,5] => {{1,2,5,6,7},{3,4}} => 7
[[[[.,[.,[.,[.,.]]]],.],.],.] => [4,3,2,1,5,6,7] => [7,6,5,1,2,3,4] => {{1,4,7},{2,3,5,6}} => 7
[[[[.,[.,[[.,.],.]]],.],.],.] => [3,4,2,1,5,6,7] => [7,6,5,1,2,4,3] => {{1,2,3,4,5,6,7}} => 7
[[[[.,[[.,.],[.,.]]],.],.],.] => [4,2,3,1,5,6,7] => [7,6,5,1,3,2,4] => {{1,4,7},{2,6},{3,5}} => 7
[[[[.,[[.,[.,.]],.]],.],.],.] => [3,2,4,1,5,6,7] => [7,6,5,1,4,2,3] => {{1,3,4,5,7},{2,6}} => 7
[[[[.,[[[.,.],.],.]],.],.],.] => [2,3,4,1,5,6,7] => [7,6,5,1,4,3,2] => {{1,2,3,4,5,6,7}} => 7
[[[[[.,.],[.,[.,.]]],.],.],.] => [4,3,1,2,5,6,7] => [7,6,5,2,1,3,4] => {{1,2,3,4,5,6,7}} => 7
[[[[[.,.],[[.,.],.]],.],.],.] => [3,4,1,2,5,6,7] => [7,6,5,2,1,4,3] => {{1,3,5,7},{2,4,6}} => 7
[[[[[.,[.,.]],[.,.]],.],.],.] => [4,2,1,3,5,6,7] => [7,6,5,3,1,2,4] => {{1,3,4,5,7},{2,6}} => 7
[[[[[[.,.],.],[.,.]],.],.],.] => [4,1,2,3,5,6,7] => [7,6,5,3,2,1,4] => {{1,2,3,4,5,6,7}} => 7
[[[[[.,[.,[.,.]]],.],.],.],.] => [3,2,1,4,5,6,7] => [7,6,5,4,1,2,3] => {{1,3,5,7},{2,6},{4}} => 7
[[[[[.,[[.,.],.]],.],.],.],.] => [2,3,1,4,5,6,7] => [7,6,5,4,1,3,2] => {{1,2,3,5,6,7},{4}} => 7
[[[[[[.,.],[.,.]],.],.],.],.] => [3,1,2,4,5,6,7] => [7,6,5,4,2,1,3] => {{1,2,3,5,6,7},{4}} => 7
[[[[[[.,[.,.]],.],.],.],.],.] => [2,1,3,4,5,6,7] => [7,6,5,4,3,1,2] => {{1,2,6,7},{3,5},{4}} => 7
[[[[[[[.,.],.],.],.],.],.],.] => [1,2,3,4,5,6,7] => [7,6,5,4,3,2,1] => {{1,7},{2,6},{3,5},{4}} => 7
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]] => [7,6,5,4,3,8,2,1] => [1,2,8,3,4,5,6,7] => {{1},{2},{3,4,5,6,7,8}} => 1
[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]] => [7,5,4,6,3,8,2,1] => [1,2,8,3,6,4,5,7] => {{1},{2},{3,4,5,6,7,8}} => 1
[.,[.,[[.,[[.,[[.,.],.]],.]],.]]] => [5,6,4,7,3,8,2,1] => [1,2,8,3,7,4,6,5] => {{1},{2},{3,4,5,6,7,8}} => 1
[.,[.,[[.,[[[.,.],[.,.]],.]],.]]] => [6,4,5,7,3,8,2,1] => [1,2,8,3,7,5,4,6] => {{1},{2},{3,4,5,6,7,8}} => 1
[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]] => [7,6,4,3,5,8,2,1] => [1,2,8,5,3,4,6,7] => {{1},{2},{3,4,5,6,7,8}} => 1
[.,[.,[[[[.,.],[.,.]],[.,.]],.]]] => [7,5,3,4,6,8,2,1] => [1,2,8,6,4,3,5,7] => {{1},{2},{3,4,5,6,7,8}} => 1
[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]] => [6,5,4,3,7,8,2,1] => [1,2,8,7,3,4,5,6] => {{1},{2},{3,4,5,6,7,8}} => 1
[.,[.,[[[[.,.],[[.,.],.]],.],.]]] => [5,6,3,4,7,8,2,1] => [1,2,8,7,4,3,6,5] => {{1},{2},{3,4,5,6,7,8}} => 1
[.,[.,[[[[.,[[.,.],.]],.],.],.]]] => [4,5,3,6,7,8,2,1] => [1,2,8,7,6,3,5,4] => {{1},{2},{3,4,5,6,7,8}} => 1
[.,[.,[[[[[.,.],[.,.]],.],.],.]]] => [5,3,4,6,7,8,2,1] => [1,2,8,7,6,4,3,5] => {{1},{2},{3,4,5,6,7,8}} => 1
[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]] => [8,6,5,4,3,2,7,1] => [1,7,2,3,4,5,6,8] => {{1},{2,3,4,5,6,7},{8}} => 1
[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]] => [8,5,4,6,3,2,7,1] => [1,7,2,3,6,4,5,8] => {{1},{2,3,4,5,6,7},{8}} => 1
[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]] => [8,6,4,3,5,2,7,1] => [1,7,2,5,3,4,6,8] => {{1},{2,3,4,5,6,7},{8}} => 1
[.,[[.,[[.,[[.,.],.]],.]],[.,.]]] => [8,4,5,3,6,2,7,1] => [1,7,2,6,3,5,4,8] => {{1},{2,3,4,5,6,7},{8}} => 1
[.,[[.,[[[.,.],[.,.]],.]],[.,.]]] => [8,5,3,4,6,2,7,1] => [1,7,2,6,4,3,5,8] => {{1},{2,3,4,5,6,7},{8}} => 1
[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [8,6,5,3,2,4,7,1] => [1,7,4,2,3,5,6,8] => {{1},{2,3,4,5,6,7},{8}} => 1
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => [8,6,4,2,3,5,7,1] => [1,7,5,3,2,4,6,8] => {{1},{2,3,4,5,6,7},{8}} => 1
[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]] => [8,5,4,3,2,6,7,1] => [1,7,6,2,3,4,5,8] => {{1},{2,3,4,5,6,7},{8}} => 1
[.,[[[[.,.],[[.,.],.]],.],[.,.]]] => [8,4,5,2,3,6,7,1] => [1,7,6,3,2,5,4,8] => {{1},{2,3,4,5,6,7},{8}} => 1
[.,[[[[.,[[.,.],.]],.],.],[.,.]]] => [8,3,4,2,5,6,7,1] => [1,7,6,5,2,4,3,8] => {{1},{2,3,4,5,6,7},{8}} => 1
[.,[[[[[.,.],[.,.]],.],.],[.,.]]] => [8,4,2,3,5,6,7,1] => [1,7,6,5,3,2,4,8] => {{1},{2,3,4,5,6,7},{8}} => 1
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [7,6,5,4,3,2,8,1] => [1,8,2,3,4,5,6,7] => {{1},{2,3,4,5,6,7,8}} => 1
[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]] => [6,7,5,4,3,2,8,1] => [1,8,2,3,4,5,7,6] => {{1},{2,3,4,5,6,8},{7}} => 1
[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]] => [7,5,6,4,3,2,8,1] => [1,8,2,3,4,6,5,7] => {{1},{2,3,4,5,7,8},{6}} => 1
[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]] => [6,5,7,4,3,2,8,1] => [1,8,2,3,4,7,5,6] => {{1},{2,3,4,5,6,7,8}} => 1
[.,[[.,[.,[.,[[[.,.],.],.]]]],.]] => [5,6,7,4,3,2,8,1] => [1,8,2,3,4,7,6,5] => {{1},{2,3,4,5,8},{6,7}} => 1
[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]] => [7,6,4,5,3,2,8,1] => [1,8,2,3,5,4,6,7] => {{1},{2,3,4,6,7,8},{5}} => 1
[.,[[.,[.,[[.,[.,.]],[.,.]]]],.]] => [7,5,4,6,3,2,8,1] => [1,8,2,3,6,4,5,7] => {{1},{2,3,4,5,6,7,8}} => 1
[.,[[.,[.,[[[.,.],[.,.]],.]]],.]] => [6,4,5,7,3,2,8,1] => [1,8,2,3,7,5,4,6] => {{1},{2,3,4,5,6,7,8}} => 1
[.,[[.,[.,[[[.,[.,.]],.],.]]],.]] => [5,4,6,7,3,2,8,1] => [1,8,2,3,7,6,4,5] => {{1},{2,3,4,5,7,8},{6}} => 1
[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]] => [7,6,5,3,4,2,8,1] => [1,8,2,4,3,5,6,7] => {{1},{2,3,5,6,7,8},{4}} => 1
[.,[[.,[[.,.],[[.,[.,.]],.]]],.]] => [6,5,7,3,4,2,8,1] => [1,8,2,4,3,7,5,6] => {{1},{2,3,5,6,7,8},{4}} => 1
[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]] => [7,6,4,3,5,2,8,1] => [1,8,2,5,3,4,6,7] => {{1},{2,3,4,5,6,7,8}} => 1
[.,[[.,[[.,[.,.]],[[.,.],.]]],.]] => [6,7,4,3,5,2,8,1] => [1,8,2,5,3,4,7,6] => {{1},{2,3,4,5,6,8},{7}} => 1
[.,[[.,[[.,[[.,.],.]],[.,.]]],.]] => [7,4,5,3,6,2,8,1] => [1,8,2,6,3,5,4,7] => {{1},{2,3,4,5,6,7,8}} => 1
[.,[[.,[[[.,.],[.,.]],[.,.]]],.]] => [7,5,3,4,6,2,8,1] => [1,8,2,6,4,3,5,7] => {{1},{2,3,4,5,6,7,8}} => 1
[.,[[.,[[[.,[.,.]],.],[.,.]]],.]] => [7,4,3,5,6,2,8,1] => [1,8,2,6,5,3,4,7] => {{1},{2,3,4,6,7,8},{5}} => 1
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]] => [6,5,4,3,7,2,8,1] => [1,8,2,7,3,4,5,6] => {{1},{2,3,4,5,6,7,8}} => 1
[.,[[.,[[.,[[[.,.],.],.]],.]],.]] => [4,5,6,3,7,2,8,1] => [1,8,2,7,3,6,5,4] => {{1},{2,3,4,5,7,8},{6}} => 1
[.,[[.,[[[.,.],[[.,.],.]],.]],.]] => [5,6,3,4,7,2,8,1] => [1,8,2,7,4,3,6,5] => {{1},{2,3,4,5,6,7,8}} => 1
[.,[[.,[[[[.,.],.],[.,.]],.]],.]] => [6,3,4,5,7,2,8,1] => [1,8,2,7,5,4,3,6] => {{1},{2,3,4,6,7,8},{5}} => 1
[.,[[.,[[[.,[[.,.],.]],.],.]],.]] => [4,5,3,6,7,2,8,1] => [1,8,2,7,6,3,5,4] => {{1},{2,3,4,5,6,7,8}} => 1
[.,[[.,[[[[.,.],[.,.]],.],.]],.]] => [5,3,4,6,7,2,8,1] => [1,8,2,7,6,4,3,5] => {{1},{2,3,4,5,6,7,8}} => 1
[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]] => [7,6,5,4,2,3,8,1] => [1,8,3,2,4,5,6,7] => {{1},{2,4,5,6,7,8},{3}} => 1
[.,[[[.,.],[.,[[.,[.,.]],.]]],.]] => [6,5,7,4,2,3,8,1] => [1,8,3,2,4,7,5,6] => {{1},{2,4,5,6,7,8},{3}} => 1
[.,[[[.,.],[[.,[.,.]],[.,.]]],.]] => [7,5,4,6,2,3,8,1] => [1,8,3,2,6,4,5,7] => {{1},{2,4,5,6,7,8},{3}} => 1
[.,[[[.,.],[[[.,.],[.,.]],.]],.]] => [6,4,5,7,2,3,8,1] => [1,8,3,2,7,5,4,6] => {{1},{2,4,5,6,7,8},{3}} => 1
[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]] => [7,6,5,3,2,4,8,1] => [1,8,4,2,3,5,6,7] => {{1},{2,3,4,5,6,7,8}} => 1
[.,[[[.,[.,.]],[.,[[.,.],.]]],.]] => [6,7,5,3,2,4,8,1] => [1,8,4,2,3,5,7,6] => {{1},{2,3,4,5,6,8},{7}} => 1
[.,[[[.,[.,.]],[[.,.],[.,.]]],.]] => [7,5,6,3,2,4,8,1] => [1,8,4,2,3,6,5,7] => {{1},{2,3,4,5,7,8},{6}} => 1
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]] => [6,5,7,3,2,4,8,1] => [1,8,4,2,3,7,5,6] => {{1},{2,3,4,5,6,7,8}} => 1
[.,[[[.,[.,.]],[[[.,.],.],.]],.]] => [5,6,7,3,2,4,8,1] => [1,8,4,2,3,7,6,5] => {{1},{2,3,4,5,8},{6,7}} => 1
[.,[[[[.,.],[.,.]],[.,[.,.]]],.]] => [7,6,4,2,3,5,8,1] => [1,8,5,3,2,4,6,7] => {{1},{2,3,4,5,6,7,8}} => 1
[.,[[[[.,.],[.,.]],[[.,.],.]],.]] => [6,7,4,2,3,5,8,1] => [1,8,5,3,2,4,7,6] => {{1},{2,3,4,5,6,8},{7}} => 1
[.,[[[[.,[.,.]],.],[.,[.,.]]],.]] => [7,6,3,2,4,5,8,1] => [1,8,5,4,2,3,6,7] => {{1},{2,3,5,6,7,8},{4}} => 1
[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]] => [7,5,4,3,2,6,8,1] => [1,8,6,2,3,4,5,7] => {{1},{2,3,4,5,6,7,8}} => 1
[.,[[[[.,.],[[.,.],.]],[.,.]],.]] => [7,4,5,2,3,6,8,1] => [1,8,6,3,2,5,4,7] => {{1},{2,3,4,5,6,7,8}} => 1
[.,[[[[[.,.],[.,.]],.],[.,.]],.]] => [7,4,2,3,5,6,8,1] => [1,8,6,5,3,2,4,7] => {{1},{2,3,4,5,6,7,8}} => 1
[.,[[[.,[.,[.,[[.,.],.]]]],.],.]] => [5,6,4,3,2,7,8,1] => [1,8,7,2,3,4,6,5] => {{1},{2,3,4,5,6,7,8}} => 1
[.,[[[.,[.,[[.,.],[.,.]]]],.],.]] => [6,4,5,3,2,7,8,1] => [1,8,7,2,3,5,4,6] => {{1},{2,3,4,5,6,7,8}} => 1
[.,[[[.,[.,[[.,[.,.]],.]]],.],.]] => [5,4,6,3,2,7,8,1] => [1,8,7,2,3,6,4,5] => {{1},{2,3,4,5,7,8},{6}} => 1
[.,[[[.,[[.,[.,.]],[.,.]]],.],.]] => [6,4,3,5,2,7,8,1] => [1,8,7,2,5,3,4,6] => {{1},{2,3,4,6,7,8},{5}} => 1
[.,[[[.,[[.,[.,[.,.]]],.]],.],.]] => [5,4,3,6,2,7,8,1] => [1,8,7,2,6,3,4,5] => {{1},{2,3,4,5,6,7,8}} => 1
[.,[[[[.,.],[.,[.,[.,.]]]],.],.]] => [6,5,4,2,3,7,8,1] => [1,8,7,3,2,4,5,6] => {{1},{2,3,4,5,6,7,8}} => 1
[.,[[[[.,[.,.]],[.,[.,.]]],.],.]] => [6,5,3,2,4,7,8,1] => [1,8,7,4,2,3,5,6] => {{1},{2,3,5,6,7,8},{4}} => 1
[.,[[[[[.,.],.],[[.,.],.]],.],.]] => [5,6,2,3,4,7,8,1] => [1,8,7,4,3,2,6,5] => {{1},{2,3,5,6,7,8},{4}} => 1
[.,[[[[.,[.,[.,.]]],[.,.]],.],.]] => [6,4,3,2,5,7,8,1] => [1,8,7,5,2,3,4,6] => {{1},{2,3,4,5,6,7,8}} => 1
[.,[[[[.,[[[.,.],.],.]],.],.],.]] => [3,4,5,2,6,7,8,1] => [1,8,7,6,2,5,4,3] => {{1},{2,3,4,5,6,7,8}} => 1
[.,[[[[[.,.],[.,[.,.]]],.],.],.]] => [5,4,2,3,6,7,8,1] => [1,8,7,6,3,2,4,5] => {{1},{2,3,4,5,6,7,8}} => 1
[.,[[[[[[.,.],.],[.,.]],.],.],.]] => [5,2,3,4,6,7,8,1] => [1,8,7,6,4,3,2,5] => {{1},{2,3,4,5,6,7,8}} => 1
[.,[[[[[.,[[.,.],.]],.],.],.],.]] => [3,4,2,5,6,7,8,1] => [1,8,7,6,5,2,4,3] => {{1},{2,3,4,6,7,8},{5}} => 1
[.,[[[[[[.,.],[.,.]],.],.],.],.]] => [4,2,3,5,6,7,8,1] => [1,8,7,6,5,3,2,4] => {{1},{2,3,4,6,7,8},{5}} => 1
[[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [7,8,5,6,3,4,1,2] => [2,1,4,3,6,5,8,7] => {{1,2},{3,4},{5,6},{7,8}} => 2
[[.,.],[[.,.],[[[[.,.],.],.],.]]] => [5,6,7,8,3,4,1,2] => [2,1,4,3,8,7,6,5] => {{1,2},{3,4},{5,8},{6,7}} => 2
[[.,.],[[[[.,.],.],.],[[.,.],.]]] => [7,8,3,4,5,6,1,2] => [2,1,6,5,4,3,8,7] => {{1,2},{3,6},{4,5},{7,8}} => 2
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => [7,6,5,4,3,8,1,2] => [2,1,8,3,4,5,6,7] => {{1,2},{3,4,5,6,7,8}} => 2
[[.,.],[[.,[[.,[.,.]],[.,.]]],.]] => [7,5,4,6,3,8,1,2] => [2,1,8,3,6,4,5,7] => {{1,2},{3,4,5,6,7,8}} => 2
[[.,.],[[.,[[.,[[.,.],.]],.]],.]] => [5,6,4,7,3,8,1,2] => [2,1,8,3,7,4,6,5] => {{1,2},{3,4,5,6,7,8}} => 2
[[.,.],[[.,[[[.,.],[.,.]],.]],.]] => [6,4,5,7,3,8,1,2] => [2,1,8,3,7,5,4,6] => {{1,2},{3,4,5,6,7,8}} => 2
[[.,.],[[[.,[.,.]],[.,[.,.]]],.]] => [7,6,4,3,5,8,1,2] => [2,1,8,5,3,4,6,7] => {{1,2},{3,4,5,6,7,8}} => 2
[[.,.],[[[.,[[.,.],.]],[.,.]],.]] => [7,4,5,3,6,8,1,2] => [2,1,8,6,3,5,4,7] => {{1,2},{3,4,5,6,7,8}} => 2
[[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [7,5,3,4,6,8,1,2] => [2,1,8,6,4,3,5,7] => {{1,2},{3,4,5,6,7,8}} => 2
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]] => [6,5,4,3,7,8,1,2] => [2,1,8,7,3,4,5,6] => {{1,2},{3,4,5,6,7,8}} => 2
[[.,.],[[[[.,.],[[.,.],.]],.],.]] => [5,6,3,4,7,8,1,2] => [2,1,8,7,4,3,6,5] => {{1,2},{3,4,5,6,7,8}} => 2
[[.,.],[[[[.,[[.,.],.]],.],.],.]] => [4,5,3,6,7,8,1,2] => [2,1,8,7,6,3,5,4] => {{1,2},{3,4,5,6,7,8}} => 2
[[.,.],[[[[[.,.],[.,.]],.],.],.]] => [5,3,4,6,7,8,1,2] => [2,1,8,7,6,4,3,5] => {{1,2},{3,4,5,6,7,8}} => 2
[[.,.],[[[[[[.,.],.],.],.],.],.]] => [3,4,5,6,7,8,1,2] => [2,1,8,7,6,5,4,3] => {{1,2},{3,8},{4,7},{5,6}} => 2
[[[[.,.],.],.],[[.,.],[[.,.],.]]] => [7,8,5,6,1,2,3,4] => [4,3,2,1,6,5,8,7] => {{1,4},{2,3},{5,6},{7,8}} => 4
[[[[.,.],.],.],[[[[.,.],.],.],.]] => [5,6,7,8,1,2,3,4] => [4,3,2,1,8,7,6,5] => {{1,4},{2,3},{5,8},{6,7}} => 4
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [7,8,5,4,3,2,1,6] => [6,1,2,3,4,5,8,7] => {{1,2,3,4,5,6},{7,8}} => 6
[[.,[[.,[.,.]],[.,.]]],[[.,.],.]] => [7,8,5,3,2,4,1,6] => [6,1,4,2,3,5,8,7] => {{1,2,3,4,5,6},{7,8}} => 6
[[.,[[.,[[.,.],.]],.]],[[.,.],.]] => [7,8,3,4,2,5,1,6] => [6,1,5,2,4,3,8,7] => {{1,2,3,4,5,6},{7,8}} => 6
[[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [7,8,5,4,2,1,3,6] => [6,3,1,2,4,5,8,7] => {{1,2,3,4,5,6},{7,8}} => 6
[[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [7,8,5,3,1,2,4,6] => [6,4,2,1,3,5,8,7] => {{1,2,3,4,5,6},{7,8}} => 6
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]] => [7,8,4,3,2,1,5,6] => [6,5,1,2,3,4,8,7] => {{1,2,3,4,5,6},{7,8}} => 6
[[[[.,.],[[.,.],.]],.],[[.,.],.]] => [7,8,3,4,1,2,5,6] => [6,5,2,1,4,3,8,7] => {{1,2,3,4,5,6},{7,8}} => 6
[[[[.,[[.,.],.]],.],.],[[.,.],.]] => [7,8,2,3,1,4,5,6] => [6,5,4,1,3,2,8,7] => {{1,2,3,4,5,6},{7,8}} => 6
[[[[[.,.],[.,.]],.],.],[[.,.],.]] => [7,8,3,1,2,4,5,6] => [6,5,4,2,1,3,8,7] => {{1,2,3,4,5,6},{7,8}} => 6
[[[[[[.,.],.],.],.],.],[[.,.],.]] => [7,8,1,2,3,4,5,6] => [6,5,4,3,2,1,8,7] => {{1,6},{2,5},{3,4},{7,8}} => 6
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [8,6,5,4,3,2,1,7] => [7,1,2,3,4,5,6,8] => {{1,2,3,4,5,6,7},{8}} => 7
[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]] => [8,5,6,4,3,2,1,7] => [7,1,2,3,4,6,5,8] => {{1,2,3,4,5,7},{6},{8}} => 7
[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]] => [8,5,4,6,3,2,1,7] => [7,1,2,3,6,4,5,8] => {{1,2,3,4,5,6,7},{8}} => 7
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]] => [8,4,5,6,3,2,1,7] => [7,1,2,3,6,5,4,8] => {{1,2,3,4,7},{5,6},{8}} => 7
[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]] => [8,6,4,3,5,2,1,7] => [7,1,2,5,3,4,6,8] => {{1,2,3,4,5,6,7},{8}} => 7
[[.,[.,[[.,[[.,.],.]],.]]],[.,.]] => [8,4,5,3,6,2,1,7] => [7,1,2,6,3,5,4,8] => {{1,2,3,4,5,6,7},{8}} => 7
[[.,[.,[[[.,.],[.,.]],.]]],[.,.]] => [8,5,3,4,6,2,1,7] => [7,1,2,6,4,3,5,8] => {{1,2,3,4,5,6,7},{8}} => 7
[[.,[.,[[[.,[.,.]],.],.]]],[.,.]] => [8,4,3,5,6,2,1,7] => [7,1,2,6,5,3,4,8] => {{1,2,3,4,6,7},{5},{8}} => 7
[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]] => [8,6,5,3,2,4,1,7] => [7,1,4,2,3,5,6,8] => {{1,2,3,4,5,6,7},{8}} => 7
[[.,[[.,[[.,.],.]],[.,.]]],[.,.]] => [8,6,3,4,2,5,1,7] => [7,1,5,2,4,3,6,8] => {{1,2,3,4,5,6,7},{8}} => 7
[[.,[[[.,.],[.,.]],[.,.]]],[.,.]] => [8,6,4,2,3,5,1,7] => [7,1,5,3,2,4,6,8] => {{1,2,3,4,5,6,7},{8}} => 7
[[.,[[[.,[.,.]],.],[.,.]]],[.,.]] => [8,6,3,2,4,5,1,7] => [7,1,5,4,2,3,6,8] => {{1,2,3,5,6,7},{4},{8}} => 7
[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]] => [8,5,4,3,2,6,1,7] => [7,1,6,2,3,4,5,8] => {{1,2,3,4,5,6,7},{8}} => 7
[[.,[[.,[[[.,.],.],.]],.]],[.,.]] => [8,3,4,5,2,6,1,7] => [7,1,6,2,5,4,3,8] => {{1,2,3,4,6,7},{5},{8}} => 7
[[.,[[[.,.],[[.,.],.]],.]],[.,.]] => [8,4,5,2,3,6,1,7] => [7,1,6,3,2,5,4,8] => {{1,2,3,4,5,6,7},{8}} => 7
[[.,[[[.,[[.,.],.]],.],.]],[.,.]] => [8,3,4,2,5,6,1,7] => [7,1,6,5,2,4,3,8] => {{1,2,3,4,5,6,7},{8}} => 7
[[.,[[[[.,.],[.,.]],.],.]],[.,.]] => [8,4,2,3,5,6,1,7] => [7,1,6,5,3,2,4,8] => {{1,2,3,4,5,6,7},{8}} => 7
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [8,6,5,4,2,1,3,7] => [7,3,1,2,4,5,6,8] => {{1,2,3,4,5,6,7},{8}} => 7
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [8,5,6,4,2,1,3,7] => [7,3,1,2,4,6,5,8] => {{1,2,3,4,5,7},{6},{8}} => 7
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [8,6,4,5,2,1,3,7] => [7,3,1,2,5,4,6,8] => {{1,2,3,4,6,7},{5},{8}} => 7
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [8,5,4,6,2,1,3,7] => [7,3,1,2,6,4,5,8] => {{1,2,3,4,5,6,7},{8}} => 7
[[[.,[[.,.],.]],[.,[.,.]]],[.,.]] => [8,6,5,2,3,1,4,7] => [7,4,1,3,2,5,6,8] => {{1,2,3,4,5,6,7},{8}} => 7
[[[.,[[.,.],.]],[[.,.],.]],[.,.]] => [8,5,6,2,3,1,4,7] => [7,4,1,3,2,6,5,8] => {{1,2,3,4,5,7},{6},{8}} => 7
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [8,6,4,3,2,1,5,7] => [7,5,1,2,3,4,6,8] => {{1,2,3,4,5,6,7},{8}} => 7
[[[[.,[[.,.],.]],.],[.,.]],[.,.]] => [8,6,2,3,1,4,5,7] => [7,5,4,1,3,2,6,8] => {{1,2,3,4,5,6,7},{8}} => 7
[[[.,[.,[.,[[.,.],.]]]],.],[.,.]] => [8,4,5,3,2,1,6,7] => [7,6,1,2,3,5,4,8] => {{1,2,3,4,5,6,7},{8}} => 7
[[[.,[[.,[.,.]],[.,.]]],.],[.,.]] => [8,5,3,2,4,1,6,7] => [7,6,1,4,2,3,5,8] => {{1,2,3,5,6,7},{4},{8}} => 7
[[[[.,[.,[[.,.],.]]],.],.],[.,.]] => [8,3,4,2,1,5,6,7] => [7,6,5,1,2,4,3,8] => {{1,2,3,4,5,6,7},{8}} => 7
[[[[.,[[[.,.],.],.]],.],.],[.,.]] => [8,2,3,4,1,5,6,7] => [7,6,5,1,4,3,2,8] => {{1,2,3,4,5,6,7},{8}} => 7
[[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [8,4,3,1,2,5,6,7] => [7,6,5,2,1,3,4,8] => {{1,2,3,4,5,6,7},{8}} => 7
[[[[[[.,.],.],[.,.]],.],.],[.,.]] => [8,4,1,2,3,5,6,7] => [7,6,5,3,2,1,4,8] => {{1,2,3,4,5,6,7},{8}} => 7
[[[[[.,[[.,.],.]],.],.],.],[.,.]] => [8,2,3,1,4,5,6,7] => [7,6,5,4,1,3,2,8] => {{1,2,3,5,6,7},{4},{8}} => 7
[[[[[[.,.],[.,.]],.],.],.],[.,.]] => [8,3,1,2,4,5,6,7] => [7,6,5,4,2,1,3,8] => {{1,2,3,5,6,7},{4},{8}} => 7
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [7,6,5,4,3,2,1,8] => [8,1,2,3,4,5,6,7] => {{1,2,3,4,5,6,7,8}} => 8
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => [6,7,5,4,3,2,1,8] => [8,1,2,3,4,5,7,6] => {{1,2,3,4,5,6,8},{7}} => 8
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.] => [7,5,6,4,3,2,1,8] => [8,1,2,3,4,6,5,7] => {{1,2,3,4,5,7,8},{6}} => 8
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => [6,5,7,4,3,2,1,8] => [8,1,2,3,4,7,5,6] => {{1,2,3,4,5,6,7,8}} => 8
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.] => [5,6,7,4,3,2,1,8] => [8,1,2,3,4,7,6,5] => {{1,2,3,4,5,8},{6,7}} => 8
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => [7,6,4,5,3,2,1,8] => [8,1,2,3,5,4,6,7] => {{1,2,3,4,6,7,8},{5}} => 8
[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.] => [7,5,4,6,3,2,1,8] => [8,1,2,3,6,4,5,7] => {{1,2,3,4,5,6,7,8}} => 8
[[.,[.,[.,[[[.,.],.],[.,.]]]]],.] => [7,4,5,6,3,2,1,8] => [8,1,2,3,6,5,4,7] => {{1,2,3,4,7,8},{5,6}} => 8
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => [6,5,4,7,3,2,1,8] => [8,1,2,3,7,4,5,6] => {{1,2,3,4,6,8},{5,7}} => 8
[[.,[.,[.,[[[.,.],[.,.]],.]]]],.] => [6,4,5,7,3,2,1,8] => [8,1,2,3,7,5,4,6] => {{1,2,3,4,5,6,7,8}} => 8
[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.] => [7,6,5,3,4,2,1,8] => [8,1,2,4,3,5,6,7] => {{1,2,3,5,6,7,8},{4}} => 8
[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.] => [7,6,4,3,5,2,1,8] => [8,1,2,5,3,4,6,7] => {{1,2,3,4,5,6,7,8}} => 8
[[.,[.,[[.,[.,.]],[[.,.],.]]]],.] => [6,7,4,3,5,2,1,8] => [8,1,2,5,3,4,7,6] => {{1,2,3,4,5,6,8},{7}} => 8
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.] => [7,6,3,4,5,2,1,8] => [8,1,2,5,4,3,6,7] => {{1,2,3,6,7,8},{4,5}} => 8
[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.] => [7,5,4,3,6,2,1,8] => [8,1,2,6,3,4,5,7] => {{1,2,3,5,7,8},{4,6}} => 8
[[.,[.,[[[.,[.,.]],.],[.,.]]]],.] => [7,4,3,5,6,2,1,8] => [8,1,2,6,5,3,4,7] => {{1,2,3,4,6,7,8},{5}} => 8
[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.] => [6,5,4,3,7,2,1,8] => [8,1,2,7,3,4,5,6] => {{1,2,3,4,5,6,7,8}} => 8
[[.,[.,[[.,[[.,.],[.,.]]],.]]],.] => [6,4,5,3,7,2,1,8] => [8,1,2,7,3,5,4,6] => {{1,2,3,5,6,8},{4,7}} => 8
[[.,[.,[[.,[[[.,.],.],.]],.]]],.] => [4,5,6,3,7,2,1,8] => [8,1,2,7,3,6,5,4] => {{1,2,3,4,5,7,8},{6}} => 8
[[.,[.,[[[.,.],[[.,.],.]],.]]],.] => [5,6,3,4,7,2,1,8] => [8,1,2,7,4,3,6,5] => {{1,2,3,4,5,6,7,8}} => 8
[[.,[.,[[[[.,.],.],[.,.]],.]]],.] => [6,3,4,5,7,2,1,8] => [8,1,2,7,5,4,3,6] => {{1,2,3,4,6,7,8},{5}} => 8
[[.,[.,[[[.,[.,[.,.]]],.],.]]],.] => [5,4,3,6,7,2,1,8] => [8,1,2,7,6,3,4,5] => {{1,2,3,5,6,8},{4,7}} => 8
[[.,[.,[[[.,[[.,.],.]],.],.]]],.] => [4,5,3,6,7,2,1,8] => [8,1,2,7,6,3,5,4] => {{1,2,3,4,5,6,7,8}} => 8
[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.] => [7,6,5,4,2,3,1,8] => [8,1,3,2,4,5,6,7] => {{1,2,4,5,6,7,8},{3}} => 8
[[.,[[.,.],[[.,[[.,.],.]],.]]],.] => [5,6,4,7,2,3,1,8] => [8,1,3,2,7,4,6,5] => {{1,2,4,5,6,7,8},{3}} => 8
[[.,[[.,.],[[[.,.],[.,.]],.]]],.] => [6,4,5,7,2,3,1,8] => [8,1,3,2,7,5,4,6] => {{1,2,4,5,6,7,8},{3}} => 8
[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.] => [7,6,5,3,2,4,1,8] => [8,1,4,2,3,5,6,7] => {{1,2,3,4,5,6,7,8}} => 8
[[.,[[.,[.,.]],[.,[[.,.],.]]]],.] => [6,7,5,3,2,4,1,8] => [8,1,4,2,3,5,7,6] => {{1,2,3,4,5,6,8},{7}} => 8
[[.,[[.,[.,.]],[[.,.],[.,.]]]],.] => [7,5,6,3,2,4,1,8] => [8,1,4,2,3,6,5,7] => {{1,2,3,4,5,7,8},{6}} => 8
[[.,[[.,[.,.]],[[.,[.,.]],.]]],.] => [6,5,7,3,2,4,1,8] => [8,1,4,2,3,7,5,6] => {{1,2,3,4,5,6,7,8}} => 8
[[.,[[.,[.,.]],[[[.,.],.],.]]],.] => [5,6,7,3,2,4,1,8] => [8,1,4,2,3,7,6,5] => {{1,2,3,4,5,8},{6,7}} => 8
[[.,[[[.,.],.],[.,[.,[.,.]]]]],.] => [7,6,5,2,3,4,1,8] => [8,1,4,3,2,5,6,7] => {{1,2,5,6,7,8},{3,4}} => 8
[[.,[[[.,.],.],[[.,[.,.]],.]]],.] => [6,5,7,2,3,4,1,8] => [8,1,4,3,2,7,5,6] => {{1,2,5,6,7,8},{3,4}} => 8
[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.] => [7,6,4,3,2,5,1,8] => [8,1,5,2,3,4,6,7] => {{1,2,4,6,7,8},{3,5}} => 8
[[.,[[.,[[.,.],.]],[[.,.],.]]],.] => [6,7,3,4,2,5,1,8] => [8,1,5,2,4,3,7,6] => {{1,2,3,4,5,6,8},{7}} => 8
[[.,[[[.,.],[.,.]],[.,[.,.]]]],.] => [7,6,4,2,3,5,1,8] => [8,1,5,3,2,4,6,7] => {{1,2,3,4,5,6,7,8}} => 8
[[.,[[[.,.],[.,.]],[[.,.],.]]],.] => [6,7,4,2,3,5,1,8] => [8,1,5,3,2,4,7,6] => {{1,2,3,4,5,6,8},{7}} => 8
[[.,[[[.,[.,.]],.],[.,[.,.]]]],.] => [7,6,3,2,4,5,1,8] => [8,1,5,4,2,3,6,7] => {{1,2,3,5,6,7,8},{4}} => 8
[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.] => [7,5,4,3,2,6,1,8] => [8,1,6,2,3,4,5,7] => {{1,2,3,4,5,6,7,8}} => 8
[[.,[[.,[[.,.],[.,.]]],[.,.]]],.] => [7,5,3,4,2,6,1,8] => [8,1,6,2,4,3,5,7] => {{1,2,4,5,7,8},{3,6}} => 8
[[.,[[[.,.],[[.,.],.]],[.,.]]],.] => [7,4,5,2,3,6,1,8] => [8,1,6,3,2,5,4,7] => {{1,2,3,4,5,6,7,8}} => 8
[[.,[[[.,[.,[.,.]]],.],[.,.]]],.] => [7,4,3,2,5,6,1,8] => [8,1,6,5,2,3,4,7] => {{1,2,4,5,7,8},{3,6}} => 8
[[.,[[.,[.,[[.,[.,.]],.]]],.]],.] => [5,4,6,3,2,7,1,8] => [8,1,7,2,3,6,4,5] => {{1,2,3,4,5,7,8},{6}} => 8
[[.,[[.,[[.,.],[.,[.,.]]]],.]],.] => [6,5,3,4,2,7,1,8] => [8,1,7,2,4,3,5,6] => {{1,2,3,4,5,6,7,8}} => 8
[[.,[[.,[[.,[.,.]],[.,.]]],.]],.] => [6,4,3,5,2,7,1,8] => [8,1,7,2,5,3,4,6] => {{1,2,3,4,6,7,8},{5}} => 8
[[.,[[.,[[.,[.,[.,.]]],.]],.]],.] => [5,4,3,6,2,7,1,8] => [8,1,7,2,6,3,4,5] => {{1,2,3,4,5,6,7,8}} => 8
[[.,[[.,[[[.,.],[.,.]],.]],.]],.] => [5,3,4,6,2,7,1,8] => [8,1,7,2,6,4,3,5] => {{1,2,4,5,6,8},{3,7}} => 8
[[.,[[.,[[[[.,.],.],.],.]],.]],.] => [3,4,5,6,2,7,1,8] => [8,1,7,2,6,5,4,3] => {{1,2,3,4,7,8},{5,6}} => 8
[[.,[[[.,.],[.,[.,[.,.]]]],.]],.] => [6,5,4,2,3,7,1,8] => [8,1,7,3,2,4,5,6] => {{1,2,3,4,5,6,7,8}} => 8
[[.,[[[.,.],[[[.,.],.],.]],.]],.] => [4,5,6,2,3,7,1,8] => [8,1,7,3,2,6,5,4] => {{1,2,3,4,5,7,8},{6}} => 8
[[.,[[[.,[.,.]],[.,[.,.]]],.]],.] => [6,5,3,2,4,7,1,8] => [8,1,7,4,2,3,5,6] => {{1,2,3,5,6,7,8},{4}} => 8
[[.,[[[[.,.],.],[[.,.],.]],.]],.] => [5,6,2,3,4,7,1,8] => [8,1,7,4,3,2,6,5] => {{1,2,3,5,6,7,8},{4}} => 8
[[.,[[[.,[.,[.,.]]],[.,.]],.]],.] => [6,4,3,2,5,7,1,8] => [8,1,7,5,2,3,4,6] => {{1,2,3,4,5,6,7,8}} => 8
[[.,[[[.,[[.,.],.]],[.,.]],.]],.] => [6,3,4,2,5,7,1,8] => [8,1,7,5,2,4,3,6] => {{1,2,4,5,6,8},{3,7}} => 8
[[.,[[[[[.,.],.],.],[.,.]],.]],.] => [6,2,3,4,5,7,1,8] => [8,1,7,5,4,3,2,6] => {{1,2,3,6,7,8},{4,5}} => 8
[[.,[[[.,[[[.,.],.],.]],.],.]],.] => [3,4,5,2,6,7,1,8] => [8,1,7,6,2,5,4,3] => {{1,2,3,4,5,6,7,8}} => 8
[[.,[[[[.,.],[.,[.,.]]],.],.]],.] => [5,4,2,3,6,7,1,8] => [8,1,7,6,3,2,4,5] => {{1,2,3,4,5,6,7,8}} => 8
[[.,[[[[.,[.,.]],[.,.]],.],.]],.] => [5,3,2,4,6,7,1,8] => [8,1,7,6,4,2,3,5] => {{1,2,4,5,6,8},{3,7}} => 8
[[.,[[[[[.,.],.],[.,.]],.],.]],.] => [5,2,3,4,6,7,1,8] => [8,1,7,6,4,3,2,5] => {{1,2,3,4,5,6,7,8}} => 8
[[.,[[[[.,[[.,.],.]],.],.],.]],.] => [3,4,2,5,6,7,1,8] => [8,1,7,6,5,2,4,3] => {{1,2,3,4,6,7,8},{5}} => 8
[[.,[[[[[.,.],[.,.]],.],.],.]],.] => [4,2,3,5,6,7,1,8] => [8,1,7,6,5,3,2,4] => {{1,2,3,4,6,7,8},{5}} => 8
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [7,6,5,4,3,1,2,8] => [8,2,1,3,4,5,6,7] => {{1,3,4,5,6,7,8},{2}} => 8
[[[.,.],[.,[.,[[.,[.,.]],.]]]],.] => [6,5,7,4,3,1,2,8] => [8,2,1,3,4,7,5,6] => {{1,3,4,5,6,7,8},{2}} => 8
[[[.,.],[.,[[.,[.,.]],[.,.]]]],.] => [7,5,4,6,3,1,2,8] => [8,2,1,3,6,4,5,7] => {{1,3,4,5,6,7,8},{2}} => 8
[[[.,.],[.,[[.,[[.,.],.]],.]]],.] => [5,6,4,7,3,1,2,8] => [8,2,1,3,7,4,6,5] => {{1,3,4,5,6,7,8},{2}} => 8
[[[.,.],[[.,.],[[.,[.,.]],.]]],.] => [6,5,7,3,4,1,2,8] => [8,2,1,4,3,7,5,6] => {{1,3,5,6,7,8},{2},{4}} => 8
[[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [7,5,3,4,6,1,2,8] => [8,2,1,6,4,3,5,7] => {{1,3,4,5,6,7,8},{2}} => 8
[[[.,.],[[.,[.,[.,[.,.]]]],.]],.] => [6,5,4,3,7,1,2,8] => [8,2,1,7,3,4,5,6] => {{1,3,4,5,6,7,8},{2}} => 8
[[[.,.],[[[.,.],[[.,.],.]],.]],.] => [5,6,3,4,7,1,2,8] => [8,2,1,7,4,3,6,5] => {{1,3,4,5,6,7,8},{2}} => 8
[[[.,.],[[[.,[[.,.],.]],.],.]],.] => [4,5,3,6,7,1,2,8] => [8,2,1,7,6,3,5,4] => {{1,3,4,5,6,7,8},{2}} => 8
[[[.,.],[[[[.,.],[.,.]],.],.]],.] => [5,3,4,6,7,1,2,8] => [8,2,1,7,6,4,3,5] => {{1,3,4,5,6,7,8},{2}} => 8
[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [7,6,5,4,2,1,3,8] => [8,3,1,2,4,5,6,7] => {{1,2,3,4,5,6,7,8}} => 8
[[[.,[.,.]],[.,[.,[[.,.],.]]]],.] => [6,7,5,4,2,1,3,8] => [8,3,1,2,4,5,7,6] => {{1,2,3,4,5,6,8},{7}} => 8
[[[.,[.,.]],[.,[[.,.],[.,.]]]],.] => [7,5,6,4,2,1,3,8] => [8,3,1,2,4,6,5,7] => {{1,2,3,4,5,7,8},{6}} => 8
[[[.,[.,.]],[.,[[.,[.,.]],.]]],.] => [6,5,7,4,2,1,3,8] => [8,3,1,2,4,7,5,6] => {{1,2,3,4,5,6,7,8}} => 8
[[[.,[.,.]],[.,[[[.,.],.],.]]],.] => [5,6,7,4,2,1,3,8] => [8,3,1,2,4,7,6,5] => {{1,2,3,4,5,8},{6,7}} => 8
[[[.,[.,.]],[[.,.],[.,[.,.]]]],.] => [7,6,4,5,2,1,3,8] => [8,3,1,2,5,4,6,7] => {{1,2,3,4,6,7,8},{5}} => 8
[[[.,[.,.]],[[.,[.,.]],[.,.]]],.] => [7,5,4,6,2,1,3,8] => [8,3,1,2,6,4,5,7] => {{1,2,3,4,5,6,7,8}} => 8
[[[.,[.,.]],[[[.,.],.],[.,.]]],.] => [7,4,5,6,2,1,3,8] => [8,3,1,2,6,5,4,7] => {{1,2,3,4,7,8},{5,6}} => 8
[[[.,[.,.]],[[.,[.,[.,.]]],.]],.] => [6,5,4,7,2,1,3,8] => [8,3,1,2,7,4,5,6] => {{1,2,3,4,6,8},{5,7}} => 8
[[[.,[.,.]],[[[.,[.,.]],.],.]],.] => [5,4,6,7,2,1,3,8] => [8,3,1,2,7,6,4,5] => {{1,2,3,4,5,7,8},{6}} => 8
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [7,6,5,4,1,2,3,8] => [8,3,2,1,4,5,6,7] => {{1,4,5,6,7,8},{2,3}} => 8
[[[[.,.],.],[.,[[.,[.,.]],.]]],.] => [6,5,7,4,1,2,3,8] => [8,3,2,1,4,7,5,6] => {{1,4,5,6,7,8},{2,3}} => 8
[[[[.,.],.],[[.,[.,.]],[.,.]]],.] => [7,5,4,6,1,2,3,8] => [8,3,2,1,6,4,5,7] => {{1,4,5,6,7,8},{2,3}} => 8
[[[[.,.],.],[[.,[[.,.],.]],.]],.] => [5,6,4,7,1,2,3,8] => [8,3,2,1,7,4,6,5] => {{1,4,5,6,7,8},{2,3}} => 8
[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.] => [7,6,5,3,2,1,4,8] => [8,4,1,2,3,5,6,7] => {{1,3,5,6,7,8},{2,4}} => 8
[[[.,[.,[.,.]]],[[.,[.,.]],.]],.] => [6,5,7,3,2,1,4,8] => [8,4,1,2,3,7,5,6] => {{1,3,5,6,7,8},{2,4}} => 8
[[[.,[[.,.],.]],[.,[.,[.,.]]]],.] => [7,6,5,2,3,1,4,8] => [8,4,1,3,2,5,6,7] => {{1,2,3,4,5,6,7,8}} => 8
[[[.,[[.,.],.]],[.,[[.,.],.]]],.] => [6,7,5,2,3,1,4,8] => [8,4,1,3,2,5,7,6] => {{1,2,3,4,5,6,8},{7}} => 8
[[[.,[[.,.],.]],[[.,.],[.,.]]],.] => [7,5,6,2,3,1,4,8] => [8,4,1,3,2,6,5,7] => {{1,2,3,4,5,7,8},{6}} => 8
[[[.,[[.,.],.]],[[[.,.],.],.]],.] => [5,6,7,2,3,1,4,8] => [8,4,1,3,2,7,6,5] => {{1,2,3,4,5,8},{6,7}} => 8
[[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [7,6,5,3,1,2,4,8] => [8,4,2,1,3,5,6,7] => {{1,2,3,4,5,6,7,8}} => 8
[[[[.,.],[.,.]],[.,[[.,.],.]]],.] => [6,7,5,3,1,2,4,8] => [8,4,2,1,3,5,7,6] => {{1,2,3,4,5,6,8},{7}} => 8
[[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [7,5,6,3,1,2,4,8] => [8,4,2,1,3,6,5,7] => {{1,2,3,4,5,7,8},{6}} => 8
[[[[.,.],[.,.]],[[.,[.,.]],.]],.] => [6,5,7,3,1,2,4,8] => [8,4,2,1,3,7,5,6] => {{1,2,3,4,5,6,7,8}} => 8
[[[[.,.],[.,.]],[[[.,.],.],.]],.] => [5,6,7,3,1,2,4,8] => [8,4,2,1,3,7,6,5] => {{1,2,3,4,5,8},{6,7}} => 8
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.] => [7,6,4,3,2,1,5,8] => [8,5,1,2,3,4,6,7] => {{1,2,3,4,5,6,7,8}} => 8
[[[.,[[.,.],[.,.]]],[.,[.,.]]],.] => [7,6,4,2,3,1,5,8] => [8,5,1,3,2,4,6,7] => {{1,3,4,6,7,8},{2,5}} => 8
[[[[.,.],[[.,.],.]],[.,[.,.]]],.] => [7,6,3,4,1,2,5,8] => [8,5,2,1,4,3,6,7] => {{1,2,3,4,5,6,7,8}} => 8
[[[[.,.],[[.,.],.]],[[.,.],.]],.] => [6,7,3,4,1,2,5,8] => [8,5,2,1,4,3,7,6] => {{1,2,3,4,5,6,8},{7}} => 8
[[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [7,6,4,1,2,3,5,8] => [8,5,3,2,1,4,6,7] => {{1,2,4,5,6,7,8},{3}} => 8
[[[[.,[.,[.,.]]],.],[.,[.,.]]],.] => [7,6,3,2,1,4,5,8] => [8,5,4,1,2,3,6,7] => {{1,3,4,6,7,8},{2,5}} => 8
[[[[.,[[.,.],.]],.],[.,[.,.]]],.] => [7,6,2,3,1,4,5,8] => [8,5,4,1,3,2,6,7] => {{1,2,3,4,5,6,7,8}} => 8
[[[[.,[[.,.],.]],.],[[.,.],.]],.] => [6,7,2,3,1,4,5,8] => [8,5,4,1,3,2,7,6] => {{1,2,3,4,5,6,8},{7}} => 8
[[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [7,6,3,1,2,4,5,8] => [8,5,4,2,1,3,6,7] => {{1,2,3,4,5,6,7,8}} => 8
[[[[[.,.],[.,.]],.],[[.,.],.]],.] => [6,7,3,1,2,4,5,8] => [8,5,4,2,1,3,7,6] => {{1,2,3,4,5,6,8},{7}} => 8
[[[.,[.,[.,[[.,.],.]]]],[.,.]],.] => [7,4,5,3,2,1,6,8] => [8,6,1,2,3,5,4,7] => {{1,2,3,4,5,6,7,8}} => 8
[[[.,[.,[[.,.],[.,.]]]],[.,.]],.] => [7,5,3,4,2,1,6,8] => [8,6,1,2,4,3,5,7] => {{1,2,3,4,5,6,7,8}} => 8
[[[.,[.,[[.,[.,.]],.]]],[.,.]],.] => [7,4,3,5,2,1,6,8] => [8,6,1,2,5,3,4,7] => {{1,2,3,4,6,7,8},{5}} => 8
[[[.,[[.,.],[.,[.,.]]]],[.,.]],.] => [7,5,4,2,3,1,6,8] => [8,6,1,3,2,4,5,7] => {{1,2,3,4,5,6,7,8}} => 8
[[[.,[[.,[.,.]],[.,.]]],[.,.]],.] => [7,5,3,2,4,1,6,8] => [8,6,1,4,2,3,5,7] => {{1,2,3,5,6,7,8},{4}} => 8
[[[.,[[.,[.,[.,.]]],.]],[.,.]],.] => [7,4,3,2,5,1,6,8] => [8,6,1,5,2,3,4,7] => {{1,2,3,4,5,6,7,8}} => 8
[[[.,[[[.,.],[.,.]],.]],[.,.]],.] => [7,4,2,3,5,1,6,8] => [8,6,1,5,3,2,4,7] => {{1,3,4,5,7,8},{2,6}} => 8
[[[.,[[[[.,.],.],.],.]],[.,.]],.] => [7,2,3,4,5,1,6,8] => [8,6,1,5,4,3,2,7] => {{1,2,3,6,7,8},{4,5}} => 8
[[[[.,.],[[[.,.],.],.]],[.,.]],.] => [7,3,4,5,1,2,6,8] => [8,6,2,1,5,4,3,7] => {{1,2,3,4,6,7,8},{5}} => 8
[[[[[.,.],.],[[.,.],.]],[.,.]],.] => [7,4,5,1,2,3,6,8] => [8,6,3,2,1,5,4,7] => {{1,2,4,5,6,7,8},{3}} => 8
[[[[.,[.,[.,.]]],[.,.]],[.,.]],.] => [7,5,3,2,1,4,6,8] => [8,6,4,1,2,3,5,7] => {{1,2,3,4,5,6,7,8}} => 8
[[[[.,[[.,.],.]],[.,.]],[.,.]],.] => [7,5,2,3,1,4,6,8] => [8,6,4,1,3,2,5,7] => {{1,3,4,5,7,8},{2,6}} => 8
[[[[[[.,.],.],.],[.,.]],[.,.]],.] => [7,5,1,2,3,4,6,8] => [8,6,4,3,2,1,5,7] => {{1,2,5,6,7,8},{3,4}} => 8
[[[[.,[.,[[.,.],.]]],.],[.,.]],.] => [7,3,4,2,1,5,6,8] => [8,6,5,1,2,4,3,7] => {{1,2,3,4,5,6,7,8}} => 8
[[[[.,[[[.,.],.],.]],.],[.,.]],.] => [7,2,3,4,1,5,6,8] => [8,6,5,1,4,3,2,7] => {{1,2,3,4,5,6,7,8}} => 8
[[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [7,4,3,1,2,5,6,8] => [8,6,5,2,1,3,4,7] => {{1,2,3,4,5,6,7,8}} => 8
[[[[[[.,.],.],[.,.]],.],[.,.]],.] => [7,4,1,2,3,5,6,8] => [8,6,5,3,2,1,4,7] => {{1,2,3,4,5,6,7,8}} => 8
[[[[[.,[[.,.],.]],.],.],[.,.]],.] => [7,2,3,1,4,5,6,8] => [8,6,5,4,1,3,2,7] => {{1,2,3,5,6,7,8},{4}} => 8
[[[[[[.,.],[.,.]],.],.],[.,.]],.] => [7,3,1,2,4,5,6,8] => [8,6,5,4,2,1,3,7] => {{1,2,3,5,6,7,8},{4}} => 8
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.] => [6,5,4,3,2,1,7,8] => [8,7,1,2,3,4,5,6] => {{1,2,3,4,5,6,7,8}} => 8
[[[.,[.,[.,[[[.,.],.],.]]]],.],.] => [4,5,6,3,2,1,7,8] => [8,7,1,2,3,6,5,4] => {{1,2,3,4,5,7,8},{6}} => 8
[[[.,[.,[[.,.],[[.,.],.]]]],.],.] => [5,6,3,4,2,1,7,8] => [8,7,1,2,4,3,6,5] => {{1,2,3,4,5,6,7,8}} => 8
[[[.,[.,[[[.,.],.],[.,.]]]],.],.] => [6,3,4,5,2,1,7,8] => [8,7,1,2,5,4,3,6] => {{1,2,3,4,6,7,8},{5}} => 8
[[[.,[.,[[[.,[.,.]],.],.]]],.],.] => [4,3,5,6,2,1,7,8] => [8,7,1,2,6,5,3,4] => {{1,2,3,4,7,8},{5,6}} => 8
[[[.,[[.,.],[.,[[.,.],.]]]],.],.] => [5,6,4,2,3,1,7,8] => [8,7,1,3,2,4,6,5] => {{1,2,3,4,5,6,7,8}} => 8
[[[.,[[.,.],[[.,.],[.,.]]]],.],.] => [6,4,5,2,3,1,7,8] => [8,7,1,3,2,5,4,6] => {{1,2,3,4,5,6,7,8}} => 8
[[[.,[[.,.],[[.,[.,.]],.]]],.],.] => [5,4,6,2,3,1,7,8] => [8,7,1,3,2,6,4,5] => {{1,2,3,4,5,7,8},{6}} => 8
[[[.,[[[.,[.,.]],.],[.,.]]],.],.] => [6,3,2,4,5,1,7,8] => [8,7,1,5,4,2,3,6] => {{1,2,3,6,7,8},{4,5}} => 8
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.] => [5,4,3,2,6,1,7,8] => [8,7,1,6,2,3,4,5] => {{1,2,3,4,5,6,7,8}} => 8
[[[.,[[.,[[.,[.,.]],.]],.]],.],.] => [4,3,5,2,6,1,7,8] => [8,7,1,6,2,5,3,4] => {{1,2,3,4,5,6,7,8}} => 8
[[[.,[[[.,[.,.]],[.,.]],.]],.],.] => [5,3,2,4,6,1,7,8] => [8,7,1,6,4,2,3,5] => {{1,2,3,4,5,6,7,8}} => 8
[[[.,[[[[.,.],.],[.,.]],.]],.],.] => [5,2,3,4,6,1,7,8] => [8,7,1,6,4,3,2,5] => {{1,3,4,5,6,8},{2,7}} => 8
[[[.,[[[.,[.,[.,.]]],.],.]],.],.] => [4,3,2,5,6,1,7,8] => [8,7,1,6,5,2,3,4] => {{1,2,3,4,6,7,8},{5}} => 8
[[[[.,.],[.,[.,[[.,.],.]]]],.],.] => [5,6,4,3,1,2,7,8] => [8,7,2,1,3,4,6,5] => {{1,2,3,4,5,6,7,8}} => 8
[[[[.,.],[.,[[.,.],[.,.]]]],.],.] => [6,4,5,3,1,2,7,8] => [8,7,2,1,3,5,4,6] => {{1,2,3,4,5,6,7,8}} => 8
[[[[.,.],[.,[[.,[.,.]],.]]],.],.] => [5,4,6,3,1,2,7,8] => [8,7,2,1,3,6,4,5] => {{1,2,3,4,5,7,8},{6}} => 8
[[[[.,.],[[.,.],[.,[.,.]]]],.],.] => [6,5,3,4,1,2,7,8] => [8,7,2,1,4,3,5,6] => {{1,2,3,4,5,6,7,8}} => 8
[[[[.,.],[[.,[.,.]],[.,.]]],.],.] => [6,4,3,5,1,2,7,8] => [8,7,2,1,5,3,4,6] => {{1,2,3,4,6,7,8},{5}} => 8
[[[[.,.],[[.,[.,[.,.]]],.]],.],.] => [5,4,3,6,1,2,7,8] => [8,7,2,1,6,3,4,5] => {{1,2,3,4,5,6,7,8}} => 8
[[[[.,.],[[[[.,.],.],.],.]],.],.] => [3,4,5,6,1,2,7,8] => [8,7,2,1,6,5,4,3] => {{1,2,3,4,7,8},{5,6}} => 8
[[[[.,[.,.]],[.,[[.,.],.]]],.],.] => [5,6,4,2,1,3,7,8] => [8,7,3,1,2,4,6,5] => {{1,2,4,5,6,7,8},{3}} => 8
[[[[[.,.],.],[.,[.,[.,.]]]],.],.] => [6,5,4,1,2,3,7,8] => [8,7,3,2,1,4,5,6] => {{1,2,4,5,6,7,8},{3}} => 8
[[[[.,[.,[.,.]]],[[.,.],.]],.],.] => [5,6,3,2,1,4,7,8] => [8,7,4,1,2,3,6,5] => {{1,2,3,4,5,6,7,8}} => 8
[[[[[.,.],[.,.]],[.,[.,.]]],.],.] => [6,5,3,1,2,4,7,8] => [8,7,4,2,1,3,5,6] => {{1,2,3,4,5,6,7,8}} => 8
[[[[[[.,.],.],.],[[.,.],.]],.],.] => [5,6,1,2,3,4,7,8] => [8,7,4,3,2,1,6,5] => {{1,2,5,6,7,8},{3,4}} => 8
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.] => [6,4,3,2,1,5,7,8] => [8,7,5,1,2,3,4,6] => {{1,2,3,4,5,6,7,8}} => 8
[[[[.,[[.,[.,.]],.]],[.,.]],.],.] => [6,3,2,4,1,5,7,8] => [8,7,5,1,4,2,3,6] => {{1,2,3,4,5,6,7,8}} => 8
[[[[.,[[[.,.],.],.]],[.,.]],.],.] => [6,2,3,4,1,5,7,8] => [8,7,5,1,4,3,2,6] => {{1,3,4,5,6,8},{2,7}} => 8
[[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [6,4,2,1,3,5,7,8] => [8,7,5,3,1,2,4,6] => {{1,2,3,4,5,6,7,8}} => 8
[[[[[.,[.,[.,.]]],.],[.,.]],.],.] => [6,3,2,1,4,5,7,8] => [8,7,5,4,1,2,3,6] => {{1,2,3,5,6,7,8},{4}} => 8
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.] => [5,4,3,2,1,6,7,8] => [8,7,6,1,2,3,4,5] => {{1,2,4,5,7,8},{3,6}} => 8
[[[[.,[.,[[.,.],[.,.]]]],.],.],.] => [5,3,4,2,1,6,7,8] => [8,7,6,1,2,4,3,5] => {{1,2,3,4,5,6,7,8}} => 8
[[[[.,[.,[[[.,.],.],.]]],.],.],.] => [3,4,5,2,1,6,7,8] => [8,7,6,1,2,5,4,3] => {{1,2,3,4,5,6,7,8}} => 8
[[[[.,[[.,.],[.,[.,.]]]],.],.],.] => [5,4,2,3,1,6,7,8] => [8,7,6,1,3,2,4,5] => {{1,2,3,4,5,6,7,8}} => 8
[[[[.,[[.,[[.,.],.]],.]],.],.],.] => [3,4,2,5,1,6,7,8] => [8,7,6,1,5,2,4,3] => {{1,2,3,4,6,7,8},{5}} => 8
[[[[.,[[[[.,.],.],.],.]],.],.],.] => [2,3,4,5,1,6,7,8] => [8,7,6,1,5,4,3,2] => {{1,2,3,4,6,7,8},{5}} => 8
[[[[[.,.],[[.,[.,.]],.]],.],.],.] => [4,3,5,1,2,6,7,8] => [8,7,6,2,1,5,3,4] => {{1,2,3,4,5,6,7,8}} => 8
[[[[[[.,.],.],[.,[.,.]]],.],.],.] => [5,4,1,2,3,6,7,8] => [8,7,6,3,2,1,4,5] => {{1,2,3,4,5,6,7,8}} => 8
[[[[[[.,.],[.,.]],[.,.]],.],.],.] => [5,3,1,2,4,6,7,8] => [8,7,6,4,2,1,3,5] => {{1,2,3,5,6,7,8},{4}} => 8
[[[[[[[.,.],.],.],[.,.]],.],.],.] => [5,1,2,3,4,6,7,8] => [8,7,6,4,3,2,1,5] => {{1,2,3,5,6,7,8},{4}} => 8
[[[[[.,[.,[[.,.],.]]],.],.],.],.] => [3,4,2,1,5,6,7,8] => [8,7,6,5,1,2,4,3] => {{1,2,3,4,5,6,7,8}} => 8
[[[[[.,[[.,[.,.]],.]],.],.],.],.] => [3,2,4,1,5,6,7,8] => [8,7,6,5,1,4,2,3] => {{1,3,4,5,6,8},{2,7}} => 8
[[[[[.,[[[.,.],.],.]],.],.],.],.] => [2,3,4,1,5,6,7,8] => [8,7,6,5,1,4,3,2] => {{1,2,3,4,5,6,7,8}} => 8
[[[[[[.,.],[.,[.,.]]],.],.],.],.] => [4,3,1,2,5,6,7,8] => [8,7,6,5,2,1,3,4] => {{1,2,3,4,5,6,7,8}} => 8
[[[[[[.,[.,.]],[.,.]],.],.],.],.] => [4,2,1,3,5,6,7,8] => [8,7,6,5,3,1,2,4] => {{1,3,4,5,6,8},{2,7}} => 8
[[[[[[[.,.],.],[.,.]],.],.],.],.] => [4,1,2,3,5,6,7,8] => [8,7,6,5,3,2,1,4] => {{1,2,3,4,5,6,7,8}} => 8
[[[[[[.,[[.,.],.]],.],.],.],.],.] => [2,3,1,4,5,6,7,8] => [8,7,6,5,4,1,3,2] => {{1,2,3,6,7,8},{4,5}} => 8
[[[[[[[.,.],[.,.]],.],.],.],.],.] => [3,1,2,4,5,6,7,8] => [8,7,6,5,4,2,1,3] => {{1,2,3,6,7,8},{4,5}} => 8
[[[[[[[[.,.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8] => [8,7,6,5,4,3,2,1] => {{1,8},{2,7},{3,6},{4,5}} => 8
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9,10] => [10,9,8,7,6,5,4,3,2,1] => {{1,10},{2,9},{3,8},{4,7},{5,6}} => 10
[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]] => [8,7,6,5,4,3,2,9,1] => [1,9,2,3,4,5,6,7,8] => {{1},{2,3,4,5,6,7,8,9}} => 1
[.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]] => [9,8,7,6,5,4,3,2,10,1] => [1,10,2,3,4,5,6,7,8,9] => {{1},{2,3,4,5,6,7,8,9,10}} => 1
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [9,10,7,8,5,6,3,4,1,2] => [2,1,4,3,6,5,8,7,10,9] => {{1,2},{3,4},{5,6},{7,8},{9,10}} => 2
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]] => [11,12,9,10,7,8,5,6,3,4,1,2] => [2,1,4,3,6,5,8,7,10,9,12,11] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}} => 2
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [10,8,6,4,2,1,3,5,7,9] => [9,7,5,3,1,2,4,6,8,10] => {{1,2,3,4,5,6,7,8,9},{10}} => 9
[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]] => [9,10,1,2,3,4,5,6,7,8] => [8,7,6,5,4,3,2,1,10,9] => {{1,8},{2,7},{3,6},{4,5},{9,10}} => 8
[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]] => [7,8,9,10,1,2,3,4,5,6] => [6,5,4,3,2,1,10,9,8,7] => {{1,6},{2,5},{3,4},{7,10},{8,9}} => 6
[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]] => [5,6,7,8,9,10,1,2,3,4] => [4,3,2,1,10,9,8,7,6,5] => {{1,4},{2,3},{5,10},{6,9},{7,8}} => 4
[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]] => [3,4,5,6,7,8,9,10,1,2] => [2,1,10,9,8,7,6,5,4,3] => {{1,2},{3,10},{4,9},{5,8},{6,7}} => 2
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => [9,7,6,5,4,3,2,1,8] => [8,1,2,3,4,5,6,7,9] => {{1,2,3,4,5,6,7,8},{9}} => 8
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]] => [10,8,7,6,5,4,3,2,1,9] => [9,1,2,3,4,5,6,7,8,10] => {{1,2,3,4,5,6,7,8,9},{10}} => 9
[.,[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]] => [6,2,3,4,5,7,8,9,10,1] => [1,10,9,8,7,5,4,3,2,6] => {{1},{2,3,4,5,6,7,8,9,10}} => 1
[.,[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]] => [10,9,8,7,6,5,4,3,2,11,1] => [1,11,2,3,4,5,6,7,8,9,10] => {{1},{2,3,4,5,6,7,8,9,10,11}} => 1
[.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]] => [7,8,6,5,4,3,2,9,1] => [1,9,2,3,4,5,6,8,7] => {{1},{2,3,4,5,6,7,9},{8}} => 1
[.,[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]] => [8,9,7,6,5,4,3,2,10,1] => [1,10,2,3,4,5,6,7,9,8] => {{1},{2,3,4,5,6,7,8,10},{9}} => 1
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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:
1,1 2,1,2 5,2,2,5 14,5,4,5,14 42,14,10,10,14,42 132,42,28,25,28,42,132
F1=q
F2=q+q2
F3=2 q+q2+2 q3
F4=5 q+2 q2+2 q3+5 q4
F5=14 q+5 q2+4 q3+5 q4+14 q5
F6=42 q+14 q2+10 q3+10 q4+14 q5+42 q6
F7=132 q+42 q2+28 q3+25 q4+28 q5+42 q6+132 q7
Description
The biggest entry in the block containing the 1.
Map
reverse
Description
Sends a permutation to its reverse.
The reverse of a permutation σ of length n is given by τ with τ(i)=σ(n+1−i).
The reverse of a permutation σ of length n is given by τ with τ(i)=σ(n+1−i).
Map
to cycle type
Description
Let π=c1…cr a permutation of size n decomposed in its cyclic parts. The associated set partition of [n] then is S=S1∪⋯∪Sr such that Si is the set of integers in the cycle ci.
A permutation is cyclic [1] if and only if its cycle type is a hook partition [2].
A permutation is cyclic [1] if and only if its cycle type is a hook partition [2].
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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