Identifier
-
Mp00012:
Binary trees
—to Dyck path: up step, left tree, down step, right tree⟶
Dyck paths
Mp00138: Dyck paths —to noncrossing partition⟶ Set partitions
St000505: Set partitions ⟶ ℤ
Values
[.,.] => [1,0] => {{1}} => 1
[.,[.,.]] => [1,0,1,0] => {{1},{2}} => 1
[[.,.],.] => [1,1,0,0] => {{1,2}} => 2
[.,[.,[.,.]]] => [1,0,1,0,1,0] => {{1},{2},{3}} => 1
[.,[[.,.],.]] => [1,0,1,1,0,0] => {{1},{2,3}} => 1
[[.,.],[.,.]] => [1,1,0,0,1,0] => {{1,2},{3}} => 2
[[.,[.,.]],.] => [1,1,0,1,0,0] => {{1,3},{2}} => 3
[[[.,.],.],.] => [1,1,1,0,0,0] => {{1,2,3}} => 3
[.,[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0] => {{1},{2},{3},{4}} => 1
[.,[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0] => {{1},{2},{3,4}} => 1
[.,[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0] => {{1},{2,3},{4}} => 1
[.,[[.,[.,.]],.]] => [1,0,1,1,0,1,0,0] => {{1},{2,4},{3}} => 1
[.,[[[.,.],.],.]] => [1,0,1,1,1,0,0,0] => {{1},{2,3,4}} => 1
[[.,.],[.,[.,.]]] => [1,1,0,0,1,0,1,0] => {{1,2},{3},{4}} => 2
[[.,.],[[.,.],.]] => [1,1,0,0,1,1,0,0] => {{1,2},{3,4}} => 2
[[.,[.,.]],[.,.]] => [1,1,0,1,0,0,1,0] => {{1,3},{2},{4}} => 3
[[[.,.],.],[.,.]] => [1,1,1,0,0,0,1,0] => {{1,2,3},{4}} => 3
[[.,[.,[.,.]]],.] => [1,1,0,1,0,1,0,0] => {{1,4},{2},{3}} => 4
[[.,[[.,.],.]],.] => [1,1,0,1,1,0,0,0] => {{1,3,4},{2}} => 4
[[[.,.],[.,.]],.] => [1,1,1,0,0,1,0,0] => {{1,4},{2,3}} => 4
[[[.,[.,.]],.],.] => [1,1,1,0,1,0,0,0] => {{1,2,4},{3}} => 4
[[[[.,.],.],.],.] => [1,1,1,1,0,0,0,0] => {{1,2,3,4}} => 4
[.,[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5}} => 1
[.,[.,[.,[[.,.],.]]]] => [1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4,5}} => 1
[.,[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5}} => 1
[.,[.,[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,0,0] => {{1},{2},{3,5},{4}} => 1
[.,[.,[[[.,.],.],.]]] => [1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3,4,5}} => 1
[.,[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4},{5}} => 1
[.,[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5}} => 1
[.,[[.,[.,.]],[.,.]]] => [1,0,1,1,0,1,0,0,1,0] => {{1},{2,4},{3},{5}} => 1
[.,[[[.,.],.],[.,.]]] => [1,0,1,1,1,0,0,0,1,0] => {{1},{2,3,4},{5}} => 1
[.,[[.,[.,[.,.]]],.]] => [1,0,1,1,0,1,0,1,0,0] => {{1},{2,5},{3},{4}} => 1
[.,[[.,[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,0,0] => {{1},{2,4,5},{3}} => 1
[.,[[[.,.],[.,.]],.]] => [1,0,1,1,1,0,0,1,0,0] => {{1},{2,5},{3,4}} => 1
[.,[[[.,[.,.]],.],.]] => [1,0,1,1,1,0,1,0,0,0] => {{1},{2,3,5},{4}} => 1
[.,[[[[.,.],.],.],.]] => [1,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4,5}} => 1
[[.,.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5}} => 2
[[.,.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,0] => {{1,2},{3},{4,5}} => 2
[[.,.],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5}} => 2
[[.,.],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,1,0,0] => {{1,2},{3,5},{4}} => 2
[[.,.],[[[.,.],.],.]] => [1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5}} => 2
[[.,[.,.]],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,0] => {{1,3},{2},{4},{5}} => 3
[[.,[.,.]],[[.,.],.]] => [1,1,0,1,0,0,1,1,0,0] => {{1,3},{2},{4,5}} => 3
[[[.,.],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,0] => {{1,2,3},{4},{5}} => 3
[[[.,.],.],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5}} => 3
[[.,[.,[.,.]]],[.,.]] => [1,1,0,1,0,1,0,0,1,0] => {{1,4},{2},{3},{5}} => 4
[[.,[[.,.],.]],[.,.]] => [1,1,0,1,1,0,0,0,1,0] => {{1,3,4},{2},{5}} => 4
[[[.,.],[.,.]],[.,.]] => [1,1,1,0,0,1,0,0,1,0] => {{1,4},{2,3},{5}} => 4
[[[.,[.,.]],.],[.,.]] => [1,1,1,0,1,0,0,0,1,0] => {{1,2,4},{3},{5}} => 4
[[[[.,.],.],.],[.,.]] => [1,1,1,1,0,0,0,0,1,0] => {{1,2,3,4},{5}} => 4
[[.,[.,[.,[.,.]]]],.] => [1,1,0,1,0,1,0,1,0,0] => {{1,5},{2},{3},{4}} => 5
[[.,[.,[[.,.],.]]],.] => [1,1,0,1,0,1,1,0,0,0] => {{1,4,5},{2},{3}} => 5
[[.,[[.,.],[.,.]]],.] => [1,1,0,1,1,0,0,1,0,0] => {{1,5},{2},{3,4}} => 5
[[.,[[.,[.,.]],.]],.] => [1,1,0,1,1,0,1,0,0,0] => {{1,3,5},{2},{4}} => 5
[[.,[[[.,.],.],.]],.] => [1,1,0,1,1,1,0,0,0,0] => {{1,3,4,5},{2}} => 5
[[[.,.],[.,[.,.]]],.] => [1,1,1,0,0,1,0,1,0,0] => {{1,5},{2,3},{4}} => 5
[[[.,.],[[.,.],.]],.] => [1,1,1,0,0,1,1,0,0,0] => {{1,4,5},{2,3}} => 5
[[[.,[.,.]],[.,.]],.] => [1,1,1,0,1,0,0,1,0,0] => {{1,5},{2,4},{3}} => 5
[[[[.,.],.],[.,.]],.] => [1,1,1,1,0,0,0,1,0,0] => {{1,5},{2,3,4}} => 5
[[[.,[.,[.,.]]],.],.] => [1,1,1,0,1,0,1,0,0,0] => {{1,2,5},{3},{4}} => 5
[[[.,[[.,.],.]],.],.] => [1,1,1,0,1,1,0,0,0,0] => {{1,2,4,5},{3}} => 5
[[[[.,.],[.,.]],.],.] => [1,1,1,1,0,0,1,0,0,0] => {{1,2,5},{3,4}} => 5
[[[[.,[.,.]],.],.],.] => [1,1,1,1,0,1,0,0,0,0] => {{1,2,3,5},{4}} => 5
[[[[[.,.],.],.],.],.] => [1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4,5}} => 5
[.,[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6}} => 1
[.,[.,[.,[.,[[.,.],.]]]]] => [1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5,6}} => 1
[.,[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4,5},{6}} => 1
[.,[.,[.,[[.,[.,.]],.]]]] => [1,0,1,0,1,0,1,1,0,1,0,0] => {{1},{2},{3},{4,6},{5}} => 1
[.,[.,[.,[[[.,.],.],.]]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4,5,6}} => 1
[.,[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3,4},{5},{6}} => 1
[.,[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6}} => 1
[.,[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,0,1,0,0,1,0] => {{1},{2},{3,5},{4},{6}} => 1
[.,[.,[[[.,.],.],[.,.]]]] => [1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3,4,5},{6}} => 1
[.,[.,[[.,[.,[.,.]]],.]]] => [1,0,1,0,1,1,0,1,0,1,0,0] => {{1},{2},{3,6},{4},{5}} => 1
[.,[.,[[.,[[.,.],.]],.]]] => [1,0,1,0,1,1,0,1,1,0,0,0] => {{1},{2},{3,5,6},{4}} => 1
[.,[.,[[[.,.],[.,.]],.]]] => [1,0,1,0,1,1,1,0,0,1,0,0] => {{1},{2},{3,6},{4,5}} => 1
[.,[.,[[[.,[.,.]],.],.]]] => [1,0,1,0,1,1,1,0,1,0,0,0] => {{1},{2},{3,4,6},{5}} => 1
[.,[.,[[[[.,.],.],.],.]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3,4,5,6}} => 1
[.,[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6}} => 1
[.,[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5,6}} => 1
[.,[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 1
[.,[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,0,1,1,0,1,0,0] => {{1},{2,3},{4,6},{5}} => 1
[.,[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5,6}} => 1
[.,[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,0,1,0] => {{1},{2,4},{3},{5},{6}} => 1
[.,[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,0,0] => {{1},{2,4},{3},{5,6}} => 1
[.,[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2,3,4},{5},{6}} => 1
[.,[[[.,.],.],[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => 1
[.,[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,0] => {{1},{2,5},{3},{4},{6}} => 1
[.,[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,0] => {{1},{2,4,5},{3},{6}} => 1
[.,[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,0,0,1,0] => {{1},{2,5},{3,4},{6}} => 1
[.,[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,1,0,0,0,1,0] => {{1},{2,3,5},{4},{6}} => 1
[.,[[[[.,.],.],.],[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2,3,4,5},{6}} => 1
[.,[[.,[.,[.,[.,.]]]],.]] => [1,0,1,1,0,1,0,1,0,1,0,0] => {{1},{2,6},{3},{4},{5}} => 1
[.,[[.,[.,[[.,.],.]]],.]] => [1,0,1,1,0,1,0,1,1,0,0,0] => {{1},{2,5,6},{3},{4}} => 1
[.,[[.,[[.,.],[.,.]]],.]] => [1,0,1,1,0,1,1,0,0,1,0,0] => {{1},{2,6},{3},{4,5}} => 1
[.,[[.,[[.,[.,.]],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,0] => {{1},{2,4,6},{3},{5}} => 1
[.,[[.,[[[.,.],.],.]],.]] => [1,0,1,1,0,1,1,1,0,0,0,0] => {{1},{2,4,5,6},{3}} => 1
[.,[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,1,0,0,1,0,1,0,0] => {{1},{2,6},{3,4},{5}} => 1
[.,[[[.,.],[[.,.],.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,0] => {{1},{2,5,6},{3,4}} => 1
[.,[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,1,0,0,1,0,0] => {{1},{2,6},{3,5},{4}} => 1
[.,[[[[.,.],.],[.,.]],.]] => [1,0,1,1,1,1,0,0,0,1,0,0] => {{1},{2,6},{3,4,5}} => 1
>>> Load all 718 entries. <<<[.,[[[.,[.,[.,.]]],.],.]] => [1,0,1,1,1,0,1,0,1,0,0,0] => {{1},{2,3,6},{4},{5}} => 1
[.,[[[.,[[.,.],.]],.],.]] => [1,0,1,1,1,0,1,1,0,0,0,0] => {{1},{2,3,5,6},{4}} => 1
[.,[[[[.,.],[.,.]],.],.]] => [1,0,1,1,1,1,0,0,1,0,0,0] => {{1},{2,3,6},{4,5}} => 1
[.,[[[[.,[.,.]],.],.],.]] => [1,0,1,1,1,1,0,1,0,0,0,0] => {{1},{2,3,4,6},{5}} => 1
[.,[[[[[.,.],.],.],.],.]] => [1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3,4,5,6}} => 1
[[.,.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5},{6}} => 2
[[.,.],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5,6}} => 2
[[.,.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4,5},{6}} => 2
[[.,.],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,0,1,1,0,1,0,0] => {{1,2},{3},{4,6},{5}} => 2
[[.,.],[.,[[[.,.],.],.]]] => [1,1,0,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4,5,6}} => 2
[[.,.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,0,1,0] => {{1,2},{3,4},{5},{6}} => 2
[[.,.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 2
[[.,.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,0] => {{1,2},{3,5},{4},{6}} => 2
[[.,.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4,5},{6}} => 2
[[.,.],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,0,1,0,0] => {{1,2},{3,6},{4},{5}} => 2
[[.,.],[[.,[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,0] => {{1,2},{3,5,6},{4}} => 2
[[.,.],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,0,0] => {{1,2},{3,6},{4,5}} => 2
[[.,.],[[[.,[.,.]],.],.]] => [1,1,0,0,1,1,1,0,1,0,0,0] => {{1,2},{3,4,6},{5}} => 2
[[.,.],[[[[.,.],.],.],.]] => [1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4,5,6}} => 2
[[.,[.,.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,0,1,0,1,0] => {{1,3},{2},{4},{5},{6}} => 3
[[.,[.,.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,0,1,1,0,0] => {{1,3},{2},{4},{5,6}} => 3
[[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,0,1,0] => {{1,3},{2},{4,5},{6}} => 3
[[.,[.,.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,0,1,0,0] => {{1,3},{2},{4,6},{5}} => 3
[[.,[.,.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,1,0,0,0] => {{1,3},{2},{4,5,6}} => 3
[[[.,.],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6}} => 3
[[[.,.],.],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,0,1,1,0,0] => {{1,2,3},{4},{5,6}} => 3
[[[.,.],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6}} => 3
[[[.,.],.],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,0,1,0,0] => {{1,2,3},{4,6},{5}} => 3
[[[.,.],.],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2,3},{4,5,6}} => 3
[[.,[.,[.,.]]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,0,1,0] => {{1,4},{2},{3},{5},{6}} => 4
[[.,[.,[.,.]]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,0] => {{1,4},{2},{3},{5,6}} => 4
[[.,[[.,.],.]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,0,1,0] => {{1,3,4},{2},{5},{6}} => 4
[[.,[[.,.],.]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,0] => {{1,3,4},{2},{5,6}} => 4
[[[.,.],[.,.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,0,1,0] => {{1,4},{2,3},{5},{6}} => 4
[[[.,.],[.,.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,0] => {{1,4},{2,3},{5,6}} => 4
[[[.,[.,.]],.],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,0,1,0] => {{1,2,4},{3},{5},{6}} => 4
[[[.,[.,.]],.],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,0] => {{1,2,4},{3},{5,6}} => 4
[[[[.,.],.],.],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,0,1,0] => {{1,2,3,4},{5},{6}} => 4
[[[[.,.],.],.],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2,3,4},{5,6}} => 4
[[.,[.,[.,[.,.]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,0,1,0] => {{1,5},{2},{3},{4},{6}} => 5
[[.,[.,[[.,.],.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,0] => {{1,4,5},{2},{3},{6}} => 5
[[.,[[.,.],[.,.]]],[.,.]] => [1,1,0,1,1,0,0,1,0,0,1,0] => {{1,5},{2},{3,4},{6}} => 5
[[.,[[.,[.,.]],.]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,0] => {{1,3,5},{2},{4},{6}} => 5
[[.,[[[.,.],.],.]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,0] => {{1,3,4,5},{2},{6}} => 5
[[[.,.],[.,[.,.]]],[.,.]] => [1,1,1,0,0,1,0,1,0,0,1,0] => {{1,5},{2,3},{4},{6}} => 5
[[[.,.],[[.,.],.]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,0] => {{1,4,5},{2,3},{6}} => 5
[[[.,[.,.]],[.,.]],[.,.]] => [1,1,1,0,1,0,0,1,0,0,1,0] => {{1,5},{2,4},{3},{6}} => 5
[[[[.,.],.],[.,.]],[.,.]] => [1,1,1,1,0,0,0,1,0,0,1,0] => {{1,5},{2,3,4},{6}} => 5
[[[.,[.,[.,.]]],.],[.,.]] => [1,1,1,0,1,0,1,0,0,0,1,0] => {{1,2,5},{3},{4},{6}} => 5
[[[.,[[.,.],.]],.],[.,.]] => [1,1,1,0,1,1,0,0,0,0,1,0] => {{1,2,4,5},{3},{6}} => 5
[[[[.,.],[.,.]],.],[.,.]] => [1,1,1,1,0,0,1,0,0,0,1,0] => {{1,2,5},{3,4},{6}} => 5
[[[[.,[.,.]],.],.],[.,.]] => [1,1,1,1,0,1,0,0,0,0,1,0] => {{1,2,3,5},{4},{6}} => 5
[[[[[.,.],.],.],.],[.,.]] => [1,1,1,1,1,0,0,0,0,0,1,0] => {{1,2,3,4,5},{6}} => 5
[[.,[.,[.,[.,[.,.]]]]],.] => [1,1,0,1,0,1,0,1,0,1,0,0] => {{1,6},{2},{3},{4},{5}} => 6
[[.,[.,[.,[[.,.],.]]]],.] => [1,1,0,1,0,1,0,1,1,0,0,0] => {{1,5,6},{2},{3},{4}} => 6
[[.,[.,[[.,.],[.,.]]]],.] => [1,1,0,1,0,1,1,0,0,1,0,0] => {{1,6},{2},{3},{4,5}} => 6
[[.,[.,[[.,[.,.]],.]]],.] => [1,1,0,1,0,1,1,0,1,0,0,0] => {{1,4,6},{2},{3},{5}} => 6
[[.,[.,[[[.,.],.],.]]],.] => [1,1,0,1,0,1,1,1,0,0,0,0] => {{1,4,5,6},{2},{3}} => 6
[[.,[[.,.],[.,[.,.]]]],.] => [1,1,0,1,1,0,0,1,0,1,0,0] => {{1,6},{2},{3,4},{5}} => 6
[[.,[[.,.],[[.,.],.]]],.] => [1,1,0,1,1,0,0,1,1,0,0,0] => {{1,5,6},{2},{3,4}} => 6
[[.,[[.,[.,.]],[.,.]]],.] => [1,1,0,1,1,0,1,0,0,1,0,0] => {{1,6},{2},{3,5},{4}} => 6
[[.,[[[.,.],.],[.,.]]],.] => [1,1,0,1,1,1,0,0,0,1,0,0] => {{1,6},{2},{3,4,5}} => 6
[[.,[[.,[.,[.,.]]],.]],.] => [1,1,0,1,1,0,1,0,1,0,0,0] => {{1,3,6},{2},{4},{5}} => 6
[[.,[[.,[[.,.],.]],.]],.] => [1,1,0,1,1,0,1,1,0,0,0,0] => {{1,3,5,6},{2},{4}} => 6
[[.,[[[.,.],[.,.]],.]],.] => [1,1,0,1,1,1,0,0,1,0,0,0] => {{1,3,6},{2},{4,5}} => 6
[[.,[[[.,[.,.]],.],.]],.] => [1,1,0,1,1,1,0,1,0,0,0,0] => {{1,3,4,6},{2},{5}} => 6
[[.,[[[[.,.],.],.],.]],.] => [1,1,0,1,1,1,1,0,0,0,0,0] => {{1,3,4,5,6},{2}} => 6
[[[.,.],[.,[.,[.,.]]]],.] => [1,1,1,0,0,1,0,1,0,1,0,0] => {{1,6},{2,3},{4},{5}} => 6
[[[.,.],[.,[[.,.],.]]],.] => [1,1,1,0,0,1,0,1,1,0,0,0] => {{1,5,6},{2,3},{4}} => 6
[[[.,.],[[.,.],[.,.]]],.] => [1,1,1,0,0,1,1,0,0,1,0,0] => {{1,6},{2,3},{4,5}} => 6
[[[.,.],[[.,[.,.]],.]],.] => [1,1,1,0,0,1,1,0,1,0,0,0] => {{1,4,6},{2,3},{5}} => 6
[[[.,.],[[[.,.],.],.]],.] => [1,1,1,0,0,1,1,1,0,0,0,0] => {{1,4,5,6},{2,3}} => 6
[[[.,[.,.]],[.,[.,.]]],.] => [1,1,1,0,1,0,0,1,0,1,0,0] => {{1,6},{2,4},{3},{5}} => 6
[[[.,[.,.]],[[.,.],.]],.] => [1,1,1,0,1,0,0,1,1,0,0,0] => {{1,5,6},{2,4},{3}} => 6
[[[[.,.],.],[.,[.,.]]],.] => [1,1,1,1,0,0,0,1,0,1,0,0] => {{1,6},{2,3,4},{5}} => 6
[[[[.,.],.],[[.,.],.]],.] => [1,1,1,1,0,0,0,1,1,0,0,0] => {{1,5,6},{2,3,4}} => 6
[[[.,[.,[.,.]]],[.,.]],.] => [1,1,1,0,1,0,1,0,0,1,0,0] => {{1,6},{2,5},{3},{4}} => 6
[[[.,[[.,.],.]],[.,.]],.] => [1,1,1,0,1,1,0,0,0,1,0,0] => {{1,6},{2,4,5},{3}} => 6
[[[[.,.],[.,.]],[.,.]],.] => [1,1,1,1,0,0,1,0,0,1,0,0] => {{1,6},{2,5},{3,4}} => 6
[[[[.,[.,.]],.],[.,.]],.] => [1,1,1,1,0,1,0,0,0,1,0,0] => {{1,6},{2,3,5},{4}} => 6
[[[[[.,.],.],.],[.,.]],.] => [1,1,1,1,1,0,0,0,0,1,0,0] => {{1,6},{2,3,4,5}} => 6
[[[.,[.,[.,[.,.]]]],.],.] => [1,1,1,0,1,0,1,0,1,0,0,0] => {{1,2,6},{3},{4},{5}} => 6
[[[.,[.,[[.,.],.]]],.],.] => [1,1,1,0,1,0,1,1,0,0,0,0] => {{1,2,5,6},{3},{4}} => 6
[[[.,[[.,.],[.,.]]],.],.] => [1,1,1,0,1,1,0,0,1,0,0,0] => {{1,2,6},{3},{4,5}} => 6
[[[.,[[.,[.,.]],.]],.],.] => [1,1,1,0,1,1,0,1,0,0,0,0] => {{1,2,4,6},{3},{5}} => 6
[[[.,[[[.,.],.],.]],.],.] => [1,1,1,0,1,1,1,0,0,0,0,0] => {{1,2,4,5,6},{3}} => 6
[[[[.,.],[.,[.,.]]],.],.] => [1,1,1,1,0,0,1,0,1,0,0,0] => {{1,2,6},{3,4},{5}} => 6
[[[[.,.],[[.,.],.]],.],.] => [1,1,1,1,0,0,1,1,0,0,0,0] => {{1,2,5,6},{3,4}} => 6
[[[[.,[.,.]],[.,.]],.],.] => [1,1,1,1,0,1,0,0,1,0,0,0] => {{1,2,6},{3,5},{4}} => 6
[[[[[.,.],.],[.,.]],.],.] => [1,1,1,1,1,0,0,0,1,0,0,0] => {{1,2,6},{3,4,5}} => 6
[[[[.,[.,[.,.]]],.],.],.] => [1,1,1,1,0,1,0,1,0,0,0,0] => {{1,2,3,6},{4},{5}} => 6
[[[[.,[[.,.],.]],.],.],.] => [1,1,1,1,0,1,1,0,0,0,0,0] => {{1,2,3,5,6},{4}} => 6
[[[[[.,.],[.,.]],.],.],.] => [1,1,1,1,1,0,0,1,0,0,0,0] => {{1,2,3,6},{4,5}} => 6
[[[[[.,[.,.]],.],.],.],.] => [1,1,1,1,1,0,1,0,0,0,0,0] => {{1,2,3,4,6},{5}} => 6
[[[[[[.,.],.],.],.],.],.] => [1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3,4,5,6}} => 6
[.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6},{7}} => 1
[.,[.,[.,[.,[.,[[.,.],.]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6,7}} => 1
[.,[.,[.,[.,[[.,.],[.,.]]]]]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4},{5,6},{7}} => 1
[.,[.,[.,[.,[[.,[.,.]],.]]]]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => {{1},{2},{3},{4},{5,7},{6}} => 1
[.,[.,[.,[.,[[[.,.],.],.]]]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4},{5,6,7}} => 1
[.,[.,[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3},{4,5},{6},{7}} => 1
[.,[.,[.,[[.,.],[[.,.],.]]]]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 1
[.,[.,[.,[[.,[.,.]],[.,.]]]]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => {{1},{2},{3},{4,6},{5},{7}} => 1
[.,[.,[.,[[[.,.],.],[.,.]]]]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}} => 1
[.,[.,[.,[[.,[.,[.,.]]],.]]]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => {{1},{2},{3},{4,7},{5},{6}} => 1
[.,[.,[.,[[.,[[.,.],.]],.]]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => {{1},{2},{3},{4,6,7},{5}} => 1
[.,[.,[.,[[[.,.],[.,.]],.]]]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => {{1},{2},{3},{4,7},{5,6}} => 1
[.,[.,[.,[[[.,[.,.]],.],.]]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => {{1},{2},{3},{4,5,7},{6}} => 1
[.,[.,[.,[[[[.,.],.],.],.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3},{4,5,6,7}} => 1
[.,[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2},{3,4},{5},{6},{7}} => 1
[.,[.,[[.,.],[.,[[.,.],.]]]]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 1
[.,[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 1
[.,[.,[[.,.],[[.,[.,.]],.]]]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => {{1},{2},{3,4},{5,7},{6}} => 1
[.,[.,[[.,.],[[[.,.],.],.]]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 1
[.,[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => {{1},{2},{3,5},{4},{6},{7}} => 1
[.,[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => {{1},{2},{3,5},{4},{6,7}} => 1
[.,[.,[[[.,.],.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 1
[.,[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 1
[.,[.,[[.,[.,[.,.]]],[.,.]]]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => {{1},{2},{3,6},{4},{5},{7}} => 1
[.,[.,[[.,[[.,.],.]],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => {{1},{2},{3,5,6},{4},{7}} => 1
[.,[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => {{1},{2},{3,6},{4,5},{7}} => 1
[.,[.,[[[.,[.,.]],.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => {{1},{2},{3,4,6},{5},{7}} => 1
[.,[.,[[[[.,.],.],.],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => 1
[.,[.,[[.,[.,[.,[.,.]]]],.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => {{1},{2},{3,7},{4},{5},{6}} => 1
[.,[.,[[.,[.,[[.,.],.]]],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => {{1},{2},{3,6,7},{4},{5}} => 1
[.,[.,[[.,[[.,.],[.,.]]],.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => {{1},{2},{3,7},{4},{5,6}} => 1
[.,[.,[[.,[[.,[.,.]],.]],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => {{1},{2},{3,5,7},{4},{6}} => 1
[.,[.,[[.,[[[.,.],.],.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => {{1},{2},{3,5,6,7},{4}} => 1
[.,[.,[[[.,.],[.,[.,.]]],.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => {{1},{2},{3,7},{4,5},{6}} => 1
[.,[.,[[[.,.],[[.,.],.]],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => {{1},{2},{3,6,7},{4,5}} => 1
[.,[.,[[[.,[.,.]],[.,.]],.]]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => {{1},{2},{3,7},{4,6},{5}} => 1
[.,[.,[[[[.,.],.],[.,.]],.]]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => {{1},{2},{3,7},{4,5,6}} => 1
[.,[.,[[[.,[.,[.,.]]],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => {{1},{2},{3,4,7},{5},{6}} => 1
[.,[.,[[[.,[[.,.],.]],.],.]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => {{1},{2},{3,4,6,7},{5}} => 1
[.,[.,[[[[.,.],[.,.]],.],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => {{1},{2},{3,4,7},{5,6}} => 1
[.,[.,[[[[.,[.,.]],.],.],.]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => {{1},{2},{3,4,5,7},{6}} => 1
[.,[.,[[[[[.,.],.],.],.],.]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2},{3,4,5,6,7}} => 1
[.,[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6},{7}} => 1
[.,[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 1
[.,[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 1
[.,[[.,.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => {{1},{2,3},{4},{5,7},{6}} => 1
[.,[[.,.],[.,[[[.,.],.],.]]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 1
[.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 1
[.,[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 1
[.,[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => {{1},{2,3},{4,6},{5},{7}} => 1
[.,[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 1
[.,[[.,.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => {{1},{2,3},{4,7},{5},{6}} => 1
[.,[[.,.],[[.,[[.,.],.]],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => {{1},{2,3},{4,6,7},{5}} => 1
[.,[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => {{1},{2,3},{4,7},{5,6}} => 1
[.,[[.,.],[[[.,[.,.]],.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => {{1},{2,3},{4,5,7},{6}} => 1
[.,[[.,.],[[[[.,.],.],.],.]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 1
[.,[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => {{1},{2,4},{3},{5},{6},{7}} => 1
[.,[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => {{1},{2,4},{3},{5},{6,7}} => 1
[.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => {{1},{2,4},{3},{5,6},{7}} => 1
[.,[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => {{1},{2,4},{3},{5,7},{6}} => 1
[.,[[.,[.,.]],[[[.,.],.],.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => {{1},{2,4},{3},{5,6,7}} => 1
[.,[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}} => 1
[.,[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 1
[.,[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 1
[.,[[[.,.],.],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => {{1},{2,3,4},{5,7},{6}} => 1
[.,[[[.,.],.],[[[.,.],.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 1
[.,[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => {{1},{2,5},{3},{4},{6},{7}} => 1
[.,[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => {{1},{2,5},{3},{4},{6,7}} => 1
[.,[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => {{1},{2,4,5},{3},{6},{7}} => 1
[.,[[.,[[.,.],.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => {{1},{2,4,5},{3},{6,7}} => 1
[.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => {{1},{2,5},{3,4},{6},{7}} => 1
[.,[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => {{1},{2,5},{3,4},{6,7}} => 1
[.,[[[.,[.,.]],.],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => {{1},{2,3,5},{4},{6},{7}} => 1
[.,[[[.,[.,.]],.],[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => {{1},{2,3,5},{4},{6,7}} => 1
[.,[[[[.,.],.],.],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => 1
[.,[[[[.,.],.],.],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 1
[.,[[.,[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => {{1},{2,6},{3},{4},{5},{7}} => 1
[.,[[.,[.,[[.,.],.]]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => {{1},{2,5,6},{3},{4},{7}} => 1
[.,[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => {{1},{2,6},{3},{4,5},{7}} => 1
[.,[[.,[[.,[.,.]],.]],[.,.]]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => {{1},{2,4,6},{3},{5},{7}} => 1
[.,[[.,[[[.,.],.],.]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => {{1},{2,4,5,6},{3},{7}} => 1
[.,[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => {{1},{2,6},{3,4},{5},{7}} => 1
[.,[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => {{1},{2,5,6},{3,4},{7}} => 1
[.,[[[.,[.,.]],[.,.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => {{1},{2,6},{3,5},{4},{7}} => 1
[.,[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => {{1},{2,6},{3,4,5},{7}} => 1
[.,[[[.,[.,[.,.]]],.],[.,.]]] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => {{1},{2,3,6},{4},{5},{7}} => 1
[.,[[[.,[[.,.],.]],.],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => {{1},{2,3,5,6},{4},{7}} => 1
[.,[[[[.,.],[.,.]],.],[.,.]]] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => {{1},{2,3,6},{4,5},{7}} => 1
[.,[[[[.,[.,.]],.],.],[.,.]]] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => {{1},{2,3,4,6},{5},{7}} => 1
[.,[[[[[.,.],.],.],.],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6},{7}} => 1
[.,[[.,[.,[.,[.,[.,.]]]]],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => {{1},{2,7},{3},{4},{5},{6}} => 1
[.,[[.,[.,[.,[[.,.],.]]]],.]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => {{1},{2,6,7},{3},{4},{5}} => 1
[.,[[.,[.,[[.,.],[.,.]]]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => {{1},{2,7},{3},{4},{5,6}} => 1
[.,[[.,[.,[[.,[.,.]],.]]],.]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => {{1},{2,5,7},{3},{4},{6}} => 1
[.,[[.,[.,[[[.,.],.],.]]],.]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => {{1},{2,5,6,7},{3},{4}} => 1
[.,[[.,[[.,.],[.,[.,.]]]],.]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => {{1},{2,7},{3},{4,5},{6}} => 1
[.,[[.,[[.,.],[[.,.],.]]],.]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => {{1},{2,6,7},{3},{4,5}} => 1
[.,[[.,[[.,[.,.]],[.,.]]],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => {{1},{2,7},{3},{4,6},{5}} => 1
[.,[[.,[[[.,.],.],[.,.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => {{1},{2,7},{3},{4,5,6}} => 1
[.,[[.,[[.,[.,[.,.]]],.]],.]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => {{1},{2,4,7},{3},{5},{6}} => 1
[.,[[.,[[.,[[.,.],.]],.]],.]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => {{1},{2,4,6,7},{3},{5}} => 1
[.,[[.,[[[.,.],[.,.]],.]],.]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => {{1},{2,4,7},{3},{5,6}} => 1
[.,[[.,[[[.,[.,.]],.],.]],.]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => {{1},{2,4,5,7},{3},{6}} => 1
[.,[[.,[[[[.,.],.],.],.]],.]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => {{1},{2,4,5,6,7},{3}} => 1
[.,[[[.,.],[.,[.,[.,.]]]],.]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => {{1},{2,7},{3,4},{5},{6}} => 1
[.,[[[.,.],[.,[[.,.],.]]],.]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => {{1},{2,6,7},{3,4},{5}} => 1
[.,[[[.,.],[[.,.],[.,.]]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => {{1},{2,7},{3,4},{5,6}} => 1
[.,[[[.,.],[[.,[.,.]],.]],.]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => {{1},{2,5,7},{3,4},{6}} => 1
[.,[[[.,.],[[[.,.],.],.]],.]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => {{1},{2,5,6,7},{3,4}} => 1
[.,[[[.,[.,.]],[.,[.,.]]],.]] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => {{1},{2,7},{3,5},{4},{6}} => 1
[.,[[[.,[.,.]],[[.,.],.]],.]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => {{1},{2,6,7},{3,5},{4}} => 1
[.,[[[[.,.],.],[.,[.,.]]],.]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => {{1},{2,7},{3,4,5},{6}} => 1
[.,[[[[.,.],.],[[.,.],.]],.]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => {{1},{2,6,7},{3,4,5}} => 1
[.,[[[.,[.,[.,.]]],[.,.]],.]] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => {{1},{2,7},{3,6},{4},{5}} => 1
[.,[[[.,[[.,.],.]],[.,.]],.]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => {{1},{2,7},{3,5,6},{4}} => 1
[.,[[[[.,.],[.,.]],[.,.]],.]] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => {{1},{2,7},{3,6},{4,5}} => 1
[.,[[[[.,[.,.]],.],[.,.]],.]] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => {{1},{2,7},{3,4,6},{5}} => 1
[.,[[[[[.,.],.],.],[.,.]],.]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => {{1},{2,7},{3,4,5,6}} => 1
[.,[[[.,[.,[.,[.,.]]]],.],.]] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => {{1},{2,3,7},{4},{5},{6}} => 1
[.,[[[.,[.,[[.,.],.]]],.],.]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => {{1},{2,3,6,7},{4},{5}} => 1
[.,[[[.,[[.,.],[.,.]]],.],.]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => {{1},{2,3,7},{4},{5,6}} => 1
[.,[[[.,[[.,[.,.]],.]],.],.]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => {{1},{2,3,5,7},{4},{6}} => 1
[.,[[[.,[[[.,.],.],.]],.],.]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => {{1},{2,3,5,6,7},{4}} => 1
[.,[[[[.,.],[.,[.,.]]],.],.]] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => {{1},{2,3,7},{4,5},{6}} => 1
[.,[[[[.,.],[[.,.],.]],.],.]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => {{1},{2,3,6,7},{4,5}} => 1
[.,[[[[.,[.,.]],[.,.]],.],.]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => {{1},{2,3,7},{4,6},{5}} => 1
[.,[[[[[.,.],.],[.,.]],.],.]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => {{1},{2,3,7},{4,5,6}} => 1
[.,[[[[.,[.,[.,.]]],.],.],.]] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => {{1},{2,3,4,7},{5},{6}} => 1
[.,[[[[.,[[.,.],.]],.],.],.]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => {{1},{2,3,4,6,7},{5}} => 1
[.,[[[[[.,.],[.,.]],.],.],.]] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => {{1},{2,3,4,7},{5,6}} => 1
[.,[[[[[.,[.,.]],.],.],.],.]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => {{1},{2,3,4,5,7},{6}} => 1
[.,[[[[[[.,.],.],.],.],.],.]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7}} => 1
[[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5},{6},{7}} => 2
[[.,.],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6,7}} => 2
[[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 2
[[.,.],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => {{1,2},{3},{4},{5,7},{6}} => 2
[[.,.],[.,[.,[[[.,.],.],.]]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => 2
[[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 2
[[.,.],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 2
[[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => {{1,2},{3},{4,6},{5},{7}} => 2
[[.,.],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 2
[[.,.],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => {{1,2},{3},{4,7},{5},{6}} => 2
[[.,.],[.,[[.,[[.,.],.]],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => {{1,2},{3},{4,6,7},{5}} => 2
[[.,.],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => {{1,2},{3},{4,7},{5,6}} => 2
[[.,.],[.,[[[.,[.,.]],.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => {{1,2},{3},{4,5,7},{6}} => 2
[[.,.],[.,[[[[.,.],.],.],.]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}} => 2
[[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 2
[[.,.],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 2
[[.,.],[[.,.],[[.,.],[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 2
[[.,.],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => {{1,2},{3,4},{5,7},{6}} => 2
[[.,.],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 2
[[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => {{1,2},{3,5},{4},{6},{7}} => 2
[[.,.],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => {{1,2},{3,5},{4},{6,7}} => 2
[[.,.],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 2
[[.,.],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 2
[[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => {{1,2},{3,6},{4},{5},{7}} => 2
[[.,.],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => {{1,2},{3,5,6},{4},{7}} => 2
[[.,.],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => {{1,2},{3,6},{4,5},{7}} => 2
[[.,.],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => {{1,2},{3,4,6},{5},{7}} => 2
[[.,.],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 2
[[.,.],[[.,[.,[.,[.,.]]]],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => {{1,2},{3,7},{4},{5},{6}} => 2
[[.,.],[[.,[.,[[.,.],.]]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => {{1,2},{3,6,7},{4},{5}} => 2
[[.,.],[[.,[[.,.],[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => {{1,2},{3,7},{4},{5,6}} => 2
[[.,.],[[.,[[.,[.,.]],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => {{1,2},{3,5,7},{4},{6}} => 2
[[.,.],[[.,[[[.,.],.],.]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => {{1,2},{3,5,6,7},{4}} => 2
[[.,.],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => {{1,2},{3,7},{4,5},{6}} => 2
[[.,.],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => {{1,2},{3,6,7},{4,5}} => 2
[[.,.],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => {{1,2},{3,7},{4,6},{5}} => 2
[[.,.],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => {{1,2},{3,7},{4,5,6}} => 2
[[.,.],[[[.,[.,[.,.]]],.],.]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => {{1,2},{3,4,7},{5},{6}} => 2
[[.,.],[[[.,[[.,.],.]],.],.]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => {{1,2},{3,4,6,7},{5}} => 2
[[.,.],[[[[.,.],[.,.]],.],.]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => {{1,2},{3,4,7},{5,6}} => 2
[[.,.],[[[[.,[.,.]],.],.],.]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => {{1,2},{3,4,5,7},{6}} => 2
[[.,.],[[[[[.,.],.],.],.],.]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3,4,5,6,7}} => 2
[[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => {{1,3},{2},{4},{5},{6},{7}} => 3
[[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => {{1,3},{2},{4},{5},{6,7}} => 3
[[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => {{1,3},{2},{4},{5,6},{7}} => 3
[[.,[.,.]],[.,[[.,[.,.]],.]]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => {{1,3},{2},{4},{5,7},{6}} => 3
[[.,[.,.]],[.,[[[.,.],.],.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => {{1,3},{2},{4},{5,6,7}} => 3
[[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => {{1,3},{2},{4,5},{6},{7}} => 3
[[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => {{1,3},{2},{4,5},{6,7}} => 3
[[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => {{1,3},{2},{4,6},{5},{7}} => 3
[[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => {{1,3},{2},{4,5,6},{7}} => 3
[[.,[.,.]],[[.,[.,[.,.]]],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => {{1,3},{2},{4,7},{5},{6}} => 3
[[.,[.,.]],[[.,[[.,.],.]],.]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => {{1,3},{2},{4,6,7},{5}} => 3
[[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => {{1,3},{2},{4,7},{5,6}} => 3
[[.,[.,.]],[[[.,[.,.]],.],.]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => {{1,3},{2},{4,5,7},{6}} => 3
[[.,[.,.]],[[[[.,.],.],.],.]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => {{1,3},{2},{4,5,6,7}} => 3
[[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6},{7}} => 3
[[[.,.],.],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => 3
[[[.,.],.],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 3
[[[.,.],.],[.,[[.,[.,.]],.]]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => {{1,2,3},{4},{5,7},{6}} => 3
[[[.,.],.],[.,[[[.,.],.],.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 3
[[[.,.],.],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 3
[[[.,.],.],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 3
[[[.,.],.],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => {{1,2,3},{4,6},{5},{7}} => 3
[[[.,.],.],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 3
[[[.,.],.],[[.,[.,[.,.]]],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => {{1,2,3},{4,7},{5},{6}} => 3
[[[.,.],.],[[.,[[.,.],.]],.]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => {{1,2,3},{4,6,7},{5}} => 3
[[[.,.],.],[[[.,.],[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => {{1,2,3},{4,7},{5,6}} => 3
[[[.,.],.],[[[.,[.,.]],.],.]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => {{1,2,3},{4,5,7},{6}} => 3
[[[.,.],.],[[[[.,.],.],.],.]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}} => 3
[[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => {{1,4},{2},{3},{5},{6},{7}} => 4
[[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => {{1,4},{2},{3},{5},{6,7}} => 4
[[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => {{1,4},{2},{3},{5,6},{7}} => 4
[[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => {{1,4},{2},{3},{5,7},{6}} => 4
[[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => {{1,4},{2},{3},{5,6,7}} => 4
[[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => {{1,3,4},{2},{5},{6},{7}} => 4
[[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => {{1,3,4},{2},{5},{6,7}} => 4
[[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => {{1,3,4},{2},{5,6},{7}} => 4
[[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => {{1,3,4},{2},{5,7},{6}} => 4
[[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => {{1,3,4},{2},{5,6,7}} => 4
[[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => {{1,4},{2,3},{5},{6},{7}} => 4
[[[.,.],[.,.]],[.,[[.,.],.]]] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => {{1,4},{2,3},{5},{6,7}} => 4
[[[.,.],[.,.]],[[.,.],[.,.]]] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => {{1,4},{2,3},{5,6},{7}} => 4
[[[.,.],[.,.]],[[.,[.,.]],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => {{1,4},{2,3},{5,7},{6}} => 4
[[[.,.],[.,.]],[[[.,.],.],.]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => {{1,4},{2,3},{5,6,7}} => 4
[[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => {{1,2,4},{3},{5},{6},{7}} => 4
[[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => {{1,2,4},{3},{5},{6,7}} => 4
[[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => {{1,2,4},{3},{5,6},{7}} => 4
[[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => {{1,2,4},{3},{5,7},{6}} => 4
[[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => {{1,2,4},{3},{5,6,7}} => 4
[[[[.,.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => {{1,2,3,4},{5},{6},{7}} => 4
[[[[.,.],.],.],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}} => 4
[[[[.,.],.],.],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 4
[[[[.,.],.],.],[[.,[.,.]],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => {{1,2,3,4},{5,7},{6}} => 4
[[[[.,.],.],.],[[[.,.],.],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7}} => 4
[[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => {{1,5},{2},{3},{4},{6},{7}} => 5
[[.,[.,[.,[.,.]]]],[[.,.],.]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => {{1,5},{2},{3},{4},{6,7}} => 5
[[.,[.,[[.,.],.]]],[.,[.,.]]] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => {{1,4,5},{2},{3},{6},{7}} => 5
[[.,[.,[[.,.],.]]],[[.,.],.]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => {{1,4,5},{2},{3},{6,7}} => 5
[[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => {{1,5},{2},{3,4},{6},{7}} => 5
[[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => {{1,5},{2},{3,4},{6,7}} => 5
[[.,[[.,[.,.]],.]],[.,[.,.]]] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => {{1,3,5},{2},{4},{6},{7}} => 5
[[.,[[.,[.,.]],.]],[[.,.],.]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => {{1,3,5},{2},{4},{6,7}} => 5
[[.,[[[.,.],.],.]],[.,[.,.]]] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => {{1,3,4,5},{2},{6},{7}} => 5
[[.,[[[.,.],.],.]],[[.,.],.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => {{1,3,4,5},{2},{6,7}} => 5
[[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => {{1,5},{2,3},{4},{6},{7}} => 5
[[[.,.],[.,[.,.]]],[[.,.],.]] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => {{1,5},{2,3},{4},{6,7}} => 5
[[[.,.],[[.,.],.]],[.,[.,.]]] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => {{1,4,5},{2,3},{6},{7}} => 5
[[[.,.],[[.,.],.]],[[.,.],.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => {{1,4,5},{2,3},{6,7}} => 5
[[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => {{1,5},{2,4},{3},{6},{7}} => 5
[[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => {{1,5},{2,4},{3},{6,7}} => 5
[[[[.,.],.],[.,.]],[.,[.,.]]] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => {{1,5},{2,3,4},{6},{7}} => 5
[[[[.,.],.],[.,.]],[[.,.],.]] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => {{1,5},{2,3,4},{6,7}} => 5
[[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => {{1,2,5},{3},{4},{6},{7}} => 5
[[[.,[.,[.,.]]],.],[[.,.],.]] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => {{1,2,5},{3},{4},{6,7}} => 5
[[[.,[[.,.],.]],.],[.,[.,.]]] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => {{1,2,4,5},{3},{6},{7}} => 5
[[[.,[[.,.],.]],.],[[.,.],.]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => {{1,2,4,5},{3},{6,7}} => 5
[[[[.,.],[.,.]],.],[.,[.,.]]] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => {{1,2,5},{3,4},{6},{7}} => 5
[[[[.,.],[.,.]],.],[[.,.],.]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => {{1,2,5},{3,4},{6,7}} => 5
[[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => {{1,2,3,5},{4},{6},{7}} => 5
[[[[.,[.,.]],.],.],[[.,.],.]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => {{1,2,3,5},{4},{6,7}} => 5
[[[[[.,.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => {{1,2,3,4,5},{6},{7}} => 5
[[[[[.,.],.],.],.],[[.,.],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5},{6,7}} => 5
[[.,[.,[.,[.,[.,.]]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => {{1,6},{2},{3},{4},{5},{7}} => 6
[[.,[.,[.,[[.,.],.]]]],[.,.]] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => {{1,5,6},{2},{3},{4},{7}} => 6
[[.,[.,[[.,.],[.,.]]]],[.,.]] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => {{1,6},{2},{3},{4,5},{7}} => 6
[[.,[.,[[.,[.,.]],.]]],[.,.]] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => {{1,4,6},{2},{3},{5},{7}} => 6
[[.,[.,[[[.,.],.],.]]],[.,.]] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => {{1,4,5,6},{2},{3},{7}} => 6
[[.,[[.,.],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => {{1,6},{2},{3,4},{5},{7}} => 6
[[.,[[.,.],[[.,.],.]]],[.,.]] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => {{1,5,6},{2},{3,4},{7}} => 6
[[.,[[.,[.,.]],[.,.]]],[.,.]] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => {{1,6},{2},{3,5},{4},{7}} => 6
[[.,[[[.,.],.],[.,.]]],[.,.]] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => {{1,6},{2},{3,4,5},{7}} => 6
[[.,[[.,[.,[.,.]]],.]],[.,.]] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => {{1,3,6},{2},{4},{5},{7}} => 6
[[.,[[.,[[.,.],.]],.]],[.,.]] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => {{1,3,5,6},{2},{4},{7}} => 6
[[.,[[[.,.],[.,.]],.]],[.,.]] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => {{1,3,6},{2},{4,5},{7}} => 6
[[.,[[[.,[.,.]],.],.]],[.,.]] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => {{1,3,4,6},{2},{5},{7}} => 6
[[.,[[[[.,.],.],.],.]],[.,.]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => {{1,3,4,5,6},{2},{7}} => 6
[[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => {{1,6},{2,3},{4},{5},{7}} => 6
[[[.,.],[.,[[.,.],.]]],[.,.]] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => {{1,5,6},{2,3},{4},{7}} => 6
[[[.,.],[[.,.],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => {{1,6},{2,3},{4,5},{7}} => 6
[[[.,.],[[.,[.,.]],.]],[.,.]] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => {{1,4,6},{2,3},{5},{7}} => 6
[[[.,.],[[[.,.],.],.]],[.,.]] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => {{1,4,5,6},{2,3},{7}} => 6
[[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => {{1,6},{2,4},{3},{5},{7}} => 6
[[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => {{1,5,6},{2,4},{3},{7}} => 6
[[[[.,.],.],[.,[.,.]]],[.,.]] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => {{1,6},{2,3,4},{5},{7}} => 6
[[[[.,.],.],[[.,.],.]],[.,.]] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => {{1,5,6},{2,3,4},{7}} => 6
[[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => {{1,6},{2,5},{3},{4},{7}} => 6
[[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => {{1,6},{2,4,5},{3},{7}} => 6
[[[[.,.],[.,.]],[.,.]],[.,.]] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => {{1,6},{2,5},{3,4},{7}} => 6
[[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => {{1,6},{2,3,5},{4},{7}} => 6
[[[[[.,.],.],.],[.,.]],[.,.]] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => {{1,6},{2,3,4,5},{7}} => 6
[[[.,[.,[.,[.,.]]]],.],[.,.]] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => {{1,2,6},{3},{4},{5},{7}} => 6
[[[.,[.,[[.,.],.]]],.],[.,.]] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => {{1,2,5,6},{3},{4},{7}} => 6
[[[.,[[.,.],[.,.]]],.],[.,.]] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => {{1,2,6},{3},{4,5},{7}} => 6
[[[.,[[.,[.,.]],.]],.],[.,.]] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => {{1,2,4,6},{3},{5},{7}} => 6
[[[.,[[[.,.],.],.]],.],[.,.]] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => {{1,2,4,5,6},{3},{7}} => 6
[[[[.,.],[.,[.,.]]],.],[.,.]] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => {{1,2,6},{3,4},{5},{7}} => 6
[[[[.,.],[[.,.],.]],.],[.,.]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => {{1,2,5,6},{3,4},{7}} => 6
[[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => {{1,2,6},{3,5},{4},{7}} => 6
[[[[[.,.],.],[.,.]],.],[.,.]] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => {{1,2,6},{3,4,5},{7}} => 6
[[[[.,[.,[.,.]]],.],.],[.,.]] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => {{1,2,3,6},{4},{5},{7}} => 6
[[[[.,[[.,.],.]],.],.],[.,.]] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => {{1,2,3,5,6},{4},{7}} => 6
[[[[[.,.],[.,.]],.],.],[.,.]] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => {{1,2,3,6},{4,5},{7}} => 6
[[[[[.,[.,.]],.],.],.],[.,.]] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,6},{5},{7}} => 6
[[[[[[.,.],.],.],.],.],[.,.]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6},{7}} => 6
[[.,[.,[.,[.,[.,[.,.]]]]]],.] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1,7},{2},{3},{4},{5},{6}} => 7
[[.,[.,[.,[.,[[.,.],.]]]]],.] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => {{1,6,7},{2},{3},{4},{5}} => 7
[[.,[.,[.,[[.,.],[.,.]]]]],.] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => {{1,7},{2},{3},{4},{5,6}} => 7
[[.,[.,[.,[[.,[.,.]],.]]]],.] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => {{1,5,7},{2},{3},{4},{6}} => 7
[[.,[.,[.,[[[.,.],.],.]]]],.] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => {{1,5,6,7},{2},{3},{4}} => 7
[[.,[.,[[.,.],[.,[.,.]]]]],.] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => {{1,7},{2},{3},{4,5},{6}} => 7
[[.,[.,[[.,.],[[.,.],.]]]],.] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => {{1,6,7},{2},{3},{4,5}} => 7
[[.,[.,[[.,[.,.]],[.,.]]]],.] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => {{1,7},{2},{3},{4,6},{5}} => 7
[[.,[.,[[[.,.],.],[.,.]]]],.] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => {{1,7},{2},{3},{4,5,6}} => 7
[[.,[.,[[.,[.,[.,.]]],.]]],.] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => {{1,4,7},{2},{3},{5},{6}} => 7
[[.,[.,[[.,[[.,.],.]],.]]],.] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => {{1,4,6,7},{2},{3},{5}} => 7
[[.,[.,[[[.,.],[.,.]],.]]],.] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => {{1,4,7},{2},{3},{5,6}} => 7
[[.,[.,[[[.,[.,.]],.],.]]],.] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => {{1,4,5,7},{2},{3},{6}} => 7
[[.,[.,[[[[.,.],.],.],.]]],.] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => {{1,4,5,6,7},{2},{3}} => 7
[[.,[[.,.],[.,[.,[.,.]]]]],.] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => {{1,7},{2},{3,4},{5},{6}} => 7
[[.,[[.,.],[.,[[.,.],.]]]],.] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => {{1,6,7},{2},{3,4},{5}} => 7
[[.,[[.,.],[[.,.],[.,.]]]],.] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => {{1,7},{2},{3,4},{5,6}} => 7
[[.,[[.,.],[[.,[.,.]],.]]],.] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => {{1,5,7},{2},{3,4},{6}} => 7
[[.,[[.,.],[[[.,.],.],.]]],.] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => {{1,5,6,7},{2},{3,4}} => 7
[[.,[[.,[.,.]],[.,[.,.]]]],.] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => {{1,7},{2},{3,5},{4},{6}} => 7
[[.,[[.,[.,.]],[[.,.],.]]],.] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => {{1,6,7},{2},{3,5},{4}} => 7
[[.,[[[.,.],.],[.,[.,.]]]],.] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => {{1,7},{2},{3,4,5},{6}} => 7
[[.,[[[.,.],.],[[.,.],.]]],.] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => {{1,6,7},{2},{3,4,5}} => 7
[[.,[[.,[.,[.,.]]],[.,.]]],.] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => {{1,7},{2},{3,6},{4},{5}} => 7
[[.,[[.,[[.,.],.]],[.,.]]],.] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => {{1,7},{2},{3,5,6},{4}} => 7
[[.,[[[.,.],[.,.]],[.,.]]],.] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => {{1,7},{2},{3,6},{4,5}} => 7
[[.,[[[.,[.,.]],.],[.,.]]],.] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => {{1,7},{2},{3,4,6},{5}} => 7
[[.,[[[[.,.],.],.],[.,.]]],.] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => {{1,7},{2},{3,4,5,6}} => 7
[[.,[[.,[.,[.,[.,.]]]],.]],.] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => {{1,3,7},{2},{4},{5},{6}} => 7
[[.,[[.,[.,[[.,.],.]]],.]],.] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => {{1,3,6,7},{2},{4},{5}} => 7
[[.,[[.,[[.,.],[.,.]]],.]],.] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => {{1,3,7},{2},{4},{5,6}} => 7
[[.,[[.,[[.,[.,.]],.]],.]],.] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => {{1,3,5,7},{2},{4},{6}} => 7
[[.,[[.,[[[.,.],.],.]],.]],.] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => {{1,3,5,6,7},{2},{4}} => 7
[[.,[[[.,.],[.,[.,.]]],.]],.] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => {{1,3,7},{2},{4,5},{6}} => 7
[[.,[[[.,.],[[.,.],.]],.]],.] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => {{1,3,6,7},{2},{4,5}} => 7
[[.,[[[.,[.,.]],[.,.]],.]],.] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => {{1,3,7},{2},{4,6},{5}} => 7
[[.,[[[[.,.],.],[.,.]],.]],.] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => {{1,3,7},{2},{4,5,6}} => 7
[[.,[[[.,[.,[.,.]]],.],.]],.] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => {{1,3,4,7},{2},{5},{6}} => 7
[[.,[[[.,[[.,.],.]],.],.]],.] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => {{1,3,4,6,7},{2},{5}} => 7
[[.,[[[[.,.],[.,.]],.],.]],.] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => {{1,3,4,7},{2},{5,6}} => 7
[[.,[[[[.,[.,.]],.],.],.]],.] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => {{1,3,4,5,7},{2},{6}} => 7
[[.,[[[[[.,.],.],.],.],.]],.] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => {{1,3,4,5,6,7},{2}} => 7
[[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => {{1,7},{2,3},{4},{5},{6}} => 7
[[[.,.],[.,[.,[[.,.],.]]]],.] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => {{1,6,7},{2,3},{4},{5}} => 7
[[[.,.],[.,[[.,.],[.,.]]]],.] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => {{1,7},{2,3},{4},{5,6}} => 7
[[[.,.],[.,[[.,[.,.]],.]]],.] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => {{1,5,7},{2,3},{4},{6}} => 7
[[[.,.],[.,[[[.,.],.],.]]],.] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => {{1,5,6,7},{2,3},{4}} => 7
[[[.,.],[[.,.],[.,[.,.]]]],.] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => {{1,7},{2,3},{4,5},{6}} => 7
[[[.,.],[[.,.],[[.,.],.]]],.] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => {{1,6,7},{2,3},{4,5}} => 7
[[[.,.],[[.,[.,.]],[.,.]]],.] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => {{1,7},{2,3},{4,6},{5}} => 7
[[[.,.],[[[.,.],.],[.,.]]],.] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => {{1,7},{2,3},{4,5,6}} => 7
[[[.,.],[[.,[.,[.,.]]],.]],.] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => {{1,4,7},{2,3},{5},{6}} => 7
[[[.,.],[[.,[[.,.],.]],.]],.] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => {{1,4,6,7},{2,3},{5}} => 7
[[[.,.],[[[.,.],[.,.]],.]],.] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => {{1,4,7},{2,3},{5,6}} => 7
[[[.,.],[[[.,[.,.]],.],.]],.] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => {{1,4,5,7},{2,3},{6}} => 7
[[[.,.],[[[[.,.],.],.],.]],.] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => {{1,4,5,6,7},{2,3}} => 7
[[[.,[.,.]],[.,[.,[.,.]]]],.] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => {{1,7},{2,4},{3},{5},{6}} => 7
[[[.,[.,.]],[.,[[.,.],.]]],.] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => {{1,6,7},{2,4},{3},{5}} => 7
[[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => {{1,7},{2,4},{3},{5,6}} => 7
[[[.,[.,.]],[[.,[.,.]],.]],.] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => {{1,5,7},{2,4},{3},{6}} => 7
[[[.,[.,.]],[[[.,.],.],.]],.] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => {{1,5,6,7},{2,4},{3}} => 7
[[[[.,.],.],[.,[.,[.,.]]]],.] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => {{1,7},{2,3,4},{5},{6}} => 7
[[[[.,.],.],[.,[[.,.],.]]],.] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => {{1,6,7},{2,3,4},{5}} => 7
[[[[.,.],.],[[.,.],[.,.]]],.] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => {{1,7},{2,3,4},{5,6}} => 7
[[[[.,.],.],[[.,[.,.]],.]],.] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => {{1,5,7},{2,3,4},{6}} => 7
[[[[.,.],.],[[[.,.],.],.]],.] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => {{1,5,6,7},{2,3,4}} => 7
[[[.,[.,[.,.]]],[.,[.,.]]],.] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => {{1,7},{2,5},{3},{4},{6}} => 7
[[[.,[.,[.,.]]],[[.,.],.]],.] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => {{1,6,7},{2,5},{3},{4}} => 7
[[[.,[[.,.],.]],[.,[.,.]]],.] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => {{1,7},{2,4,5},{3},{6}} => 7
[[[.,[[.,.],.]],[[.,.],.]],.] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => {{1,6,7},{2,4,5},{3}} => 7
[[[[.,.],[.,.]],[.,[.,.]]],.] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => {{1,7},{2,5},{3,4},{6}} => 7
[[[[.,.],[.,.]],[[.,.],.]],.] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => {{1,6,7},{2,5},{3,4}} => 7
[[[[.,[.,.]],.],[.,[.,.]]],.] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => {{1,7},{2,3,5},{4},{6}} => 7
[[[[.,[.,.]],.],[[.,.],.]],.] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => {{1,6,7},{2,3,5},{4}} => 7
[[[[[.,.],.],.],[.,[.,.]]],.] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => {{1,7},{2,3,4,5},{6}} => 7
[[[[[.,.],.],.],[[.,.],.]],.] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => {{1,6,7},{2,3,4,5}} => 7
[[[.,[.,[.,[.,.]]]],[.,.]],.] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => {{1,7},{2,6},{3},{4},{5}} => 7
[[[.,[.,[[.,.],.]]],[.,.]],.] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => {{1,7},{2,5,6},{3},{4}} => 7
[[[.,[[.,.],[.,.]]],[.,.]],.] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => {{1,7},{2,6},{3},{4,5}} => 7
[[[.,[[.,[.,.]],.]],[.,.]],.] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => {{1,7},{2,4,6},{3},{5}} => 7
[[[.,[[[.,.],.],.]],[.,.]],.] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => {{1,7},{2,4,5,6},{3}} => 7
[[[[.,.],[.,[.,.]]],[.,.]],.] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => {{1,7},{2,6},{3,4},{5}} => 7
[[[[.,.],[[.,.],.]],[.,.]],.] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => {{1,7},{2,5,6},{3,4}} => 7
[[[[.,[.,.]],[.,.]],[.,.]],.] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => {{1,7},{2,6},{3,5},{4}} => 7
[[[[[.,.],.],[.,.]],[.,.]],.] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => {{1,7},{2,6},{3,4,5}} => 7
[[[[.,[.,[.,.]]],.],[.,.]],.] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => {{1,7},{2,3,6},{4},{5}} => 7
[[[[.,[[.,.],.]],.],[.,.]],.] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => {{1,7},{2,3,5,6},{4}} => 7
[[[[[.,.],[.,.]],.],[.,.]],.] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => {{1,7},{2,3,6},{4,5}} => 7
[[[[[.,[.,.]],.],.],[.,.]],.] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => {{1,7},{2,3,4,6},{5}} => 7
[[[[[[.,.],.],.],.],[.,.]],.] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => {{1,7},{2,3,4,5,6}} => 7
[[[.,[.,[.,[.,[.,.]]]]],.],.] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => {{1,2,7},{3},{4},{5},{6}} => 7
[[[.,[.,[.,[[.,.],.]]]],.],.] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => {{1,2,6,7},{3},{4},{5}} => 7
[[[.,[.,[[.,.],[.,.]]]],.],.] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => {{1,2,7},{3},{4},{5,6}} => 7
[[[.,[.,[[.,[.,.]],.]]],.],.] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => {{1,2,5,7},{3},{4},{6}} => 7
[[[.,[.,[[[.,.],.],.]]],.],.] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => {{1,2,5,6,7},{3},{4}} => 7
[[[.,[[.,.],[.,[.,.]]]],.],.] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => {{1,2,7},{3},{4,5},{6}} => 7
[[[.,[[.,.],[[.,.],.]]],.],.] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => {{1,2,6,7},{3},{4,5}} => 7
[[[.,[[.,[.,.]],[.,.]]],.],.] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => {{1,2,7},{3},{4,6},{5}} => 7
[[[.,[[[.,.],.],[.,.]]],.],.] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => {{1,2,7},{3},{4,5,6}} => 7
[[[.,[[.,[.,[.,.]]],.]],.],.] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => {{1,2,4,7},{3},{5},{6}} => 7
[[[.,[[.,[[.,.],.]],.]],.],.] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => {{1,2,4,6,7},{3},{5}} => 7
[[[.,[[[.,.],[.,.]],.]],.],.] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => {{1,2,4,7},{3},{5,6}} => 7
[[[.,[[[.,[.,.]],.],.]],.],.] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => {{1,2,4,5,7},{3},{6}} => 7
[[[.,[[[[.,.],.],.],.]],.],.] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => {{1,2,4,5,6,7},{3}} => 7
[[[[.,.],[.,[.,[.,.]]]],.],.] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => {{1,2,7},{3,4},{5},{6}} => 7
[[[[.,.],[.,[[.,.],.]]],.],.] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => {{1,2,6,7},{3,4},{5}} => 7
[[[[.,.],[[.,.],[.,.]]],.],.] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => {{1,2,7},{3,4},{5,6}} => 7
[[[[.,.],[[.,[.,.]],.]],.],.] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => {{1,2,5,7},{3,4},{6}} => 7
[[[[.,.],[[[.,.],.],.]],.],.] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => {{1,2,5,6,7},{3,4}} => 7
[[[[.,[.,.]],[.,[.,.]]],.],.] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => {{1,2,7},{3,5},{4},{6}} => 7
[[[[.,[.,.]],[[.,.],.]],.],.] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => {{1,2,6,7},{3,5},{4}} => 7
[[[[[.,.],.],[.,[.,.]]],.],.] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => {{1,2,7},{3,4,5},{6}} => 7
[[[[[.,.],.],[[.,.],.]],.],.] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => {{1,2,6,7},{3,4,5}} => 7
[[[[.,[.,[.,.]]],[.,.]],.],.] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => {{1,2,7},{3,6},{4},{5}} => 7
[[[[.,[[.,.],.]],[.,.]],.],.] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => {{1,2,7},{3,5,6},{4}} => 7
[[[[[.,.],[.,.]],[.,.]],.],.] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => {{1,2,7},{3,6},{4,5}} => 7
[[[[[.,[.,.]],.],[.,.]],.],.] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => {{1,2,7},{3,4,6},{5}} => 7
[[[[[[.,.],.],.],[.,.]],.],.] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => {{1,2,7},{3,4,5,6}} => 7
[[[[.,[.,[.,[.,.]]]],.],.],.] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => {{1,2,3,7},{4},{5},{6}} => 7
[[[[.,[.,[[.,.],.]]],.],.],.] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => {{1,2,3,6,7},{4},{5}} => 7
[[[[.,[[.,.],[.,.]]],.],.],.] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => {{1,2,3,7},{4},{5,6}} => 7
[[[[.,[[.,[.,.]],.]],.],.],.] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => {{1,2,3,5,7},{4},{6}} => 7
[[[[.,[[[.,.],.],.]],.],.],.] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => {{1,2,3,5,6,7},{4}} => 7
[[[[[.,.],[.,[.,.]]],.],.],.] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => {{1,2,3,7},{4,5},{6}} => 7
[[[[[.,.],[[.,.],.]],.],.],.] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => {{1,2,3,6,7},{4,5}} => 7
[[[[[.,[.,.]],[.,.]],.],.],.] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => {{1,2,3,7},{4,6},{5}} => 7
[[[[[[.,.],.],[.,.]],.],.],.] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => {{1,2,3,7},{4,5,6}} => 7
[[[[[.,[.,[.,.]]],.],.],.],.] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => {{1,2,3,4,7},{5},{6}} => 7
[[[[[.,[[.,.],.]],.],.],.],.] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => {{1,2,3,4,6,7},{5}} => 7
[[[[[[.,.],[.,.]],.],.],.],.] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => {{1,2,3,4,7},{5,6}} => 7
[[[[[[.,[.,.]],.],.],.],.],.] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => {{1,2,3,4,5,7},{6}} => 7
[[[[[[[.,.],.],.],.],.],.],.] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,7}} => 7
[.,[.,[[[[[[.,.],.],.],.],.],.]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2},{3,4,5,6,7,8}} => 1
[.,[[[[[[.,.],.],.],.],.],[.,.]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7},{8}} => 1
[.,[[.,[[[[[.,.],.],.],.],.]],.]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2,4,5,6,7,8},{3}} => 1
[.,[[[.,[[[[.,.],.],.],.]],.],.]] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => {{1},{2,3,5,6,7,8},{4}} => 1
[.,[[[[.,[[[.,.],.],.]],.],.],.]] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => {{1},{2,3,4,6,7,8},{5}} => 1
[.,[[[[[[.,.],.],[.,.]],.],.],.]] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => {{1},{2,3,4,8},{5,6,7}} => 1
[.,[[[[[.,[.,[.,.]]],.],.],.],.]] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => {{1},{2,3,4,5,8},{6},{7}} => 1
[.,[[[[[.,[[.,.],.]],.],.],.],.]] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => {{1},{2,3,4,5,7,8},{6}} => 1
[.,[[[[[[.,.],[.,.]],.],.],.],.]] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => {{1},{2,3,4,5,8},{6,7}} => 1
[.,[[[[[[.,[.,.]],.],.],.],.],.]] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => {{1},{2,3,4,5,6,8},{7}} => 1
[.,[[[[[[[.,.],.],.],.],.],.],.]] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8}} => 1
[[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8}} => 2
[[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => {{1,2},{3,4},{5,8},{6,7}} => 2
[[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => {{1,2},{3,6},{4,5},{7,8}} => 2
[[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => {{1,2},{3,8},{4,5},{6,7}} => 2
[[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => {{1,2},{3,8},{4,7},{5,6}} => 2
[[.,.],[[[[[[.,.],.],.],.],.],.]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8}} => 2
[[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => {{1,4},{2,3},{5,6},{7,8}} => 4
[[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => {{1,4},{2,3},{5,8},{6,7}} => 4
[[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => {{1,6},{2,3},{4,5},{7,8}} => 6
[[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => {{1,6},{2,5},{3,4},{7,8}} => 6
[[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6},{7,8}} => 6
[[[[.,[[[.,.],.],.]],.],.],[.,.]] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,5,6,7},{4},{8}} => 7
[[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => {{1,2,3,7},{4,5,6},{8}} => 7
[[[[[.,[.,[.,.]]],.],.],.],[.,.]] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5},{6},{8}} => 7
[[[[[.,[[.,.],.]],.],.],.],[.,.]] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,6,7},{5},{8}} => 7
[[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5,6},{8}} => 7
[[[[[[.,[.,.]],.],.],.],.],[.,.]] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,7},{6},{8}} => 7
[[[[[[[.,.],.],.],.],.],.],[.,.]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7},{8}} => 7
[[.,[.,[[[[[.,.],.],.],.],.]]],.] => [1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => {{1,4,5,6,7,8},{2},{3}} => 8
[[.,[[.,[[[[.,.],.],.],.]],.]],.] => [1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => {{1,3,5,6,7,8},{2},{4}} => 8
[[.,[[[[[[.,.],.],.],.],.],.]],.] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,3,4,5,6,7,8},{2}} => 8
[[[.,.],[[.,.],[[.,.],[.,.]]]],.] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => {{1,8},{2,3},{4,5},{6,7}} => 8
[[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => {{1,8},{2,3},{4,7},{5,6}} => 8
[[[.,.],[[[[[.,.],.],.],.],.]],.] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => {{1,4,5,6,7,8},{2,3}} => 8
[[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => {{1,8},{2,5},{3,4},{6,7}} => 8
[[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => {{1,8},{2,7},{3,4},{5,6}} => 8
[[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,8},{2,7},{3,6},{4,5}} => 8
[[[[[[[.,.],.],.],.],.],[.,.]],.] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => {{1,8},{2,3,4,5,6,7}} => 8
[[[.,[[[[[.,.],.],.],.],.]],.],.] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2,4,5,6,7,8},{3}} => 8
[[[[.,.],[[[[.,.],.],.],.]],.],.] => [1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => {{1,2,5,6,7,8},{3,4}} => 8
[[[[.,[[[[.,.],.],.],.]],.],.],.] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => {{1,2,3,5,6,7,8},{4}} => 8
[[[[[.,.],[[[.,.],.],.]],.],.],.] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => {{1,2,3,6,7,8},{4,5}} => 8
[[[[[.,[[[.,.],.],.]],.],.],.],.] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => {{1,2,3,4,6,7,8},{5}} => 8
[[[[[[.,.],[[.,.],.]],.],.],.],.] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => {{1,2,3,4,7,8},{5,6}} => 8
[[[[[[.,[[.,.],.]],.],.],.],.],.] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => {{1,2,3,4,5,7,8},{6}} => 8
[[[[[[[.,.],[.,.]],.],.],.],.],.] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => {{1,2,3,4,5,8},{6,7}} => 8
[[[[[[[.,[.,.]],.],.],.],.],.],.] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,8},{7}} => 8
[[[[[[[[.,.],.],.],.],.],.],.],.] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,7,8}} => 8
[.,[[[[[[[[.,.],.],.],.],.],.],.],.]] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8,9}} => 1
[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8,9,10}} => 1
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,10}} => 2
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}} => 2
[[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8},{9}} => 8
[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9},{10}} => 9
[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,8},{6,7},{9}} => 8
[[[[[[.,[[.,.],.]],.],.],.],.],[.,.]] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,7,8},{6},{9}} => 8
[.,[[[[[[[.,.],[.,.]],.],.],.],.],.]] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => {{1},{2,3,4,5,6,9},{7,8}} => 1
[[[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]],.] => [1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => {{1,10},{2,5},{3,4},{6,7},{8,9}} => 10
[[[[.,.],[[.,.],[.,.]]],[[.,.],[.,.]]],.] => [1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => {{1,10},{2,7},{3,4},{5,6},{8,9}} => 10
[[[.,.],[[[.,.],[.,.]],[[.,.],[.,.]]]],.] => [1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => {{1,10},{2,3},{4,7},{5,6},{8,9}} => 10
[[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]],.] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => {{1,10},{2,3},{4,5},{6,7},{8,9}} => 10
[[[[.,.],[.,.]],[[.,.],[.,.]]],[[.,.],.]] => [1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => {{1,8},{2,5},{3,4},{6,7},{9,10}} => 8
[[[.,.],[[.,.],[[.,.],[.,.]]]],[[.,.],.]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => {{1,8},{2,3},{4,5},{6,7},{9,10}} => 8
[[.,.],[[[.,.],[[.,.],[.,.]]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => {{1,2},{3,8},{4,5},{6,7},{9,10}} => 2
[[[.,.],[.,.]],[[[.,.],[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => {{1,4},{2,3},{5,8},{6,7},{9,10}} => 4
[[.,.],[[.,.],[[[.,.],[.,.]],[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,8},{6,7},{9,10}} => 2
[[[[.,.],[[.,.],[[.,.],[.,.]]]],[[.,.],[.,.]]],.] => [1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => {{1,12},{2,9},{3,4},{5,6},{7,8},{10,11}} => 12
[[[[.,.],[[.,.],[.,.]]],[[.,.],[[.,.],[.,.]]]],.] => [1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => {{1,12},{2,7},{3,4},{5,6},{8,9},{10,11}} => 12
[[[[.,.],[.,.]],[[[.,.],[.,.]],[[.,.],[.,.]]]],.] => [1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => {{1,12},{2,5},{3,4},{6,9},{7,8},{10,11}} => 12
[[[[.,.],[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]],.] => [1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => {{1,12},{2,5},{3,4},{6,7},{8,9},{10,11}} => 12
[[[.,.],[[[.,.],[[.,.],[.,.]]],[[.,.],[.,.]]]],.] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => {{1,12},{2,3},{4,9},{5,6},{7,8},{10,11}} => 12
[[[.,.],[[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]]],.] => [1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => {{1,12},{2,3},{4,7},{5,6},{8,9},{10,11}} => 12
[[[.,.],[[.,.],[[[.,.],[.,.]],[[.,.],[.,.]]]]],.] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => {{1,12},{2,3},{4,5},{6,9},{7,8},{10,11}} => 12
[[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]],.] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => {{1,12},{2,3},{4,5},{6,7},{8,9},{10,11}} => 12
[[[[.,.],[[.,.],[.,.]]],[[.,.],[.,.]]],[[.,.],.]] => [1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => {{1,10},{2,7},{3,4},{5,6},{8,9},{11,12}} => 10
[[[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]],[[.,.],.]] => [1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => {{1,10},{2,5},{3,4},{6,7},{8,9},{11,12}} => 10
[[[.,.],[[[.,.],[.,.]],[[.,.],[.,.]]]],[[.,.],.]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => {{1,10},{2,3},{4,7},{5,6},{8,9},{11,12}} => 10
[[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]],[[.,.],.]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => {{1,10},{2,3},{4,5},{6,7},{8,9},{11,12}} => 10
[[[[.,.],[.,.]],[[.,.],[.,.]]],[[[.,.],[.,.]],.]] => [1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => {{1,8},{2,5},{3,4},{6,7},{9,12},{10,11}} => 8
[[[[.,.],[.,.]],[[.,.],[.,.]]],[[.,.],[[.,.],.]]] => [1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => {{1,8},{2,5},{3,4},{6,7},{9,10},{11,12}} => 8
[[.,.],[[[.,.],[[.,.],[[.,.],[.,.]]]],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => {{1,2},{3,10},{4,5},{6,7},{8,9},{11,12}} => 2
[[[.,.],[[.,.],[.,.]]],[[[.,.],[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => {{1,6},{2,3},{4,5},{7,10},{8,9},{11,12}} => 6
[[.,.],[[.,.],[[[.,.],[[.,.],[.,.]]],[[.,.],.]]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,10},{6,7},{8,9},{11,12}} => 2
[[[.,.],[.,.]],[[[.,.],[[.,.],[.,.]]],[[.,.],.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => {{1,4},{2,3},{5,10},{6,7},{8,9},{11,12}} => 4
[[[.,.],[.,.]],[[.,.],[[[.,.],[.,.]],[[.,.],.]]]] => [1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => {{1,4},{2,3},{5,6},{7,10},{8,9},{11,12}} => 4
[[.,.],[[[.,.],[.,.]],[[[.,.],[.,.]],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => {{1,2},{3,6},{4,5},{7,10},{8,9},{11,12}} => 2
[[.,.],[[.,.],[[.,.],[[[.,.],[.,.]],[[.,.],.]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,10},{8,9},{11,12}} => 2
[[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]],.] => [1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => {{1,10},{2,7},{3,6},{4,5},{8,9}} => 10
[[[[.,.],[.,.]],[.,.]],[[.,.],[[.,.],.]]] => [1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => {{1,6},{2,5},{3,4},{7,8},{9,10}} => 6
[[[[.,.],[.,.]],[.,.]],[[[.,.],[.,.]],.]] => [1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => {{1,6},{2,5},{3,4},{7,10},{8,9}} => 6
[[.,.],[[.,.],[[.,.],[[[.,.],[.,.]],.]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => {{1,2},{3,4},{5,6},{7,10},{8,9}} => 2
[[.,.],[[.,.],[[.,.],[[.,.],[[[.,.],[.,.]],.]]]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,12},{10,11}} => 2
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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
$F_{1} = q$
$F_{2} = q + q^{2}$
$F_{3} = 2\ q + q^{2} + 2\ q^{3}$
$F_{4} = 5\ q + 2\ q^{2} + 2\ q^{3} + 5\ q^{4}$
$F_{5} = 14\ q + 5\ q^{2} + 4\ q^{3} + 5\ q^{4} + 14\ q^{5}$
$F_{6} = 42\ q + 14\ q^{2} + 10\ q^{3} + 10\ q^{4} + 14\ q^{5} + 42\ q^{6}$
$F_{7} = 132\ q + 42\ q^{2} + 28\ q^{3} + 25\ q^{4} + 28\ q^{5} + 42\ q^{6} + 132\ q^{7}$
Description
The biggest entry in the block containing the 1.
Map
to Dyck path: up step, left tree, down step, right tree
Description
Return the associated Dyck path, using the bijection 1L0R.
This is given recursively as follows:
This is given recursively as follows:
- a leaf is associated to the empty Dyck Word
- a tree with children $l,r$ is associated with the Dyck path described by 1L0R where $L$ and $R$ are respectively the Dyck words associated with the trees $l$ and $r$.
Map
to noncrossing partition
Description
Biane's map to noncrossing set partitions.
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