Identifier
-
Mp00051:
Ordered trees
—to Dyck path⟶
Dyck paths
Mp00138: Dyck paths —to noncrossing partition⟶ Set partitions
Mp00079: Set partitions —shape⟶ Integer partitions
St000707: Integer partitions ⟶ ℤ
Values
[[],[]] => [1,0,1,0] => {{1},{2}} => [1,1] => 1
[[[]]] => [1,1,0,0] => {{1,2}} => [2] => 2
[[],[],[]] => [1,0,1,0,1,0] => {{1},{2},{3}} => [1,1,1] => 1
[[],[[]]] => [1,0,1,1,0,0] => {{1},{2,3}} => [2,1] => 2
[[[]],[]] => [1,1,0,0,1,0] => {{1,2},{3}} => [2,1] => 2
[[[],[]]] => [1,1,0,1,0,0] => {{1,3},{2}} => [2,1] => 2
[[[[]]]] => [1,1,1,0,0,0] => {{1,2,3}} => [3] => 6
[[],[],[],[]] => [1,0,1,0,1,0,1,0] => {{1},{2},{3},{4}} => [1,1,1,1] => 1
[[],[],[[]]] => [1,0,1,0,1,1,0,0] => {{1},{2},{3,4}} => [2,1,1] => 2
[[],[[]],[]] => [1,0,1,1,0,0,1,0] => {{1},{2,3},{4}} => [2,1,1] => 2
[[],[[],[]]] => [1,0,1,1,0,1,0,0] => {{1},{2,4},{3}} => [2,1,1] => 2
[[],[[[]]]] => [1,0,1,1,1,0,0,0] => {{1},{2,3,4}} => [3,1] => 6
[[[]],[],[]] => [1,1,0,0,1,0,1,0] => {{1,2},{3},{4}} => [2,1,1] => 2
[[[]],[[]]] => [1,1,0,0,1,1,0,0] => {{1,2},{3,4}} => [2,2] => 4
[[[],[]],[]] => [1,1,0,1,0,0,1,0] => {{1,3},{2},{4}} => [2,1,1] => 2
[[[[]]],[]] => [1,1,1,0,0,0,1,0] => {{1,2,3},{4}} => [3,1] => 6
[[[],[],[]]] => [1,1,0,1,0,1,0,0] => {{1,4},{2},{3}} => [2,1,1] => 2
[[[],[[]]]] => [1,1,0,1,1,0,0,0] => {{1,3,4},{2}} => [3,1] => 6
[[[[]],[]]] => [1,1,1,0,0,1,0,0] => {{1,4},{2,3}} => [2,2] => 4
[[[[],[]]]] => [1,1,1,0,1,0,0,0] => {{1,2,4},{3}} => [3,1] => 6
[[[[[]]]]] => [1,1,1,1,0,0,0,0] => {{1,2,3,4}} => [4] => 24
[[],[],[],[],[]] => [1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5}} => [1,1,1,1,1] => 1
[[],[],[],[[]]] => [1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4,5}} => [2,1,1,1] => 2
[[],[],[[]],[]] => [1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5}} => [2,1,1,1] => 2
[[],[],[[],[]]] => [1,0,1,0,1,1,0,1,0,0] => {{1},{2},{3,5},{4}} => [2,1,1,1] => 2
[[],[],[[[]]]] => [1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3,4,5}} => [3,1,1] => 6
[[],[[]],[],[]] => [1,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4},{5}} => [2,1,1,1] => 2
[[],[[]],[[]]] => [1,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5}} => [2,2,1] => 4
[[],[[],[]],[]] => [1,0,1,1,0,1,0,0,1,0] => {{1},{2,4},{3},{5}} => [2,1,1,1] => 2
[[],[[[]]],[]] => [1,0,1,1,1,0,0,0,1,0] => {{1},{2,3,4},{5}} => [3,1,1] => 6
[[],[[],[],[]]] => [1,0,1,1,0,1,0,1,0,0] => {{1},{2,5},{3},{4}} => [2,1,1,1] => 2
[[],[[],[[]]]] => [1,0,1,1,0,1,1,0,0,0] => {{1},{2,4,5},{3}} => [3,1,1] => 6
[[],[[[]],[]]] => [1,0,1,1,1,0,0,1,0,0] => {{1},{2,5},{3,4}} => [2,2,1] => 4
[[],[[[],[]]]] => [1,0,1,1,1,0,1,0,0,0] => {{1},{2,3,5},{4}} => [3,1,1] => 6
[[],[[[[]]]]] => [1,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4,5}} => [4,1] => 24
[[[]],[],[],[]] => [1,1,0,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5}} => [2,1,1,1] => 2
[[[]],[],[[]]] => [1,1,0,0,1,0,1,1,0,0] => {{1,2},{3},{4,5}} => [2,2,1] => 4
[[[]],[[]],[]] => [1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5}} => [2,2,1] => 4
[[[]],[[],[]]] => [1,1,0,0,1,1,0,1,0,0] => {{1,2},{3,5},{4}} => [2,2,1] => 4
[[[]],[[[]]]] => [1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5}} => [3,2] => 12
[[[],[]],[],[]] => [1,1,0,1,0,0,1,0,1,0] => {{1,3},{2},{4},{5}} => [2,1,1,1] => 2
[[[[]]],[],[]] => [1,1,1,0,0,0,1,0,1,0] => {{1,2,3},{4},{5}} => [3,1,1] => 6
[[[],[]],[[]]] => [1,1,0,1,0,0,1,1,0,0] => {{1,3},{2},{4,5}} => [2,2,1] => 4
[[[[]]],[[]]] => [1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5}} => [3,2] => 12
[[[],[],[]],[]] => [1,1,0,1,0,1,0,0,1,0] => {{1,4},{2},{3},{5}} => [2,1,1,1] => 2
[[[],[[]]],[]] => [1,1,0,1,1,0,0,0,1,0] => {{1,3,4},{2},{5}} => [3,1,1] => 6
[[[[]],[]],[]] => [1,1,1,0,0,1,0,0,1,0] => {{1,4},{2,3},{5}} => [2,2,1] => 4
[[[[],[]]],[]] => [1,1,1,0,1,0,0,0,1,0] => {{1,2,4},{3},{5}} => [3,1,1] => 6
[[[[[]]]],[]] => [1,1,1,1,0,0,0,0,1,0] => {{1,2,3,4},{5}} => [4,1] => 24
[[[],[],[],[]]] => [1,1,0,1,0,1,0,1,0,0] => {{1,5},{2},{3},{4}} => [2,1,1,1] => 2
[[[],[],[[]]]] => [1,1,0,1,0,1,1,0,0,0] => {{1,4,5},{2},{3}} => [3,1,1] => 6
[[[],[[]],[]]] => [1,1,0,1,1,0,0,1,0,0] => {{1,5},{2},{3,4}} => [2,2,1] => 4
[[[],[[],[]]]] => [1,1,0,1,1,0,1,0,0,0] => {{1,3,5},{2},{4}} => [3,1,1] => 6
[[[],[[[]]]]] => [1,1,0,1,1,1,0,0,0,0] => {{1,3,4,5},{2}} => [4,1] => 24
[[[[]],[],[]]] => [1,1,1,0,0,1,0,1,0,0] => {{1,5},{2,3},{4}} => [2,2,1] => 4
[[[[]],[[]]]] => [1,1,1,0,0,1,1,0,0,0] => {{1,4,5},{2,3}} => [3,2] => 12
[[[[],[]],[]]] => [1,1,1,0,1,0,0,1,0,0] => {{1,5},{2,4},{3}} => [2,2,1] => 4
[[[[[]]],[]]] => [1,1,1,1,0,0,0,1,0,0] => {{1,5},{2,3,4}} => [3,2] => 12
[[[[],[],[]]]] => [1,1,1,0,1,0,1,0,0,0] => {{1,2,5},{3},{4}} => [3,1,1] => 6
[[[[],[[]]]]] => [1,1,1,0,1,1,0,0,0,0] => {{1,2,4,5},{3}} => [4,1] => 24
[[[[[]],[]]]] => [1,1,1,1,0,0,1,0,0,0] => {{1,2,5},{3,4}} => [3,2] => 12
[[[[[],[]]]]] => [1,1,1,1,0,1,0,0,0,0] => {{1,2,3,5},{4}} => [4,1] => 24
[[[[[[]]]]]] => [1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4,5}} => [5] => 120
[[],[],[],[],[],[]] => [1,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6}} => [1,1,1,1,1,1] => 1
[[],[],[],[],[[]]] => [1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5,6}} => [2,1,1,1,1] => 2
[[],[],[],[[]],[]] => [1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4,5},{6}} => [2,1,1,1,1] => 2
[[],[],[],[[],[]]] => [1,0,1,0,1,0,1,1,0,1,0,0] => {{1},{2},{3},{4,6},{5}} => [2,1,1,1,1] => 2
[[],[],[],[[[]]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4,5,6}} => [3,1,1,1] => 6
[[],[],[[]],[],[]] => [1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3,4},{5},{6}} => [2,1,1,1,1] => 2
[[],[],[[]],[[]]] => [1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6}} => [2,2,1,1] => 4
[[],[],[[],[]],[]] => [1,0,1,0,1,1,0,1,0,0,1,0] => {{1},{2},{3,5},{4},{6}} => [2,1,1,1,1] => 2
[[],[],[[[]]],[]] => [1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3,4,5},{6}} => [3,1,1,1] => 6
[[],[],[[],[],[]]] => [1,0,1,0,1,1,0,1,0,1,0,0] => {{1},{2},{3,6},{4},{5}} => [2,1,1,1,1] => 2
[[],[],[[],[[]]]] => [1,0,1,0,1,1,0,1,1,0,0,0] => {{1},{2},{3,5,6},{4}} => [3,1,1,1] => 6
[[],[],[[[]],[]]] => [1,0,1,0,1,1,1,0,0,1,0,0] => {{1},{2},{3,6},{4,5}} => [2,2,1,1] => 4
[[],[],[[[],[]]]] => [1,0,1,0,1,1,1,0,1,0,0,0] => {{1},{2},{3,4,6},{5}} => [3,1,1,1] => 6
[[],[],[[[[]]]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3,4,5,6}} => [4,1,1] => 24
[[],[[]],[],[],[]] => [1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6}} => [2,1,1,1,1] => 2
[[],[[]],[],[[]]] => [1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5,6}} => [2,2,1,1] => 4
[[],[[]],[[]],[]] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => [2,2,1,1] => 4
[[],[[]],[[],[]]] => [1,0,1,1,0,0,1,1,0,1,0,0] => {{1},{2,3},{4,6},{5}} => [2,2,1,1] => 4
[[],[[]],[[[]]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5,6}} => [3,2,1] => 12
[[],[[],[]],[],[]] => [1,0,1,1,0,1,0,0,1,0,1,0] => {{1},{2,4},{3},{5},{6}} => [2,1,1,1,1] => 2
[[],[[[]]],[],[]] => [1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2,3,4},{5},{6}} => [3,1,1,1] => 6
[[],[[],[]],[[]]] => [1,0,1,1,0,1,0,0,1,1,0,0] => {{1},{2,4},{3},{5,6}} => [2,2,1,1] => 4
[[],[[[]]],[[]]] => [1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => [3,2,1] => 12
[[],[[],[],[]],[]] => [1,0,1,1,0,1,0,1,0,0,1,0] => {{1},{2,5},{3},{4},{6}} => [2,1,1,1,1] => 2
[[],[[],[[]]],[]] => [1,0,1,1,0,1,1,0,0,0,1,0] => {{1},{2,4,5},{3},{6}} => [3,1,1,1] => 6
[[],[[[]],[]],[]] => [1,0,1,1,1,0,0,1,0,0,1,0] => {{1},{2,5},{3,4},{6}} => [2,2,1,1] => 4
[[],[[[],[]]],[]] => [1,0,1,1,1,0,1,0,0,0,1,0] => {{1},{2,3,5},{4},{6}} => [3,1,1,1] => 6
[[],[[[[]]]],[]] => [1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2,3,4,5},{6}} => [4,1,1] => 24
[[],[[],[],[],[]]] => [1,0,1,1,0,1,0,1,0,1,0,0] => {{1},{2,6},{3},{4},{5}} => [2,1,1,1,1] => 2
[[],[[],[],[[]]]] => [1,0,1,1,0,1,0,1,1,0,0,0] => {{1},{2,5,6},{3},{4}} => [3,1,1,1] => 6
[[],[[],[[]],[]]] => [1,0,1,1,0,1,1,0,0,1,0,0] => {{1},{2,6},{3},{4,5}} => [2,2,1,1] => 4
[[],[[],[[],[]]]] => [1,0,1,1,0,1,1,0,1,0,0,0] => {{1},{2,4,6},{3},{5}} => [3,1,1,1] => 6
[[],[[],[[[]]]]] => [1,0,1,1,0,1,1,1,0,0,0,0] => {{1},{2,4,5,6},{3}} => [4,1,1] => 24
[[],[[[]],[],[]]] => [1,0,1,1,1,0,0,1,0,1,0,0] => {{1},{2,6},{3,4},{5}} => [2,2,1,1] => 4
[[],[[[]],[[]]]] => [1,0,1,1,1,0,0,1,1,0,0,0] => {{1},{2,5,6},{3,4}} => [3,2,1] => 12
[[],[[[],[]],[]]] => [1,0,1,1,1,0,1,0,0,1,0,0] => {{1},{2,6},{3,5},{4}} => [2,2,1,1] => 4
[[],[[[[]]],[]]] => [1,0,1,1,1,1,0,0,0,1,0,0] => {{1},{2,6},{3,4,5}} => [3,2,1] => 12
[[],[[[],[],[]]]] => [1,0,1,1,1,0,1,0,1,0,0,0] => {{1},{2,3,6},{4},{5}} => [3,1,1,1] => 6
>>> Load all 1539 entries. <<<[[],[[[],[[]]]]] => [1,0,1,1,1,0,1,1,0,0,0,0] => {{1},{2,3,5,6},{4}} => [4,1,1] => 24
[[],[[[[]],[]]]] => [1,0,1,1,1,1,0,0,1,0,0,0] => {{1},{2,3,6},{4,5}} => [3,2,1] => 12
[[],[[[[],[]]]]] => [1,0,1,1,1,1,0,1,0,0,0,0] => {{1},{2,3,4,6},{5}} => [4,1,1] => 24
[[],[[[[[]]]]]] => [1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3,4,5,6}} => [5,1] => 120
[[[]],[],[],[],[]] => [1,1,0,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5},{6}} => [2,1,1,1,1] => 2
[[[]],[],[],[[]]] => [1,1,0,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5,6}} => [2,2,1,1] => 4
[[[]],[],[[]],[]] => [1,1,0,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4,5},{6}} => [2,2,1,1] => 4
[[[]],[],[[],[]]] => [1,1,0,0,1,0,1,1,0,1,0,0] => {{1,2},{3},{4,6},{5}} => [2,2,1,1] => 4
[[[]],[],[[[]]]] => [1,1,0,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4,5,6}} => [3,2,1] => 12
[[[]],[[]],[],[]] => [1,1,0,0,1,1,0,0,1,0,1,0] => {{1,2},{3,4},{5},{6}} => [2,2,1,1] => 4
[[[]],[[]],[[]]] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => [2,2,2] => 8
[[[]],[[],[]],[]] => [1,1,0,0,1,1,0,1,0,0,1,0] => {{1,2},{3,5},{4},{6}} => [2,2,1,1] => 4
[[[]],[[[]]],[]] => [1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4,5},{6}} => [3,2,1] => 12
[[[]],[[],[],[]]] => [1,1,0,0,1,1,0,1,0,1,0,0] => {{1,2},{3,6},{4},{5}} => [2,2,1,1] => 4
[[[]],[[],[[]]]] => [1,1,0,0,1,1,0,1,1,0,0,0] => {{1,2},{3,5,6},{4}} => [3,2,1] => 12
[[[]],[[[]],[]]] => [1,1,0,0,1,1,1,0,0,1,0,0] => {{1,2},{3,6},{4,5}} => [2,2,2] => 8
[[[]],[[[],[]]]] => [1,1,0,0,1,1,1,0,1,0,0,0] => {{1,2},{3,4,6},{5}} => [3,2,1] => 12
[[[]],[[[[]]]]] => [1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4,5,6}} => [4,2] => 48
[[[],[]],[],[],[]] => [1,1,0,1,0,0,1,0,1,0,1,0] => {{1,3},{2},{4},{5},{6}} => [2,1,1,1,1] => 2
[[[[]]],[],[],[]] => [1,1,1,0,0,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6}} => [3,1,1,1] => 6
[[[],[]],[],[[]]] => [1,1,0,1,0,0,1,0,1,1,0,0] => {{1,3},{2},{4},{5,6}} => [2,2,1,1] => 4
[[[[]]],[],[[]]] => [1,1,1,0,0,0,1,0,1,1,0,0] => {{1,2,3},{4},{5,6}} => [3,2,1] => 12
[[[],[]],[[]],[]] => [1,1,0,1,0,0,1,1,0,0,1,0] => {{1,3},{2},{4,5},{6}} => [2,2,1,1] => 4
[[[[]]],[[]],[]] => [1,1,1,0,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6}} => [3,2,1] => 12
[[[],[]],[[],[]]] => [1,1,0,1,0,0,1,1,0,1,0,0] => {{1,3},{2},{4,6},{5}} => [2,2,1,1] => 4
[[[],[]],[[[]]]] => [1,1,0,1,0,0,1,1,1,0,0,0] => {{1,3},{2},{4,5,6}} => [3,2,1] => 12
[[[[]]],[[],[]]] => [1,1,1,0,0,0,1,1,0,1,0,0] => {{1,2,3},{4,6},{5}} => [3,2,1] => 12
[[[[]]],[[[]]]] => [1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2,3},{4,5,6}} => [3,3] => 36
[[[],[],[]],[],[]] => [1,1,0,1,0,1,0,0,1,0,1,0] => {{1,4},{2},{3},{5},{6}} => [2,1,1,1,1] => 2
[[[],[[]]],[],[]] => [1,1,0,1,1,0,0,0,1,0,1,0] => {{1,3,4},{2},{5},{6}} => [3,1,1,1] => 6
[[[[]],[]],[],[]] => [1,1,1,0,0,1,0,0,1,0,1,0] => {{1,4},{2,3},{5},{6}} => [2,2,1,1] => 4
[[[[],[]]],[],[]] => [1,1,1,0,1,0,0,0,1,0,1,0] => {{1,2,4},{3},{5},{6}} => [3,1,1,1] => 6
[[[[[]]]],[],[]] => [1,1,1,1,0,0,0,0,1,0,1,0] => {{1,2,3,4},{5},{6}} => [4,1,1] => 24
[[[],[],[]],[[]]] => [1,1,0,1,0,1,0,0,1,1,0,0] => {{1,4},{2},{3},{5,6}} => [2,2,1,1] => 4
[[[],[[]]],[[]]] => [1,1,0,1,1,0,0,0,1,1,0,0] => {{1,3,4},{2},{5,6}} => [3,2,1] => 12
[[[[]],[]],[[]]] => [1,1,1,0,0,1,0,0,1,1,0,0] => {{1,4},{2,3},{5,6}} => [2,2,2] => 8
[[[[],[]]],[[]]] => [1,1,1,0,1,0,0,0,1,1,0,0] => {{1,2,4},{3},{5,6}} => [3,2,1] => 12
[[[[[]]]],[[]]] => [1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2,3,4},{5,6}} => [4,2] => 48
[[[],[],[],[]],[]] => [1,1,0,1,0,1,0,1,0,0,1,0] => {{1,5},{2},{3},{4},{6}} => [2,1,1,1,1] => 2
[[[],[],[[]]],[]] => [1,1,0,1,0,1,1,0,0,0,1,0] => {{1,4,5},{2},{3},{6}} => [3,1,1,1] => 6
[[[],[[]],[]],[]] => [1,1,0,1,1,0,0,1,0,0,1,0] => {{1,5},{2},{3,4},{6}} => [2,2,1,1] => 4
[[[],[[],[]]],[]] => [1,1,0,1,1,0,1,0,0,0,1,0] => {{1,3,5},{2},{4},{6}} => [3,1,1,1] => 6
[[[],[[[]]]],[]] => [1,1,0,1,1,1,0,0,0,0,1,0] => {{1,3,4,5},{2},{6}} => [4,1,1] => 24
[[[[]],[],[]],[]] => [1,1,1,0,0,1,0,1,0,0,1,0] => {{1,5},{2,3},{4},{6}} => [2,2,1,1] => 4
[[[[]],[[]]],[]] => [1,1,1,0,0,1,1,0,0,0,1,0] => {{1,4,5},{2,3},{6}} => [3,2,1] => 12
[[[[],[]],[]],[]] => [1,1,1,0,1,0,0,1,0,0,1,0] => {{1,5},{2,4},{3},{6}} => [2,2,1,1] => 4
[[[[[]]],[]],[]] => [1,1,1,1,0,0,0,1,0,0,1,0] => {{1,5},{2,3,4},{6}} => [3,2,1] => 12
[[[[],[],[]]],[]] => [1,1,1,0,1,0,1,0,0,0,1,0] => {{1,2,5},{3},{4},{6}} => [3,1,1,1] => 6
[[[[],[[]]]],[]] => [1,1,1,0,1,1,0,0,0,0,1,0] => {{1,2,4,5},{3},{6}} => [4,1,1] => 24
[[[[[]],[]]],[]] => [1,1,1,1,0,0,1,0,0,0,1,0] => {{1,2,5},{3,4},{6}} => [3,2,1] => 12
[[[[[],[]]]],[]] => [1,1,1,1,0,1,0,0,0,0,1,0] => {{1,2,3,5},{4},{6}} => [4,1,1] => 24
[[[[[[]]]]],[]] => [1,1,1,1,1,0,0,0,0,0,1,0] => {{1,2,3,4,5},{6}} => [5,1] => 120
[[[],[],[],[],[]]] => [1,1,0,1,0,1,0,1,0,1,0,0] => {{1,6},{2},{3},{4},{5}} => [2,1,1,1,1] => 2
[[[],[],[],[[]]]] => [1,1,0,1,0,1,0,1,1,0,0,0] => {{1,5,6},{2},{3},{4}} => [3,1,1,1] => 6
[[[],[],[[]],[]]] => [1,1,0,1,0,1,1,0,0,1,0,0] => {{1,6},{2},{3},{4,5}} => [2,2,1,1] => 4
[[[],[],[[],[]]]] => [1,1,0,1,0,1,1,0,1,0,0,0] => {{1,4,6},{2},{3},{5}} => [3,1,1,1] => 6
[[[],[],[[[]]]]] => [1,1,0,1,0,1,1,1,0,0,0,0] => {{1,4,5,6},{2},{3}} => [4,1,1] => 24
[[[],[[]],[],[]]] => [1,1,0,1,1,0,0,1,0,1,0,0] => {{1,6},{2},{3,4},{5}} => [2,2,1,1] => 4
[[[],[[]],[[]]]] => [1,1,0,1,1,0,0,1,1,0,0,0] => {{1,5,6},{2},{3,4}} => [3,2,1] => 12
[[[],[[],[]],[]]] => [1,1,0,1,1,0,1,0,0,1,0,0] => {{1,6},{2},{3,5},{4}} => [2,2,1,1] => 4
[[[],[[[]]],[]]] => [1,1,0,1,1,1,0,0,0,1,0,0] => {{1,6},{2},{3,4,5}} => [3,2,1] => 12
[[[],[[],[],[]]]] => [1,1,0,1,1,0,1,0,1,0,0,0] => {{1,3,6},{2},{4},{5}} => [3,1,1,1] => 6
[[[],[[],[[]]]]] => [1,1,0,1,1,0,1,1,0,0,0,0] => {{1,3,5,6},{2},{4}} => [4,1,1] => 24
[[[],[[[]],[]]]] => [1,1,0,1,1,1,0,0,1,0,0,0] => {{1,3,6},{2},{4,5}} => [3,2,1] => 12
[[[],[[[],[]]]]] => [1,1,0,1,1,1,0,1,0,0,0,0] => {{1,3,4,6},{2},{5}} => [4,1,1] => 24
[[[],[[[[]]]]]] => [1,1,0,1,1,1,1,0,0,0,0,0] => {{1,3,4,5,6},{2}} => [5,1] => 120
[[[[]],[],[],[]]] => [1,1,1,0,0,1,0,1,0,1,0,0] => {{1,6},{2,3},{4},{5}} => [2,2,1,1] => 4
[[[[]],[],[[]]]] => [1,1,1,0,0,1,0,1,1,0,0,0] => {{1,5,6},{2,3},{4}} => [3,2,1] => 12
[[[[]],[[]],[]]] => [1,1,1,0,0,1,1,0,0,1,0,0] => {{1,6},{2,3},{4,5}} => [2,2,2] => 8
[[[[]],[[],[]]]] => [1,1,1,0,0,1,1,0,1,0,0,0] => {{1,4,6},{2,3},{5}} => [3,2,1] => 12
[[[[]],[[[]]]]] => [1,1,1,0,0,1,1,1,0,0,0,0] => {{1,4,5,6},{2,3}} => [4,2] => 48
[[[[],[]],[],[]]] => [1,1,1,0,1,0,0,1,0,1,0,0] => {{1,6},{2,4},{3},{5}} => [2,2,1,1] => 4
[[[[[]]],[],[]]] => [1,1,1,1,0,0,0,1,0,1,0,0] => {{1,6},{2,3,4},{5}} => [3,2,1] => 12
[[[[],[]],[[]]]] => [1,1,1,0,1,0,0,1,1,0,0,0] => {{1,5,6},{2,4},{3}} => [3,2,1] => 12
[[[[[]]],[[]]]] => [1,1,1,1,0,0,0,1,1,0,0,0] => {{1,5,6},{2,3,4}} => [3,3] => 36
[[[[],[],[]],[]]] => [1,1,1,0,1,0,1,0,0,1,0,0] => {{1,6},{2,5},{3},{4}} => [2,2,1,1] => 4
[[[[],[[]]],[]]] => [1,1,1,0,1,1,0,0,0,1,0,0] => {{1,6},{2,4,5},{3}} => [3,2,1] => 12
[[[[[]],[]],[]]] => [1,1,1,1,0,0,1,0,0,1,0,0] => {{1,6},{2,5},{3,4}} => [2,2,2] => 8
[[[[[],[]]],[]]] => [1,1,1,1,0,1,0,0,0,1,0,0] => {{1,6},{2,3,5},{4}} => [3,2,1] => 12
[[[[[[]]]],[]]] => [1,1,1,1,1,0,0,0,0,1,0,0] => {{1,6},{2,3,4,5}} => [4,2] => 48
[[[[],[],[],[]]]] => [1,1,1,0,1,0,1,0,1,0,0,0] => {{1,2,6},{3},{4},{5}} => [3,1,1,1] => 6
[[[[],[],[[]]]]] => [1,1,1,0,1,0,1,1,0,0,0,0] => {{1,2,5,6},{3},{4}} => [4,1,1] => 24
[[[[],[[]],[]]]] => [1,1,1,0,1,1,0,0,1,0,0,0] => {{1,2,6},{3},{4,5}} => [3,2,1] => 12
[[[[],[[],[]]]]] => [1,1,1,0,1,1,0,1,0,0,0,0] => {{1,2,4,6},{3},{5}} => [4,1,1] => 24
[[[[],[[[]]]]]] => [1,1,1,0,1,1,1,0,0,0,0,0] => {{1,2,4,5,6},{3}} => [5,1] => 120
[[[[[]],[],[]]]] => [1,1,1,1,0,0,1,0,1,0,0,0] => {{1,2,6},{3,4},{5}} => [3,2,1] => 12
[[[[[]],[[]]]]] => [1,1,1,1,0,0,1,1,0,0,0,0] => {{1,2,5,6},{3,4}} => [4,2] => 48
[[[[[],[]],[]]]] => [1,1,1,1,0,1,0,0,1,0,0,0] => {{1,2,6},{3,5},{4}} => [3,2,1] => 12
[[[[[[]]],[]]]] => [1,1,1,1,1,0,0,0,1,0,0,0] => {{1,2,6},{3,4,5}} => [3,3] => 36
[[[[[],[],[]]]]] => [1,1,1,1,0,1,0,1,0,0,0,0] => {{1,2,3,6},{4},{5}} => [4,1,1] => 24
[[[[[],[[]]]]]] => [1,1,1,1,0,1,1,0,0,0,0,0] => {{1,2,3,5,6},{4}} => [5,1] => 120
[[[[[[]],[]]]]] => [1,1,1,1,1,0,0,1,0,0,0,0] => {{1,2,3,6},{4,5}} => [4,2] => 48
[[[[[[],[]]]]]] => [1,1,1,1,1,0,1,0,0,0,0,0] => {{1,2,3,4,6},{5}} => [5,1] => 120
[[[[[[[]]]]]]] => [1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3,4,5,6}} => [6] => 720
[[],[],[],[],[],[],[]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6},{7}} => [1,1,1,1,1,1,1] => 1
[[],[],[],[],[],[[]]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6,7}} => [2,1,1,1,1,1] => 2
[[],[],[],[],[[]],[]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4},{5,6},{7}} => [2,1,1,1,1,1] => 2
[[],[],[],[],[[],[]]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => {{1},{2},{3},{4},{5,7},{6}} => [2,1,1,1,1,1] => 2
[[],[],[],[],[[[]]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4},{5,6,7}} => [3,1,1,1,1] => 6
[[],[],[],[[]],[],[]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3},{4,5},{6},{7}} => [2,1,1,1,1,1] => 2
[[],[],[],[[]],[[]]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => [2,2,1,1,1] => 4
[[],[],[],[[],[]],[]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => {{1},{2},{3},{4,6},{5},{7}} => [2,1,1,1,1,1] => 2
[[],[],[],[[[]]],[]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}} => [3,1,1,1,1] => 6
[[],[],[],[[],[],[]]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => {{1},{2},{3},{4,7},{5},{6}} => [2,1,1,1,1,1] => 2
[[],[],[],[[],[[]]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => {{1},{2},{3},{4,6,7},{5}} => [3,1,1,1,1] => 6
[[],[],[],[[[]],[]]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => {{1},{2},{3},{4,7},{5,6}} => [2,2,1,1,1] => 4
[[],[],[],[[[],[]]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => {{1},{2},{3},{4,5,7},{6}} => [3,1,1,1,1] => 6
[[],[],[],[[[[]]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3},{4,5,6,7}} => [4,1,1,1] => 24
[[],[],[[]],[],[],[]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2},{3,4},{5},{6},{7}} => [2,1,1,1,1,1] => 2
[[],[],[[]],[],[[]]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => [2,2,1,1,1] => 4
[[],[],[[]],[[]],[]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => [2,2,1,1,1] => 4
[[],[],[[]],[[],[]]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => {{1},{2},{3,4},{5,7},{6}} => [2,2,1,1,1] => 4
[[],[],[[]],[[[]]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => [3,2,1,1] => 12
[[],[],[[],[]],[],[]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => {{1},{2},{3,5},{4},{6},{7}} => [2,1,1,1,1,1] => 2
[[],[],[[[]]],[],[]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => [3,1,1,1,1] => 6
[[],[],[[],[]],[[]]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => {{1},{2},{3,5},{4},{6,7}} => [2,2,1,1,1] => 4
[[],[],[[[]]],[[]]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => [3,2,1,1] => 12
[[],[],[[],[],[]],[]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => {{1},{2},{3,6},{4},{5},{7}} => [2,1,1,1,1,1] => 2
[[],[],[[],[[]]],[]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => {{1},{2},{3,5,6},{4},{7}} => [3,1,1,1,1] => 6
[[],[],[[[]],[]],[]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => {{1},{2},{3,6},{4,5},{7}} => [2,2,1,1,1] => 4
[[],[],[[[],[]]],[]] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => {{1},{2},{3,4,6},{5},{7}} => [3,1,1,1,1] => 6
[[],[],[[[[]]]],[]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => [4,1,1,1] => 24
[[],[],[[],[],[],[]]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => {{1},{2},{3,7},{4},{5},{6}} => [2,1,1,1,1,1] => 2
[[],[],[[],[],[[]]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => {{1},{2},{3,6,7},{4},{5}} => [3,1,1,1,1] => 6
[[],[],[[],[[]],[]]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => {{1},{2},{3,7},{4},{5,6}} => [2,2,1,1,1] => 4
[[],[],[[],[[],[]]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => {{1},{2},{3,5,7},{4},{6}} => [3,1,1,1,1] => 6
[[],[],[[],[[[]]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => {{1},{2},{3,5,6,7},{4}} => [4,1,1,1] => 24
[[],[],[[[]],[],[]]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => {{1},{2},{3,7},{4,5},{6}} => [2,2,1,1,1] => 4
[[],[],[[[]],[[]]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => {{1},{2},{3,6,7},{4,5}} => [3,2,1,1] => 12
[[],[],[[[],[]],[]]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => {{1},{2},{3,7},{4,6},{5}} => [2,2,1,1,1] => 4
[[],[],[[[[]]],[]]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => {{1},{2},{3,7},{4,5,6}} => [3,2,1,1] => 12
[[],[],[[[],[],[]]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => {{1},{2},{3,4,7},{5},{6}} => [3,1,1,1,1] => 6
[[],[],[[[],[[]]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => {{1},{2},{3,4,6,7},{5}} => [4,1,1,1] => 24
[[],[],[[[[]],[]]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => {{1},{2},{3,4,7},{5,6}} => [3,2,1,1] => 12
[[],[],[[[[],[]]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => {{1},{2},{3,4,5,7},{6}} => [4,1,1,1] => 24
[[],[],[[[[[]]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2},{3,4,5,6,7}} => [5,1,1] => 120
[[],[[]],[],[],[],[]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6},{7}} => [2,1,1,1,1,1] => 2
[[],[[]],[],[],[[]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => [2,2,1,1,1] => 4
[[],[[]],[],[[]],[]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => [2,2,1,1,1] => 4
[[],[[]],[],[[],[]]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => {{1},{2,3},{4},{5,7},{6}} => [2,2,1,1,1] => 4
[[],[[]],[],[[[]]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => [3,2,1,1] => 12
[[],[[]],[[]],[],[]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => [2,2,1,1,1] => 4
[[],[[]],[[]],[[]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => [2,2,2,1] => 8
[[],[[]],[[],[]],[]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => {{1},{2,3},{4,6},{5},{7}} => [2,2,1,1,1] => 4
[[],[[]],[[[]]],[]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => [3,2,1,1] => 12
[[],[[]],[[],[],[]]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => {{1},{2,3},{4,7},{5},{6}} => [2,2,1,1,1] => 4
[[],[[]],[[],[[]]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => {{1},{2,3},{4,6,7},{5}} => [3,2,1,1] => 12
[[],[[]],[[[]],[]]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => {{1},{2,3},{4,7},{5,6}} => [2,2,2,1] => 8
[[],[[]],[[[],[]]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => {{1},{2,3},{4,5,7},{6}} => [3,2,1,1] => 12
[[],[[]],[[[[]]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => [4,2,1] => 48
[[],[[],[]],[],[],[]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => {{1},{2,4},{3},{5},{6},{7}} => [2,1,1,1,1,1] => 2
[[],[[[]]],[],[],[]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}} => [3,1,1,1,1] => 6
[[],[[],[]],[],[[]]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => {{1},{2,4},{3},{5},{6,7}} => [2,2,1,1,1] => 4
[[],[[[]]],[],[[]]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => [3,2,1,1] => 12
[[],[[],[]],[[]],[]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => {{1},{2,4},{3},{5,6},{7}} => [2,2,1,1,1] => 4
[[],[[[]]],[[]],[]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => [3,2,1,1] => 12
[[],[[],[]],[[],[]]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => {{1},{2,4},{3},{5,7},{6}} => [2,2,1,1,1] => 4
[[],[[],[]],[[[]]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => {{1},{2,4},{3},{5,6,7}} => [3,2,1,1] => 12
[[],[[[]]],[[],[]]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => {{1},{2,3,4},{5,7},{6}} => [3,2,1,1] => 12
[[],[[[]]],[[[]]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => [3,3,1] => 36
[[],[[],[],[]],[],[]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => {{1},{2,5},{3},{4},{6},{7}} => [2,1,1,1,1,1] => 2
[[],[[],[[]]],[],[]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => {{1},{2,4,5},{3},{6},{7}} => [3,1,1,1,1] => 6
[[],[[[]],[]],[],[]] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => {{1},{2,5},{3,4},{6},{7}} => [2,2,1,1,1] => 4
[[],[[[],[]]],[],[]] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => {{1},{2,3,5},{4},{6},{7}} => [3,1,1,1,1] => 6
[[],[[[[]]]],[],[]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => [4,1,1,1] => 24
[[],[[],[],[]],[[]]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => {{1},{2,5},{3},{4},{6,7}} => [2,2,1,1,1] => 4
[[],[[],[[]]],[[]]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => {{1},{2,4,5},{3},{6,7}} => [3,2,1,1] => 12
[[],[[[]],[]],[[]]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => {{1},{2,5},{3,4},{6,7}} => [2,2,2,1] => 8
[[],[[[],[]]],[[]]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => {{1},{2,3,5},{4},{6,7}} => [3,2,1,1] => 12
[[],[[[[]]]],[[]]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => [4,2,1] => 48
[[],[[],[],[],[]],[]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => {{1},{2,6},{3},{4},{5},{7}} => [2,1,1,1,1,1] => 2
[[],[[],[],[[]]],[]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => {{1},{2,5,6},{3},{4},{7}} => [3,1,1,1,1] => 6
[[],[[],[[]],[]],[]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => {{1},{2,6},{3},{4,5},{7}} => [2,2,1,1,1] => 4
[[],[[],[[],[]]],[]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => {{1},{2,4,6},{3},{5},{7}} => [3,1,1,1,1] => 6
[[],[[],[[[]]]],[]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => {{1},{2,4,5,6},{3},{7}} => [4,1,1,1] => 24
[[],[[[]],[],[]],[]] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => {{1},{2,6},{3,4},{5},{7}} => [2,2,1,1,1] => 4
[[],[[[]],[[]]],[]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => {{1},{2,5,6},{3,4},{7}} => [3,2,1,1] => 12
[[],[[[],[]],[]],[]] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => {{1},{2,6},{3,5},{4},{7}} => [2,2,1,1,1] => 4
[[],[[[[]]],[]],[]] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => {{1},{2,6},{3,4,5},{7}} => [3,2,1,1] => 12
[[],[[[],[],[]]],[]] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => {{1},{2,3,6},{4},{5},{7}} => [3,1,1,1,1] => 6
[[],[[[],[[]]]],[]] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => {{1},{2,3,5,6},{4},{7}} => [4,1,1,1] => 24
[[],[[[[]],[]]],[]] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => {{1},{2,3,6},{4,5},{7}} => [3,2,1,1] => 12
[[],[[[[],[]]]],[]] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => {{1},{2,3,4,6},{5},{7}} => [4,1,1,1] => 24
[[],[[[[[]]]]],[]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6},{7}} => [5,1,1] => 120
[[],[[],[],[],[],[]]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => {{1},{2,7},{3},{4},{5},{6}} => [2,1,1,1,1,1] => 2
[[],[[],[],[],[[]]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => {{1},{2,6,7},{3},{4},{5}} => [3,1,1,1,1] => 6
[[],[[],[],[[]],[]]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => {{1},{2,7},{3},{4},{5,6}} => [2,2,1,1,1] => 4
[[],[[],[],[[],[]]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => {{1},{2,5,7},{3},{4},{6}} => [3,1,1,1,1] => 6
[[],[[],[],[[[]]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => {{1},{2,5,6,7},{3},{4}} => [4,1,1,1] => 24
[[],[[],[[]],[],[]]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => {{1},{2,7},{3},{4,5},{6}} => [2,2,1,1,1] => 4
[[],[[],[[]],[[]]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => {{1},{2,6,7},{3},{4,5}} => [3,2,1,1] => 12
[[],[[],[[],[]],[]]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => {{1},{2,7},{3},{4,6},{5}} => [2,2,1,1,1] => 4
[[],[[],[[[]]],[]]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => {{1},{2,7},{3},{4,5,6}} => [3,2,1,1] => 12
[[],[[],[[],[],[]]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => {{1},{2,4,7},{3},{5},{6}} => [3,1,1,1,1] => 6
[[],[[],[[],[[]]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => {{1},{2,4,6,7},{3},{5}} => [4,1,1,1] => 24
[[],[[],[[[]],[]]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => {{1},{2,4,7},{3},{5,6}} => [3,2,1,1] => 12
[[],[[],[[[],[]]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => {{1},{2,4,5,7},{3},{6}} => [4,1,1,1] => 24
[[],[[],[[[[]]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => {{1},{2,4,5,6,7},{3}} => [5,1,1] => 120
[[],[[[]],[],[],[]]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => {{1},{2,7},{3,4},{5},{6}} => [2,2,1,1,1] => 4
[[],[[[]],[],[[]]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => {{1},{2,6,7},{3,4},{5}} => [3,2,1,1] => 12
[[],[[[]],[[]],[]]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => {{1},{2,7},{3,4},{5,6}} => [2,2,2,1] => 8
[[],[[[]],[[],[]]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => {{1},{2,5,7},{3,4},{6}} => [3,2,1,1] => 12
[[],[[[]],[[[]]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => {{1},{2,5,6,7},{3,4}} => [4,2,1] => 48
[[],[[[],[]],[],[]]] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => {{1},{2,7},{3,5},{4},{6}} => [2,2,1,1,1] => 4
[[],[[[[]]],[],[]]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => {{1},{2,7},{3,4,5},{6}} => [3,2,1,1] => 12
[[],[[[],[]],[[]]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => {{1},{2,6,7},{3,5},{4}} => [3,2,1,1] => 12
[[],[[[[]]],[[]]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => {{1},{2,6,7},{3,4,5}} => [3,3,1] => 36
[[],[[[],[],[]],[]]] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => {{1},{2,7},{3,6},{4},{5}} => [2,2,1,1,1] => 4
[[],[[[],[[]]],[]]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => {{1},{2,7},{3,5,6},{4}} => [3,2,1,1] => 12
[[],[[[[]],[]],[]]] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => {{1},{2,7},{3,6},{4,5}} => [2,2,2,1] => 8
[[],[[[[],[]]],[]]] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => {{1},{2,7},{3,4,6},{5}} => [3,2,1,1] => 12
[[],[[[[[]]]],[]]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => {{1},{2,7},{3,4,5,6}} => [4,2,1] => 48
[[],[[[],[],[],[]]]] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => {{1},{2,3,7},{4},{5},{6}} => [3,1,1,1,1] => 6
[[],[[[],[],[[]]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => {{1},{2,3,6,7},{4},{5}} => [4,1,1,1] => 24
[[],[[[],[[]],[]]]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => {{1},{2,3,7},{4},{5,6}} => [3,2,1,1] => 12
[[],[[[],[[],[]]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => {{1},{2,3,5,7},{4},{6}} => [4,1,1,1] => 24
[[],[[[],[[[]]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => {{1},{2,3,5,6,7},{4}} => [5,1,1] => 120
[[],[[[[]],[],[]]]] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => {{1},{2,3,7},{4,5},{6}} => [3,2,1,1] => 12
[[],[[[[]],[[]]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => {{1},{2,3,6,7},{4,5}} => [4,2,1] => 48
[[],[[[[],[]],[]]]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => {{1},{2,3,7},{4,6},{5}} => [3,2,1,1] => 12
[[],[[[[[]]],[]]]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => {{1},{2,3,7},{4,5,6}} => [3,3,1] => 36
[[],[[[[],[],[]]]]] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => {{1},{2,3,4,7},{5},{6}} => [4,1,1,1] => 24
[[],[[[[],[[]]]]]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => {{1},{2,3,4,6,7},{5}} => [5,1,1] => 120
[[],[[[[[]],[]]]]] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => {{1},{2,3,4,7},{5,6}} => [4,2,1] => 48
[[],[[[[[],[]]]]]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => {{1},{2,3,4,5,7},{6}} => [5,1,1] => 120
[[],[[[[[[]]]]]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7}} => [6,1] => 720
[[[]],[],[],[],[],[]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5},{6},{7}} => [2,1,1,1,1,1] => 2
[[[]],[],[],[],[[]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6,7}} => [2,2,1,1,1] => 4
[[[]],[],[],[[]],[]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => [2,2,1,1,1] => 4
[[[]],[],[],[[],[]]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => {{1,2},{3},{4},{5,7},{6}} => [2,2,1,1,1] => 4
[[[]],[],[],[[[]]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => [3,2,1,1] => 12
[[[]],[],[[]],[],[]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => [2,2,1,1,1] => 4
[[[]],[],[[]],[[]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => [2,2,2,1] => 8
[[[]],[],[[],[]],[]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => {{1,2},{3},{4,6},{5},{7}} => [2,2,1,1,1] => 4
[[[]],[],[[[]]],[]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => [3,2,1,1] => 12
[[[]],[],[[],[],[]]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => {{1,2},{3},{4,7},{5},{6}} => [2,2,1,1,1] => 4
[[[]],[],[[],[[]]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => {{1,2},{3},{4,6,7},{5}} => [3,2,1,1] => 12
[[[]],[],[[[]],[]]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => {{1,2},{3},{4,7},{5,6}} => [2,2,2,1] => 8
[[[]],[],[[[],[]]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => {{1,2},{3},{4,5,7},{6}} => [3,2,1,1] => 12
[[[]],[],[[[[]]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}} => [4,2,1] => 48
[[[]],[[]],[],[],[]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => [2,2,1,1,1] => 4
[[[]],[[]],[],[[]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => [2,2,2,1] => 8
[[[]],[[]],[[]],[]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => [2,2,2,1] => 8
[[[]],[[]],[[],[]]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => {{1,2},{3,4},{5,7},{6}} => [2,2,2,1] => 8
[[[]],[[]],[[[]]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => [3,2,2] => 24
[[[]],[[],[]],[],[]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => {{1,2},{3,5},{4},{6},{7}} => [2,2,1,1,1] => 4
[[[]],[[[]]],[],[]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => [3,2,1,1] => 12
[[[]],[[],[]],[[]]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => {{1,2},{3,5},{4},{6,7}} => [2,2,2,1] => 8
[[[]],[[[]]],[[]]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => [3,2,2] => 24
[[[]],[[],[],[]],[]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => {{1,2},{3,6},{4},{5},{7}} => [2,2,1,1,1] => 4
[[[]],[[],[[]]],[]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => {{1,2},{3,5,6},{4},{7}} => [3,2,1,1] => 12
[[[]],[[[]],[]],[]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => {{1,2},{3,6},{4,5},{7}} => [2,2,2,1] => 8
[[[]],[[[],[]]],[]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => {{1,2},{3,4,6},{5},{7}} => [3,2,1,1] => 12
[[[]],[[[[]]]],[]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => [4,2,1] => 48
[[[]],[[],[],[],[]]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => {{1,2},{3,7},{4},{5},{6}} => [2,2,1,1,1] => 4
[[[]],[[],[],[[]]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => {{1,2},{3,6,7},{4},{5}} => [3,2,1,1] => 12
[[[]],[[],[[]],[]]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => {{1,2},{3,7},{4},{5,6}} => [2,2,2,1] => 8
[[[]],[[],[[],[]]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => {{1,2},{3,5,7},{4},{6}} => [3,2,1,1] => 12
[[[]],[[],[[[]]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => {{1,2},{3,5,6,7},{4}} => [4,2,1] => 48
[[[]],[[[]],[],[]]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => {{1,2},{3,7},{4,5},{6}} => [2,2,2,1] => 8
[[[]],[[[]],[[]]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => {{1,2},{3,6,7},{4,5}} => [3,2,2] => 24
[[[]],[[[],[]],[]]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => {{1,2},{3,7},{4,6},{5}} => [2,2,2,1] => 8
[[[]],[[[[]]],[]]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => {{1,2},{3,7},{4,5,6}} => [3,2,2] => 24
[[[]],[[[],[],[]]]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => {{1,2},{3,4,7},{5},{6}} => [3,2,1,1] => 12
[[[]],[[[],[[]]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => {{1,2},{3,4,6,7},{5}} => [4,2,1] => 48
[[[]],[[[[]],[]]]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => {{1,2},{3,4,7},{5,6}} => [3,2,2] => 24
[[[]],[[[[],[]]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => {{1,2},{3,4,5,7},{6}} => [4,2,1] => 48
[[[]],[[[[[]]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3,4,5,6,7}} => [5,2] => 240
[[[],[]],[],[],[],[]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => {{1,3},{2},{4},{5},{6},{7}} => [2,1,1,1,1,1] => 2
[[[[]]],[],[],[],[]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6},{7}} => [3,1,1,1,1] => 6
[[[],[]],[],[],[[]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => {{1,3},{2},{4},{5},{6,7}} => [2,2,1,1,1] => 4
[[[[]]],[],[],[[]]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => [3,2,1,1] => 12
[[[],[]],[],[[]],[]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => {{1,3},{2},{4},{5,6},{7}} => [2,2,1,1,1] => 4
[[[[]]],[],[[]],[]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => [3,2,1,1] => 12
[[[],[]],[],[[],[]]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => {{1,3},{2},{4},{5,7},{6}} => [2,2,1,1,1] => 4
[[[],[]],[],[[[]]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => {{1,3},{2},{4},{5,6,7}} => [3,2,1,1] => 12
[[[[]]],[],[[],[]]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => {{1,2,3},{4},{5,7},{6}} => [3,2,1,1] => 12
[[[[]]],[],[[[]]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => [3,3,1] => 36
[[[],[]],[[]],[],[]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => {{1,3},{2},{4,5},{6},{7}} => [2,2,1,1,1] => 4
[[[[]]],[[]],[],[]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => [3,2,1,1] => 12
[[[],[]],[[]],[[]]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => {{1,3},{2},{4,5},{6,7}} => [2,2,2,1] => 8
[[[[]]],[[]],[[]]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => [3,2,2] => 24
[[[],[]],[[],[]],[]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => {{1,3},{2},{4,6},{5},{7}} => [2,2,1,1,1] => 4
[[[],[]],[[[]]],[]] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => {{1,3},{2},{4,5,6},{7}} => [3,2,1,1] => 12
[[[[]]],[[],[]],[]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => {{1,2,3},{4,6},{5},{7}} => [3,2,1,1] => 12
[[[[]]],[[[]]],[]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => [3,3,1] => 36
[[[],[]],[[],[],[]]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => {{1,3},{2},{4,7},{5},{6}} => [2,2,1,1,1] => 4
[[[],[]],[[],[[]]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => {{1,3},{2},{4,6,7},{5}} => [3,2,1,1] => 12
[[[],[]],[[[]],[]]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => {{1,3},{2},{4,7},{5,6}} => [2,2,2,1] => 8
[[[],[]],[[[],[]]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => {{1,3},{2},{4,5,7},{6}} => [3,2,1,1] => 12
[[[],[]],[[[[]]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => {{1,3},{2},{4,5,6,7}} => [4,2,1] => 48
[[[[]]],[[],[],[]]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => {{1,2,3},{4,7},{5},{6}} => [3,2,1,1] => 12
[[[[]]],[[],[[]]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => {{1,2,3},{4,6,7},{5}} => [3,3,1] => 36
[[[[]]],[[[]],[]]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => {{1,2,3},{4,7},{5,6}} => [3,2,2] => 24
[[[[]]],[[[],[]]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => {{1,2,3},{4,5,7},{6}} => [3,3,1] => 36
[[[[]]],[[[[]]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}} => [4,3] => 144
[[[],[],[]],[],[],[]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => {{1,4},{2},{3},{5},{6},{7}} => [2,1,1,1,1,1] => 2
[[[],[[]]],[],[],[]] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => {{1,3,4},{2},{5},{6},{7}} => [3,1,1,1,1] => 6
[[[[]],[]],[],[],[]] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => {{1,4},{2,3},{5},{6},{7}} => [2,2,1,1,1] => 4
[[[[],[]]],[],[],[]] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => {{1,2,4},{3},{5},{6},{7}} => [3,1,1,1,1] => 6
[[[[[]]]],[],[],[]] => [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] => 24
[[[],[],[]],[],[[]]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => {{1,4},{2},{3},{5},{6,7}} => [2,2,1,1,1] => 4
[[[],[[]]],[],[[]]] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => {{1,3,4},{2},{5},{6,7}} => [3,2,1,1] => 12
[[[[]],[]],[],[[]]] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => {{1,4},{2,3},{5},{6,7}} => [2,2,2,1] => 8
[[[[],[]]],[],[[]]] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => {{1,2,4},{3},{5},{6,7}} => [3,2,1,1] => 12
[[[[[]]]],[],[[]]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}} => [4,2,1] => 48
[[[],[],[]],[[]],[]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => {{1,4},{2},{3},{5,6},{7}} => [2,2,1,1,1] => 4
[[[],[[]]],[[]],[]] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => {{1,3,4},{2},{5,6},{7}} => [3,2,1,1] => 12
[[[[]],[]],[[]],[]] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => {{1,4},{2,3},{5,6},{7}} => [2,2,2,1] => 8
[[[[],[]]],[[]],[]] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => {{1,2,4},{3},{5,6},{7}} => [3,2,1,1] => 12
[[[[[]]]],[[]],[]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => [4,2,1] => 48
[[[],[],[]],[[],[]]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => {{1,4},{2},{3},{5,7},{6}} => [2,2,1,1,1] => 4
[[[],[],[]],[[[]]]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => {{1,4},{2},{3},{5,6,7}} => [3,2,1,1] => 12
[[[],[[]]],[[],[]]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => {{1,3,4},{2},{5,7},{6}} => [3,2,1,1] => 12
[[[],[[]]],[[[]]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => {{1,3,4},{2},{5,6,7}} => [3,3,1] => 36
[[[[]],[]],[[],[]]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => {{1,4},{2,3},{5,7},{6}} => [2,2,2,1] => 8
[[[[]],[]],[[[]]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => {{1,4},{2,3},{5,6,7}} => [3,2,2] => 24
[[[[],[]]],[[],[]]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => {{1,2,4},{3},{5,7},{6}} => [3,2,1,1] => 12
[[[[],[]]],[[[]]]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => {{1,2,4},{3},{5,6,7}} => [3,3,1] => 36
[[[[[]]]],[[],[]]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => {{1,2,3,4},{5,7},{6}} => [4,2,1] => 48
[[[[[]]]],[[[]]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7}} => [4,3] => 144
[[[],[],[],[]],[],[]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => {{1,5},{2},{3},{4},{6},{7}} => [2,1,1,1,1,1] => 2
[[[],[],[[]]],[],[]] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => {{1,4,5},{2},{3},{6},{7}} => [3,1,1,1,1] => 6
[[[],[[]],[]],[],[]] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => {{1,5},{2},{3,4},{6},{7}} => [2,2,1,1,1] => 4
[[[],[[],[]]],[],[]] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => {{1,3,5},{2},{4},{6},{7}} => [3,1,1,1,1] => 6
[[[],[[[]]]],[],[]] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => {{1,3,4,5},{2},{6},{7}} => [4,1,1,1] => 24
[[[[]],[],[]],[],[]] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => {{1,5},{2,3},{4},{6},{7}} => [2,2,1,1,1] => 4
[[[[]],[[]]],[],[]] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => {{1,4,5},{2,3},{6},{7}} => [3,2,1,1] => 12
[[[[],[]],[]],[],[]] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => {{1,5},{2,4},{3},{6},{7}} => [2,2,1,1,1] => 4
[[[[[]]],[]],[],[]] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => {{1,5},{2,3,4},{6},{7}} => [3,2,1,1] => 12
[[[[],[],[]]],[],[]] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => {{1,2,5},{3},{4},{6},{7}} => [3,1,1,1,1] => 6
[[[[],[[]]]],[],[]] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => {{1,2,4,5},{3},{6},{7}} => [4,1,1,1] => 24
[[[[[]],[]]],[],[]] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => {{1,2,5},{3,4},{6},{7}} => [3,2,1,1] => 12
[[[[[],[]]]],[],[]] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => {{1,2,3,5},{4},{6},{7}} => [4,1,1,1] => 24
[[[[[[]]]]],[],[]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => {{1,2,3,4,5},{6},{7}} => [5,1,1] => 120
[[[],[],[],[]],[[]]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => {{1,5},{2},{3},{4},{6,7}} => [2,2,1,1,1] => 4
[[[],[],[[]]],[[]]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => {{1,4,5},{2},{3},{6,7}} => [3,2,1,1] => 12
[[[],[[]],[]],[[]]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => {{1,5},{2},{3,4},{6,7}} => [2,2,2,1] => 8
[[[],[[],[]]],[[]]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => {{1,3,5},{2},{4},{6,7}} => [3,2,1,1] => 12
[[[],[[[]]]],[[]]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => {{1,3,4,5},{2},{6,7}} => [4,2,1] => 48
[[[[]],[],[]],[[]]] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => {{1,5},{2,3},{4},{6,7}} => [2,2,2,1] => 8
[[[[]],[[]]],[[]]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => {{1,4,5},{2,3},{6,7}} => [3,2,2] => 24
[[[[],[]],[]],[[]]] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => {{1,5},{2,4},{3},{6,7}} => [2,2,2,1] => 8
[[[[[]]],[]],[[]]] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => {{1,5},{2,3,4},{6,7}} => [3,2,2] => 24
[[[[],[],[]]],[[]]] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => {{1,2,5},{3},{4},{6,7}} => [3,2,1,1] => 12
[[[[],[[]]]],[[]]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => {{1,2,4,5},{3},{6,7}} => [4,2,1] => 48
[[[[[]],[]]],[[]]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => {{1,2,5},{3,4},{6,7}} => [3,2,2] => 24
[[[[[],[]]]],[[]]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => {{1,2,3,5},{4},{6,7}} => [4,2,1] => 48
[[[[[[]]]]],[[]]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5},{6,7}} => [5,2] => 240
[[[],[],[],[],[]],[]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => {{1,6},{2},{3},{4},{5},{7}} => [2,1,1,1,1,1] => 2
[[[],[],[],[[]]],[]] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => {{1,5,6},{2},{3},{4},{7}} => [3,1,1,1,1] => 6
[[[],[],[[]],[]],[]] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => {{1,6},{2},{3},{4,5},{7}} => [2,2,1,1,1] => 4
[[[],[],[[],[]]],[]] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => {{1,4,6},{2},{3},{5},{7}} => [3,1,1,1,1] => 6
[[[],[],[[[]]]],[]] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => {{1,4,5,6},{2},{3},{7}} => [4,1,1,1] => 24
[[[],[[]],[],[]],[]] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => {{1,6},{2},{3,4},{5},{7}} => [2,2,1,1,1] => 4
[[[],[[]],[[]]],[]] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => {{1,5,6},{2},{3,4},{7}} => [3,2,1,1] => 12
[[[],[[],[]],[]],[]] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => {{1,6},{2},{3,5},{4},{7}} => [2,2,1,1,1] => 4
[[[],[[[]]],[]],[]] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => {{1,6},{2},{3,4,5},{7}} => [3,2,1,1] => 12
[[[],[[],[],[]]],[]] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => {{1,3,6},{2},{4},{5},{7}} => [3,1,1,1,1] => 6
[[[],[[],[[]]]],[]] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => {{1,3,5,6},{2},{4},{7}} => [4,1,1,1] => 24
[[[],[[[]],[]]],[]] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => {{1,3,6},{2},{4,5},{7}} => [3,2,1,1] => 12
[[[],[[[],[]]]],[]] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => {{1,3,4,6},{2},{5},{7}} => [4,1,1,1] => 24
[[[],[[[[]]]]],[]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => {{1,3,4,5,6},{2},{7}} => [5,1,1] => 120
[[[[]],[],[],[]],[]] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => {{1,6},{2,3},{4},{5},{7}} => [2,2,1,1,1] => 4
[[[[]],[],[[]]],[]] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => {{1,5,6},{2,3},{4},{7}} => [3,2,1,1] => 12
[[[[]],[[]],[]],[]] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => {{1,6},{2,3},{4,5},{7}} => [2,2,2,1] => 8
[[[[]],[[],[]]],[]] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => {{1,4,6},{2,3},{5},{7}} => [3,2,1,1] => 12
[[[[]],[[[]]]],[]] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => {{1,4,5,6},{2,3},{7}} => [4,2,1] => 48
[[[[],[]],[],[]],[]] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => {{1,6},{2,4},{3},{5},{7}} => [2,2,1,1,1] => 4
[[[[[]]],[],[]],[]] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => {{1,6},{2,3,4},{5},{7}} => [3,2,1,1] => 12
[[[[],[]],[[]]],[]] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => {{1,5,6},{2,4},{3},{7}} => [3,2,1,1] => 12
[[[[[]]],[[]]],[]] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => {{1,5,6},{2,3,4},{7}} => [3,3,1] => 36
[[[[],[],[]],[]],[]] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => {{1,6},{2,5},{3},{4},{7}} => [2,2,1,1,1] => 4
[[[[],[[]]],[]],[]] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => {{1,6},{2,4,5},{3},{7}} => [3,2,1,1] => 12
[[[[[]],[]],[]],[]] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => {{1,6},{2,5},{3,4},{7}} => [2,2,2,1] => 8
[[[[[],[]]],[]],[]] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => {{1,6},{2,3,5},{4},{7}} => [3,2,1,1] => 12
[[[[[[]]]],[]],[]] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => {{1,6},{2,3,4,5},{7}} => [4,2,1] => 48
[[[[],[],[],[]]],[]] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => {{1,2,6},{3},{4},{5},{7}} => [3,1,1,1,1] => 6
[[[[],[],[[]]]],[]] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => {{1,2,5,6},{3},{4},{7}} => [4,1,1,1] => 24
[[[[],[[]],[]]],[]] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => {{1,2,6},{3},{4,5},{7}} => [3,2,1,1] => 12
[[[[],[[],[]]]],[]] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => {{1,2,4,6},{3},{5},{7}} => [4,1,1,1] => 24
[[[[],[[[]]]]],[]] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => {{1,2,4,5,6},{3},{7}} => [5,1,1] => 120
[[[[[]],[],[]]],[]] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => {{1,2,6},{3,4},{5},{7}} => [3,2,1,1] => 12
[[[[[]],[[]]]],[]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => {{1,2,5,6},{3,4},{7}} => [4,2,1] => 48
[[[[[],[]],[]]],[]] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => {{1,2,6},{3,5},{4},{7}} => [3,2,1,1] => 12
[[[[[[]]],[]]],[]] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => {{1,2,6},{3,4,5},{7}} => [3,3,1] => 36
[[[[[],[],[]]]],[]] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => {{1,2,3,6},{4},{5},{7}} => [4,1,1,1] => 24
[[[[[],[[]]]]],[]] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => {{1,2,3,5,6},{4},{7}} => [5,1,1] => 120
[[[[[[]],[]]]],[]] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => {{1,2,3,6},{4,5},{7}} => [4,2,1] => 48
[[[[[[],[]]]]],[]] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,6},{5},{7}} => [5,1,1] => 120
[[[[[[[]]]]]],[]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6},{7}} => [6,1] => 720
[[[],[],[],[],[],[]]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1,7},{2},{3},{4},{5},{6}} => [2,1,1,1,1,1] => 2
[[[],[],[],[],[[]]]] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => {{1,6,7},{2},{3},{4},{5}} => [3,1,1,1,1] => 6
[[[],[],[],[[]],[]]] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => {{1,7},{2},{3},{4},{5,6}} => [2,2,1,1,1] => 4
[[[],[],[],[[],[]]]] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => {{1,5,7},{2},{3},{4},{6}} => [3,1,1,1,1] => 6
[[[],[],[],[[[]]]]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => {{1,5,6,7},{2},{3},{4}} => [4,1,1,1] => 24
[[[],[],[[]],[],[]]] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => {{1,7},{2},{3},{4,5},{6}} => [2,2,1,1,1] => 4
[[[],[],[[]],[[]]]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => {{1,6,7},{2},{3},{4,5}} => [3,2,1,1] => 12
[[[],[],[[],[]],[]]] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => {{1,7},{2},{3},{4,6},{5}} => [2,2,1,1,1] => 4
[[[],[],[[[]]],[]]] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => {{1,7},{2},{3},{4,5,6}} => [3,2,1,1] => 12
[[[],[],[[],[],[]]]] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => {{1,4,7},{2},{3},{5},{6}} => [3,1,1,1,1] => 6
[[[],[],[[],[[]]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => {{1,4,6,7},{2},{3},{5}} => [4,1,1,1] => 24
[[[],[],[[[]],[]]]] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => {{1,4,7},{2},{3},{5,6}} => [3,2,1,1] => 12
[[[],[],[[[],[]]]]] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => {{1,4,5,7},{2},{3},{6}} => [4,1,1,1] => 24
[[[],[],[[[[]]]]]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => {{1,4,5,6,7},{2},{3}} => [5,1,1] => 120
[[[],[[]],[],[],[]]] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => {{1,7},{2},{3,4},{5},{6}} => [2,2,1,1,1] => 4
[[[],[[]],[],[[]]]] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => {{1,6,7},{2},{3,4},{5}} => [3,2,1,1] => 12
[[[],[[]],[[]],[]]] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => {{1,7},{2},{3,4},{5,6}} => [2,2,2,1] => 8
[[[],[[]],[[],[]]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => {{1,5,7},{2},{3,4},{6}} => [3,2,1,1] => 12
[[[],[[]],[[[]]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => {{1,5,6,7},{2},{3,4}} => [4,2,1] => 48
[[[],[[],[]],[],[]]] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => {{1,7},{2},{3,5},{4},{6}} => [2,2,1,1,1] => 4
[[[],[[[]]],[],[]]] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => {{1,7},{2},{3,4,5},{6}} => [3,2,1,1] => 12
[[[],[[],[]],[[]]]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => {{1,6,7},{2},{3,5},{4}} => [3,2,1,1] => 12
[[[],[[[]]],[[]]]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => {{1,6,7},{2},{3,4,5}} => [3,3,1] => 36
[[[],[[],[],[]],[]]] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => {{1,7},{2},{3,6},{4},{5}} => [2,2,1,1,1] => 4
[[[],[[],[[]]],[]]] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => {{1,7},{2},{3,5,6},{4}} => [3,2,1,1] => 12
[[[],[[[]],[]],[]]] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => {{1,7},{2},{3,6},{4,5}} => [2,2,2,1] => 8
[[[],[[[],[]]],[]]] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => {{1,7},{2},{3,4,6},{5}} => [3,2,1,1] => 12
[[[],[[[[]]]],[]]] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => {{1,7},{2},{3,4,5,6}} => [4,2,1] => 48
[[[],[[],[],[],[]]]] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => {{1,3,7},{2},{4},{5},{6}} => [3,1,1,1,1] => 6
[[[],[[],[],[[]]]]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => {{1,3,6,7},{2},{4},{5}} => [4,1,1,1] => 24
[[[],[[],[[]],[]]]] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => {{1,3,7},{2},{4},{5,6}} => [3,2,1,1] => 12
[[[],[[],[[],[]]]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => {{1,3,5,7},{2},{4},{6}} => [4,1,1,1] => 24
[[[],[[],[[[]]]]]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => {{1,3,5,6,7},{2},{4}} => [5,1,1] => 120
[[[],[[[]],[],[]]]] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => {{1,3,7},{2},{4,5},{6}} => [3,2,1,1] => 12
[[[],[[[]],[[]]]]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => {{1,3,6,7},{2},{4,5}} => [4,2,1] => 48
[[[],[[[],[]],[]]]] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => {{1,3,7},{2},{4,6},{5}} => [3,2,1,1] => 12
[[[],[[[[]]],[]]]] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => {{1,3,7},{2},{4,5,6}} => [3,3,1] => 36
[[[],[[[],[],[]]]]] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => {{1,3,4,7},{2},{5},{6}} => [4,1,1,1] => 24
[[[],[[[],[[]]]]]] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => {{1,3,4,6,7},{2},{5}} => [5,1,1] => 120
[[[],[[[[]],[]]]]] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => {{1,3,4,7},{2},{5,6}} => [4,2,1] => 48
[[[],[[[[],[]]]]]] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => {{1,3,4,5,7},{2},{6}} => [5,1,1] => 120
[[[],[[[[[]]]]]]] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => {{1,3,4,5,6,7},{2}} => [6,1] => 720
[[[[]],[],[],[],[]]] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => {{1,7},{2,3},{4},{5},{6}} => [2,2,1,1,1] => 4
[[[[]],[],[],[[]]]] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => {{1,6,7},{2,3},{4},{5}} => [3,2,1,1] => 12
[[[[]],[],[[]],[]]] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => {{1,7},{2,3},{4},{5,6}} => [2,2,2,1] => 8
[[[[]],[],[[],[]]]] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => {{1,5,7},{2,3},{4},{6}} => [3,2,1,1] => 12
[[[[]],[],[[[]]]]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => {{1,5,6,7},{2,3},{4}} => [4,2,1] => 48
[[[[]],[[]],[],[]]] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => {{1,7},{2,3},{4,5},{6}} => [2,2,2,1] => 8
[[[[]],[[]],[[]]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => {{1,6,7},{2,3},{4,5}} => [3,2,2] => 24
[[[[]],[[],[]],[]]] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => {{1,7},{2,3},{4,6},{5}} => [2,2,2,1] => 8
[[[[]],[[[]]],[]]] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => {{1,7},{2,3},{4,5,6}} => [3,2,2] => 24
[[[[]],[[],[],[]]]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => {{1,4,7},{2,3},{5},{6}} => [3,2,1,1] => 12
[[[[]],[[],[[]]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => {{1,4,6,7},{2,3},{5}} => [4,2,1] => 48
[[[[]],[[[]],[]]]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => {{1,4,7},{2,3},{5,6}} => [3,2,2] => 24
[[[[]],[[[],[]]]]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => {{1,4,5,7},{2,3},{6}} => [4,2,1] => 48
[[[[]],[[[[]]]]]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => {{1,4,5,6,7},{2,3}} => [5,2] => 240
[[[[],[]],[],[],[]]] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => {{1,7},{2,4},{3},{5},{6}} => [2,2,1,1,1] => 4
[[[[[]]],[],[],[]]] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => {{1,7},{2,3,4},{5},{6}} => [3,2,1,1] => 12
[[[[],[]],[],[[]]]] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => {{1,6,7},{2,4},{3},{5}} => [3,2,1,1] => 12
[[[[[]]],[],[[]]]] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => {{1,6,7},{2,3,4},{5}} => [3,3,1] => 36
[[[[],[]],[[]],[]]] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => {{1,7},{2,4},{3},{5,6}} => [2,2,2,1] => 8
[[[[[]]],[[]],[]]] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => {{1,7},{2,3,4},{5,6}} => [3,2,2] => 24
[[[[],[]],[[],[]]]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => {{1,5,7},{2,4},{3},{6}} => [3,2,1,1] => 12
[[[[],[]],[[[]]]]] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => {{1,5,6,7},{2,4},{3}} => [4,2,1] => 48
[[[[[]]],[[],[]]]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => {{1,5,7},{2,3,4},{6}} => [3,3,1] => 36
[[[[[]]],[[[]]]]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => {{1,5,6,7},{2,3,4}} => [4,3] => 144
[[[[],[],[]],[],[]]] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => {{1,7},{2,5},{3},{4},{6}} => [2,2,1,1,1] => 4
[[[[],[[]]],[],[]]] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => {{1,7},{2,4,5},{3},{6}} => [3,2,1,1] => 12
[[[[[]],[]],[],[]]] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => {{1,7},{2,5},{3,4},{6}} => [2,2,2,1] => 8
[[[[[],[]]],[],[]]] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => {{1,7},{2,3,5},{4},{6}} => [3,2,1,1] => 12
[[[[[[]]]],[],[]]] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => {{1,7},{2,3,4,5},{6}} => [4,2,1] => 48
[[[[],[],[]],[[]]]] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => {{1,6,7},{2,5},{3},{4}} => [3,2,1,1] => 12
[[[[],[[]]],[[]]]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => {{1,6,7},{2,4,5},{3}} => [3,3,1] => 36
[[[[[]],[]],[[]]]] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => {{1,6,7},{2,5},{3,4}} => [3,2,2] => 24
[[[[[],[]]],[[]]]] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => {{1,6,7},{2,3,5},{4}} => [3,3,1] => 36
[[[[[[]]]],[[]]]] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => {{1,6,7},{2,3,4,5}} => [4,3] => 144
[[[[],[],[],[]],[]]] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => {{1,7},{2,6},{3},{4},{5}} => [2,2,1,1,1] => 4
[[[[],[],[[]]],[]]] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => {{1,7},{2,5,6},{3},{4}} => [3,2,1,1] => 12
[[[[],[[]],[]],[]]] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => {{1,7},{2,6},{3},{4,5}} => [2,2,2,1] => 8
[[[[],[[],[]]],[]]] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => {{1,7},{2,4,6},{3},{5}} => [3,2,1,1] => 12
[[[[],[[[]]]],[]]] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => {{1,7},{2,4,5,6},{3}} => [4,2,1] => 48
[[[[[]],[],[]],[]]] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => {{1,7},{2,6},{3,4},{5}} => [2,2,2,1] => 8
[[[[[]],[[]]],[]]] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => {{1,7},{2,5,6},{3,4}} => [3,2,2] => 24
[[[[[],[]],[]],[]]] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => {{1,7},{2,6},{3,5},{4}} => [2,2,2,1] => 8
[[[[[[]]],[]],[]]] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => {{1,7},{2,6},{3,4,5}} => [3,2,2] => 24
[[[[[],[],[]]],[]]] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => {{1,7},{2,3,6},{4},{5}} => [3,2,1,1] => 12
[[[[[],[[]]]],[]]] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => {{1,7},{2,3,5,6},{4}} => [4,2,1] => 48
[[[[[[]],[]]],[]]] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => {{1,7},{2,3,6},{4,5}} => [3,2,2] => 24
[[[[[[],[]]]],[]]] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => {{1,7},{2,3,4,6},{5}} => [4,2,1] => 48
[[[[[[[]]]]],[]]] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => {{1,7},{2,3,4,5,6}} => [5,2] => 240
[[[[],[],[],[],[]]]] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => {{1,2,7},{3},{4},{5},{6}} => [3,1,1,1,1] => 6
[[[[],[],[],[[]]]]] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => {{1,2,6,7},{3},{4},{5}} => [4,1,1,1] => 24
[[[[],[],[[]],[]]]] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => {{1,2,7},{3},{4},{5,6}} => [3,2,1,1] => 12
[[[[],[],[[],[]]]]] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => {{1,2,5,7},{3},{4},{6}} => [4,1,1,1] => 24
[[[[],[],[[[]]]]]] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => {{1,2,5,6,7},{3},{4}} => [5,1,1] => 120
[[[[],[[]],[],[]]]] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => {{1,2,7},{3},{4,5},{6}} => [3,2,1,1] => 12
[[[[],[[]],[[]]]]] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => {{1,2,6,7},{3},{4,5}} => [4,2,1] => 48
[[[[],[[],[]],[]]]] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => {{1,2,7},{3},{4,6},{5}} => [3,2,1,1] => 12
[[[[],[[[]]],[]]]] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => {{1,2,7},{3},{4,5,6}} => [3,3,1] => 36
[[[[],[[],[],[]]]]] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => {{1,2,4,7},{3},{5},{6}} => [4,1,1,1] => 24
[[[[],[[],[[]]]]]] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => {{1,2,4,6,7},{3},{5}} => [5,1,1] => 120
[[[[],[[[]],[]]]]] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => {{1,2,4,7},{3},{5,6}} => [4,2,1] => 48
[[[[],[[[],[]]]]]] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => {{1,2,4,5,7},{3},{6}} => [5,1,1] => 120
[[[[],[[[[]]]]]]] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => {{1,2,4,5,6,7},{3}} => [6,1] => 720
[[[[[]],[],[],[]]]] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => {{1,2,7},{3,4},{5},{6}} => [3,2,1,1] => 12
[[[[[]],[],[[]]]]] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => {{1,2,6,7},{3,4},{5}} => [4,2,1] => 48
[[[[[]],[[]],[]]]] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => {{1,2,7},{3,4},{5,6}} => [3,2,2] => 24
[[[[[]],[[],[]]]]] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => {{1,2,5,7},{3,4},{6}} => [4,2,1] => 48
[[[[[]],[[[]]]]]] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => {{1,2,5,6,7},{3,4}} => [5,2] => 240
[[[[[],[]],[],[]]]] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => {{1,2,7},{3,5},{4},{6}} => [3,2,1,1] => 12
[[[[[[]]],[],[]]]] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => {{1,2,7},{3,4,5},{6}} => [3,3,1] => 36
[[[[[],[]],[[]]]]] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => {{1,2,6,7},{3,5},{4}} => [4,2,1] => 48
[[[[[[]]],[[]]]]] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => {{1,2,6,7},{3,4,5}} => [4,3] => 144
[[[[[],[],[]],[]]]] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => {{1,2,7},{3,6},{4},{5}} => [3,2,1,1] => 12
[[[[[],[[]]],[]]]] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => {{1,2,7},{3,5,6},{4}} => [3,3,1] => 36
[[[[[[]],[]],[]]]] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => {{1,2,7},{3,6},{4,5}} => [3,2,2] => 24
[[[[[[],[]]],[]]]] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => {{1,2,7},{3,4,6},{5}} => [3,3,1] => 36
[[[[[[[]]]],[]]]] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => {{1,2,7},{3,4,5,6}} => [4,3] => 144
[[[[[],[],[],[]]]]] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => {{1,2,3,7},{4},{5},{6}} => [4,1,1,1] => 24
[[[[[],[],[[]]]]]] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => {{1,2,3,6,7},{4},{5}} => [5,1,1] => 120
[[[[[],[[]],[]]]]] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => {{1,2,3,7},{4},{5,6}} => [4,2,1] => 48
[[[[[],[[],[]]]]]] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => {{1,2,3,5,7},{4},{6}} => [5,1,1] => 120
[[[[[],[[[]]]]]]] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => {{1,2,3,5,6,7},{4}} => [6,1] => 720
[[[[[[]],[],[]]]]] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => {{1,2,3,7},{4,5},{6}} => [4,2,1] => 48
[[[[[[]],[[]]]]]] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => {{1,2,3,6,7},{4,5}} => [5,2] => 240
[[[[[[],[]],[]]]]] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => {{1,2,3,7},{4,6},{5}} => [4,2,1] => 48
[[[[[[[]]],[]]]]] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => {{1,2,3,7},{4,5,6}} => [4,3] => 144
[[[[[[],[],[]]]]]] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => {{1,2,3,4,7},{5},{6}} => [5,1,1] => 120
[[[[[[],[[]]]]]]] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => {{1,2,3,4,6,7},{5}} => [6,1] => 720
[[[[[[[]],[]]]]]] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => {{1,2,3,4,7},{5,6}} => [5,2] => 240
[[[[[[[],[]]]]]]] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => {{1,2,3,4,5,7},{6}} => [6,1] => 720
[[[[[[[[]]]]]]]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,7}} => [7] => 5040
[[],[],[],[],[],[],[],[]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6},{7},{8}} => [1,1,1,1,1,1,1,1] => 1
[[],[],[],[],[],[],[[]]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6},{7,8}} => [2,1,1,1,1,1,1] => 2
[[],[],[],[],[],[[],[]]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => {{1},{2},{3},{4},{5},{6,8},{7}} => [2,1,1,1,1,1,1] => 2
[[],[],[],[],[],[[[]]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4},{5},{6,7,8}} => [3,1,1,1,1,1] => 6
[[],[],[],[],[[]],[],[]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3},{4},{5,6},{7},{8}} => [2,1,1,1,1,1,1] => 2
[[],[],[],[],[[]],[[]]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4},{5,6},{7,8}} => [2,2,1,1,1,1] => 4
[[],[],[],[],[[],[]],[]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => {{1},{2},{3},{4},{5,7},{6},{8}} => [2,1,1,1,1,1,1] => 2
[[],[],[],[],[[[]]],[]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4},{5,6,7},{8}} => [3,1,1,1,1,1] => 6
[[],[],[],[],[[],[],[]]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => {{1},{2},{3},{4},{5,8},{6},{7}} => [2,1,1,1,1,1,1] => 2
[[],[],[],[],[[],[[]]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => {{1},{2},{3},{4},{5,7,8},{6}} => [3,1,1,1,1,1] => 6
[[],[],[],[],[[[]],[]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => {{1},{2},{3},{4},{5,8},{6,7}} => [2,2,1,1,1,1] => 4
[[],[],[],[],[[[],[]]]] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => {{1},{2},{3},{4},{5,6,8},{7}} => [3,1,1,1,1,1] => 6
[[],[],[],[],[[[[]]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3},{4},{5,6,7,8}} => [4,1,1,1,1] => 24
[[],[],[],[[]],[],[[]]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3},{4,5},{6},{7,8}} => [2,2,1,1,1,1] => 4
[[],[],[],[[],[],[],[]]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => {{1},{2},{3},{4,8},{5},{6},{7}} => [2,1,1,1,1,1,1] => 2
[[],[],[],[[],[[[]]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => {{1},{2},{3},{4,6,7,8},{5}} => [4,1,1,1,1] => 24
[[],[],[],[[[]],[],[]]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => {{1},{2},{3},{4,8},{5,6},{7}} => [2,2,1,1,1,1] => 4
[[],[],[],[[[]],[[]]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => {{1},{2},{3},{4,7,8},{5,6}} => [3,2,1,1,1] => 12
[[],[],[],[[[],[]],[]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => {{1},{2},{3},{4,8},{5,7},{6}} => [2,2,1,1,1,1] => 4
[[],[],[],[[[[]]],[]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => {{1},{2},{3},{4,8},{5,6,7}} => [3,2,1,1,1] => 12
[[],[],[],[[[[[]]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2},{3},{4,5,6,7,8}} => [5,1,1,1] => 120
[[],[],[[]],[],[],[[]]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6},{7,8}} => [2,2,1,1,1,1] => 4
[[],[],[[]],[],[[],[]]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => {{1},{2},{3,4},{5},{6,8},{7}} => [2,2,1,1,1,1] => 4
[[],[],[[]],[[[[]]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2},{3,4},{5,6,7,8}} => [4,2,1,1] => 48
[[],[],[[[]]],[],[],[]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7},{8}} => [3,1,1,1,1,1] => 6
[[],[],[[],[]],[[[]]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,5},{4},{6,7,8}} => [3,2,1,1,1] => 12
[[],[],[[[]]],[[[]]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2},{3,4,5},{6,7,8}} => [3,3,1,1] => 36
[[],[],[[[[]]]],[[]]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2},{3,4,5,6},{7,8}} => [4,2,1,1] => 48
[[],[],[[[[[]]]]],[]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2},{3,4,5,6,7},{8}} => [5,1,1,1] => 120
[[],[],[[],[],[],[],[]]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => {{1},{2},{3,8},{4},{5},{6},{7}} => [2,1,1,1,1,1,1] => 2
[[],[],[[],[[]],[[]]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => {{1},{2},{3,7,8},{4},{5,6}} => [3,2,1,1,1] => 12
[[],[],[[],[[[]]],[]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => {{1},{2},{3,8},{4},{5,6,7}} => [3,2,1,1,1] => 12
[[],[],[[],[[],[[]]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => {{1},{2},{3,5,7,8},{4},{6}} => [4,1,1,1,1] => 24
[[],[],[[],[[[]],[]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => {{1},{2},{3,5,8},{4},{6,7}} => [3,2,1,1,1] => 12
[[],[],[[],[[[[]]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => {{1},{2},{3,5,6,7,8},{4}} => [5,1,1,1] => 120
[[],[],[[[]],[],[],[]]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => {{1},{2},{3,8},{4,5},{6},{7}} => [2,2,1,1,1,1] => 4
[[],[],[[[]],[[[]]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => {{1},{2},{3,6,7,8},{4,5}} => [4,2,1,1] => 48
[[],[],[[[],[]],[],[]]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => {{1},{2},{3,8},{4,6},{5},{7}} => [2,2,1,1,1,1] => 4
[[],[],[[[[]]],[],[]]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => {{1},{2},{3,8},{4,5,6},{7}} => [3,2,1,1,1] => 12
[[],[],[[[],[]],[[]]]] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => {{1},{2},{3,7,8},{4,6},{5}} => [3,2,1,1,1] => 12
[[],[],[[[[]]],[[]]]] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => {{1},{2},{3,7,8},{4,5,6}} => [3,3,1,1] => 36
[[],[],[[[],[],[]],[]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => {{1},{2},{3,8},{4,7},{5},{6}} => [2,2,1,1,1,1] => 4
[[],[],[[[],[[]]],[]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => {{1},{2},{3,8},{4,6,7},{5}} => [3,2,1,1,1] => 12
[[],[],[[[[]],[]],[]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => {{1},{2},{3,8},{4,7},{5,6}} => [2,2,2,1,1] => 8
[[],[],[[[[[]]]],[]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => {{1},{2},{3,8},{4,5,6,7}} => [4,2,1,1] => 48
[[],[],[[[[[]]],[]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => {{1},{2},{3,4,8},{5,6,7}} => [3,3,1,1] => 36
[[],[],[[[[],[],[]]]]] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => {{1},{2},{3,4,5,8},{6},{7}} => [4,1,1,1,1] => 24
[[],[],[[[[[]],[]]]]] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => {{1},{2},{3,4,5,8},{6,7}} => [4,2,1,1] => 48
[[],[],[[[[[],[]]]]]] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => {{1},{2},{3,4,5,6,8},{7}} => [5,1,1,1] => 120
[[],[],[[[[[[]]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2},{3,4,5,6,7,8}} => [6,1,1] => 720
[[],[[]],[],[],[],[[]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6},{7,8}} => [2,2,1,1,1,1] => 4
[[],[[]],[],[],[[],[]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => {{1},{2,3},{4},{5},{6,8},{7}} => [2,2,1,1,1,1] => 4
[[],[[]],[],[[[[]]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4},{5,6,7,8}} => [4,2,1,1] => 48
[[],[[]],[[]],[[]],[]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6,7},{8}} => [2,2,2,1,1] => 8
[[],[[]],[[]],[[],[]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => {{1},{2,3},{4,5},{6,8},{7}} => [2,2,2,1,1] => 8
[[],[[]],[[]],[[[]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5},{6,7,8}} => [3,2,2,1] => 24
[[],[[]],[[[]]],[[]]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3},{4,5,6},{7,8}} => [3,2,2,1] => 24
[[],[[]],[[],[[]]],[]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => {{1},{2,3},{4,6,7},{5},{8}} => [3,2,1,1,1] => 12
[[],[[]],[[[]],[]],[]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => {{1},{2,3},{4,7},{5,6},{8}} => [2,2,2,1,1] => 8
[[],[[]],[[],[[],[]]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => {{1},{2,3},{4,6,8},{5},{7}} => [3,2,1,1,1] => 12
[[],[[]],[[],[[[]]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => {{1},{2,3},{4,6,7,8},{5}} => [4,2,1,1] => 48
[[],[[]],[[[]],[],[]]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => {{1},{2,3},{4,8},{5,6},{7}} => [2,2,2,1,1] => 8
[[],[[]],[[[]],[[]]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => {{1},{2,3},{4,7,8},{5,6}} => [3,2,2,1] => 24
[[],[[]],[[[],[]],[]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => {{1},{2,3},{4,8},{5,7},{6}} => [2,2,2,1,1] => 8
[[],[[]],[[[[]]],[]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => {{1},{2,3},{4,8},{5,6,7}} => [3,2,2,1] => 24
[[],[[]],[[[],[],[]]]] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => {{1},{2,3},{4,5,8},{6},{7}} => [3,2,1,1,1] => 12
[[],[[]],[[[[]],[]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => {{1},{2,3},{4,5,8},{6,7}} => [3,2,2,1] => 24
[[],[[]],[[[[],[]]]]] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => {{1},{2,3},{4,5,6,8},{7}} => [4,2,1,1] => 48
[[],[[]],[[[[[]]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3},{4,5,6,7,8}} => [5,2,1] => 240
[[],[[[]]],[],[],[],[]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7},{8}} => [3,1,1,1,1,1] => 6
[[],[[],[]],[],[],[[]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,4},{3},{5},{6},{7,8}} => [2,2,1,1,1,1] => 4
[[],[[],[]],[],[[],[]]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => {{1},{2,4},{3},{5},{6,8},{7}} => [2,2,1,1,1,1] => 4
[[],[[],[]],[],[[[]]]] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,4},{3},{5},{6,7,8}} => [3,2,1,1,1] => 12
[[],[[[]]],[],[[[]]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3,4},{5},{6,7,8}} => [3,3,1,1] => 36
[[],[[],[]],[[]],[[]]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,4},{3},{5,6},{7,8}} => [2,2,2,1,1] => 8
[[],[[[]]],[[]],[[]]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3,4},{5,6},{7,8}} => [3,2,2,1] => 24
[[],[[],[]],[[],[[]]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => {{1},{2,4},{3},{5,7,8},{6}} => [3,2,1,1,1] => 12
[[],[[],[]],[[[]],[]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => {{1},{2,4},{3},{5,8},{6,7}} => [2,2,2,1,1] => 8
[[],[[],[]],[[[[]]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,4},{3},{5,6,7,8}} => [4,2,1,1] => 48
[[],[[[]]],[[[]],[]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => {{1},{2,3,4},{5,8},{6,7}} => [3,2,2,1] => 24
[[],[[[]]],[[[],[]]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => {{1},{2,3,4},{5,6,8},{7}} => [3,3,1,1] => 36
[[],[[[],[]]],[],[],[]] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,5},{4},{6},{7},{8}} => [3,1,1,1,1,1] => 6
[[],[[],[[]]],[[]],[]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,4,5},{3},{6,7},{8}} => [3,2,1,1,1] => 12
[[],[[[]],[]],[[]],[]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => {{1},{2,5},{3,4},{6,7},{8}} => [2,2,2,1,1] => 8
[[],[[],[],[]],[[],[]]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => {{1},{2,5},{3},{4},{6,8},{7}} => [2,2,1,1,1,1] => 4
[[],[[],[[]]],[[],[]]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => {{1},{2,4,5},{3},{6,8},{7}} => [3,2,1,1,1] => 12
[[],[[],[[]]],[[[]]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,4,5},{3},{6,7,8}} => [3,3,1,1] => 36
[[],[[[]],[]],[[],[]]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => {{1},{2,5},{3,4},{6,8},{7}} => [2,2,2,1,1] => 8
[[],[[[]],[]],[[[]]]] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => {{1},{2,5},{3,4},{6,7,8}} => [3,2,2,1] => 24
[[],[[[],[]]],[[[]]]] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,5},{4},{6,7,8}} => [3,3,1,1] => 36
[[],[[[],[],[]]],[],[]] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => {{1},{2,3,6},{4},{5},{7},{8}} => [3,1,1,1,1,1] => 6
[[],[[[[[]]]]],[],[]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5,6},{7},{8}} => [5,1,1,1] => 120
[[],[[],[[]],[]],[[]]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => {{1},{2,6},{3},{4,5},{7,8}} => [2,2,2,1,1] => 8
[[],[[],[[],[]]],[[]]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => {{1},{2,4,6},{3},{5},{7,8}} => [3,2,1,1,1] => 12
[[],[[[],[]],[]],[[]]] => [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => {{1},{2,6},{3,5},{4},{7,8}} => [2,2,2,1,1] => 8
[[],[[[[]],[]]],[[]]] => [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => {{1},{2,3,6},{4,5},{7,8}} => [3,2,2,1] => 24
[[],[[[[],[]]]],[[]]] => [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,6},{5},{7,8}} => [4,2,1,1] => 48
[[],[[[[[]]]]],[[]]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5,6},{7,8}} => [5,2,1] => 240
[[],[[],[[],[[]]]],[]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => {{1},{2,4,6,7},{3},{5},{8}} => [4,1,1,1,1] => 24
[[],[[],[[[]],[]]],[]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => {{1},{2,4,7},{3},{5,6},{8}} => [3,2,1,1,1] => 12
[[],[[[]],[],[[]]],[]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => {{1},{2,6,7},{3,4},{5},{8}} => [3,2,1,1,1] => 12
[[],[[[]],[[]],[]],[]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => {{1},{2,7},{3,4},{5,6},{8}} => [2,2,2,1,1] => 8
[[],[[[],[]],[],[]],[]] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => {{1},{2,7},{3,5},{4},{6},{8}} => [2,2,1,1,1,1] => 4
[[],[[[],[]],[[]]],[]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => {{1},{2,6,7},{3,5},{4},{8}} => [3,2,1,1,1] => 12
[[],[[[],[[]]],[]],[]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => {{1},{2,7},{3,5,6},{4},{8}} => [3,2,1,1,1] => 12
[[],[[[[]],[]],[]],[]] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => {{1},{2,7},{3,6},{4,5},{8}} => [2,2,2,1,1] => 8
[[],[[[],[],[],[]]],[]] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => {{1},{2,3,7},{4},{5},{6},{8}} => [3,1,1,1,1,1] => 6
[[],[[[],[],[[]]]],[]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => {{1},{2,3,6,7},{4},{5},{8}} => [4,1,1,1,1] => 24
[[],[[[],[[]],[]]],[]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => {{1},{2,3,7},{4},{5,6},{8}} => [3,2,1,1,1] => 12
[[],[[[],[[],[]]]],[]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => {{1},{2,3,5,7},{4},{6},{8}} => [4,1,1,1,1] => 24
[[],[[[],[[[]]]]],[]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => {{1},{2,3,5,6,7},{4},{8}} => [5,1,1,1] => 120
[[],[[[[]],[[]]]],[]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => {{1},{2,3,6,7},{4,5},{8}} => [4,2,1,1] => 48
[[],[[[[[],[]]]]],[]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => {{1},{2,3,4,5,7},{6},{8}} => [5,1,1,1] => 120
[[],[[],[],[],[],[],[]]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1},{2,8},{3},{4},{5},{6},{7}} => [2,1,1,1,1,1,1] => 2
[[],[[],[],[[[]]],[]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => {{1},{2,8},{3},{4},{5,6,7}} => [3,2,1,1,1] => 12
[[],[[],[],[[],[],[]]]] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => {{1},{2,5,8},{3},{4},{6},{7}} => [3,1,1,1,1,1] => 6
[[],[[],[],[[[],[]]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => {{1},{2,5,6,8},{3},{4},{7}} => [4,1,1,1,1] => 24
[[],[[],[],[[[[]]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => {{1},{2,5,6,7,8},{3},{4}} => [5,1,1,1] => 120
[[],[[],[[]],[[],[]]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => {{1},{2,6,8},{3},{4,5},{7}} => [3,2,1,1,1] => 12
[[],[[],[[]],[[[]]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => {{1},{2,6,7,8},{3},{4,5}} => [4,2,1,1] => 48
[[],[[],[[[]]],[[]]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => {{1},{2,7,8},{3},{4,5,6}} => [3,3,1,1] => 36
[[],[[],[[],[[]]],[]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => {{1},{2,8},{3},{4,6,7},{5}} => [3,2,1,1,1] => 12
[[],[[],[[[]],[]],[]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => {{1},{2,8},{3},{4,7},{5,6}} => [2,2,2,1,1] => 8
[[],[[],[[],[[]],[]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => {{1},{2,4,8},{3},{5},{6,7}} => [3,2,1,1,1] => 12
[[],[[],[[],[[],[]]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => {{1},{2,4,6,8},{3},{5},{7}} => [4,1,1,1,1] => 24
[[],[[],[[],[[[]]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => {{1},{2,4,6,7,8},{3},{5}} => [5,1,1,1] => 120
[[],[[],[[[]],[],[]]]] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => {{1},{2,4,8},{3},{5,6},{7}} => [3,2,1,1,1] => 12
[[],[[],[[[]],[[]]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => {{1},{2,4,7,8},{3},{5,6}} => [4,2,1,1] => 48
[[],[[],[[[],[]],[]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => {{1},{2,4,8},{3},{5,7},{6}} => [3,2,1,1,1] => 12
[[],[[],[[[[]]],[]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => {{1},{2,4,8},{3},{5,6,7}} => [3,3,1,1] => 36
[[],[[],[[[],[[]]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => {{1},{2,4,5,7,8},{3},{6}} => [5,1,1,1] => 120
[[],[[],[[[[]],[]]]]] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => {{1},{2,4,5,8},{3},{6,7}} => [4,2,1,1] => 48
[[],[[],[[[[],[]]]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => {{1},{2,4,5,6,8},{3},{7}} => [5,1,1,1] => 120
[[],[[],[[[[[]]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2,4,5,6,7,8},{3}} => [6,1,1] => 720
[[],[[[]],[],[],[],[]]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => {{1},{2,8},{3,4},{5},{6},{7}} => [2,2,1,1,1,1] => 4
[[],[[[]],[],[[],[]]]] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => {{1},{2,6,8},{3,4},{5},{7}} => [3,2,1,1,1] => 12
[[],[[[]],[[]],[],[]]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => {{1},{2,8},{3,4},{5,6},{7}} => [2,2,2,1,1] => 8
[[],[[[]],[[]],[[]]]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => {{1},{2,7,8},{3,4},{5,6}} => [3,2,2,1] => 24
[[],[[[]],[[],[]],[]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => {{1},{2,8},{3,4},{5,7},{6}} => [2,2,2,1,1] => 8
[[],[[[]],[[[]]],[]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => {{1},{2,8},{3,4},{5,6,7}} => [3,2,2,1] => 24
[[],[[[]],[[[]],[]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => {{1},{2,5,8},{3,4},{6,7}} => [3,2,2,1] => 24
[[],[[[]],[[[[]]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => {{1},{2,5,6,7,8},{3,4}} => [5,2,1] => 240
[[],[[[],[]],[],[],[]]] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => {{1},{2,8},{3,5},{4},{6},{7}} => [2,2,1,1,1,1] => 4
[[],[[[[]]],[],[],[]]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => {{1},{2,8},{3,4,5},{6},{7}} => [3,2,1,1,1] => 12
[[],[[[],[]],[[]],[]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => {{1},{2,8},{3,5},{4},{6,7}} => [2,2,2,1,1] => 8
[[],[[[[]]],[[]],[]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => {{1},{2,8},{3,4,5},{6,7}} => [3,2,2,1] => 24
[[],[[[],[]],[[],[]]]] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => {{1},{2,6,8},{3,5},{4},{7}} => [3,2,1,1,1] => 12
[[],[[[],[]],[[[]]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => {{1},{2,6,7,8},{3,5},{4}} => [4,2,1,1] => 48
[[],[[[[]]],[[],[]]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => {{1},{2,6,8},{3,4,5},{7}} => [3,3,1,1] => 36
[[],[[[[]]],[[[]]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => {{1},{2,6,7,8},{3,4,5}} => [4,3,1] => 144
[[],[[[],[[]]],[],[]]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => {{1},{2,8},{3,5,6},{4},{7}} => [3,2,1,1,1] => 12
[[],[[[[]],[]],[],[]]] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => {{1},{2,8},{3,6},{4,5},{7}} => [2,2,2,1,1] => 8
[[],[[[[],[]]],[],[]]] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => {{1},{2,8},{3,4,6},{5},{7}} => [3,2,1,1,1] => 12
[[],[[[[[]]]],[],[]]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => {{1},{2,8},{3,4,5,6},{7}} => [4,2,1,1] => 48
[[],[[[[]],[]],[[]]]] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => {{1},{2,7,8},{3,6},{4,5}} => [3,2,2,1] => 24
[[],[[[[],[]]],[[]]]] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => {{1},{2,7,8},{3,4,6},{5}} => [3,3,1,1] => 36
[[],[[[],[],[],[]],[]]] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => {{1},{2,8},{3,7},{4},{5},{6}} => [2,2,1,1,1,1] => 4
[[],[[[],[[]],[]],[]]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => {{1},{2,8},{3,7},{4},{5,6}} => [2,2,2,1,1] => 8
[[],[[[],[[],[]]],[]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => {{1},{2,8},{3,5,7},{4},{6}} => [3,2,1,1,1] => 12
[[],[[[],[[[]]]],[]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => {{1},{2,8},{3,5,6,7},{4}} => [4,2,1,1] => 48
[[],[[[[]],[],[]],[]]] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => {{1},{2,8},{3,7},{4,5},{6}} => [2,2,2,1,1] => 8
[[],[[[[]],[[]]],[]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => {{1},{2,8},{3,6,7},{4,5}} => [3,2,2,1] => 24
[[],[[[[],[]],[]],[]]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => {{1},{2,8},{3,7},{4,6},{5}} => [2,2,2,1,1] => 8
[[],[[[[[]]],[]],[]]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => {{1},{2,8},{3,7},{4,5,6}} => [3,2,2,1] => 24
[[],[[[[],[[]]]],[]]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => {{1},{2,8},{3,4,6,7},{5}} => [4,2,1,1] => 48
[[],[[[[[]],[]]],[]]] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => {{1},{2,8},{3,4,7},{5,6}} => [3,2,2,1] => 24
[[],[[[[[],[]]]],[]]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => {{1},{2,8},{3,4,5,7},{6}} => [4,2,1,1] => 48
[[],[[[],[],[],[],[]]]] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => {{1},{2,3,8},{4},{5},{6},{7}} => [3,1,1,1,1,1] => 6
[[],[[[],[],[],[[]]]]] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => {{1},{2,3,7,8},{4},{5},{6}} => [4,1,1,1,1] => 24
[[],[[[],[],[[],[]]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => {{1},{2,3,6,8},{4},{5},{7}} => [4,1,1,1,1] => 24
[[],[[[],[],[[[]]]]]] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => {{1},{2,3,6,7,8},{4},{5}} => [5,1,1,1] => 120
[[],[[[],[[[]]],[]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => {{1},{2,3,8},{4},{5,6,7}} => [3,3,1,1] => 36
[[],[[[],[[],[],[]]]]] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => {{1},{2,3,5,8},{4},{6},{7}} => [4,1,1,1,1] => 24
[[],[[[],[[],[[]]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => {{1},{2,3,5,7,8},{4},{6}} => [5,1,1,1] => 120
[[],[[[],[[[]],[]]]]] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => {{1},{2,3,5,8},{4},{6,7}} => [4,2,1,1] => 48
[[],[[[],[[[],[]]]]]] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => {{1},{2,3,5,6,8},{4},{7}} => [5,1,1,1] => 120
[[],[[[[]],[],[],[]]]] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => {{1},{2,3,8},{4,5},{6},{7}} => [3,2,1,1,1] => 12
[[],[[[[]],[[]],[]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => {{1},{2,3,8},{4,5},{6,7}} => [3,2,2,1] => 24
[[],[[[[]],[[],[]]]]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => {{1},{2,3,6,8},{4,5},{7}} => [4,2,1,1] => 48
[[],[[[[],[]],[],[]]]] => [1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => {{1},{2,3,8},{4,6},{5},{7}} => [3,2,1,1,1] => 12
[[],[[[[[]]],[],[]]]] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => {{1},{2,3,8},{4,5,6},{7}} => [3,3,1,1] => 36
[[],[[[[],[]],[[]]]]] => [1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => {{1},{2,3,7,8},{4,6},{5}} => [4,2,1,1] => 48
[[],[[[[],[[]]],[]]]] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => {{1},{2,3,8},{4,6,7},{5}} => [3,3,1,1] => 36
[[],[[[[[]],[]],[]]]] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => {{1},{2,3,8},{4,7},{5,6}} => [3,2,2,1] => 24
[[],[[[[[],[]]],[]]]] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => {{1},{2,3,8},{4,5,7},{6}} => [3,3,1,1] => 36
[[],[[[[],[],[],[]]]]] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => {{1},{2,3,4,8},{5},{6},{7}} => [4,1,1,1,1] => 24
[[],[[[[],[],[[]]]]]] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => {{1},{2,3,4,7,8},{5},{6}} => [5,1,1,1] => 120
[[],[[[[],[[],[]]]]]] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => {{1},{2,3,4,6,8},{5},{7}} => [5,1,1,1] => 120
[[],[[[[],[[[]]]]]]] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => {{1},{2,3,4,6,7,8},{5}} => [6,1,1] => 720
[[],[[[[[]],[],[]]]]] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => {{1},{2,3,4,8},{5,6},{7}} => [4,2,1,1] => 48
[[],[[[[[],[]],[]]]]] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => {{1},{2,3,4,8},{5,7},{6}} => [4,2,1,1] => 48
[[],[[[[[[]]],[]]]]] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => {{1},{2,3,4,8},{5,6,7}} => [4,3,1] => 144
[[],[[[[[],[],[]]]]]] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => {{1},{2,3,4,5,8},{6},{7}} => [5,1,1,1] => 120
[[],[[[[[],[[]]]]]]] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => {{1},{2,3,4,5,7,8},{6}} => [6,1,1] => 720
[[],[[[[[[]],[]]]]]] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => {{1},{2,3,4,5,8},{6,7}} => [5,2,1] => 240
[[],[[[[[[],[]]]]]]] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => {{1},{2,3,4,5,6,8},{7}} => [6,1,1] => 720
[[],[[[[[[[]]]]]]]] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8}} => [7,1] => 5040
[[[]],[],[],[],[],[],[]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5},{6},{7},{8}} => [2,1,1,1,1,1,1] => 2
[[[]],[],[],[],[],[[]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6},{7,8}} => [2,2,1,1,1,1] => 4
[[[]],[],[],[],[[],[]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => {{1,2},{3},{4},{5},{6,8},{7}} => [2,2,1,1,1,1] => 4
[[[]],[],[],[[[[]]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4},{5,6,7,8}} => [4,2,1,1] => 48
[[[]],[],[[]],[[[]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3},{4,5},{6,7,8}} => [3,2,2,1] => 24
[[[]],[],[[[]]],[[]]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3},{4,5,6},{7,8}} => [3,2,2,1] => 24
[[[]],[],[[],[[[]]]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => {{1,2},{3},{4,6,7,8},{5}} => [4,2,1,1] => 48
[[[]],[],[[[],[],[]]]] => [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => {{1,2},{3},{4,5,8},{6},{7}} => [3,2,1,1,1] => 12
[[[]],[],[[[[]],[]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => {{1,2},{3},{4,5,8},{6,7}} => [3,2,2,1] => 24
[[[]],[],[[[[],[]]]]] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => {{1,2},{3},{4,5,6,8},{7}} => [4,2,1,1] => 48
[[[]],[],[[[[[]]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3},{4,5,6,7,8}} => [5,2,1] => 240
[[[]],[[]],[],[[[]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1,2},{3,4},{5},{6,7,8}} => [3,2,2,1] => 24
[[[]],[[]],[[]],[[]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8}} => [2,2,2,2] => 16
[[[]],[[]],[[],[[]]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => {{1,2},{3,4},{5,7,8},{6}} => [3,2,2,1] => 24
[[[]],[[]],[[[]],[]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => {{1,2},{3,4},{5,8},{6,7}} => [2,2,2,2] => 16
[[[]],[[]],[[[],[]]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => {{1,2},{3,4},{5,6,8},{7}} => [3,2,2,1] => 24
[[[]],[[]],[[[[]]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4},{5,6,7,8}} => [4,2,2] => 96
[[[]],[[[]]],[],[],[]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7},{8}} => [3,2,1,1,1] => 12
[[[]],[[],[]],[[[]]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => {{1,2},{3,5},{4},{6,7,8}} => [3,2,2,1] => 24
[[[]],[[],[[]]],[[]]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => {{1,2},{3,5,6},{4},{7,8}} => [3,2,2,1] => 24
[[[]],[[[]],[]],[[]]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => {{1,2},{3,6},{4,5},{7,8}} => [2,2,2,2] => 16
[[[]],[[[],[]]],[[]]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => {{1,2},{3,4,6},{5},{7,8}} => [3,2,2,1] => 24
[[[]],[[[[]]]],[[]]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2},{3,4,5,6},{7,8}} => [4,2,2] => 96
[[[]],[[[[[]]]]],[]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1,2},{3,4,5,6,7},{8}} => [5,2,1] => 240
[[[]],[[],[],[[[]]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => {{1,2},{3,6,7,8},{4},{5}} => [4,2,1,1] => 48
[[[]],[[],[[]],[[]]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => {{1,2},{3,7,8},{4},{5,6}} => [3,2,2,1] => 24
[[[]],[[],[[[]]],[]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => {{1,2},{3,8},{4},{5,6,7}} => [3,2,2,1] => 24
[[[]],[[],[[],[[]]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => {{1,2},{3,5,7,8},{4},{6}} => [4,2,1,1] => 48
[[[]],[[],[[[]],[]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => {{1,2},{3,5,8},{4},{6,7}} => [3,2,2,1] => 24
[[[]],[[],[[[],[]]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => {{1,2},{3,5,6,8},{4},{7}} => [4,2,1,1] => 48
[[[]],[[],[[[[]]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => {{1,2},{3,5,6,7,8},{4}} => [5,2,1] => 240
[[[]],[[[]],[],[],[]]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => {{1,2},{3,8},{4,5},{6},{7}} => [2,2,2,1,1] => 8
[[[]],[[[]],[],[[]]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => {{1,2},{3,7,8},{4,5},{6}} => [3,2,2,1] => 24
[[[]],[[[]],[[]],[]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => {{1,2},{3,8},{4,5},{6,7}} => [2,2,2,2] => 16
[[[]],[[[]],[[],[]]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => {{1,2},{3,6,8},{4,5},{7}} => [3,2,2,1] => 24
[[[]],[[[]],[[[]]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => {{1,2},{3,6,7,8},{4,5}} => [4,2,2] => 96
[[[]],[[[[]]],[],[]]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => {{1,2},{3,8},{4,5,6},{7}} => [3,2,2,1] => 24
[[[]],[[[],[]],[[]]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => {{1,2},{3,7,8},{4,6},{5}} => [3,2,2,1] => 24
[[[]],[[[],[[]]],[]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => {{1,2},{3,8},{4,6,7},{5}} => [3,2,2,1] => 24
[[[]],[[[[]],[]],[]]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => {{1,2},{3,8},{4,7},{5,6}} => [2,2,2,2] => 16
[[[]],[[[[],[]]],[]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => {{1,2},{3,8},{4,5,7},{6}} => [3,2,2,1] => 24
[[[]],[[[[[]]]],[]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => {{1,2},{3,8},{4,5,6,7}} => [4,2,2] => 96
[[[]],[[[],[],[],[]]]] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => {{1,2},{3,4,8},{5},{6},{7}} => [3,2,1,1,1] => 12
[[[]],[[[],[],[[]]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => {{1,2},{3,4,7,8},{5},{6}} => [4,2,1,1] => 48
[[[]],[[[],[[]],[]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => {{1,2},{3,4,8},{5},{6,7}} => [3,2,2,1] => 24
[[[]],[[[],[[],[]]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => {{1,2},{3,4,6,8},{5},{7}} => [4,2,1,1] => 48
[[[]],[[[],[[[]]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => {{1,2},{3,4,6,7,8},{5}} => [5,2,1] => 240
[[[]],[[[[]],[],[]]]] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => {{1,2},{3,4,8},{5,6},{7}} => [3,2,2,1] => 24
[[[]],[[[[],[]],[]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => {{1,2},{3,4,8},{5,7},{6}} => [3,2,2,1] => 24
[[[]],[[[[[]]],[]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => {{1,2},{3,4,8},{5,6,7}} => [3,3,2] => 72
[[[]],[[[[],[],[]]]]] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => {{1,2},{3,4,5,8},{6},{7}} => [4,2,1,1] => 48
[[[]],[[[[],[[]]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => {{1,2},{3,4,5,7,8},{6}} => [5,2,1] => 240
[[[]],[[[[[]],[]]]]] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => {{1,2},{3,4,5,8},{6,7}} => [4,2,2] => 96
[[[]],[[[[[],[]]]]]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => {{1,2},{3,4,5,6,8},{7}} => [5,2,1] => 240
[[[]],[[[[[[]]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8}} => [6,2] => 1440
[[[],[]],[],[],[],[],[]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,3},{2},{4},{5},{6},{7},{8}} => [2,1,1,1,1,1,1] => 2
[[[[]]],[],[],[],[],[]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6},{7},{8}} => [3,1,1,1,1,1] => 6
[[[],[]],[],[],[],[[]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,3},{2},{4},{5},{6},{7,8}} => [2,2,1,1,1,1] => 4
[[[[]]],[],[],[],[[]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6},{7,8}} => [3,2,1,1,1] => 12
[[[],[]],[],[],[[],[]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => {{1,3},{2},{4},{5},{6,8},{7}} => [2,2,1,1,1,1] => 4
[[[],[]],[],[],[[[]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,3},{2},{4},{5},{6,7,8}} => [3,2,1,1,1] => 12
[[[[]]],[],[],[[],[]]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => {{1,2,3},{4},{5},{6,8},{7}} => [3,2,1,1,1] => 12
[[[],[]],[],[[],[[]]]] => [1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => {{1,3},{2},{4},{5,7,8},{6}} => [3,2,1,1,1] => 12
[[[],[]],[],[[[]],[]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => {{1,3},{2},{4},{5,8},{6,7}} => [2,2,2,1,1] => 8
[[[],[]],[],[[[[]]]]] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,3},{2},{4},{5,6,7,8}} => [4,2,1,1] => 48
[[[],[]],[[]],[[]],[]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,3},{2},{4,5},{6,7},{8}} => [2,2,2,1,1] => 8
[[[],[]],[[]],[[],[]]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => {{1,3},{2},{4,5},{6,8},{7}} => [2,2,2,1,1] => 8
[[[],[]],[[]],[[[]]]] => [1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,3},{2},{4,5},{6,7,8}} => [3,2,2,1] => 24
[[[],[]],[[],[]],[[]]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => {{1,3},{2},{4,6},{5},{7,8}} => [2,2,2,1,1] => 8
[[[],[]],[[[]]],[[]]] => [1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,3},{2},{4,5,6},{7,8}} => [3,2,2,1] => 24
[[[],[]],[[],[[]]],[]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => {{1,3},{2},{4,6,7},{5},{8}} => [3,2,1,1,1] => 12
[[[],[]],[[[]],[]],[]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => {{1,3},{2},{4,7},{5,6},{8}} => [2,2,2,1,1] => 8
[[[[]]],[[],[[]]],[]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => {{1,2,3},{4,6,7},{5},{8}} => [3,3,1,1] => 36
[[[[]]],[[[[]]]],[]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2,3},{4,5,6,7},{8}} => [4,3,1] => 144
[[[],[]],[[],[[]],[]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => {{1,3},{2},{4,8},{5},{6,7}} => [2,2,2,1,1] => 8
[[[],[]],[[],[[],[]]]] => [1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => {{1,3},{2},{4,6,8},{5},{7}} => [3,2,1,1,1] => 12
[[[],[]],[[],[[[]]]]] => [1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => {{1,3},{2},{4,6,7,8},{5}} => [4,2,1,1] => 48
[[[],[]],[[[]],[],[]]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => {{1,3},{2},{4,8},{5,6},{7}} => [2,2,2,1,1] => 8
[[[],[]],[[[]],[[]]]] => [1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => {{1,3},{2},{4,7,8},{5,6}} => [3,2,2,1] => 24
[[[],[]],[[[],[]],[]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => {{1,3},{2},{4,8},{5,7},{6}} => [2,2,2,1,1] => 8
[[[],[]],[[[[]]],[]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => {{1,3},{2},{4,8},{5,6,7}} => [3,2,2,1] => 24
[[[],[]],[[[],[[]]]]] => [1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => {{1,3},{2},{4,5,7,8},{6}} => [4,2,1,1] => 48
[[[],[]],[[[[]],[]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => {{1,3},{2},{4,5,8},{6,7}} => [3,2,2,1] => 24
[[[],[]],[[[[],[]]]]] => [1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => {{1,3},{2},{4,5,6,8},{7}} => [4,2,1,1] => 48
[[[],[]],[[[[[]]]]]] => [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,3},{2},{4,5,6,7,8}} => [5,2,1] => 240
[[[[]]],[[[],[],[]]]] => [1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => {{1,2,3},{4,5,8},{6},{7}} => [3,3,1,1] => 36
[[[[]]],[[[],[[]]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => {{1,2,3},{4,5,7,8},{6}} => [4,3,1] => 144
[[[[]]],[[[[]],[]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => {{1,2,3},{4,5,8},{6,7}} => [3,3,2] => 72
[[[[]]],[[[[[]]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8}} => [5,3] => 720
[[[],[],[]],[],[],[],[]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => {{1,4},{2},{3},{5},{6},{7},{8}} => [2,1,1,1,1,1,1] => 2
[[[],[[]]],[],[],[],[]] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => {{1,3,4},{2},{5},{6},{7},{8}} => [3,1,1,1,1,1] => 6
[[[[]],[]],[],[],[],[]] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => {{1,4},{2,3},{5},{6},{7},{8}} => [2,2,1,1,1,1] => 4
[[[[],[]]],[],[],[],[]] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => {{1,2,4},{3},{5},{6},{7},{8}} => [3,1,1,1,1,1] => 6
[[[[[]]]],[],[],[],[]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => {{1,2,3,4},{5},{6},{7},{8}} => [4,1,1,1,1] => 24
[[[],[[]]],[],[],[[]]] => [1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,3,4},{2},{5},{6},{7,8}} => [3,2,1,1,1] => 12
[[[[[]]]],[],[[]],[]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3,4},{5},{6,7},{8}} => [4,2,1,1] => 48
[[[],[],[]],[],[[],[]]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => {{1,4},{2},{3},{5},{6,8},{7}} => [2,2,1,1,1,1] => 4
[[[],[],[]],[],[[[]]]] => [1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => {{1,4},{2},{3},{5},{6,7,8}} => [3,2,1,1,1] => 12
[[[],[[]]],[],[[],[]]] => [1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => {{1,3,4},{2},{5},{6,8},{7}} => [3,2,1,1,1] => 12
[[[],[[]]],[],[[[]]]] => [1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,3,4},{2},{5},{6,7,8}} => [3,3,1,1] => 36
[[[],[],[]],[[]],[[]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => {{1,4},{2},{3},{5,6},{7,8}} => [2,2,2,1,1] => 8
[[[],[[]]],[[]],[[]]] => [1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,3,4},{2},{5,6},{7,8}} => [3,2,2,1] => 24
[[[[]],[]],[[]],[[]]] => [1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => {{1,4},{2,3},{5,6},{7,8}} => [2,2,2,2] => 16
[[[[],[]]],[[]],[[]]] => [1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,4},{3},{5,6},{7,8}} => [3,2,2,1] => 24
[[[[[]]]],[[]],[[]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3,4},{5,6},{7,8}} => [4,2,2] => 96
[[[[[]]]],[[[]]],[]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3,4},{5,6,7},{8}} => [4,3,1] => 144
[[[],[],[]],[[],[],[]]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => {{1,4},{2},{3},{5,8},{6},{7}} => [2,2,1,1,1,1] => 4
[[[],[],[]],[[[[]]]]] => [1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => {{1,4},{2},{3},{5,6,7,8}} => [4,2,1,1] => 48
[[[],[[]]],[[],[[]]]] => [1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => {{1,3,4},{2},{5,7,8},{6}} => [3,3,1,1] => 36
[[[],[[]]],[[[]],[]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => {{1,3,4},{2},{5,8},{6,7}} => [3,2,2,1] => 24
[[[],[[]]],[[[],[]]]] => [1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => {{1,3,4},{2},{5,6,8},{7}} => [3,3,1,1] => 36
[[[],[[]]],[[[[]]]]] => [1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,3,4},{2},{5,6,7,8}} => [4,3,1] => 144
[[[[]],[]],[[],[[]]]] => [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => {{1,4},{2,3},{5,7,8},{6}} => [3,2,2,1] => 24
[[[[]],[]],[[[]],[]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => {{1,4},{2,3},{5,8},{6,7}} => [2,2,2,2] => 16
[[[[]],[]],[[[],[]]]] => [1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => {{1,4},{2,3},{5,6,8},{7}} => [3,2,2,1] => 24
[[[[]],[]],[[[[]]]]] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => {{1,4},{2,3},{5,6,7,8}} => [4,2,2] => 96
[[[[],[]]],[[[]],[]]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => {{1,2,4},{3},{5,8},{6,7}} => [3,2,2,1] => 24
[[[[],[]]],[[[],[]]]] => [1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => {{1,2,4},{3},{5,6,8},{7}} => [3,3,1,1] => 36
[[[[],[]]],[[[[]]]]] => [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,4},{3},{5,6,7,8}} => [4,3,1] => 144
[[[[[]]]],[[],[[]]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => {{1,2,3,4},{5,7,8},{6}} => [4,3,1] => 144
[[[[[]]]],[[[]],[]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => {{1,2,3,4},{5,8},{6,7}} => [4,2,2] => 96
[[[[[]]]],[[[],[]]]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => {{1,2,3,4},{5,6,8},{7}} => [4,3,1] => 144
[[[[[]]]],[[[[]]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4},{5,6,7,8}} => [4,4] => 576
[[[],[],[],[]],[],[],[]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => {{1,5},{2},{3},{4},{6},{7},{8}} => [2,1,1,1,1,1,1] => 2
[[[],[],[[]]],[],[],[]] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => {{1,4,5},{2},{3},{6},{7},{8}} => [3,1,1,1,1,1] => 6
[[[],[[]],[]],[],[],[]] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => {{1,5},{2},{3,4},{6},{7},{8}} => [2,2,1,1,1,1] => 4
[[[],[[],[]]],[],[],[]] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => {{1,3,5},{2},{4},{6},{7},{8}} => [3,1,1,1,1,1] => 6
[[[[]],[],[]],[],[],[]] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => {{1,5},{2,3},{4},{6},{7},{8}} => [2,2,1,1,1,1] => 4
[[[[],[]],[]],[],[],[]] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => {{1,5},{2,4},{3},{6},{7},{8}} => [2,2,1,1,1,1] => 4
[[[[[]]],[]],[],[],[]] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => {{1,5},{2,3,4},{6},{7},{8}} => [3,2,1,1,1] => 12
[[[[],[],[]]],[],[],[]] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => {{1,2,5},{3},{4},{6},{7},{8}} => [3,1,1,1,1,1] => 6
[[[[[]],[]]],[],[],[]] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => {{1,2,5},{3,4},{6},{7},{8}} => [3,2,1,1,1] => 12
[[[[[[]]]]],[],[],[]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => {{1,2,3,4,5},{6},{7},{8}} => [5,1,1,1] => 120
[[[],[[]],[]],[],[[]]] => [1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => {{1,5},{2},{3,4},{6},{7,8}} => [2,2,2,1,1] => 8
[[[],[[],[]]],[],[[]]] => [1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => {{1,3,5},{2},{4},{6},{7,8}} => [3,2,1,1,1] => 12
[[[],[[[]]]],[],[[]]] => [1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,3,4,5},{2},{6},{7,8}} => [4,2,1,1] => 48
[[[[],[]],[]],[],[[]]] => [1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => {{1,5},{2,4},{3},{6},{7,8}} => [2,2,2,1,1] => 8
[[[[],[],[]]],[],[[]]] => [1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => {{1,2,5},{3},{4},{6},{7,8}} => [3,2,1,1,1] => 12
[[[[[],[]]]],[],[[]]] => [1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,5},{4},{6},{7,8}} => [4,2,1,1] => 48
[[[],[[],[]]],[[]],[]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => {{1,3,5},{2},{4},{6,7},{8}} => [3,2,1,1,1] => 12
[[[],[[[]]]],[[]],[]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,3,4,5},{2},{6,7},{8}} => [4,2,1,1] => 48
[[[[]],[],[]],[[]],[]] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => {{1,5},{2,3},{4},{6,7},{8}} => [2,2,2,1,1] => 8
[[[[]],[[]]],[[]],[]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => {{1,4,5},{2,3},{6,7},{8}} => [3,2,2,1] => 24
[[[[],[]],[]],[[]],[]] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => {{1,5},{2,4},{3},{6,7},{8}} => [2,2,2,1,1] => 8
[[[[[]],[]]],[[]],[]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => {{1,2,5},{3,4},{6,7},{8}} => [3,2,2,1] => 24
[[[[[[]]]]],[[]],[]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4,5},{6,7},{8}} => [5,2,1] => 240
[[[],[],[],[]],[[[]]]] => [1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => {{1,5},{2},{3},{4},{6,7,8}} => [3,2,1,1,1] => 12
[[[],[],[[]]],[[],[]]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => {{1,4,5},{2},{3},{6,8},{7}} => [3,2,1,1,1] => 12
[[[],[],[[]]],[[[]]]] => [1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => {{1,4,5},{2},{3},{6,7,8}} => [3,3,1,1] => 36
[[[],[[]],[]],[[],[]]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => {{1,5},{2},{3,4},{6,8},{7}} => [2,2,2,1,1] => 8
[[[],[[],[]]],[[],[]]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => {{1,3,5},{2},{4},{6,8},{7}} => [3,2,1,1,1] => 12
[[[],[[],[]]],[[[]]]] => [1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => {{1,3,5},{2},{4},{6,7,8}} => [3,3,1,1] => 36
[[[],[[[]]]],[[],[]]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => {{1,3,4,5},{2},{6,8},{7}} => [4,2,1,1] => 48
[[[],[[[]]]],[[[]]]] => [1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,3,4,5},{2},{6,7,8}} => [4,3,1] => 144
[[[[]],[],[]],[[],[]]] => [1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => {{1,5},{2,3},{4},{6,8},{7}} => [2,2,2,1,1] => 8
[[[[],[]],[]],[[],[]]] => [1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => {{1,5},{2,4},{3},{6,8},{7}} => [2,2,2,1,1] => 8
[[[[],[]],[]],[[[]]]] => [1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => {{1,5},{2,4},{3},{6,7,8}} => [3,2,2,1] => 24
[[[[[]]],[]],[[],[]]] => [1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => {{1,5},{2,3,4},{6,8},{7}} => [3,2,2,1] => 24
[[[[[]],[]]],[[],[]]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => {{1,2,5},{3,4},{6,8},{7}} => [3,2,2,1] => 24
[[[[[]],[]]],[[[]]]] => [1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => {{1,2,5},{3,4},{6,7,8}} => [3,3,2] => 72
[[[[[],[]]]],[[[]]]] => [1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,5},{4},{6,7,8}} => [4,3,1] => 144
[[[[[[]]]]],[[],[]]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => {{1,2,3,4,5},{6,8},{7}} => [5,2,1] => 240
[[[[[[]]]]],[[[]]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4,5},{6,7,8}} => [5,3] => 720
[[[],[],[],[],[]],[],[]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => {{1,6},{2},{3},{4},{5},{7},{8}} => [2,1,1,1,1,1,1] => 2
[[[],[],[[]],[]],[],[]] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => {{1,6},{2},{3},{4,5},{7},{8}} => [2,2,1,1,1,1] => 4
[[[],[[],[]],[]],[],[]] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => {{1,6},{2},{3,5},{4},{7},{8}} => [2,2,1,1,1,1] => 4
[[[],[[[]]],[]],[],[]] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => {{1,6},{2},{3,4,5},{7},{8}} => [3,2,1,1,1] => 12
[[[],[[],[],[]]],[],[]] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => {{1,3,6},{2},{4},{5},{7},{8}} => [3,1,1,1,1,1] => 6
[[[],[[[[]]]]],[],[]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => {{1,3,4,5,6},{2},{7},{8}} => [5,1,1,1] => 120
[[[[[]]],[],[]],[],[]] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => {{1,6},{2,3,4},{5},{7},{8}} => [3,2,1,1,1] => 12
[[[[[]]],[[]]],[],[]] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => {{1,5,6},{2,3,4},{7},{8}} => [3,3,1,1] => 36
[[[[],[],[]],[]],[],[]] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => {{1,6},{2,5},{3},{4},{7},{8}} => [2,2,1,1,1,1] => 4
[[[[[[]]]],[]],[],[]] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => {{1,6},{2,3,4,5},{7},{8}} => [4,2,1,1] => 48
[[[[],[],[],[]]],[],[]] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => {{1,2,6},{3},{4},{5},{7},{8}} => [3,1,1,1,1,1] => 6
[[[[[]],[[]]]],[],[]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => {{1,2,5,6},{3,4},{7},{8}} => [4,2,1,1] => 48
[[[[[[]]],[]]],[],[]] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => {{1,2,6},{3,4,5},{7},{8}} => [3,3,1,1] => 36
[[[[[],[[]]]]],[],[]] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => {{1,2,3,5,6},{4},{7},{8}} => [5,1,1,1] => 120
[[[[[[]],[]]]],[],[]] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => {{1,2,3,6},{4,5},{7},{8}} => [4,2,1,1] => 48
[[[[[[],[]]]]],[],[]] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => {{1,2,3,4,6},{5},{7},{8}} => [5,1,1,1] => 120
[[[[[[[]]]]]],[],[]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => {{1,2,3,4,5,6},{7},{8}} => [6,1,1] => 720
[[[],[],[],[],[]],[[]]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => {{1,6},{2},{3},{4},{5},{7,8}} => [2,2,1,1,1,1] => 4
[[[],[],[[[]]]],[[]]] => [1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => {{1,4,5,6},{2},{3},{7,8}} => [4,2,1,1] => 48
[[[],[[]],[[]]],[[]]] => [1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => {{1,5,6},{2},{3,4},{7,8}} => [3,2,2,1] => 24
[[[],[[],[]],[]],[[]]] => [1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => {{1,6},{2},{3,5},{4},{7,8}} => [2,2,2,1,1] => 8
[[[],[[[]]],[]],[[]]] => [1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => {{1,6},{2},{3,4,5},{7,8}} => [3,2,2,1] => 24
[[[],[[],[[]]]],[[]]] => [1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => {{1,3,5,6},{2},{4},{7,8}} => [4,2,1,1] => 48
[[[],[[[]],[]]],[[]]] => [1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => {{1,3,6},{2},{4,5},{7,8}} => [3,2,2,1] => 24
[[[],[[[],[]]]],[[]]] => [1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => {{1,3,4,6},{2},{5},{7,8}} => [4,2,1,1] => 48
[[[],[[[[]]]]],[[]]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1,3,4,5,6},{2},{7,8}} => [5,2,1] => 240
[[[[]],[],[],[]],[[]]] => [1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => {{1,6},{2,3},{4},{5},{7,8}} => [2,2,2,1,1] => 8
[[[[]],[],[[]]],[[]]] => [1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => {{1,5,6},{2,3},{4},{7,8}} => [3,2,2,1] => 24
[[[[]],[[]],[]],[[]]] => [1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => {{1,6},{2,3},{4,5},{7,8}} => [2,2,2,2] => 16
[[[[]],[[],[]]],[[]]] => [1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => {{1,4,6},{2,3},{5},{7,8}} => [3,2,2,1] => 24
[[[[]],[[[]]]],[[]]] => [1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => {{1,4,5,6},{2,3},{7,8}} => [4,2,2] => 96
[[[[[]]],[],[]],[[]]] => [1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => {{1,6},{2,3,4},{5},{7,8}} => [3,2,2,1] => 24
[[[[],[]],[[]]],[[]]] => [1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => {{1,5,6},{2,4},{3},{7,8}} => [3,2,2,1] => 24
[[[[],[],[]],[]],[[]]] => [1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => {{1,6},{2,5},{3},{4},{7,8}} => [2,2,2,1,1] => 8
[[[[],[[]]],[]],[[]]] => [1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => {{1,6},{2,4,5},{3},{7,8}} => [3,2,2,1] => 24
[[[[[]],[]],[]],[[]]] => [1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => {{1,6},{2,5},{3,4},{7,8}} => [2,2,2,2] => 16
[[[[[],[]]],[]],[[]]] => [1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => {{1,6},{2,3,5},{4},{7,8}} => [3,2,2,1] => 24
[[[[],[],[],[]]],[[]]] => [1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => {{1,2,6},{3},{4},{5},{7,8}} => [3,2,1,1,1] => 12
[[[[],[],[[]]]],[[]]] => [1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => {{1,2,5,6},{3},{4},{7,8}} => [4,2,1,1] => 48
[[[[],[[]],[]]],[[]]] => [1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => {{1,2,6},{3},{4,5},{7,8}} => [3,2,2,1] => 24
[[[[],[[],[]]]],[[]]] => [1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => {{1,2,4,6},{3},{5},{7,8}} => [4,2,1,1] => 48
[[[[],[[[]]]]],[[]]] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => {{1,2,4,5,6},{3},{7,8}} => [5,2,1] => 240
[[[[[]],[],[]]],[[]]] => [1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => {{1,2,6},{3,4},{5},{7,8}} => [3,2,2,1] => 24
[[[[[],[]],[]]],[[]]] => [1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => {{1,2,6},{3,5},{4},{7,8}} => [3,2,2,1] => 24
[[[[[[]]],[]]],[[]]] => [1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => {{1,2,6},{3,4,5},{7,8}} => [3,3,2] => 72
[[[[[],[],[]]]],[[]]] => [1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => {{1,2,3,6},{4},{5},{7,8}} => [4,2,1,1] => 48
[[[[[],[[]]]]],[[]]] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => {{1,2,3,5,6},{4},{7,8}} => [5,2,1] => 240
[[[[[[]],[]]]],[[]]] => [1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => {{1,2,3,6},{4,5},{7,8}} => [4,2,2] => 96
[[[[[[],[]]]]],[[]]] => [1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,6},{5},{7,8}} => [5,2,1] => 240
[[[[[[[]]]]]],[[]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6},{7,8}} => [6,2] => 1440
[[[],[],[],[],[],[]],[]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => {{1,7},{2},{3},{4},{5},{6},{8}} => [2,1,1,1,1,1,1] => 2
[[[],[],[],[[]],[]],[]] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => {{1,7},{2},{3},{4},{5,6},{8}} => [2,2,1,1,1,1] => 4
[[[],[],[],[[],[]]],[]] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => {{1,5,7},{2},{3},{4},{6},{8}} => [3,1,1,1,1,1] => 6
[[[],[],[[]],[[]]],[]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => {{1,6,7},{2},{3},{4,5},{8}} => [3,2,1,1,1] => 12
[[[],[],[[],[]],[]],[]] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => {{1,7},{2},{3},{4,6},{5},{8}} => [2,2,1,1,1,1] => 4
[[[],[],[[[]]],[]],[]] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0] => {{1,7},{2},{3},{4,5,6},{8}} => [3,2,1,1,1] => 12
[[[],[],[[[[]]]]],[]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => {{1,4,5,6,7},{2},{3},{8}} => [5,1,1,1] => 120
[[[],[[]],[[],[]]],[]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0] => {{1,5,7},{2},{3,4},{6},{8}} => [3,2,1,1,1] => 12
[[[],[[]],[[[]]]],[]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => {{1,5,6,7},{2},{3,4},{8}} => [4,2,1,1] => 48
[[[],[[],[[]]],[]],[]] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => {{1,7},{2},{3,5,6},{4},{8}} => [3,2,1,1,1] => 12
[[[],[[[]],[]],[]],[]] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => {{1,7},{2},{3,6},{4,5},{8}} => [2,2,2,1,1] => 8
[[[],[[],[],[],[]]],[]] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => {{1,3,7},{2},{4},{5},{6},{8}} => [3,1,1,1,1,1] => 6
[[[],[[],[[]],[]]],[]] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => {{1,3,7},{2},{4},{5,6},{8}} => [3,2,1,1,1] => 12
[[[],[[],[[],[]]]],[]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => {{1,3,5,7},{2},{4},{6},{8}} => [4,1,1,1,1] => 24
[[[],[[[]],[],[]]],[]] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => {{1,3,7},{2},{4,5},{6},{8}} => [3,2,1,1,1] => 12
[[[],[[[],[]],[]]],[]] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => {{1,3,7},{2},{4,6},{5},{8}} => [3,2,1,1,1] => 12
[[[],[[[[]]],[]]],[]] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => {{1,3,7},{2},{4,5,6},{8}} => [3,3,1,1] => 36
[[[],[[[[[]]]]]],[]] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,3,4,5,6,7},{2},{8}} => [6,1,1] => 720
[[[[]],[],[],[],[]],[]] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => {{1,7},{2,3},{4},{5},{6},{8}} => [2,2,1,1,1,1] => 4
[[[[]],[],[[]],[]],[]] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => {{1,7},{2,3},{4},{5,6},{8}} => [2,2,2,1,1] => 8
[[[[]],[],[[],[]]],[]] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => {{1,5,7},{2,3},{4},{6},{8}} => [3,2,1,1,1] => 12
[[[[]],[],[[[]]]],[]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0] => {{1,5,6,7},{2,3},{4},{8}} => [4,2,1,1] => 48
[[[[]],[[]],[],[]],[]] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => {{1,7},{2,3},{4,5},{6},{8}} => [2,2,2,1,1] => 8
[[[[]],[[]],[[]]],[]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => {{1,6,7},{2,3},{4,5},{8}} => [3,2,2,1] => 24
[[[[]],[[],[]],[]],[]] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0] => {{1,7},{2,3},{4,6},{5},{8}} => [2,2,2,1,1] => 8
[[[[]],[[[]]],[]],[]] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => {{1,7},{2,3},{4,5,6},{8}} => [3,2,2,1] => 24
[[[[]],[[],[[]]]],[]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => {{1,4,6,7},{2,3},{5},{8}} => [4,2,1,1] => 48
[[[[]],[[[]],[]]],[]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => {{1,4,7},{2,3},{5,6},{8}} => [3,2,2,1] => 24
[[[[]],[[[],[]]]],[]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => {{1,4,5,7},{2,3},{6},{8}} => [4,2,1,1] => 48
[[[[]],[[[[]]]]],[]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => {{1,4,5,6,7},{2,3},{8}} => [5,2,1] => 240
[[[[],[]],[],[],[]],[]] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => {{1,7},{2,4},{3},{5},{6},{8}} => [2,2,1,1,1,1] => 4
[[[[[]]],[],[],[]],[]] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => {{1,7},{2,3,4},{5},{6},{8}} => [3,2,1,1,1] => 12
[[[[],[]],[[]],[]],[]] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => {{1,7},{2,4},{3},{5,6},{8}} => [2,2,2,1,1] => 8
[[[[[]]],[[]],[]],[]] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => {{1,7},{2,3,4},{5,6},{8}} => [3,2,2,1] => 24
[[[[],[]],[[],[]]],[]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => {{1,5,7},{2,4},{3},{6},{8}} => [3,2,1,1,1] => 12
[[[[[]]],[[],[]]],[]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => {{1,5,7},{2,3,4},{6},{8}} => [3,3,1,1] => 36
[[[[[]]],[[[]]]],[]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => {{1,5,6,7},{2,3,4},{8}} => [4,3,1] => 144
[[[[],[],[]],[],[]],[]] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => {{1,7},{2,5},{3},{4},{6},{8}} => [2,2,1,1,1,1] => 4
[[[[],[[]]],[],[]],[]] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => {{1,7},{2,4,5},{3},{6},{8}} => [3,2,1,1,1] => 12
[[[[[]],[]],[],[]],[]] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0] => {{1,7},{2,5},{3,4},{6},{8}} => [2,2,2,1,1] => 8
[[[[[[]]]],[],[]],[]] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => {{1,7},{2,3,4,5},{6},{8}} => [4,2,1,1] => 48
[[[[],[[]]],[[]]],[]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => {{1,6,7},{2,4,5},{3},{8}} => [3,3,1,1] => 36
[[[[[]],[]],[[]]],[]] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => {{1,6,7},{2,5},{3,4},{8}} => [3,2,2,1] => 24
[[[[[],[]]],[[]]],[]] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => {{1,6,7},{2,3,5},{4},{8}} => [3,3,1,1] => 36
[[[[],[[]],[]],[]],[]] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => {{1,7},{2,6},{3},{4,5},{8}} => [2,2,2,1,1] => 8
[[[[],[[],[]]],[]],[]] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => {{1,7},{2,4,6},{3},{5},{8}} => [3,2,1,1,1] => 12
[[[[],[[[]]]],[]],[]] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => {{1,7},{2,4,5,6},{3},{8}} => [4,2,1,1] => 48
[[[[[]],[],[]],[]],[]] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => {{1,7},{2,6},{3,4},{5},{8}} => [2,2,2,1,1] => 8
[[[[[],[]],[]],[]],[]] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => {{1,7},{2,6},{3,5},{4},{8}} => [2,2,2,1,1] => 8
[[[[[[]]],[]],[]],[]] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => {{1,7},{2,6},{3,4,5},{8}} => [3,2,2,1] => 24
[[[[[],[[]]]],[]],[]] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => {{1,7},{2,3,5,6},{4},{8}} => [4,2,1,1] => 48
[[[[[[[]]]]],[]],[]] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => {{1,7},{2,3,4,5,6},{8}} => [5,2,1] => 240
[[[[],[],[],[],[]]],[]] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => {{1,2,7},{3},{4},{5},{6},{8}} => [3,1,1,1,1,1] => 6
[[[[],[],[[[]]]]],[]] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => {{1,2,5,6,7},{3},{4},{8}} => [5,1,1,1] => 120
[[[[],[[[]],[]]]],[]] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => {{1,2,4,7},{3},{5,6},{8}} => [4,2,1,1] => 48
[[[[[]],[[]],[]]],[]] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => {{1,2,7},{3,4},{5,6},{8}} => [3,2,2,1] => 24
[[[[[]],[[],[]]]],[]] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => {{1,2,5,7},{3,4},{6},{8}} => [4,2,1,1] => 48
[[[[[],[[]]],[]]],[]] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => {{1,2,7},{3,5,6},{4},{8}} => [3,3,1,1] => 36
[[[[[[[]]]],[]]],[]] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => {{1,2,7},{3,4,5,6},{8}} => [4,3,1] => 144
[[[[[],[[]],[]]]],[]] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => {{1,2,3,7},{4},{5,6},{8}} => [4,2,1,1] => 48
[[[[[],[[],[]]]]],[]] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,5,7},{4},{6},{8}} => [5,1,1,1] => 120
[[[[[],[[[]]]]]],[]] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,5,6,7},{4},{8}} => [6,1,1] => 720
[[[[[[]],[],[]]]],[]] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => {{1,2,3,7},{4,5},{6},{8}} => [4,2,1,1] => 48
[[[[[[]],[[]]]]],[]] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => {{1,2,3,6,7},{4,5},{8}} => [5,2,1] => 240
[[[[[[],[]],[]]]],[]] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => {{1,2,3,7},{4,6},{5},{8}} => [4,2,1,1] => 48
[[[[[[[]]],[]]]],[]] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => {{1,2,3,7},{4,5,6},{8}} => [4,3,1] => 144
[[[[[[],[],[]]]]],[]] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5},{6},{8}} => [5,1,1,1] => 120
[[[[[[],[[]]]]]],[]] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,6,7},{5},{8}} => [6,1,1] => 720
[[[[[[[]],[]]]]],[]] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5,6},{8}} => [5,2,1] => 240
[[[[[[[],[]]]]]],[]] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,7},{6},{8}} => [6,1,1] => 720
[[[[[[[[]]]]]]],[]] => [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] => 5040
[[[],[],[],[],[],[],[]]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => {{1,8},{2},{3},{4},{5},{6},{7}} => [2,1,1,1,1,1,1] => 2
[[[],[],[],[],[],[[]]]] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => {{1,7,8},{2},{3},{4},{5},{6}} => [3,1,1,1,1,1] => 6
[[[],[],[],[],[[]],[]]] => [1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => {{1,8},{2},{3},{4},{5},{6,7}} => [2,2,1,1,1,1] => 4
[[[],[],[],[],[[],[]]]] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => {{1,6,8},{2},{3},{4},{5},{7}} => [3,1,1,1,1,1] => 6
[[[],[],[],[],[[[]]]]] => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => {{1,6,7,8},{2},{3},{4},{5}} => [4,1,1,1,1] => 24
[[[],[],[],[[],[]],[]]] => [1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => {{1,8},{2},{3},{4},{5,7},{6}} => [2,2,1,1,1,1] => 4
[[[],[],[],[[[]]],[]]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => {{1,8},{2},{3},{4},{5,6,7}} => [3,2,1,1,1] => 12
[[[],[],[],[[],[[]]]]] => [1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => {{1,5,7,8},{2},{3},{4},{6}} => [4,1,1,1,1] => 24
[[[],[],[],[[[],[]]]]] => [1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => {{1,5,6,8},{2},{3},{4},{7}} => [4,1,1,1,1] => 24
[[[],[],[],[[[[]]]]]] => [1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => {{1,5,6,7,8},{2},{3},{4}} => [5,1,1,1] => 120
[[[],[],[[]],[],[],[]]] => [1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => {{1,8},{2},{3},{4,5},{6},{7}} => [2,2,1,1,1,1] => 4
[[[],[],[[]],[[[]]]]] => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => {{1,6,7,8},{2},{3},{4,5}} => [4,2,1,1] => 48
[[[],[],[[],[[],[]]]]] => [1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => {{1,4,6,8},{2},{3},{5},{7}} => [4,1,1,1,1] => 24
[[[],[],[[[]],[],[]]]] => [1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => {{1,4,8},{2},{3},{5,6},{7}} => [3,2,1,1,1] => 12
[[[],[],[[[]],[[]]]]] => [1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => {{1,4,7,8},{2},{3},{5,6}} => [4,2,1,1] => 48
[[[],[],[[[[]]],[]]]] => [1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => {{1,4,8},{2},{3},{5,6,7}} => [3,3,1,1] => 36
[[[],[],[[[],[],[]]]]] => [1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => {{1,4,5,8},{2},{3},{6},{7}} => [4,1,1,1,1] => 24
[[[],[],[[[[]],[]]]]] => [1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => {{1,4,5,8},{2},{3},{6,7}} => [4,2,1,1] => 48
[[[],[],[[[[],[]]]]]] => [1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => {{1,4,5,6,8},{2},{3},{7}} => [5,1,1,1] => 120
[[[],[[]],[],[],[],[]]] => [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => {{1,8},{2},{3,4},{5},{6},{7}} => [2,2,1,1,1,1] => 4
[[[],[[]],[],[[[]]]]] => [1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => {{1,6,7,8},{2},{3,4},{5}} => [4,2,1,1] => 48
[[[],[[]],[[]],[[]]]] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => {{1,7,8},{2},{3,4},{5,6}} => [3,2,2,1] => 24
[[[],[[]],[[[]]],[]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => {{1,8},{2},{3,4},{5,6,7}} => [3,2,2,1] => 24
[[[],[[]],[[],[[]]]]] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => {{1,5,7,8},{2},{3,4},{6}} => [4,2,1,1] => 48
[[[],[[]],[[[]],[]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => {{1,5,8},{2},{3,4},{6,7}} => [3,2,2,1] => 24
[[[],[[]],[[[],[]]]]] => [1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => {{1,5,6,8},{2},{3,4},{7}} => [4,2,1,1] => 48
[[[],[[],[]],[],[],[]]] => [1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => {{1,8},{2},{3,5},{4},{6},{7}} => [2,2,1,1,1,1] => 4
[[[],[[[]]],[],[],[]]] => [1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => {{1,8},{2},{3,4,5},{6},{7}} => [3,2,1,1,1] => 12
[[[],[[[]]],[],[[]]]] => [1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => {{1,7,8},{2},{3,4,5},{6}} => [3,3,1,1] => 36
[[[],[[[]]],[[]],[]]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => {{1,8},{2},{3,4,5},{6,7}} => [3,2,2,1] => 24
[[[],[[],[]],[[],[]]]] => [1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => {{1,6,8},{2},{3,5},{4},{7}} => [3,2,1,1,1] => 12
[[[],[[],[]],[[[]]]]] => [1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => {{1,6,7,8},{2},{3,5},{4}} => [4,2,1,1] => 48
[[[],[[[]]],[[],[]]]] => [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => {{1,6,8},{2},{3,4,5},{7}} => [3,3,1,1] => 36
[[[],[[[[]]]],[],[]]] => [1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => {{1,8},{2},{3,4,5,6},{7}} => [4,2,1,1] => 48
[[[],[[],[[]]],[[]]]] => [1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => {{1,7,8},{2},{3,5,6},{4}} => [3,3,1,1] => 36
[[[],[[[]],[]],[[]]]] => [1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => {{1,7,8},{2},{3,6},{4,5}} => [3,2,2,1] => 24
[[[],[[[]],[[]]],[]]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => {{1,8},{2},{3,6,7},{4,5}} => [3,2,2,1] => 24
[[[],[[[],[[]]]],[]]] => [1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => {{1,8},{2},{3,4,6,7},{5}} => [4,2,1,1] => 48
[[[],[[[[]],[]]],[]]] => [1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => {{1,8},{2},{3,4,7},{5,6}} => [3,2,2,1] => 24
[[[],[[[[],[]]]],[]]] => [1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => {{1,8},{2},{3,4,5,7},{6}} => [4,2,1,1] => 48
[[[],[[],[],[],[],[]]]] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => {{1,3,8},{2},{4},{5},{6},{7}} => [3,1,1,1,1,1] => 6
[[[],[[],[],[],[[]]]]] => [1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => {{1,3,7,8},{2},{4},{5},{6}} => [4,1,1,1,1] => 24
[[[],[[],[[[]]],[]]]] => [1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => {{1,3,8},{2},{4},{5,6,7}} => [3,3,1,1] => 36
[[[],[[],[[],[],[]]]]] => [1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => {{1,3,5,8},{2},{4},{6},{7}} => [4,1,1,1,1] => 24
[[[],[[],[[],[[]]]]]] => [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => {{1,3,5,7,8},{2},{4},{6}} => [5,1,1,1] => 120
[[[],[[],[[[]],[]]]]] => [1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => {{1,3,5,8},{2},{4},{6,7}} => [4,2,1,1] => 48
[[[],[[],[[[],[]]]]]] => [1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => {{1,3,5,6,8},{2},{4},{7}} => [5,1,1,1] => 120
[[[],[[[]],[],[[]]]]] => [1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => {{1,3,7,8},{2},{4,5},{6}} => [4,2,1,1] => 48
[[[],[[[]],[[]],[]]]] => [1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => {{1,3,8},{2},{4,5},{6,7}} => [3,2,2,1] => 24
[[[],[[[]],[[],[]]]]] => [1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => {{1,3,6,8},{2},{4,5},{7}} => [4,2,1,1] => 48
[[[],[[[[]]],[],[]]]] => [1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => {{1,3,8},{2},{4,5,6},{7}} => [3,3,1,1] => 36
[[[],[[[],[]],[[]]]]] => [1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => {{1,3,7,8},{2},{4,6},{5}} => [4,2,1,1] => 48
[[[],[[[],[[]]],[]]]] => [1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => {{1,3,8},{2},{4,6,7},{5}} => [3,3,1,1] => 36
[[[],[[[[]],[]],[]]]] => [1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => {{1,3,8},{2},{4,7},{5,6}} => [3,2,2,1] => 24
[[[],[[[[],[]]],[]]]] => [1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => {{1,3,8},{2},{4,5,7},{6}} => [3,3,1,1] => 36
[[[],[[[],[],[],[]]]]] => [1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => {{1,3,4,8},{2},{5},{6},{7}} => [4,1,1,1,1] => 24
[[[],[[[],[],[[]]]]]] => [1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => {{1,3,4,7,8},{2},{5},{6}} => [5,1,1,1] => 120
[[[],[[[],[[],[]]]]]] => [1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => {{1,3,4,6,8},{2},{5},{7}} => [5,1,1,1] => 120
[[[],[[[[]],[],[]]]]] => [1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => {{1,3,4,8},{2},{5,6},{7}} => [4,2,1,1] => 48
[[[],[[[[],[]],[]]]]] => [1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => {{1,3,4,8},{2},{5,7},{6}} => [4,2,1,1] => 48
[[[],[[[[],[],[]]]]]] => [1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => {{1,3,4,5,8},{2},{6},{7}} => [5,1,1,1] => 120
[[[],[[[[[]],[]]]]]] => [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => {{1,3,4,5,8},{2},{6,7}} => [5,2,1] => 240
[[[],[[[[[],[]]]]]]] => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => {{1,3,4,5,6,8},{2},{7}} => [6,1,1] => 720
[[[],[[[[[[]]]]]]]] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,3,4,5,6,7,8},{2}} => [7,1] => 5040
[[[[]],[],[],[],[],[]]] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => {{1,8},{2,3},{4},{5},{6},{7}} => [2,2,1,1,1,1] => 4
[[[[]],[],[],[[],[]]]] => [1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => {{1,6,8},{2,3},{4},{5},{7}} => [3,2,1,1,1] => 12
[[[[]],[],[[]],[[]]]] => [1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => {{1,7,8},{2,3},{4},{5,6}} => [3,2,2,1] => 24
[[[[]],[],[[[]]],[]]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => {{1,8},{2,3},{4},{5,6,7}} => [3,2,2,1] => 24
[[[[]],[],[[],[[]]]]] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => {{1,5,7,8},{2,3},{4},{6}} => [4,2,1,1] => 48
[[[[]],[],[[[]],[]]]] => [1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => {{1,5,8},{2,3},{4},{6,7}} => [3,2,2,1] => 24
[[[[]],[],[[[],[]]]]] => [1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => {{1,5,6,8},{2,3},{4},{7}} => [4,2,1,1] => 48
[[[[]],[[]],[],[],[]]] => [1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => {{1,8},{2,3},{4,5},{6},{7}} => [2,2,2,1,1] => 8
[[[[]],[[]],[],[[]]]] => [1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => {{1,7,8},{2,3},{4,5},{6}} => [3,2,2,1] => 24
[[[[]],[[]],[[]],[]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => {{1,8},{2,3},{4,5},{6,7}} => [2,2,2,2] => 16
[[[[]],[[]],[[],[]]]] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => {{1,6,8},{2,3},{4,5},{7}} => [3,2,2,1] => 24
[[[[]],[[]],[[[]]]]] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => {{1,6,7,8},{2,3},{4,5}} => [4,2,2] => 96
[[[[]],[[],[]],[[]]]] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => {{1,7,8},{2,3},{4,6},{5}} => [3,2,2,1] => 24
[[[[]],[[],[[]]],[]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => {{1,8},{2,3},{4,6,7},{5}} => [3,2,2,1] => 24
[[[[]],[[[]],[]],[]]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => {{1,8},{2,3},{4,7},{5,6}} => [2,2,2,2] => 16
[[[[]],[[[],[]]],[]]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => {{1,8},{2,3},{4,5,7},{6}} => [3,2,2,1] => 24
[[[[]],[[],[],[],[]]]] => [1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => {{1,4,8},{2,3},{5},{6},{7}} => [3,2,1,1,1] => 12
[[[[]],[[],[],[[]]]]] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => {{1,4,7,8},{2,3},{5},{6}} => [4,2,1,1] => 48
[[[[]],[[],[[]],[]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => {{1,4,8},{2,3},{5},{6,7}} => [3,2,2,1] => 24
[[[[]],[[],[[],[]]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => {{1,4,6,8},{2,3},{5},{7}} => [4,2,1,1] => 48
[[[[]],[[],[[[]]]]]] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => {{1,4,6,7,8},{2,3},{5}} => [5,2,1] => 240
[[[[]],[[[]],[],[]]]] => [1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => {{1,4,8},{2,3},{5,6},{7}} => [3,2,2,1] => 24
[[[[]],[[[],[]],[]]]] => [1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => {{1,4,8},{2,3},{5,7},{6}} => [3,2,2,1] => 24
[[[[]],[[[[]]],[]]]] => [1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => {{1,4,8},{2,3},{5,6,7}} => [3,3,2] => 72
[[[[]],[[[],[],[]]]]] => [1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => {{1,4,5,8},{2,3},{6},{7}} => [4,2,1,1] => 48
[[[[]],[[[[]],[]]]]] => [1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => {{1,4,5,8},{2,3},{6,7}} => [4,2,2] => 96
[[[[]],[[[[],[]]]]]] => [1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => {{1,4,5,6,8},{2,3},{7}} => [5,2,1] => 240
[[[[]],[[[[[]]]]]]] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => {{1,4,5,6,7,8},{2,3}} => [6,2] => 1440
[[[[],[]],[],[],[],[]]] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => {{1,8},{2,4},{3},{5},{6},{7}} => [2,2,1,1,1,1] => 4
[[[[[]]],[],[],[],[]]] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => {{1,8},{2,3,4},{5},{6},{7}} => [3,2,1,1,1] => 12
[[[[],[]],[],[[]],[]]] => [1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => {{1,8},{2,4},{3},{5},{6,7}} => [2,2,2,1,1] => 8
[[[[[]]],[],[[]],[]]] => [1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => {{1,8},{2,3,4},{5},{6,7}} => [3,2,2,1] => 24
[[[[],[]],[],[[[]]]]] => [1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => {{1,6,7,8},{2,4},{3},{5}} => [4,2,1,1] => 48
[[[[[]]],[],[[],[]]]] => [1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => {{1,6,8},{2,3,4},{5},{7}} => [3,3,1,1] => 36
[[[[[]]],[[]],[],[]]] => [1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => {{1,8},{2,3,4},{5,6},{7}} => [3,2,2,1] => 24
[[[[],[]],[[]],[[]]]] => [1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => {{1,7,8},{2,4},{3},{5,6}} => [3,2,2,1] => 24
[[[[],[]],[[],[]],[]]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => {{1,8},{2,4},{3},{5,7},{6}} => [2,2,2,1,1] => 8
[[[[],[]],[[[]]],[]]] => [1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => {{1,8},{2,4},{3},{5,6,7}} => [3,2,2,1] => 24
[[[[[]]],[[],[]],[]]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => {{1,8},{2,3,4},{5,7},{6}} => [3,2,2,1] => 24
[[[[],[]],[[],[[]]]]] => [1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => {{1,5,7,8},{2,4},{3},{6}} => [4,2,1,1] => 48
[[[[],[]],[[[]],[]]]] => [1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => {{1,5,8},{2,4},{3},{6,7}} => [3,2,2,1] => 24
[[[[],[]],[[[],[]]]]] => [1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => {{1,5,6,8},{2,4},{3},{7}} => [4,2,1,1] => 48
[[[[[]]],[[],[],[]]]] => [1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => {{1,5,8},{2,3,4},{6},{7}} => [3,3,1,1] => 36
[[[[[]]],[[[]],[]]]] => [1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => {{1,5,8},{2,3,4},{6,7}} => [3,3,2] => 72
[[[[[]]],[[[],[]]]]] => [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => {{1,5,6,8},{2,3,4},{7}} => [4,3,1] => 144
[[[[[]]],[[[[]]]]]] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => {{1,5,6,7,8},{2,3,4}} => [5,3] => 720
[[[[],[],[]],[],[],[]]] => [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => {{1,8},{2,5},{3},{4},{6},{7}} => [2,2,1,1,1,1] => 4
[[[[[],[]]],[],[],[]]] => [1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => {{1,8},{2,3,5},{4},{6},{7}} => [3,2,1,1,1] => 12
[[[[],[],[]],[],[[]]]] => [1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => {{1,7,8},{2,5},{3},{4},{6}} => [3,2,1,1,1] => 12
[[[[],[[]]],[],[[]]]] => [1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => {{1,7,8},{2,4,5},{3},{6}} => [3,3,1,1] => 36
[[[[[]],[]],[],[[]]]] => [1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => {{1,7,8},{2,5},{3,4},{6}} => [3,2,2,1] => 24
[[[[[],[]]],[],[[]]]] => [1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => {{1,7,8},{2,3,5},{4},{6}} => [3,3,1,1] => 36
[[[[],[[]]],[[]],[]]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => {{1,8},{2,4,5},{3},{6,7}} => [3,2,2,1] => 24
[[[[[]],[]],[[]],[]]] => [1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => {{1,8},{2,5},{3,4},{6,7}} => [2,2,2,2] => 16
[[[[[],[]]],[[]],[]]] => [1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => {{1,8},{2,3,5},{4},{6,7}} => [3,2,2,1] => 24
[[[[],[],[]],[[[]]]]] => [1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => {{1,6,7,8},{2,5},{3},{4}} => [4,2,1,1] => 48
[[[[],[[]]],[[],[]]]] => [1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => {{1,6,8},{2,4,5},{3},{7}} => [3,3,1,1] => 36
[[[[[]],[]],[[],[]]]] => [1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => {{1,6,8},{2,5},{3,4},{7}} => [3,2,2,1] => 24
[[[[[]],[]],[[[]]]]] => [1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => {{1,6,7,8},{2,5},{3,4}} => [4,2,2] => 96
[[[[[],[]]],[[],[]]]] => [1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => {{1,6,8},{2,3,5},{4},{7}} => [3,3,1,1] => 36
[[[[[[]]]],[[[]]]]] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => {{1,6,7,8},{2,3,4,5}} => [4,4] => 576
[[[[],[[[]]]],[],[]]] => [1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => {{1,8},{2,4,5,6},{3},{7}} => [4,2,1,1] => 48
[[[[[]],[],[]],[],[]]] => [1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => {{1,8},{2,6},{3,4},{5},{7}} => [2,2,2,1,1] => 8
[[[[[]],[[]]],[],[]]] => [1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => {{1,8},{2,5,6},{3,4},{7}} => [3,2,2,1] => 24
[[[[[[]]],[]],[],[]]] => [1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => {{1,8},{2,6},{3,4,5},{7}} => [3,2,2,1] => 24
[[[[[],[],[]]],[],[]]] => [1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => {{1,8},{2,3,6},{4},{5},{7}} => [3,2,1,1,1] => 12
[[[[[],[[]]]],[],[]]] => [1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => {{1,8},{2,3,5,6},{4},{7}} => [4,2,1,1] => 48
[[[[[[]],[]]],[],[]]] => [1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => {{1,8},{2,3,6},{4,5},{7}} => [3,2,2,1] => 24
[[[[[[],[]]]],[],[]]] => [1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => {{1,8},{2,3,4,6},{5},{7}} => [4,2,1,1] => 48
[[[[[[[]]]]],[],[]]] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => {{1,8},{2,3,4,5,6},{7}} => [5,2,1] => 240
[[[[],[],[],[]],[[]]]] => [1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => {{1,7,8},{2,6},{3},{4},{5}} => [3,2,1,1,1] => 12
[[[[],[],[[]]],[[]]]] => [1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => {{1,7,8},{2,5,6},{3},{4}} => [3,3,1,1] => 36
[[[[],[[]],[]],[[]]]] => [1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => {{1,7,8},{2,6},{3},{4,5}} => [3,2,2,1] => 24
[[[[],[[],[]]],[[]]]] => [1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => {{1,7,8},{2,4,6},{3},{5}} => [3,3,1,1] => 36
[[[[[]],[],[]],[[]]]] => [1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => {{1,7,8},{2,6},{3,4},{5}} => [3,2,2,1] => 24
[[[[[]],[[]]],[[]]]] => [1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => {{1,7,8},{2,5,6},{3,4}} => [3,3,2] => 72
[[[[[],[]],[]],[[]]]] => [1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => {{1,7,8},{2,6},{3,5},{4}} => [3,2,2,1] => 24
[[[[[[]]],[]],[[]]]] => [1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => {{1,7,8},{2,6},{3,4,5}} => [3,3,2] => 72
[[[[[],[],[]]],[[]]]] => [1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => {{1,7,8},{2,3,6},{4},{5}} => [3,3,1,1] => 36
[[[[],[],[],[],[]],[]]] => [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => {{1,8},{2,7},{3},{4},{5},{6}} => [2,2,1,1,1,1] => 4
[[[[],[],[[],[]]],[]]] => [1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => {{1,8},{2,5,7},{3},{4},{6}} => [3,2,1,1,1] => 12
[[[[],[],[[[]]]],[]]] => [1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => {{1,8},{2,5,6,7},{3},{4}} => [4,2,1,1] => 48
[[[[],[[]],[[]]],[]]] => [1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => {{1,8},{2,6,7},{3},{4,5}} => [3,2,2,1] => 24
[[[[],[[[]]],[]],[]]] => [1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => {{1,8},{2,7},{3},{4,5,6}} => [3,2,2,1] => 24
[[[[],[[],[],[]]],[]]] => [1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => {{1,8},{2,4,7},{3},{5},{6}} => [3,2,1,1,1] => 12
[[[[],[[],[[]]]],[]]] => [1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => {{1,8},{2,4,6,7},{3},{5}} => [4,2,1,1] => 48
[[[[],[[[]],[]]],[]]] => [1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => {{1,8},{2,4,7},{3},{5,6}} => [3,2,2,1] => 24
[[[[],[[[],[]]]],[]]] => [1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => {{1,8},{2,4,5,7},{3},{6}} => [4,2,1,1] => 48
[[[[[]],[],[],[]],[]]] => [1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => {{1,8},{2,7},{3,4},{5},{6}} => [2,2,2,1,1] => 8
[[[[[]],[],[[]]],[]]] => [1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => {{1,8},{2,6,7},{3,4},{5}} => [3,2,2,1] => 24
[[[[[]],[[]],[]],[]]] => [1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => {{1,8},{2,7},{3,4},{5,6}} => [2,2,2,2] => 16
[[[[[]],[[],[]]],[]]] => [1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => {{1,8},{2,5,7},{3,4},{6}} => [3,2,2,1] => 24
[[[[[[]]],[],[]],[]]] => [1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => {{1,8},{2,7},{3,4,5},{6}} => [3,2,2,1] => 24
[[[[[],[]],[[]]],[]]] => [1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => {{1,8},{2,6,7},{3,5},{4}} => [3,2,2,1] => 24
[[[[[],[[]]],[]],[]]] => [1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => {{1,8},{2,7},{3,5,6},{4}} => [3,2,2,1] => 24
[[[[[[]],[]],[]],[]]] => [1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,8},{2,7},{3,6},{4,5}} => [2,2,2,2] => 16
[[[[[[],[]]],[]],[]]] => [1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => {{1,8},{2,7},{3,4,6},{5}} => [3,2,2,1] => 24
[[[[[],[],[],[]]],[]]] => [1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => {{1,8},{2,3,7},{4},{5},{6}} => [3,2,1,1,1] => 12
[[[[[],[],[[]]]],[]]] => [1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => {{1,8},{2,3,6,7},{4},{5}} => [4,2,1,1] => 48
[[[[[],[[]],[]]],[]]] => [1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => {{1,8},{2,3,7},{4},{5,6}} => [3,2,2,1] => 24
[[[[[],[[],[]]]],[]]] => [1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => {{1,8},{2,3,5,7},{4},{6}} => [4,2,1,1] => 48
[[[[[],[[[]]]]],[]]] => [1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => {{1,8},{2,3,5,6,7},{4}} => [5,2,1] => 240
[[[[[[]],[],[]]],[]]] => [1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => {{1,8},{2,3,7},{4,5},{6}} => [3,2,2,1] => 24
[[[[[[]],[[]]]],[]]] => [1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => {{1,8},{2,3,6,7},{4,5}} => [4,2,2] => 96
[[[[[[],[]],[]]],[]]] => [1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => {{1,8},{2,3,7},{4,6},{5}} => [3,2,2,1] => 24
[[[[[[[]]],[]]],[]]] => [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => {{1,8},{2,3,7},{4,5,6}} => [3,3,2] => 72
[[[[[[],[],[]]]],[]]] => [1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => {{1,8},{2,3,4,7},{5},{6}} => [4,2,1,1] => 48
[[[[[[],[[]]]]],[]]] => [1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => {{1,8},{2,3,4,6,7},{5}} => [5,2,1] => 240
[[[[[[[]],[]]]],[]]] => [1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => {{1,8},{2,3,4,7},{5,6}} => [4,2,2] => 96
[[[[[[[],[]]]]],[]]] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => {{1,8},{2,3,4,5,7},{6}} => [5,2,1] => 240
[[[[[[[[]]]]]],[]]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => {{1,8},{2,3,4,5,6,7}} => [6,2] => 1440
[[[[],[],[],[],[],[]]]] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => {{1,2,8},{3},{4},{5},{6},{7}} => [3,1,1,1,1,1] => 6
[[[[],[],[],[],[[]]]]] => [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => {{1,2,7,8},{3},{4},{5},{6}} => [4,1,1,1,1] => 24
[[[[],[],[[],[[]]]]]] => [1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => {{1,2,5,7,8},{3},{4},{6}} => [5,1,1,1] => 120
[[[[],[],[[[],[]]]]]] => [1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => {{1,2,5,6,8},{3},{4},{7}} => [5,1,1,1] => 120
[[[[],[[]],[],[[]]]]] => [1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => {{1,2,7,8},{3},{4,5},{6}} => [4,2,1,1] => 48
[[[[],[[]],[[]],[]]]] => [1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => {{1,2,8},{3},{4,5},{6,7}} => [3,2,2,1] => 24
[[[[],[[]],[[],[]]]]] => [1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => {{1,2,6,8},{3},{4,5},{7}} => [4,2,1,1] => 48
[[[[],[[[]]],[],[]]]] => [1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => {{1,2,8},{3},{4,5,6},{7}} => [3,3,1,1] => 36
[[[[],[[],[]],[[]]]]] => [1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => {{1,2,7,8},{3},{4,6},{5}} => [4,2,1,1] => 48
[[[[],[[],[[]]],[]]]] => [1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => {{1,2,8},{3},{4,6,7},{5}} => [3,3,1,1] => 36
[[[[],[[[]],[]],[]]]] => [1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => {{1,2,8},{3},{4,7},{5,6}} => [3,2,2,1] => 24
[[[[],[[[],[]]],[]]]] => [1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => {{1,2,8},{3},{4,5,7},{6}} => [3,3,1,1] => 36
[[[[],[[],[],[],[]]]]] => [1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => {{1,2,4,8},{3},{5},{6},{7}} => [4,1,1,1,1] => 24
[[[[],[[],[],[[]]]]]] => [1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => {{1,2,4,7,8},{3},{5},{6}} => [5,1,1,1] => 120
[[[[],[[],[[]],[]]]]] => [1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => {{1,2,4,8},{3},{5},{6,7}} => [4,2,1,1] => 48
[[[[],[[],[[],[]]]]]] => [1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => {{1,2,4,6,8},{3},{5},{7}} => [5,1,1,1] => 120
[[[[],[[],[[[]]]]]]] => [1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => {{1,2,4,6,7,8},{3},{5}} => [6,1,1] => 720
[[[[],[[[]],[],[]]]]] => [1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => {{1,2,4,8},{3},{5,6},{7}} => [4,2,1,1] => 48
[[[[],[[[],[]],[]]]]] => [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => {{1,2,4,8},{3},{5,7},{6}} => [4,2,1,1] => 48
[[[[],[[[],[[]]]]]]] => [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => {{1,2,4,5,7,8},{3},{6}} => [6,1,1] => 720
[[[[],[[[[]],[]]]]]] => [1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => {{1,2,4,5,8},{3},{6,7}} => [5,2,1] => 240
[[[[],[[[[],[]]]]]]] => [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => {{1,2,4,5,6,8},{3},{7}} => [6,1,1] => 720
[[[[],[[[[[]]]]]]]] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2,4,5,6,7,8},{3}} => [7,1] => 5040
[[[[[]],[],[],[],[]]]] => [1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => {{1,2,8},{3,4},{5},{6},{7}} => [3,2,1,1,1] => 12
[[[[[]],[],[],[[]]]]] => [1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => {{1,2,7,8},{3,4},{5},{6}} => [4,2,1,1] => 48
[[[[[]],[],[[]],[]]]] => [1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => {{1,2,8},{3,4},{5},{6,7}} => [3,2,2,1] => 24
[[[[[]],[],[[],[]]]]] => [1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => {{1,2,6,8},{3,4},{5},{7}} => [4,2,1,1] => 48
[[[[[]],[[]],[],[]]]] => [1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => {{1,2,8},{3,4},{5,6},{7}} => [3,2,2,1] => 24
[[[[[]],[[],[]],[]]]] => [1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => {{1,2,8},{3,4},{5,7},{6}} => [3,2,2,1] => 24
[[[[[]],[[],[],[]]]]] => [1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => {{1,2,5,8},{3,4},{6},{7}} => [4,2,1,1] => 48
[[[[[]],[[[],[]]]]]] => [1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => {{1,2,5,6,8},{3,4},{7}} => [5,2,1] => 240
[[[[[],[]],[],[[]]]]] => [1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => {{1,2,7,8},{3,5},{4},{6}} => [4,2,1,1] => 48
[[[[[],[]],[[]],[]]]] => [1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => {{1,2,8},{3,5},{4},{6,7}} => [3,2,2,1] => 24
[[[[[[]]],[[]],[]]]] => [1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => {{1,2,8},{3,4,5},{6,7}} => [3,3,2] => 72
[[[[[],[]],[[],[]]]]] => [1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => {{1,2,6,8},{3,5},{4},{7}} => [4,2,1,1] => 48
[[[[[[]]],[[[]]]]]] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => {{1,2,6,7,8},{3,4,5}} => [5,3] => 720
[[[[[],[[]]],[],[]]]] => [1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => {{1,2,8},{3,5,6},{4},{7}} => [3,3,1,1] => 36
[[[[[[]],[]],[],[]]]] => [1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => {{1,2,8},{3,6},{4,5},{7}} => [3,2,2,1] => 24
[[[[[[],[]]],[],[]]]] => [1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => {{1,2,8},{3,4,6},{5},{7}} => [3,3,1,1] => 36
[[[[[],[],[]],[[]]]]] => [1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => {{1,2,7,8},{3,6},{4},{5}} => [4,2,1,1] => 48
[[[[[[],[]]],[[]]]]] => [1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => {{1,2,7,8},{3,4,6},{5}} => [4,3,1] => 144
[[[[[[[]]]],[[]]]]] => [1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => {{1,2,7,8},{3,4,5,6}} => [4,4] => 576
[[[[[],[],[[]]],[]]]] => [1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => {{1,2,8},{3,6,7},{4},{5}} => [3,3,1,1] => 36
[[[[[],[[]],[]],[]]]] => [1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => {{1,2,8},{3,7},{4},{5,6}} => [3,2,2,1] => 24
[[[[[],[[],[]]],[]]]] => [1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => {{1,2,8},{3,5,7},{4},{6}} => [3,3,1,1] => 36
[[[[[[]],[],[]],[]]]] => [1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => {{1,2,8},{3,7},{4,5},{6}} => [3,2,2,1] => 24
[[[[[[],[]],[]],[]]]] => [1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => {{1,2,8},{3,7},{4,6},{5}} => [3,2,2,1] => 24
[[[[[[[]]],[]],[]]]] => [1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => {{1,2,8},{3,7},{4,5,6}} => [3,3,2] => 72
[[[[[[],[],[]]],[]]]] => [1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => {{1,2,8},{3,4,7},{5},{6}} => [3,3,1,1] => 36
[[[[[[[]],[]]],[]]]] => [1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => {{1,2,8},{3,4,7},{5,6}} => [3,3,2] => 72
[[[[[[[],[]]]],[]]]] => [1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => {{1,2,8},{3,4,5,7},{6}} => [4,3,1] => 144
[[[[[[[[]]]]],[]]]] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => {{1,2,8},{3,4,5,6,7}} => [5,3] => 720
[[[[[],[],[],[],[]]]]] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => {{1,2,3,8},{4},{5},{6},{7}} => [4,1,1,1,1] => 24
[[[[[],[],[],[[]]]]]] => [1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => {{1,2,3,7,8},{4},{5},{6}} => [5,1,1,1] => 120
[[[[[],[],[[]],[]]]]] => [1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => {{1,2,3,8},{4},{5},{6,7}} => [4,2,1,1] => 48
[[[[[],[],[[],[]]]]]] => [1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => {{1,2,3,6,8},{4},{5},{7}} => [5,1,1,1] => 120
[[[[[],[],[[[]]]]]]] => [1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => {{1,2,3,6,7,8},{4},{5}} => [6,1,1] => 720
[[[[[],[[]],[],[]]]]] => [1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => {{1,2,3,8},{4},{5,6},{7}} => [4,2,1,1] => 48
[[[[[],[[],[]],[]]]]] => [1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => {{1,2,3,8},{4},{5,7},{6}} => [4,2,1,1] => 48
[[[[[],[[],[],[]]]]]] => [1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => {{1,2,3,5,8},{4},{6},{7}} => [5,1,1,1] => 120
[[[[[],[[],[[]]]]]]] => [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => {{1,2,3,5,7,8},{4},{6}} => [6,1,1] => 720
[[[[[],[[[[]]]]]]]] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => {{1,2,3,5,6,7,8},{4}} => [7,1] => 5040
[[[[[[]],[],[],[]]]]] => [1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => {{1,2,3,8},{4,5},{6},{7}} => [4,2,1,1] => 48
[[[[[[]],[[]],[]]]]] => [1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => {{1,2,3,8},{4,5},{6,7}} => [4,2,2] => 96
[[[[[[]],[[],[]]]]]] => [1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => {{1,2,3,6,8},{4,5},{7}} => [5,2,1] => 240
[[[[[[]],[[[]]]]]]] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => {{1,2,3,6,7,8},{4,5}} => [6,2] => 1440
[[[[[[],[]],[],[]]]]] => [1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => {{1,2,3,8},{4,6},{5},{7}} => [4,2,1,1] => 48
[[[[[[[]]],[],[]]]]] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => {{1,2,3,8},{4,5,6},{7}} => [4,3,1] => 144
[[[[[[],[]],[[]]]]]] => [1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => {{1,2,3,7,8},{4,6},{5}} => [5,2,1] => 240
[[[[[[[]]],[[]]]]]] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => {{1,2,3,7,8},{4,5,6}} => [5,3] => 720
[[[[[[],[],[]],[]]]]] => [1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => {{1,2,3,8},{4,7},{5},{6}} => [4,2,1,1] => 48
[[[[[[[]],[]],[]]]]] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => {{1,2,3,8},{4,7},{5,6}} => [4,2,2] => 96
[[[[[[[],[]]],[]]]]] => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => {{1,2,3,8},{4,5,7},{6}} => [4,3,1] => 144
[[[[[[[[]]]],[]]]]] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => {{1,2,3,8},{4,5,6,7}} => [4,4] => 576
[[[[[[],[],[],[]]]]]] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => {{1,2,3,4,8},{5},{6},{7}} => [5,1,1,1] => 120
[[[[[[],[],[[]]]]]]] => [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => {{1,2,3,4,7,8},{5},{6}} => [6,1,1] => 720
[[[[[[],[[],[]]]]]]] => [1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => {{1,2,3,4,6,8},{5},{7}} => [6,1,1] => 720
[[[[[[],[[[]]]]]]]] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => {{1,2,3,4,6,7,8},{5}} => [7,1] => 5040
[[[[[[[]],[],[]]]]]] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => {{1,2,3,4,8},{5,6},{7}} => [5,2,1] => 240
[[[[[[[],[]],[]]]]]] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => {{1,2,3,4,8},{5,7},{6}} => [5,2,1] => 240
[[[[[[[[]]],[]]]]]] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => {{1,2,3,4,8},{5,6,7}} => [5,3] => 720
[[[[[[[],[[]]]]]]]] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => {{1,2,3,4,5,7,8},{6}} => [7,1] => 5040
[[[[[[[[]],[]]]]]]] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => {{1,2,3,4,5,8},{6,7}} => [6,2] => 1440
[[[[[[[[],[]]]]]]]] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,8},{7}} => [7,1] => 5040
[[[[[[[[[]]]]]]]]] => [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] => 40320
[[],[[],[[],[[],[[],[]]]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => {{1},{2,4,6,8,10},{3},{5},{7},{9}} => [5,1,1,1,1,1] => 120
[[],[[],[[],[[[],[]],[]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => {{1},{2,4,6,10},{3},{5},{7,9},{8}} => [4,2,1,1,1,1] => 48
[[],[[],[[[],[]],[[],[]]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => {{1},{2,4,8,10},{3},{5,7},{6},{9}} => [4,2,1,1,1,1] => 48
[[],[[],[[[],[[],[]]],[]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => {{1},{2,4,10},{3},{5,7,9},{6},{8}} => [3,3,1,1,1,1] => 36
[[],[[],[[[[],[]],[]],[]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => {{1},{2,4,10},{3},{5,9},{6,8},{7}} => [3,2,2,1,1,1] => 24
[[],[[[],[]],[[],[[],[]]]]] => [1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => {{1},{2,6,8,10},{3,5},{4},{7},{9}} => [4,2,1,1,1,1] => 48
[[],[[[],[]],[[[],[]],[]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => {{1},{2,6,10},{3,5},{4},{7,9},{8}} => [3,2,2,1,1,1] => 24
[[],[[[],[[],[]]],[[],[]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => {{1},{2,8,10},{3,5,7},{4},{6},{9}} => [3,3,1,1,1,1] => 36
[[],[[[[],[]],[]],[[],[]]]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => {{1},{2,8,10},{3,7},{4,6},{5},{9}} => [3,2,2,1,1,1] => 24
[[],[[[],[[],[[],[]]]],[]]] => [1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => {{1},{2,10},{3,5,7,9},{4},{6},{8}} => [4,2,1,1,1,1] => 48
[[],[[[],[[[],[]],[]]],[]]] => [1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => {{1},{2,10},{3,5,9},{4},{6,8},{7}} => [3,2,2,1,1,1] => 24
[[],[[[[],[]],[[],[]]],[]]] => [1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => {{1},{2,10},{3,7,9},{4,6},{5},{8}} => [3,2,2,1,1,1] => 24
[[],[[[[],[[],[]]],[]],[]]] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => {{1},{2,10},{3,9},{4,6,8},{5},{7}} => [3,2,2,1,1,1] => 24
[[],[[[[[],[]],[]],[]],[]]] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => {{1},{2,10},{3,9},{4,8},{5,7},{6}} => [2,2,2,2,1,1] => 16
[[[],[]],[[],[[],[[],[]]]]] => [1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => {{1,3},{2},{4,6,8,10},{5},{7},{9}} => [4,2,1,1,1,1] => 48
[[[],[]],[[],[[[],[]],[]]]] => [1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => {{1,3},{2},{4,6,10},{5},{7,9},{8}} => [3,2,2,1,1,1] => 24
[[[],[]],[[[],[]],[[],[]]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => {{1,3},{2},{4,8,10},{5,7},{6},{9}} => [3,2,2,1,1,1] => 24
[[[],[]],[[[],[[],[]]],[]]] => [1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => {{1,3},{2},{4,10},{5,7,9},{6},{8}} => [3,2,2,1,1,1] => 24
[[[],[]],[[[[],[]],[]],[]]] => [1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => {{1,3},{2},{4,10},{5,9},{6,8},{7}} => [2,2,2,2,1,1] => 16
[[[],[[],[]]],[[],[[],[]]]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => {{1,3,5},{2},{4},{6,8,10},{7},{9}} => [3,3,1,1,1,1] => 36
[[[],[[],[]]],[[[],[]],[]]] => [1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => {{1,3,5},{2},{4},{6,10},{7,9},{8}} => [3,2,2,1,1,1] => 24
[[[[],[]],[]],[[],[[],[]]]] => [1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => {{1,5},{2,4},{3},{6,8,10},{7},{9}} => [3,2,2,1,1,1] => 24
[[[[],[]],[]],[[[],[]],[]]] => [1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => {{1,5},{2,4},{3},{6,10},{7,9},{8}} => [2,2,2,2,1,1] => 16
[[[],[[],[[],[]]]],[[],[]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => {{1,3,5,7},{2},{4},{6},{8,10},{9}} => [4,2,1,1,1,1] => 48
[[[],[[[],[]],[]]],[[],[]]] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => {{1,3,7},{2},{4,6},{5},{8,10},{9}} => [3,2,2,1,1,1] => 24
[[[[],[]],[[],[]]],[[],[]]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => {{1,5,7},{2,4},{3},{6},{8,10},{9}} => [3,2,2,1,1,1] => 24
[[[[],[[],[]]],[]],[[],[]]] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => {{1,7},{2,4,6},{3},{5},{8,10},{9}} => [3,2,2,1,1,1] => 24
[[[[[],[]],[]],[]],[[],[]]] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => {{1,7},{2,6},{3,5},{4},{8,10},{9}} => [2,2,2,2,1,1] => 16
[[[],[[],[[],[[],[]]]]],[]] => [1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => {{1,3,5,7,9},{2},{4},{6},{8},{10}} => [5,1,1,1,1,1] => 120
[[[],[[],[[[],[]],[]]]],[]] => [1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => {{1,3,5,9},{2},{4},{6,8},{7},{10}} => [4,2,1,1,1,1] => 48
[[[],[[[],[]],[[],[]]]],[]] => [1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0] => {{1,3,7,9},{2},{4,6},{5},{8},{10}} => [4,2,1,1,1,1] => 48
[[[],[[[],[[],[]]],[]]],[]] => [1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0] => {{1,3,9},{2},{4,6,8},{5},{7},{10}} => [3,3,1,1,1,1] => 36
[[[],[[[[],[]],[]],[]]],[]] => [1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0] => {{1,3,9},{2},{4,8},{5,7},{6},{10}} => [3,2,2,1,1,1] => 24
[[[[],[]],[[],[[],[]]]],[]] => [1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => {{1,5,7,9},{2,4},{3},{6},{8},{10}} => [4,2,1,1,1,1] => 48
[[[[],[]],[[[],[]],[]]],[]] => [1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => {{1,5,9},{2,4},{3},{6,8},{7},{10}} => [3,2,2,1,1,1] => 24
[[[[],[[],[]]],[[],[]]],[]] => [1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => {{1,7,9},{2,4,6},{3},{5},{8},{10}} => [3,3,1,1,1,1] => 36
[[[[[],[]],[]],[[],[]]],[]] => [1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0] => {{1,7,9},{2,6},{3,5},{4},{8},{10}} => [3,2,2,1,1,1] => 24
[[[[],[[],[[],[]]]],[]],[]] => [1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => {{1,9},{2,4,6,8},{3},{5},{7},{10}} => [4,2,1,1,1,1] => 48
[[[[],[[[],[]],[]]],[]],[]] => [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0] => {{1,9},{2,4,8},{3},{5,7},{6},{10}} => [3,2,2,1,1,1] => 24
[[[[[],[]],[[],[]]],[]],[]] => [1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0] => {{1,9},{2,6,8},{3,5},{4},{7},{10}} => [3,2,2,1,1,1] => 24
[[[[[],[[],[]]],[]],[]],[]] => [1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0] => {{1,9},{2,8},{3,5,7},{4},{6},{10}} => [3,2,2,1,1,1] => 24
[[[[[[],[]],[]],[]],[]],[]] => [1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => {{1,9},{2,8},{3,7},{4,6},{5},{10}} => [2,2,2,2,1,1] => 16
[[],[[],[[],[[],[[],[[],[]]]]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => {{1},{2,4,6,8,10,12},{3},{5},{7},{9},{11}} => [6,1,1,1,1,1,1] => 720
[[],[[],[[],[[],[[[],[]],[]]]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0] => {{1},{2,4,6,8,12},{3},{5},{7},{9,11},{10}} => [5,2,1,1,1,1,1] => 240
[[],[[],[[],[[[],[]],[[],[]]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0] => {{1},{2,4,6,10,12},{3},{5},{7,9},{8},{11}} => [5,2,1,1,1,1,1] => 240
[[],[[],[[],[[[],[[],[]]],[]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0] => {{1},{2,4,6,12},{3},{5},{7,9,11},{8},{10}} => [4,3,1,1,1,1,1] => 144
[[],[[],[[],[[[[],[]],[]],[]]]]] => [1,0,1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0] => {{1},{2,4,6,12},{3},{5},{7,11},{8,10},{9}} => [4,2,2,1,1,1,1] => 96
[[],[[],[[[],[]],[[],[[],[]]]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0] => {{1},{2,4,8,10,12},{3},{5,7},{6},{9},{11}} => [5,2,1,1,1,1,1] => 240
[[],[[],[[[],[]],[[[],[]],[]]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0] => {{1},{2,4,8,12},{3},{5,7},{6},{9,11},{10}} => [4,2,2,1,1,1,1] => 96
[[],[[],[[[],[[],[]]],[[],[]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0] => {{1},{2,4,10,12},{3},{5,7,9},{6},{8},{11}} => [4,3,1,1,1,1,1] => 144
[[],[[],[[[[],[]],[]],[[],[]]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0] => {{1},{2,4,10,12},{3},{5,9},{6,8},{7},{11}} => [4,2,2,1,1,1,1] => 96
[[],[[],[[[],[[],[[],[]]]],[]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0] => {{1},{2,4,12},{3},{5,7,9,11},{6},{8},{10}} => [4,3,1,1,1,1,1] => 144
[[],[[],[[[],[[[],[]],[]]],[]]]] => [1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0] => {{1},{2,4,12},{3},{5,7,11},{6},{8,10},{9}} => [3,3,2,1,1,1,1] => 72
[[],[[],[[[[],[]],[[],[]]],[]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0] => {{1},{2,4,12},{3},{5,9,11},{6,8},{7},{10}} => [3,3,2,1,1,1,1] => 72
[[],[[],[[[[],[[],[]]],[]],[]]]] => [1,0,1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0] => {{1},{2,4,12},{3},{5,11},{6,8,10},{7},{9}} => [3,3,2,1,1,1,1] => 72
[[],[[],[[[[[],[]],[]],[]],[]]]] => [1,0,1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0] => {{1},{2,4,12},{3},{5,11},{6,10},{7,9},{8}} => [3,2,2,2,1,1,1] => 48
[[],[[[],[]],[[],[[],[[],[]]]]]] => [1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => {{1},{2,6,8,10,12},{3,5},{4},{7},{9},{11}} => [5,2,1,1,1,1,1] => 240
[[],[[[],[]],[[],[[[],[]],[]]]]] => [1,0,1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => {{1},{2,6,8,12},{3,5},{4},{7},{9,11},{10}} => [4,2,2,1,1,1,1] => 96
[[],[[[],[]],[[[],[]],[[],[]]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => {{1},{2,6,10,12},{3,5},{4},{7,9},{8},{11}} => [4,2,2,1,1,1,1] => 96
[[],[[[],[]],[[[],[[],[]]],[]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => {{1},{2,6,12},{3,5},{4},{7,9,11},{8},{10}} => [3,3,2,1,1,1,1] => 72
[[],[[[],[]],[[[[],[]],[]],[]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => {{1},{2,6,12},{3,5},{4},{7,11},{8,10},{9}} => [3,2,2,2,1,1,1] => 48
[[],[[[],[[],[]]],[[],[[],[]]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0] => {{1},{2,8,10,12},{3,5,7},{4},{6},{9},{11}} => [4,3,1,1,1,1,1] => 144
[[],[[[],[[],[]]],[[[],[]],[]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0] => {{1},{2,8,12},{3,5,7},{4},{6},{9,11},{10}} => [3,3,2,1,1,1,1] => 72
[[],[[[[],[]],[]],[[],[[],[]]]]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => {{1},{2,8,10,12},{3,7},{4,6},{5},{9},{11}} => [4,2,2,1,1,1,1] => 96
[[],[[[[],[]],[]],[[[],[]],[]]]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => {{1},{2,8,12},{3,7},{4,6},{5},{9,11},{10}} => [3,2,2,2,1,1,1] => 48
[[],[[[],[[],[[],[]]]],[[],[]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0] => {{1},{2,10,12},{3,5,7,9},{4},{6},{8},{11}} => [4,3,1,1,1,1,1] => 144
[[],[[[],[[[],[]],[]]],[[],[]]]] => [1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0] => {{1},{2,10,12},{3,5,9},{4},{6,8},{7},{11}} => [3,3,2,1,1,1,1] => 72
[[],[[[[],[]],[[],[]]],[[],[]]]] => [1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => {{1},{2,10,12},{3,7,9},{4,6},{5},{8},{11}} => [3,3,2,1,1,1,1] => 72
[[],[[[[],[[],[]]],[]],[[],[]]]] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0] => {{1},{2,10,12},{3,9},{4,6,8},{5},{7},{11}} => [3,3,2,1,1,1,1] => 72
[[],[[[[[],[]],[]],[]],[[],[]]]] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => {{1},{2,10,12},{3,9},{4,8},{5,7},{6},{11}} => [3,2,2,2,1,1,1] => 48
[[],[[[],[[],[[],[[],[]]]]],[]]] => [1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0] => {{1},{2,12},{3,5,7,9,11},{4},{6},{8},{10}} => [5,2,1,1,1,1,1] => 240
[[],[[[],[[],[[[],[]],[]]]],[]]] => [1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0] => {{1},{2,12},{3,5,7,11},{4},{6},{8,10},{9}} => [4,2,2,1,1,1,1] => 96
[[],[[[],[[[],[]],[[],[]]]],[]]] => [1,0,1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0] => {{1},{2,12},{3,5,9,11},{4},{6,8},{7},{10}} => [4,2,2,1,1,1,1] => 96
[[],[[[],[[[],[[],[]]],[]]],[]]] => [1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0] => {{1},{2,12},{3,5,11},{4},{6,8,10},{7},{9}} => [3,3,2,1,1,1,1] => 72
[[],[[[],[[[[],[]],[]],[]]],[]]] => [1,0,1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0] => {{1},{2,12},{3,5,11},{4},{6,10},{7,9},{8}} => [3,2,2,2,1,1,1] => 48
[[],[[[[],[]],[[],[[],[]]]],[]]] => [1,0,1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => {{1},{2,12},{3,7,9,11},{4,6},{5},{8},{10}} => [4,2,2,1,1,1,1] => 96
[[],[[[[],[]],[[[],[]],[]]],[]]] => [1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => {{1},{2,12},{3,7,11},{4,6},{5},{8,10},{9}} => [3,2,2,2,1,1,1] => 48
[[],[[[[],[[],[]]],[[],[]]],[]]] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0] => {{1},{2,12},{3,9,11},{4,6,8},{5},{7},{10}} => [3,3,2,1,1,1,1] => 72
[[],[[[[[],[]],[]],[[],[]]],[]]] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => {{1},{2,12},{3,9,11},{4,8},{5,7},{6},{10}} => [3,2,2,2,1,1,1] => 48
[[],[[[[],[[],[[],[]]]],[]],[]]] => [1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0] => {{1},{2,12},{3,11},{4,6,8,10},{5},{7},{9}} => [4,2,2,1,1,1,1] => 96
[[],[[[[],[[[],[]],[]]],[]],[]]] => [1,0,1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0] => {{1},{2,12},{3,11},{4,6,10},{5},{7,9},{8}} => [3,2,2,2,1,1,1] => 48
[[],[[[[[],[]],[[],[]]],[]],[]]] => [1,0,1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => {{1},{2,12},{3,11},{4,8,10},{5,7},{6},{9}} => [3,2,2,2,1,1,1] => 48
[[],[[[[[],[[],[]]],[]],[]],[]]] => [1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0] => {{1},{2,12},{3,11},{4,10},{5,7,9},{6},{8}} => [3,2,2,2,1,1,1] => 48
[[],[[[[[[],[]],[]],[]],[]],[]]] => [1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => {{1},{2,12},{3,11},{4,10},{5,9},{6,8},{7}} => [2,2,2,2,2,1,1] => 32
[[[],[]],[[],[[],[[],[[],[]]]]]] => [1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => {{1,3},{2},{4,6,8,10,12},{5},{7},{9},{11}} => [5,2,1,1,1,1,1] => 240
[[[],[]],[[],[[],[[[],[]],[]]]]] => [1,1,0,1,0,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => {{1,3},{2},{4,6,8,12},{5},{7},{9,11},{10}} => [4,2,2,1,1,1,1] => 96
[[[],[]],[[],[[[],[]],[[],[]]]]] => [1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => {{1,3},{2},{4,6,10,12},{5},{7,9},{8},{11}} => [4,2,2,1,1,1,1] => 96
[[[],[]],[[],[[[],[[],[]]],[]]]] => [1,1,0,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => {{1,3},{2},{4,6,12},{5},{7,9,11},{8},{10}} => [3,3,2,1,1,1,1] => 72
[[[],[]],[[],[[[[],[]],[]],[]]]] => [1,1,0,1,0,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => {{1,3},{2},{4,6,12},{5},{7,11},{8,10},{9}} => [3,2,2,2,1,1,1] => 48
[[[],[]],[[[],[]],[[],[[],[]]]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => {{1,3},{2},{4,8,10,12},{5,7},{6},{9},{11}} => [4,2,2,1,1,1,1] => 96
[[[],[]],[[[],[]],[[[],[]],[]]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => {{1,3},{2},{4,8,12},{5,7},{6},{9,11},{10}} => [3,2,2,2,1,1,1] => 48
[[[],[]],[[[],[[],[]]],[[],[]]]] => [1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => {{1,3},{2},{4,10,12},{5,7,9},{6},{8},{11}} => [3,3,2,1,1,1,1] => 72
[[[],[]],[[[[],[]],[]],[[],[]]]] => [1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => {{1,3},{2},{4,10,12},{5,9},{6,8},{7},{11}} => [3,2,2,2,1,1,1] => 48
[[[],[]],[[[],[[],[[],[]]]],[]]] => [1,1,0,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => {{1,3},{2},{4,12},{5,7,9,11},{6},{8},{10}} => [4,2,2,1,1,1,1] => 96
[[[],[]],[[[],[[[],[]],[]]],[]]] => [1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => {{1,3},{2},{4,12},{5,7,11},{6},{8,10},{9}} => [3,2,2,2,1,1,1] => 48
[[[],[]],[[[[],[]],[[],[]]],[]]] => [1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => {{1,3},{2},{4,12},{5,9,11},{6,8},{7},{10}} => [3,2,2,2,1,1,1] => 48
[[[],[]],[[[[],[[],[]]],[]],[]]] => [1,1,0,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => {{1,3},{2},{4,12},{5,11},{6,8,10},{7},{9}} => [3,2,2,2,1,1,1] => 48
[[[],[]],[[[[[],[]],[]],[]],[]]] => [1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => {{1,3},{2},{4,12},{5,11},{6,10},{7,9},{8}} => [2,2,2,2,2,1,1] => 32
[[[],[[],[]]],[[],[[],[[],[]]]]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => {{1,3,5},{2},{4},{6,8,10,12},{7},{9},{11}} => [4,3,1,1,1,1,1] => 144
[[[],[[],[]]],[[],[[[],[]],[]]]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => {{1,3,5},{2},{4},{6,8,12},{7},{9,11},{10}} => [3,3,2,1,1,1,1] => 72
[[[],[[],[]]],[[[],[]],[[],[]]]] => [1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => {{1,3,5},{2},{4},{6,10,12},{7,9},{8},{11}} => [3,3,2,1,1,1,1] => 72
[[[],[[],[]]],[[[],[[],[]]],[]]] => [1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => {{1,3,5},{2},{4},{6,12},{7,9,11},{8},{10}} => [3,3,2,1,1,1,1] => 72
[[[],[[],[]]],[[[[],[]],[]],[]]] => [1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => {{1,3,5},{2},{4},{6,12},{7,11},{8,10},{9}} => [3,2,2,2,1,1,1] => 48
[[[[],[]],[]],[[],[[],[[],[]]]]] => [1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => {{1,5},{2,4},{3},{6,8,10,12},{7},{9},{11}} => [4,2,2,1,1,1,1] => 96
[[[[],[]],[]],[[],[[[],[]],[]]]] => [1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => {{1,5},{2,4},{3},{6,8,12},{7},{9,11},{10}} => [3,2,2,2,1,1,1] => 48
[[[[],[]],[]],[[[],[]],[[],[]]]] => [1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => {{1,5},{2,4},{3},{6,10,12},{7,9},{8},{11}} => [3,2,2,2,1,1,1] => 48
[[[[],[]],[]],[[[],[[],[]]],[]]] => [1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => {{1,5},{2,4},{3},{6,12},{7,9,11},{8},{10}} => [3,2,2,2,1,1,1] => 48
[[[[],[]],[]],[[[[],[]],[]],[]]] => [1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => {{1,5},{2,4},{3},{6,12},{7,11},{8,10},{9}} => [2,2,2,2,2,1,1] => 32
[[[],[[],[[],[]]]],[[],[[],[]]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0] => {{1,3,5,7},{2},{4},{6},{8,10,12},{9},{11}} => [4,3,1,1,1,1,1] => 144
[[[],[[],[[],[]]]],[[[],[]],[]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0] => {{1,3,5,7},{2},{4},{6},{8,12},{9,11},{10}} => [4,2,2,1,1,1,1] => 96
[[[],[[[],[]],[]]],[[],[[],[]]]] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => {{1,3,7},{2},{4,6},{5},{8,10,12},{9},{11}} => [3,3,2,1,1,1,1] => 72
[[[],[[[],[]],[]]],[[[],[]],[]]] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => {{1,3,7},{2},{4,6},{5},{8,12},{9,11},{10}} => [3,2,2,2,1,1,1] => 48
[[[[],[]],[[],[]]],[[],[[],[]]]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => {{1,5,7},{2,4},{3},{6},{8,10,12},{9},{11}} => [3,3,2,1,1,1,1] => 72
[[[[],[]],[[],[]]],[[[],[]],[]]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => {{1,5,7},{2,4},{3},{6},{8,12},{9,11},{10}} => [3,2,2,2,1,1,1] => 48
[[[[],[[],[]]],[]],[[],[[],[]]]] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => {{1,7},{2,4,6},{3},{5},{8,10,12},{9},{11}} => [3,3,2,1,1,1,1] => 72
[[[[],[[],[]]],[]],[[[],[]],[]]] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => {{1,7},{2,4,6},{3},{5},{8,12},{9,11},{10}} => [3,2,2,2,1,1,1] => 48
[[[[[],[]],[]],[]],[[],[[],[]]]] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => {{1,7},{2,6},{3,5},{4},{8,10,12},{9},{11}} => [3,2,2,2,1,1,1] => 48
[[[[[],[]],[]],[]],[[[],[]],[]]] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => {{1,7},{2,6},{3,5},{4},{8,12},{9,11},{10}} => [2,2,2,2,2,1,1] => 32
[[[],[[],[[],[[],[]]]]],[[],[]]] => [1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0] => {{1,3,5,7,9},{2},{4},{6},{8},{10,12},{11}} => [5,2,1,1,1,1,1] => 240
[[[],[[],[[[],[]],[]]]],[[],[]]] => [1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0] => {{1,3,5,9},{2},{4},{6,8},{7},{10,12},{11}} => [4,2,2,1,1,1,1] => 96
[[[],[[[],[]],[[],[]]]],[[],[]]] => [1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => {{1,3,7,9},{2},{4,6},{5},{8},{10,12},{11}} => [4,2,2,1,1,1,1] => 96
[[[],[[[],[[],[]]],[]]],[[],[]]] => [1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0] => {{1,3,9},{2},{4,6,8},{5},{7},{10,12},{11}} => [3,3,2,1,1,1,1] => 72
[[[],[[[[],[]],[]],[]]],[[],[]]] => [1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => {{1,3,9},{2},{4,8},{5,7},{6},{10,12},{11}} => [3,2,2,2,1,1,1] => 48
[[[[],[]],[[],[[],[]]]],[[],[]]] => [1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => {{1,5,7,9},{2,4},{3},{6},{8},{10,12},{11}} => [4,2,2,1,1,1,1] => 96
[[[[],[]],[[[],[]],[]]],[[],[]]] => [1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => {{1,5,9},{2,4},{3},{6,8},{7},{10,12},{11}} => [3,2,2,2,1,1,1] => 48
[[[[],[[],[]]],[[],[]]],[[],[]]] => [1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => {{1,7,9},{2,4,6},{3},{5},{8},{10,12},{11}} => [3,3,2,1,1,1,1] => 72
[[[[[],[]],[]],[[],[]]],[[],[]]] => [1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => {{1,7,9},{2,6},{3,5},{4},{8},{10,12},{11}} => [3,2,2,2,1,1,1] => 48
[[[[],[[],[[],[]]]],[]],[[],[]]] => [1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0] => {{1,9},{2,4,6,8},{3},{5},{7},{10,12},{11}} => [4,2,2,1,1,1,1] => 96
[[[[],[[[],[]],[]]],[]],[[],[]]] => [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => {{1,9},{2,4,8},{3},{5,7},{6},{10,12},{11}} => [3,2,2,2,1,1,1] => 48
[[[[[],[]],[[],[]]],[]],[[],[]]] => [1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => {{1,9},{2,6,8},{3,5},{4},{7},{10,12},{11}} => [3,2,2,2,1,1,1] => 48
[[[[[],[[],[]]],[]],[]],[[],[]]] => [1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => {{1,9},{2,8},{3,5,7},{4},{6},{10,12},{11}} => [3,2,2,2,1,1,1] => 48
[[[[[[],[]],[]],[]],[]],[[],[]]] => [1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => {{1,9},{2,8},{3,7},{4,6},{5},{10,12},{11}} => [2,2,2,2,2,1,1] => 32
[[[],[[],[[],[[],[[],[]]]]]],[]] => [1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0] => {{1,3,5,7,9,11},{2},{4},{6},{8},{10},{12}} => [6,1,1,1,1,1,1] => 720
[[[],[[],[[],[[[],[]],[]]]]],[]] => [1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0] => {{1,3,5,7,11},{2},{4},{6},{8,10},{9},{12}} => [5,2,1,1,1,1,1] => 240
[[[],[[],[[[],[]],[[],[]]]]],[]] => [1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0,1,0] => {{1,3,5,9,11},{2},{4},{6,8},{7},{10},{12}} => [5,2,1,1,1,1,1] => 240
[[[],[[],[[[],[[],[]]],[]]]],[]] => [1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0,1,0] => {{1,3,5,11},{2},{4},{6,8,10},{7},{9},{12}} => [4,3,1,1,1,1,1] => 144
[[[],[[],[[[[],[]],[]],[]]]],[]] => [1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,1,0] => {{1,3,5,11},{2},{4},{6,10},{7,9},{8},{12}} => [4,2,2,1,1,1,1] => 96
[[[],[[[],[]],[[],[[],[]]]]],[]] => [1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => {{1,3,7,9,11},{2},{4,6},{5},{8},{10},{12}} => [5,2,1,1,1,1,1] => 240
[[[],[[[],[]],[[[],[]],[]]]],[]] => [1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => {{1,3,7,11},{2},{4,6},{5},{8,10},{9},{12}} => [4,2,2,1,1,1,1] => 96
[[[],[[[],[[],[]]],[[],[]]]],[]] => [1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0,1,0] => {{1,3,9,11},{2},{4,6,8},{5},{7},{10},{12}} => [4,3,1,1,1,1,1] => 144
[[[],[[[[],[]],[]],[[],[]]]],[]] => [1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0,1,0] => {{1,3,9,11},{2},{4,8},{5,7},{6},{10},{12}} => [4,2,2,1,1,1,1] => 96
[[[],[[[],[[],[[],[]]]],[]]],[]] => [1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0,1,0] => {{1,3,11},{2},{4,6,8,10},{5},{7},{9},{12}} => [4,3,1,1,1,1,1] => 144
[[[],[[[],[[[],[]],[]]],[]]],[]] => [1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0,1,0] => {{1,3,11},{2},{4,6,10},{5},{7,9},{8},{12}} => [3,3,2,1,1,1,1] => 72
[[[],[[[[],[]],[[],[]]],[]]],[]] => [1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0,1,0] => {{1,3,11},{2},{4,8,10},{5,7},{6},{9},{12}} => [3,3,2,1,1,1,1] => 72
[[[],[[[[],[[],[]]],[]],[]]],[]] => [1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0] => {{1,3,11},{2},{4,10},{5,7,9},{6},{8},{12}} => [3,3,2,1,1,1,1] => 72
[[[],[[[[[],[]],[]],[]],[]]],[]] => [1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0] => {{1,3,11},{2},{4,10},{5,9},{6,8},{7},{12}} => [3,2,2,2,1,1,1] => 48
[[[[],[]],[[],[[],[[],[]]]]],[]] => [1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => {{1,5,7,9,11},{2,4},{3},{6},{8},{10},{12}} => [5,2,1,1,1,1,1] => 240
[[[[],[]],[[],[[[],[]],[]]]],[]] => [1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => {{1,5,7,11},{2,4},{3},{6},{8,10},{9},{12}} => [4,2,2,1,1,1,1] => 96
[[[[],[]],[[[],[]],[[],[]]]],[]] => [1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0] => {{1,5,9,11},{2,4},{3},{6,8},{7},{10},{12}} => [4,2,2,1,1,1,1] => 96
[[[[],[]],[[[],[[],[]]],[]]],[]] => [1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0] => {{1,5,11},{2,4},{3},{6,8,10},{7},{9},{12}} => [3,3,2,1,1,1,1] => 72
[[[[],[]],[[[[],[]],[]],[]]],[]] => [1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0] => {{1,5,11},{2,4},{3},{6,10},{7,9},{8},{12}} => [3,2,2,2,1,1,1] => 48
[[[[],[[],[]]],[[],[[],[]]]],[]] => [1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => {{1,7,9,11},{2,4,6},{3},{5},{8},{10},{12}} => [4,3,1,1,1,1,1] => 144
[[[[],[[],[]]],[[[],[]],[]]],[]] => [1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => {{1,7,11},{2,4,6},{3},{5},{8,10},{9},{12}} => [3,3,2,1,1,1,1] => 72
[[[[[],[]],[]],[[],[[],[]]]],[]] => [1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => {{1,7,9,11},{2,6},{3,5},{4},{8},{10},{12}} => [4,2,2,1,1,1,1] => 96
[[[[[],[]],[]],[[[],[]],[]]],[]] => [1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => {{1,7,11},{2,6},{3,5},{4},{8,10},{9},{12}} => [3,2,2,2,1,1,1] => 48
[[[[],[[],[[],[]]]],[[],[]]],[]] => [1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0,1,0] => {{1,9,11},{2,4,6,8},{3},{5},{7},{10},{12}} => [4,3,1,1,1,1,1] => 144
[[[[],[[[],[]],[]]],[[],[]]],[]] => [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => {{1,9,11},{2,4,8},{3},{5,7},{6},{10},{12}} => [3,3,2,1,1,1,1] => 72
[[[[[],[]],[[],[]]],[[],[]]],[]] => [1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => {{1,9,11},{2,6,8},{3,5},{4},{7},{10},{12}} => [3,3,2,1,1,1,1] => 72
[[[[[],[[],[]]],[]],[[],[]]],[]] => [1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0,1,0] => {{1,9,11},{2,8},{3,5,7},{4},{6},{10},{12}} => [3,3,2,1,1,1,1] => 72
[[[[[[],[]],[]],[]],[[],[]]],[]] => [1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0] => {{1,9,11},{2,8},{3,7},{4,6},{5},{10},{12}} => [3,2,2,2,1,1,1] => 48
[[[[],[[],[[],[[],[]]]]],[]],[]] => [1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,1,0] => {{1,11},{2,4,6,8,10},{3},{5},{7},{9},{12}} => [5,2,1,1,1,1,1] => 240
[[[[],[[],[[[],[]],[]]]],[]],[]] => [1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0,1,0] => {{1,11},{2,4,6,10},{3},{5},{7,9},{8},{12}} => [4,2,2,1,1,1,1] => 96
[[[[],[[[],[]],[[],[]]]],[]],[]] => [1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => {{1,11},{2,4,8,10},{3},{5,7},{6},{9},{12}} => [4,2,2,1,1,1,1] => 96
[[[[],[[[],[[],[]]],[]]],[]],[]] => [1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0] => {{1,11},{2,4,10},{3},{5,7,9},{6},{8},{12}} => [3,3,2,1,1,1,1] => 72
[[[[],[[[[],[]],[]],[]]],[]],[]] => [1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0] => {{1,11},{2,4,10},{3},{5,9},{6,8},{7},{12}} => [3,2,2,2,1,1,1] => 48
[[[[[],[]],[[],[[],[]]]],[]],[]] => [1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => {{1,11},{2,6,8,10},{3,5},{4},{7},{9},{12}} => [4,2,2,1,1,1,1] => 96
[[[[[],[]],[[[],[]],[]]],[]],[]] => [1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0] => {{1,11},{2,6,10},{3,5},{4},{7,9},{8},{12}} => [3,2,2,2,1,1,1] => 48
[[[[[],[[],[]]],[[],[]]],[]],[]] => [1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0,1,0] => {{1,11},{2,8,10},{3,5,7},{4},{6},{9},{12}} => [3,3,2,1,1,1,1] => 72
[[[[[[],[]],[]],[[],[]]],[]],[]] => [1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0] => {{1,11},{2,8,10},{3,7},{4,6},{5},{9},{12}} => [3,2,2,2,1,1,1] => 48
[[[[[],[[],[[],[]]]],[]],[]],[]] => [1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0] => {{1,11},{2,10},{3,5,7,9},{4},{6},{8},{12}} => [4,2,2,1,1,1,1] => 96
[[[[[],[[[],[]],[]]],[]],[]],[]] => [1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0] => {{1,11},{2,10},{3,5,9},{4},{6,8},{7},{12}} => [3,2,2,2,1,1,1] => 48
[[[[[[],[]],[[],[]]],[]],[]],[]] => [1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0] => {{1,11},{2,10},{3,7,9},{4,6},{5},{8},{12}} => [3,2,2,2,1,1,1] => 48
[[[[[[],[[],[]]],[]],[]],[]],[]] => [1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0] => {{1,11},{2,10},{3,9},{4,6,8},{5},{7},{12}} => [3,2,2,2,1,1,1] => 48
[[[[[[[],[]],[]],[]],[]],[]],[]] => [1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => {{1,11},{2,10},{3,9},{4,8},{5,7},{6},{12}} => [2,2,2,2,2,1,1] => 32
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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 1,3,0,0,0,1 1,6,0,2,0,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1
F3=q+q2
F4=q+3 q2+q6
F5=q+6 q2+2 q4+4 q6+q24
F6=q+10 q2+10 q4+10 q6+5 q12+5 q24+q120
F7=q+15 q2+30 q4+20 q6+5 q8+30 q12+15 q24+3 q36+6 q48+6 q120+q720
F8=q+21 q2+70 q4+35 q6+35 q8+105 q12+56 q24+21 q36+42 q48+21 q120+7 q144+7 q240+7 q720+q5040
Description
The product of the factorials of the parts.
Map
to noncrossing partition
Description
Biane's map to noncrossing set partitions.
Map
to Dyck path
Description
Return the Dyck path of the corresponding ordered tree induced by the recurrence of the Catalan numbers, see wikipedia:Catalan_number.
This sends the maximal height of the Dyck path to the depth of the tree.
This sends the maximal height of the Dyck path to the depth of the tree.
Map
shape
Description
Sends a set partition to the integer partition obtained by the sizes of the blocks.
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