Identifier
-
Mp00051:
Ordered trees
—to Dyck path⟶
Dyck paths
Mp00023: Dyck paths —to non-crossing permutation⟶ Permutations
Mp00108: Permutations —cycle type⟶ Integer partitions
St000147: Integer partitions ⟶ ℤ
Values
[] => [] => [] => [] => 0
[[]] => [1,0] => [1] => [1] => 1
[[],[]] => [1,0,1,0] => [1,2] => [1,1] => 1
[[[]]] => [1,1,0,0] => [2,1] => [2] => 2
[[],[],[]] => [1,0,1,0,1,0] => [1,2,3] => [1,1,1] => 1
[[],[[]]] => [1,0,1,1,0,0] => [1,3,2] => [2,1] => 2
[[[]],[]] => [1,1,0,0,1,0] => [2,1,3] => [2,1] => 2
[[[],[]]] => [1,1,0,1,0,0] => [2,3,1] => [3] => 3
[[[[]]]] => [1,1,1,0,0,0] => [3,2,1] => [2,1] => 2
[[],[],[],[]] => [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] => [1,2,4,3] => [2,1,1] => 2
[[],[[]],[]] => [1,0,1,1,0,0,1,0] => [1,3,2,4] => [2,1,1] => 2
[[],[[],[]]] => [1,0,1,1,0,1,0,0] => [1,3,4,2] => [3,1] => 3
[[],[[[]]]] => [1,0,1,1,1,0,0,0] => [1,4,3,2] => [2,1,1] => 2
[[[]],[],[]] => [1,1,0,0,1,0,1,0] => [2,1,3,4] => [2,1,1] => 2
[[[]],[[]]] => [1,1,0,0,1,1,0,0] => [2,1,4,3] => [2,2] => 2
[[[],[]],[]] => [1,1,0,1,0,0,1,0] => [2,3,1,4] => [3,1] => 3
[[[[]]],[]] => [1,1,1,0,0,0,1,0] => [3,2,1,4] => [2,1,1] => 2
[[[],[],[]]] => [1,1,0,1,0,1,0,0] => [2,3,4,1] => [4] => 4
[[[],[[]]]] => [1,1,0,1,1,0,0,0] => [2,4,3,1] => [3,1] => 3
[[[[]],[]]] => [1,1,1,0,0,1,0,0] => [3,2,4,1] => [3,1] => 3
[[[[],[]]]] => [1,1,1,0,1,0,0,0] => [4,2,3,1] => [2,1,1] => 2
[[[[[]]]]] => [1,1,1,1,0,0,0,0] => [4,3,2,1] => [2,2] => 2
[[],[],[],[],[]] => [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] => [1,2,3,5,4] => [2,1,1,1] => 2
[[],[],[[]],[]] => [1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [2,1,1,1] => 2
[[],[],[[],[]]] => [1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [3,1,1] => 3
[[],[],[[[]]]] => [1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => [2,1,1,1] => 2
[[],[[]],[],[]] => [1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [2,1,1,1] => 2
[[],[[]],[[]]] => [1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [2,2,1] => 2
[[],[[],[]],[]] => [1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [3,1,1] => 3
[[],[[[]]],[]] => [1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => [2,1,1,1] => 2
[[],[[],[],[]]] => [1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [4,1] => 4
[[],[[],[[]]]] => [1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => [3,1,1] => 3
[[],[[[]],[]]] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => [3,1,1] => 3
[[],[[[],[]]]] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => [2,1,1,1] => 2
[[],[[[[]]]]] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => [2,2,1] => 2
[[[]],[],[],[]] => [1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [2,1,1,1] => 2
[[[]],[],[[]]] => [1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [2,2,1] => 2
[[[]],[[]],[]] => [1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [2,2,1] => 2
[[[]],[[],[]]] => [1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [3,2] => 3
[[[]],[[[]]]] => [1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => [2,2,1] => 2
[[[],[]],[],[]] => [1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [3,1,1] => 3
[[[[]]],[],[]] => [1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => [2,1,1,1] => 2
[[[],[]],[[]]] => [1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [3,2] => 3
[[[[]]],[[]]] => [1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => [2,2,1] => 2
[[[],[],[]],[]] => [1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [4,1] => 4
[[[],[[]]],[]] => [1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => [3,1,1] => 3
[[[[]],[]],[]] => [1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => [3,1,1] => 3
[[[[],[]]],[]] => [1,1,1,0,1,0,0,0,1,0] => [4,2,3,1,5] => [2,1,1,1] => 2
[[[[[]]]],[]] => [1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => [2,2,1] => 2
[[[],[],[],[]]] => [1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [5] => 5
[[[],[],[[]]]] => [1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1] => [4,1] => 4
[[[],[[]],[]]] => [1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => [4,1] => 4
[[[],[[],[]]]] => [1,1,0,1,1,0,1,0,0,0] => [2,5,3,4,1] => [3,1,1] => 3
[[[],[[[]]]]] => [1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => [3,2] => 3
[[[[]],[],[]]] => [1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => [4,1] => 4
[[[[]],[[]]]] => [1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => [3,1,1] => 3
[[[[],[]],[]]] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => [3,1,1] => 3
[[[[[]]],[]]] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => [3,2] => 3
[[[[],[],[]]]] => [1,1,1,0,1,0,1,0,0,0] => [5,2,3,4,1] => [2,1,1,1] => 2
[[[[],[[]]]]] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => [2,2,1] => 2
[[[[[]],[]]]] => [1,1,1,1,0,0,1,0,0,0] => [5,3,2,4,1] => [2,2,1] => 2
[[[[[],[]]]]] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => [3,2] => 3
[[[[[[]]]]]] => [1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => [2,2,1] => 2
[[],[],[],[],[],[]] => [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] => [1,2,3,4,6,5] => [2,1,1,1,1] => 2
[[],[],[],[[]],[]] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => [2,1,1,1,1] => 2
[[],[],[],[[],[]]] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [3,1,1,1] => 3
[[],[],[],[[[]]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => [2,1,1,1,1] => 2
[[],[],[[]],[],[]] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [2,1,1,1,1] => 2
[[],[],[[]],[[]]] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [2,2,1,1] => 2
[[],[],[[],[]],[]] => [1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [3,1,1,1] => 3
[[],[],[[[]]],[]] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => [2,1,1,1,1] => 2
[[],[],[[],[],[]]] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [4,1,1] => 4
[[],[],[[],[[]]]] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => [3,1,1,1] => 3
[[],[],[[[]],[]]] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => [3,1,1,1] => 3
[[],[],[[[],[]]]] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => [2,1,1,1,1] => 2
[[],[],[[[[]]]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => [2,2,1,1] => 2
[[],[[]],[],[],[]] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [2,1,1,1,1] => 2
[[],[[]],[],[[]]] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [2,2,1,1] => 2
[[],[[]],[[]],[]] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [2,2,1,1] => 2
[[],[[]],[[],[]]] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [3,2,1] => 3
[[],[[]],[[[]]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => [2,2,1,1] => 2
[[],[[],[]],[],[]] => [1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [3,1,1,1] => 3
[[],[[[]]],[],[]] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => [2,1,1,1,1] => 2
[[],[[],[]],[[]]] => [1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [3,2,1] => 3
[[],[[[]]],[[]]] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => [2,2,1,1] => 2
[[],[[],[],[]],[]] => [1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [4,1,1] => 4
[[],[[],[[]]],[]] => [1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => [3,1,1,1] => 3
[[],[[[]],[]],[]] => [1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => [3,1,1,1] => 3
[[],[[[],[]]],[]] => [1,0,1,1,1,0,1,0,0,0,1,0] => [1,5,3,4,2,6] => [2,1,1,1,1] => 2
[[],[[[[]]]],[]] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => [2,2,1,1] => 2
[[],[[],[],[],[]]] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [5,1] => 5
[[],[[],[],[[]]]] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => [4,1,1] => 4
[[],[[],[[]],[]]] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => [4,1,1] => 4
[[],[[],[[],[]]]] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,6,4,5,2] => [3,1,1,1] => 3
[[],[[],[[[]]]]] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => [3,2,1] => 3
[[],[[[]],[],[]]] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => [4,1,1] => 4
[[],[[[]],[[]]]] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => [3,1,1,1] => 3
[[],[[[],[]],[]]] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => [3,1,1,1] => 3
>>> Load all 1537 entries. <<<[[],[[[[]]],[]]] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => [3,2,1] => 3
[[],[[[],[],[]]]] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,6,3,4,5,2] => [2,1,1,1,1] => 2
[[],[[[],[[]]]]] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,6,3,5,4,2] => [2,2,1,1] => 2
[[],[[[[]],[]]]] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,6,4,3,5,2] => [2,2,1,1] => 2
[[],[[[[],[]]]]] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,6,4,5,3,2] => [3,2,1] => 3
[[],[[[[[]]]]]] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => [2,2,1,1] => 2
[[[]],[],[],[],[]] => [1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [2,1,1,1,1] => 2
[[[]],[],[],[[]]] => [1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => [2,2,1,1] => 2
[[[]],[],[[]],[]] => [1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [2,2,1,1] => 2
[[[]],[],[[],[]]] => [1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [3,2,1] => 3
[[[]],[],[[[]]]] => [1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => [2,2,1,1] => 2
[[[]],[[]],[],[]] => [1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [2,2,1,1] => 2
[[[]],[[]],[[]]] => [1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [2,2,2] => 2
[[[]],[[],[]],[]] => [1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [3,2,1] => 3
[[[]],[[[]]],[]] => [1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => [2,2,1,1] => 2
[[[]],[[],[],[]]] => [1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [4,2] => 4
[[[]],[[],[[]]]] => [1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => [3,2,1] => 3
[[[]],[[[]],[]]] => [1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => [3,2,1] => 3
[[[]],[[[],[]]]] => [1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,6,4,5,3] => [2,2,1,1] => 2
[[[]],[[[[]]]]] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => [2,2,2] => 2
[[[],[]],[],[],[]] => [1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [3,1,1,1] => 3
[[[[]]],[],[],[]] => [1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => [2,1,1,1,1] => 2
[[[],[]],[],[[]]] => [1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [3,2,1] => 3
[[[[]]],[],[[]]] => [1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => [2,2,1,1] => 2
[[[],[]],[[]],[]] => [1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [3,2,1] => 3
[[[[]]],[[]],[]] => [1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => [2,2,1,1] => 2
[[[],[]],[[],[]]] => [1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [3,3] => 3
[[[],[]],[[[]]]] => [1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => [3,2,1] => 3
[[[[]]],[[],[]]] => [1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => [3,2,1] => 3
[[[[]]],[[[]]]] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => [2,2,1,1] => 2
[[[],[],[]],[],[]] => [1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [4,1,1] => 4
[[[],[[]]],[],[]] => [1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => [3,1,1,1] => 3
[[[[]],[]],[],[]] => [1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => [3,1,1,1] => 3
[[[[],[]]],[],[]] => [1,1,1,0,1,0,0,0,1,0,1,0] => [4,2,3,1,5,6] => [2,1,1,1,1] => 2
[[[[[]]]],[],[]] => [1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => [2,2,1,1] => 2
[[[],[],[]],[[]]] => [1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [4,2] => 4
[[[],[[]]],[[]]] => [1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => [3,2,1] => 3
[[[[]],[]],[[]]] => [1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => [3,2,1] => 3
[[[[],[]]],[[]]] => [1,1,1,0,1,0,0,0,1,1,0,0] => [4,2,3,1,6,5] => [2,2,1,1] => 2
[[[[[]]]],[[]]] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => [2,2,2] => 2
[[[],[],[],[]],[]] => [1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [5,1] => 5
[[[],[],[[]]],[]] => [1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => [4,1,1] => 4
[[[],[[]],[]],[]] => [1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => [4,1,1] => 4
[[[],[[],[]]],[]] => [1,1,0,1,1,0,1,0,0,0,1,0] => [2,5,3,4,1,6] => [3,1,1,1] => 3
[[[],[[[]]]],[]] => [1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => [3,2,1] => 3
[[[[]],[],[]],[]] => [1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => [4,1,1] => 4
[[[[]],[[]]],[]] => [1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => [3,1,1,1] => 3
[[[[],[]],[]],[]] => [1,1,1,0,1,0,0,1,0,0,1,0] => [4,2,3,5,1,6] => [3,1,1,1] => 3
[[[[[]]],[]],[]] => [1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => [3,2,1] => 3
[[[[],[],[]]],[]] => [1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,3,4,1,6] => [2,1,1,1,1] => 2
[[[[],[[]]]],[]] => [1,1,1,0,1,1,0,0,0,0,1,0] => [5,2,4,3,1,6] => [2,2,1,1] => 2
[[[[[]],[]]],[]] => [1,1,1,1,0,0,1,0,0,0,1,0] => [5,3,2,4,1,6] => [2,2,1,1] => 2
[[[[[],[]]]],[]] => [1,1,1,1,0,1,0,0,0,0,1,0] => [5,3,4,2,1,6] => [3,2,1] => 3
[[[[[[]]]]],[]] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => [2,2,1,1] => 2
[[[],[],[],[],[]]] => [1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [6] => 6
[[[],[],[],[[]]]] => [1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,5,1] => [5,1] => 5
[[[],[],[[]],[]]] => [1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,4,6,1] => [5,1] => 5
[[[],[],[[],[]]]] => [1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,6,4,5,1] => [4,1,1] => 4
[[[],[],[[[]]]]] => [1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => [4,2] => 4
[[[],[[]],[],[]]] => [1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,3,5,6,1] => [5,1] => 5
[[[],[[]],[[]]]] => [1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => [4,1,1] => 4
[[[],[[],[]],[]]] => [1,1,0,1,1,0,1,0,0,1,0,0] => [2,5,3,4,6,1] => [4,1,1] => 4
[[[],[[[]]],[]]] => [1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => [4,2] => 4
[[[],[[],[],[]]]] => [1,1,0,1,1,0,1,0,1,0,0,0] => [2,6,3,4,5,1] => [3,1,1,1] => 3
[[[],[[],[[]]]]] => [1,1,0,1,1,0,1,1,0,0,0,0] => [2,6,3,5,4,1] => [3,2,1] => 3
[[[],[[[]],[]]]] => [1,1,0,1,1,1,0,0,1,0,0,0] => [2,6,4,3,5,1] => [3,2,1] => 3
[[[],[[[],[]]]]] => [1,1,0,1,1,1,0,1,0,0,0,0] => [2,6,4,5,3,1] => [3,3] => 3
[[[],[[[[]]]]]] => [1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => [3,2,1] => 3
[[[[]],[],[],[]]] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => [5,1] => 5
[[[[]],[],[[]]]] => [1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => [4,1,1] => 4
[[[[]],[[]],[]]] => [1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => [4,1,1] => 4
[[[[]],[[],[]]]] => [1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,6,4,5,1] => [3,1,1,1] => 3
[[[[]],[[[]]]]] => [1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => [3,2,1] => 3
[[[[],[]],[],[]]] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => [4,1,1] => 4
[[[[[]]],[],[]]] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => [4,2] => 4
[[[[],[]],[[]]]] => [1,1,1,0,1,0,0,1,1,0,0,0] => [4,2,3,6,5,1] => [3,1,1,1] => 3
[[[[[]]],[[]]]] => [1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => [3,2,1] => 3
[[[[],[],[]],[]]] => [1,1,1,0,1,0,1,0,0,1,0,0] => [5,2,3,4,6,1] => [3,1,1,1] => 3
[[[[],[[]]],[]]] => [1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,4,3,6,1] => [3,2,1] => 3
[[[[[]],[]],[]]] => [1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => [3,2,1] => 3
[[[[[],[]]],[]]] => [1,1,1,1,0,1,0,0,0,1,0,0] => [5,3,4,2,6,1] => [3,3] => 3
[[[[[[]]]],[]]] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => [3,2,1] => 3
[[[[],[],[],[]]]] => [1,1,1,0,1,0,1,0,1,0,0,0] => [6,2,3,4,5,1] => [2,1,1,1,1] => 2
[[[[],[],[[]]]]] => [1,1,1,0,1,0,1,1,0,0,0,0] => [6,2,3,5,4,1] => [2,2,1,1] => 2
[[[[],[[]],[]]]] => [1,1,1,0,1,1,0,0,1,0,0,0] => [6,2,4,3,5,1] => [2,2,1,1] => 2
[[[[],[[],[]]]]] => [1,1,1,0,1,1,0,1,0,0,0,0] => [6,2,4,5,3,1] => [3,2,1] => 3
[[[[],[[[]]]]]] => [1,1,1,0,1,1,1,0,0,0,0,0] => [6,2,5,4,3,1] => [2,2,1,1] => 2
[[[[[]],[],[]]]] => [1,1,1,1,0,0,1,0,1,0,0,0] => [6,3,2,4,5,1] => [2,2,1,1] => 2
[[[[[]],[[]]]]] => [1,1,1,1,0,0,1,1,0,0,0,0] => [6,3,2,5,4,1] => [2,2,2] => 2
[[[[[],[]],[]]]] => [1,1,1,1,0,1,0,0,1,0,0,0] => [6,3,4,2,5,1] => [3,2,1] => 3
[[[[[[]]],[]]]] => [1,1,1,1,1,0,0,0,1,0,0,0] => [6,4,3,2,5,1] => [2,2,1,1] => 2
[[[[[],[],[]]]]] => [1,1,1,1,0,1,0,1,0,0,0,0] => [6,3,4,5,2,1] => [4,2] => 4
[[[[[],[[]]]]]] => [1,1,1,1,0,1,1,0,0,0,0,0] => [6,3,5,4,2,1] => [3,2,1] => 3
[[[[[[]],[]]]]] => [1,1,1,1,1,0,0,1,0,0,0,0] => [6,4,3,5,2,1] => [3,2,1] => 3
[[[[[[],[]]]]]] => [1,1,1,1,1,0,1,0,0,0,0,0] => [6,5,3,4,2,1] => [2,2,1,1] => 2
[[[[[[[]]]]]]] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => [2,2,2] => 2
[[],[],[],[],[],[],[]] => [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] => [1,2,3,4,5,7,6] => [2,1,1,1,1,1] => 2
[[],[],[],[],[[]],[]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => [2,1,1,1,1,1] => 2
[[],[],[],[],[[],[]]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => [3,1,1,1,1] => 3
[[],[],[],[],[[[]]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => [2,1,1,1,1,1] => 2
[[],[],[],[[]],[],[]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,6,7] => [2,1,1,1,1,1] => 2
[[],[],[],[[]],[[]]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => [2,2,1,1,1] => 2
[[],[],[],[[],[]],[]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,5,6,4,7] => [3,1,1,1,1] => 3
[[],[],[],[[[]]],[]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,5,4,7] => [2,1,1,1,1,1] => 2
[[],[],[],[[],[],[]]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => [4,1,1,1] => 4
[[],[],[],[[],[[]]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,6,4] => [3,1,1,1,1] => 3
[[],[],[],[[[]],[]]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => [3,1,1,1,1] => 3
[[],[],[],[[[],[]]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,7,5,6,4] => [2,1,1,1,1,1] => 2
[[],[],[],[[[[]]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,6,5,4] => [2,2,1,1,1] => 2
[[],[],[[]],[],[],[]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7] => [2,1,1,1,1,1] => 2
[[],[],[[]],[],[[]]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => [2,2,1,1,1] => 2
[[],[],[[]],[[]],[]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => [2,2,1,1,1] => 2
[[],[],[[]],[[],[]]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,7,5] => [3,2,1,1] => 3
[[],[],[[]],[[[]]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,6,5] => [2,2,1,1,1] => 2
[[],[],[[],[]],[],[]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,5,3,6,7] => [3,1,1,1,1] => 3
[[],[],[[[]]],[],[]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,4,3,6,7] => [2,1,1,1,1,1] => 2
[[],[],[[],[]],[[]]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6] => [3,2,1,1] => 3
[[],[],[[[]]],[[]]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,4,3,7,6] => [2,2,1,1,1] => 2
[[],[],[[],[],[]],[]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => [4,1,1,1] => 4
[[],[],[[],[[]]],[]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,5,3,7] => [3,1,1,1,1] => 3
[[],[],[[[]],[]],[]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,5,4,6,3,7] => [3,1,1,1,1] => 3
[[],[],[[[],[]]],[]] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,6,4,5,3,7] => [2,1,1,1,1,1] => 2
[[],[],[[[[]]]],[]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,5,4,3,7] => [2,2,1,1,1] => 2
[[],[],[[],[],[],[]]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => [5,1,1] => 5
[[],[],[[],[],[[]]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,6,3] => [4,1,1,1] => 4
[[],[],[[],[[]],[]]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,5,7,3] => [4,1,1,1] => 4
[[],[],[[],[[],[]]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,7,5,6,3] => [3,1,1,1,1] => 3
[[],[],[[],[[[]]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,6,5,3] => [3,2,1,1] => 3
[[],[],[[[]],[],[]]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => [4,1,1,1] => 4
[[],[],[[[]],[[]]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,4,7,6,3] => [3,1,1,1,1] => 3
[[],[],[[[],[]],[]]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,6,4,5,7,3] => [3,1,1,1,1] => 3
[[],[],[[[[]]],[]]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,5,4,7,3] => [3,2,1,1] => 3
[[],[],[[[],[],[]]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,7,4,5,6,3] => [2,1,1,1,1,1] => 2
[[],[],[[[],[[]]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,7,4,6,5,3] => [2,2,1,1,1] => 2
[[],[],[[[[]],[]]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,7,5,4,6,3] => [2,2,1,1,1] => 2
[[],[],[[[[],[]]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,7,5,6,4,3] => [3,2,1,1] => 3
[[],[],[[[[[]]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => [2,2,1,1,1] => 2
[[],[[]],[],[],[],[]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => [2,1,1,1,1,1] => 2
[[],[[]],[],[],[[]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => [2,2,1,1,1] => 2
[[],[[]],[],[[]],[]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => [2,2,1,1,1] => 2
[[],[[]],[],[[],[]]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,4,6,7,5] => [3,2,1,1] => 3
[[],[[]],[],[[[]]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,6,5] => [2,2,1,1,1] => 2
[[],[[]],[[]],[],[]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => [2,2,1,1,1] => 2
[[],[[]],[[]],[[]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => [2,2,2,1] => 2
[[],[[]],[[],[]],[]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,6,4,7] => [3,2,1,1] => 3
[[],[[]],[[[]]],[]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,5,4,7] => [2,2,1,1,1] => 2
[[],[[]],[[],[],[]]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,6,7,4] => [4,2,1] => 4
[[],[[]],[[],[[]]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,6,4] => [3,2,1,1] => 3
[[],[[]],[[[]],[]]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,5,7,4] => [3,2,1,1] => 3
[[],[[]],[[[],[]]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,7,5,6,4] => [2,2,1,1,1] => 2
[[],[[]],[[[[]]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,6,5,4] => [2,2,2,1] => 2
[[],[[],[]],[],[],[]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7] => [3,1,1,1,1] => 3
[[],[[[]]],[],[],[]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7] => [2,1,1,1,1,1] => 2
[[],[[],[]],[],[[]]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => [3,2,1,1] => 3
[[],[[[]]],[],[[]]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,3,2,5,7,6] => [2,2,1,1,1] => 2
[[],[[],[]],[[]],[]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,7] => [3,2,1,1] => 3
[[],[[[]]],[[]],[]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,3,2,6,5,7] => [2,2,1,1,1] => 2
[[],[[],[]],[[],[]]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,2,6,7,5] => [3,3,1] => 3
[[],[[],[]],[[[]]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,6,5] => [3,2,1,1] => 3
[[],[[[]]],[[],[]]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,3,2,6,7,5] => [3,2,1,1] => 3
[[],[[[]]],[[[]]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3,2,7,6,5] => [2,2,1,1,1] => 2
[[],[[],[],[]],[],[]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,2,6,7] => [4,1,1,1] => 4
[[],[[],[[]]],[],[]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,4,2,6,7] => [3,1,1,1,1] => 3
[[],[[[]],[]],[],[]] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,3,5,2,6,7] => [3,1,1,1,1] => 3
[[],[[[],[]]],[],[]] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,5,3,4,2,6,7] => [2,1,1,1,1,1] => 2
[[],[[[[]]]],[],[]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,4,3,2,6,7] => [2,2,1,1,1] => 2
[[],[[],[],[]],[[]]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6] => [4,2,1] => 4
[[],[[],[[]]],[[]]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,4,2,7,6] => [3,2,1,1] => 3
[[],[[[]],[]],[[]]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,3,5,2,7,6] => [3,2,1,1] => 3
[[],[[[],[]]],[[]]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,5,3,4,2,7,6] => [2,2,1,1,1] => 2
[[],[[[[]]]],[[]]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,4,3,2,7,6] => [2,2,2,1] => 2
[[],[[],[],[],[]],[]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,2,7] => [5,1,1] => 5
[[],[[],[],[[]]],[]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,6,5,2,7] => [4,1,1,1] => 4
[[],[[],[[]],[]],[]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,4,6,2,7] => [4,1,1,1] => 4
[[],[[],[[],[]]],[]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,6,4,5,2,7] => [3,1,1,1,1] => 3
[[],[[],[[[]]]],[]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,5,4,2,7] => [3,2,1,1] => 3
[[],[[[]],[],[]],[]] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,3,5,6,2,7] => [4,1,1,1] => 4
[[],[[[]],[[]]],[]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,3,6,5,2,7] => [3,1,1,1,1] => 3
[[],[[[],[]],[]],[]] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,5,3,4,6,2,7] => [3,1,1,1,1] => 3
[[],[[[[]]],[]],[]] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,4,3,6,2,7] => [3,2,1,1] => 3
[[],[[[],[],[]]],[]] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,6,3,4,5,2,7] => [2,1,1,1,1,1] => 2
[[],[[[],[[]]]],[]] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,6,3,5,4,2,7] => [2,2,1,1,1] => 2
[[],[[[[]],[]]],[]] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,6,4,3,5,2,7] => [2,2,1,1,1] => 2
[[],[[[[],[]]]],[]] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,6,4,5,3,2,7] => [3,2,1,1] => 3
[[],[[[[[]]]]],[]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,5,4,3,2,7] => [2,2,1,1,1] => 2
[[],[[],[],[],[],[]]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => [6,1] => 6
[[],[[],[],[],[[]]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,6,2] => [5,1,1] => 5
[[],[[],[],[[]],[]]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,6,5,7,2] => [5,1,1] => 5
[[],[[],[],[[],[]]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,7,5,6,2] => [4,1,1,1] => 4
[[],[[],[],[[[]]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,6,5,2] => [4,2,1] => 4
[[],[[],[[]],[],[]]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,4,6,7,2] => [5,1,1] => 5
[[],[[],[[]],[[]]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,4,7,6,2] => [4,1,1,1] => 4
[[],[[],[[],[]],[]]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,6,4,5,7,2] => [4,1,1,1] => 4
[[],[[],[[[]]],[]]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,5,4,7,2] => [4,2,1] => 4
[[],[[],[[],[],[]]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,7,4,5,6,2] => [3,1,1,1,1] => 3
[[],[[],[[],[[]]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,7,4,6,5,2] => [3,2,1,1] => 3
[[],[[],[[[]],[]]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,7,5,4,6,2] => [3,2,1,1] => 3
[[],[[],[[[],[]]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,7,5,6,4,2] => [3,3,1] => 3
[[],[[],[[[[]]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => [3,2,1,1] => 3
[[],[[[]],[],[],[]]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => [5,1,1] => 5
[[],[[[]],[],[[]]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,3,5,7,6,2] => [4,1,1,1] => 4
[[],[[[]],[[]],[]]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,3,6,5,7,2] => [4,1,1,1] => 4
[[],[[[]],[[],[]]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,3,7,5,6,2] => [3,1,1,1,1] => 3
[[],[[[]],[[[]]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,3,7,6,5,2] => [3,2,1,1] => 3
[[],[[[],[]],[],[]]] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,5,3,4,6,7,2] => [4,1,1,1] => 4
[[],[[[[]]],[],[]]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,4,3,6,7,2] => [4,2,1] => 4
[[],[[[],[]],[[]]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,5,3,4,7,6,2] => [3,1,1,1,1] => 3
[[],[[[[]]],[[]]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,4,3,7,6,2] => [3,2,1,1] => 3
[[],[[[],[],[]],[]]] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,6,3,4,5,7,2] => [3,1,1,1,1] => 3
[[],[[[],[[]]],[]]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,6,3,5,4,7,2] => [3,2,1,1] => 3
[[],[[[[]],[]],[]]] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,6,4,3,5,7,2] => [3,2,1,1] => 3
[[],[[[[],[]]],[]]] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,6,4,5,3,7,2] => [3,3,1] => 3
[[],[[[[[]]]],[]]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,5,4,3,7,2] => [3,2,1,1] => 3
[[],[[[],[],[],[]]]] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,7,3,4,5,6,2] => [2,1,1,1,1,1] => 2
[[],[[[],[],[[]]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,7,3,4,6,5,2] => [2,2,1,1,1] => 2
[[],[[[],[[]],[]]]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,7,3,5,4,6,2] => [2,2,1,1,1] => 2
[[],[[[],[[],[]]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,7,3,5,6,4,2] => [3,2,1,1] => 3
[[],[[[],[[[]]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,7,3,6,5,4,2] => [2,2,1,1,1] => 2
[[],[[[[]],[],[]]]] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,7,4,3,5,6,2] => [2,2,1,1,1] => 2
[[],[[[[]],[[]]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,7,4,3,6,5,2] => [2,2,2,1] => 2
[[],[[[[],[]],[]]]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,7,4,5,3,6,2] => [3,2,1,1] => 3
[[],[[[[[]]],[]]]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,7,5,4,3,6,2] => [2,2,1,1,1] => 2
[[],[[[[],[],[]]]]] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,7,4,5,6,3,2] => [4,2,1] => 4
[[],[[[[],[[]]]]]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,7,4,6,5,3,2] => [3,2,1,1] => 3
[[],[[[[[]],[]]]]] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,7,5,4,6,3,2] => [3,2,1,1] => 3
[[],[[[[[],[]]]]]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,7,6,4,5,3,2] => [2,2,1,1,1] => 2
[[],[[[[[[]]]]]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => [2,2,2,1] => 2
[[[]],[],[],[],[],[]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => [2,1,1,1,1,1] => 2
[[[]],[],[],[],[[]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,7,6] => [2,2,1,1,1] => 2
[[[]],[],[],[[]],[]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,6,5,7] => [2,2,1,1,1] => 2
[[[]],[],[],[[],[]]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,6,7,5] => [3,2,1,1] => 3
[[[]],[],[],[[[]]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,6,5] => [2,2,1,1,1] => 2
[[[]],[],[[]],[],[]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,6,7] => [2,2,1,1,1] => 2
[[[]],[],[[]],[[]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,5,4,7,6] => [2,2,2,1] => 2
[[[]],[],[[],[]],[]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,6,4,7] => [3,2,1,1] => 3
[[[]],[],[[[]]],[]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,6,5,4,7] => [2,2,1,1,1] => 2
[[[]],[],[[],[],[]]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,5,6,7,4] => [4,2,1] => 4
[[[]],[],[[],[[]]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,5,7,6,4] => [3,2,1,1] => 3
[[[]],[],[[[]],[]]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,6,5,7,4] => [3,2,1,1] => 3
[[[]],[],[[[],[]]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,7,5,6,4] => [2,2,1,1,1] => 2
[[[]],[],[[[[]]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,6,5,4] => [2,2,2,1] => 2
[[[]],[[]],[],[],[]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7] => [2,2,1,1,1] => 2
[[[]],[[]],[],[[]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,5,7,6] => [2,2,2,1] => 2
[[[]],[[]],[[]],[]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => [2,2,2,1] => 2
[[[]],[[]],[[],[]]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,7,5] => [3,2,2] => 3
[[[]],[[]],[[[]]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,6,5] => [2,2,2,1] => 2
[[[]],[[],[]],[],[]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,5,3,6,7] => [3,2,1,1] => 3
[[[]],[[[]]],[],[]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,4,3,6,7] => [2,2,1,1,1] => 2
[[[]],[[],[]],[[]]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,4,5,3,7,6] => [3,2,2] => 3
[[[]],[[[]]],[[]]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,4,3,7,6] => [2,2,2,1] => 2
[[[]],[[],[],[]],[]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,3,7] => [4,2,1] => 4
[[[]],[[],[[]]],[]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,5,3,7] => [3,2,1,1] => 3
[[[]],[[[]],[]],[]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,4,6,3,7] => [3,2,1,1] => 3
[[[]],[[[],[]]],[]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,6,4,5,3,7] => [2,2,1,1,1] => 2
[[[]],[[[[]]]],[]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,5,4,3,7] => [2,2,2,1] => 2
[[[]],[[],[],[],[]]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,3] => [5,2] => 5
[[[]],[[],[],[[]]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,5,7,6,3] => [4,2,1] => 4
[[[]],[[],[[]],[]]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,5,7,3] => [4,2,1] => 4
[[[]],[[],[[],[]]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,7,5,6,3] => [3,2,1,1] => 3
[[[]],[[],[[[]]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,7,6,5,3] => [3,2,2] => 3
[[[]],[[[]],[],[]]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,4,6,7,3] => [4,2,1] => 4
[[[]],[[[]],[[]]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,4,7,6,3] => [3,2,1,1] => 3
[[[]],[[[],[]],[]]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,6,4,5,7,3] => [3,2,1,1] => 3
[[[]],[[[[]]],[]]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,6,5,4,7,3] => [3,2,2] => 3
[[[]],[[[],[],[]]]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,7,4,5,6,3] => [2,2,1,1,1] => 2
[[[]],[[[],[[]]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,7,4,6,5,3] => [2,2,2,1] => 2
[[[]],[[[[]],[]]]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,7,5,4,6,3] => [2,2,2,1] => 2
[[[]],[[[[],[]]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,7,5,6,4,3] => [3,2,2] => 3
[[[]],[[[[[]]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => [2,2,2,1] => 2
[[[],[]],[],[],[],[]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7] => [3,1,1,1,1] => 3
[[[[]]],[],[],[],[]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7] => [2,1,1,1,1,1] => 2
[[[],[]],[],[],[[]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,7,6] => [3,2,1,1] => 3
[[[[]]],[],[],[[]]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,7,6] => [2,2,1,1,1] => 2
[[[],[]],[],[[]],[]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,1,4,6,5,7] => [3,2,1,1] => 3
[[[[]]],[],[[]],[]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,2,1,4,6,5,7] => [2,2,1,1,1] => 2
[[[],[]],[],[[],[]]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,4,6,7,5] => [3,3,1] => 3
[[[],[]],[],[[[]]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,4,7,6,5] => [3,2,1,1] => 3
[[[[]]],[],[[],[]]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,2,1,4,6,7,5] => [3,2,1,1] => 3
[[[[]]],[],[[[]]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,2,1,4,7,6,5] => [2,2,1,1,1] => 2
[[[],[]],[[]],[],[]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,1,5,4,6,7] => [3,2,1,1] => 3
[[[[]]],[[]],[],[]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,5,4,6,7] => [2,2,1,1,1] => 2
[[[],[]],[[]],[[]]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6] => [3,2,2] => 3
[[[[]]],[[]],[[]]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,1,5,4,7,6] => [2,2,2,1] => 2
[[[],[]],[[],[]],[]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1,5,6,4,7] => [3,3,1] => 3
[[[],[]],[[[]]],[]] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1,6,5,4,7] => [3,2,1,1] => 3
[[[[]]],[[],[]],[]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,2,1,5,6,4,7] => [3,2,1,1] => 3
[[[[]]],[[[]]],[]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,2,1,6,5,4,7] => [2,2,1,1,1] => 2
[[[],[]],[[],[],[]]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,6,7,4] => [4,3] => 4
[[[],[]],[[],[[]]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,1,5,7,6,4] => [3,3,1] => 3
[[[],[]],[[[]],[]]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1,6,5,7,4] => [3,3,1] => 3
[[[],[]],[[[],[]]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,7,5,6,4] => [3,2,1,1] => 3
[[[],[]],[[[[]]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,7,6,5,4] => [3,2,2] => 3
[[[[]]],[[],[],[]]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,2,1,5,6,7,4] => [4,2,1] => 4
[[[[]]],[[],[[]]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,2,1,5,7,6,4] => [3,2,1,1] => 3
[[[[]]],[[[]],[]]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,2,1,6,5,7,4] => [3,2,1,1] => 3
[[[[]]],[[[],[]]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,2,1,7,5,6,4] => [2,2,1,1,1] => 2
[[[[]]],[[[[]]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,2,1,7,6,5,4] => [2,2,2,1] => 2
[[[],[],[]],[],[],[]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => [4,1,1,1] => 4
[[[],[[]]],[],[],[]] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7] => [3,1,1,1,1] => 3
[[[[]],[]],[],[],[]] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7] => [3,1,1,1,1] => 3
[[[[],[]]],[],[],[]] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [4,2,3,1,5,6,7] => [2,1,1,1,1,1] => 2
[[[[[]]]],[],[],[]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7] => [2,2,1,1,1] => 2
[[[],[],[]],[],[[]]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,1,5,7,6] => [4,2,1] => 4
[[[],[[]]],[],[[]]] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,4,3,1,5,7,6] => [3,2,1,1] => 3
[[[[]],[]],[],[[]]] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,2,4,1,5,7,6] => [3,2,1,1] => 3
[[[[],[]]],[],[[]]] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [4,2,3,1,5,7,6] => [2,2,1,1,1] => 2
[[[[[]]]],[],[[]]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,3,2,1,5,7,6] => [2,2,2,1] => 2
[[[],[],[]],[[]],[]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,7] => [4,2,1] => 4
[[[],[[]]],[[]],[]] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,3,1,6,5,7] => [3,2,1,1] => 3
[[[[]],[]],[[]],[]] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,2,4,1,6,5,7] => [3,2,1,1] => 3
[[[[],[]]],[[]],[]] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [4,2,3,1,6,5,7] => [2,2,1,1,1] => 2
[[[[[]]]],[[]],[]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,3,2,1,6,5,7] => [2,2,2,1] => 2
[[[],[],[]],[[],[]]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,7,5] => [4,3] => 4
[[[],[],[]],[[[]]]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,1,7,6,5] => [4,2,1] => 4
[[[],[[]]],[[],[]]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,3,1,6,7,5] => [3,3,1] => 3
[[[],[[]]],[[[]]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,3,1,7,6,5] => [3,2,1,1] => 3
[[[[]],[]],[[],[]]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,2,4,1,6,7,5] => [3,3,1] => 3
[[[[]],[]],[[[]]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,2,4,1,7,6,5] => [3,2,1,1] => 3
[[[[],[]]],[[],[]]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [4,2,3,1,6,7,5] => [3,2,1,1] => 3
[[[[],[]]],[[[]]]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,2,3,1,7,6,5] => [2,2,1,1,1] => 2
[[[[[]]]],[[],[]]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,3,2,1,6,7,5] => [3,2,2] => 3
[[[[[]]]],[[[]]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3,2,1,7,6,5] => [2,2,2,1] => 2
[[[],[],[],[]],[],[]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => [5,1,1] => 5
[[[],[],[[]]],[],[]] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,5,4,1,6,7] => [4,1,1,1] => 4
[[[],[[]],[]],[],[]] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,3,5,1,6,7] => [4,1,1,1] => 4
[[[],[[],[]]],[],[]] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,5,3,4,1,6,7] => [3,1,1,1,1] => 3
[[[],[[[]]]],[],[]] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,5,4,3,1,6,7] => [3,2,1,1] => 3
[[[[]],[],[]],[],[]] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,1,6,7] => [4,1,1,1] => 4
[[[[]],[[]]],[],[]] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,2,5,4,1,6,7] => [3,1,1,1,1] => 3
[[[[],[]],[]],[],[]] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [4,2,3,5,1,6,7] => [3,1,1,1,1] => 3
[[[[[]]],[]],[],[]] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,3,2,5,1,6,7] => [3,2,1,1] => 3
[[[[],[],[]]],[],[]] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [5,2,3,4,1,6,7] => [2,1,1,1,1,1] => 2
[[[[],[[]]]],[],[]] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [5,2,4,3,1,6,7] => [2,2,1,1,1] => 2
[[[[[]],[]]],[],[]] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [5,3,2,4,1,6,7] => [2,2,1,1,1] => 2
[[[[[],[]]]],[],[]] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [5,3,4,2,1,6,7] => [3,2,1,1] => 3
[[[[[[]]]]],[],[]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,4,3,2,1,6,7] => [2,2,1,1,1] => 2
[[[],[],[],[]],[[]]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => [5,2] => 5
[[[],[],[[]]],[[]]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,4,1,7,6] => [4,2,1] => 4
[[[],[[]],[]],[[]]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,3,5,1,7,6] => [4,2,1] => 4
[[[],[[],[]]],[[]]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,5,3,4,1,7,6] => [3,2,1,1] => 3
[[[],[[[]]]],[[]]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,4,3,1,7,6] => [3,2,2] => 3
[[[[]],[],[]],[[]]] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,2,4,5,1,7,6] => [4,2,1] => 4
[[[[]],[[]]],[[]]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,2,5,4,1,7,6] => [3,2,1,1] => 3
[[[[],[]],[]],[[]]] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [4,2,3,5,1,7,6] => [3,2,1,1] => 3
[[[[[]]],[]],[[]]] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,3,2,5,1,7,6] => [3,2,2] => 3
[[[[],[],[]]],[[]]] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [5,2,3,4,1,7,6] => [2,2,1,1,1] => 2
[[[[],[[]]]],[[]]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,2,4,3,1,7,6] => [2,2,2,1] => 2
[[[[[]],[]]],[[]]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,3,2,4,1,7,6] => [2,2,2,1] => 2
[[[[[],[]]]],[[]]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,3,4,2,1,7,6] => [3,2,2] => 3
[[[[[[]]]]],[[]]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,4,3,2,1,7,6] => [2,2,2,1] => 2
[[[],[],[],[],[]],[]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,1,7] => [6,1] => 6
[[[],[],[],[[]]],[]] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,6,5,1,7] => [5,1,1] => 5
[[[],[],[[]],[]],[]] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,4,6,1,7] => [5,1,1] => 5
[[[],[],[[],[]]],[]] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,6,4,5,1,7] => [4,1,1,1] => 4
[[[],[],[[[]]]],[]] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,6,5,4,1,7] => [4,2,1] => 4
[[[],[[]],[],[]],[]] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,3,5,6,1,7] => [5,1,1] => 5
[[[],[[]],[[]]],[]] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,3,6,5,1,7] => [4,1,1,1] => 4
[[[],[[],[]],[]],[]] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,5,3,4,6,1,7] => [4,1,1,1] => 4
[[[],[[[]]],[]],[]] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,5,4,3,6,1,7] => [4,2,1] => 4
[[[],[[],[],[]]],[]] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,6,3,4,5,1,7] => [3,1,1,1,1] => 3
[[[],[[],[[]]]],[]] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,6,3,5,4,1,7] => [3,2,1,1] => 3
[[[],[[[]],[]]],[]] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,6,4,3,5,1,7] => [3,2,1,1] => 3
[[[],[[[],[]]]],[]] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,6,4,5,3,1,7] => [3,3,1] => 3
[[[],[[[[]]]]],[]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,5,4,3,1,7] => [3,2,1,1] => 3
[[[[]],[],[],[]],[]] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,1,7] => [5,1,1] => 5
[[[[]],[],[[]]],[]] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,2,4,6,5,1,7] => [4,1,1,1] => 4
[[[[]],[[]],[]],[]] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,2,5,4,6,1,7] => [4,1,1,1] => 4
[[[[]],[[],[]]],[]] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,2,6,4,5,1,7] => [3,1,1,1,1] => 3
[[[[]],[[[]]]],[]] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,2,6,5,4,1,7] => [3,2,1,1] => 3
[[[[],[]],[],[]],[]] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [4,2,3,5,6,1,7] => [4,1,1,1] => 4
[[[[[]]],[],[]],[]] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,3,2,5,6,1,7] => [4,2,1] => 4
[[[[],[]],[[]]],[]] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [4,2,3,6,5,1,7] => [3,1,1,1,1] => 3
[[[[[]]],[[]]],[]] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,3,2,6,5,1,7] => [3,2,1,1] => 3
[[[[],[],[]],[]],[]] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [5,2,3,4,6,1,7] => [3,1,1,1,1] => 3
[[[[],[[]]],[]],[]] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [5,2,4,3,6,1,7] => [3,2,1,1] => 3
[[[[[]],[]],[]],[]] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [5,3,2,4,6,1,7] => [3,2,1,1] => 3
[[[[[],[]]],[]],[]] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [5,3,4,2,6,1,7] => [3,3,1] => 3
[[[[[[]]]],[]],[]] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,4,3,2,6,1,7] => [3,2,1,1] => 3
[[[[],[],[],[]]],[]] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,2,3,4,5,1,7] => [2,1,1,1,1,1] => 2
[[[[],[],[[]]]],[]] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,2,3,5,4,1,7] => [2,2,1,1,1] => 2
[[[[],[[]],[]]],[]] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [6,2,4,3,5,1,7] => [2,2,1,1,1] => 2
[[[[],[[],[]]]],[]] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,2,4,5,3,1,7] => [3,2,1,1] => 3
[[[[],[[[]]]]],[]] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,2,5,4,3,1,7] => [2,2,1,1,1] => 2
[[[[[]],[],[]]],[]] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1,7] => [2,2,1,1,1] => 2
[[[[[]],[[]]]],[]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,3,2,5,4,1,7] => [2,2,2,1] => 2
[[[[[],[]],[]]],[]] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,4,2,5,1,7] => [3,2,1,1] => 3
[[[[[[]]],[]]],[]] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,4,3,2,5,1,7] => [2,2,1,1,1] => 2
[[[[[],[],[]]]],[]] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,3,4,5,2,1,7] => [4,2,1] => 4
[[[[[],[[]]]]],[]] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,3,5,4,2,1,7] => [3,2,1,1] => 3
[[[[[[]],[]]]],[]] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,4,3,5,2,1,7] => [3,2,1,1] => 3
[[[[[[],[]]]]],[]] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,5,3,4,2,1,7] => [2,2,1,1,1] => 2
[[[[[[[]]]]]],[]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,5,4,3,2,1,7] => [2,2,2,1] => 2
[[[],[],[],[],[],[]]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => [7] => 7
[[[],[],[],[],[[]]]] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,7,6,1] => [6,1] => 6
[[[],[],[],[[]],[]]] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,6,5,7,1] => [6,1] => 6
[[[],[],[],[[],[]]]] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,7,5,6,1] => [5,1,1] => 5
[[[],[],[],[[[]]]]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,7,6,5,1] => [5,2] => 5
[[[],[],[[]],[],[]]] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,5,4,6,7,1] => [6,1] => 6
[[[],[],[[]],[[]]]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,4,7,6,1] => [5,1,1] => 5
[[[],[],[[],[]],[]]] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,6,4,5,7,1] => [5,1,1] => 5
[[[],[],[[[]]],[]]] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,6,5,4,7,1] => [5,2] => 5
[[[],[],[[],[],[]]]] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,7,4,5,6,1] => [4,1,1,1] => 4
[[[],[],[[],[[]]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,7,4,6,5,1] => [4,2,1] => 4
[[[],[],[[[]],[]]]] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,7,5,4,6,1] => [4,2,1] => 4
[[[],[],[[[],[]]]]] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,7,5,6,4,1] => [4,3] => 4
[[[],[],[[[[]]]]]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,7,6,5,4,1] => [4,2,1] => 4
[[[],[[]],[],[],[]]] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,1] => [6,1] => 6
[[[],[[]],[],[[]]]] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,4,3,5,7,6,1] => [5,1,1] => 5
[[[],[[]],[[]],[]]] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,3,6,5,7,1] => [5,1,1] => 5
[[[],[[]],[[],[]]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,3,7,5,6,1] => [4,1,1,1] => 4
[[[],[[]],[[[]]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,3,7,6,5,1] => [4,2,1] => 4
[[[],[[],[]],[],[]]] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,5,3,4,6,7,1] => [5,1,1] => 5
[[[],[[[]]],[],[]]] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,5,4,3,6,7,1] => [5,2] => 5
[[[],[[],[]],[[]]]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,5,3,4,7,6,1] => [4,1,1,1] => 4
[[[],[[[]]],[[]]]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,5,4,3,7,6,1] => [4,2,1] => 4
[[[],[[],[],[]],[]]] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,6,3,4,5,7,1] => [4,1,1,1] => 4
[[[],[[],[[]]],[]]] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,6,3,5,4,7,1] => [4,2,1] => 4
[[[],[[[]],[]],[]]] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,6,4,3,5,7,1] => [4,2,1] => 4
[[[],[[[],[]]],[]]] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,6,4,5,3,7,1] => [4,3] => 4
[[[],[[[[]]]],[]]] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,6,5,4,3,7,1] => [4,2,1] => 4
[[[],[[],[],[],[]]]] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,7,3,4,5,6,1] => [3,1,1,1,1] => 3
[[[],[[],[],[[]]]]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,7,3,4,6,5,1] => [3,2,1,1] => 3
[[[],[[],[[]],[]]]] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,7,3,5,4,6,1] => [3,2,1,1] => 3
[[[],[[],[[],[]]]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,7,3,5,6,4,1] => [3,3,1] => 3
[[[],[[],[[[]]]]]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,7,3,6,5,4,1] => [3,2,1,1] => 3
[[[],[[[]],[],[]]]] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,7,4,3,5,6,1] => [3,2,1,1] => 3
[[[],[[[]],[[]]]]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,7,4,3,6,5,1] => [3,2,2] => 3
[[[],[[[],[]],[]]]] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,7,4,5,3,6,1] => [3,3,1] => 3
[[[],[[[[]]],[]]]] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,7,5,4,3,6,1] => [3,2,1,1] => 3
[[[],[[[],[],[]]]]] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,7,4,5,6,3,1] => [4,3] => 4
[[[],[[[],[[]]]]]] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,7,4,6,5,3,1] => [3,3,1] => 3
[[[],[[[[]],[]]]]] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,7,5,4,6,3,1] => [3,3,1] => 3
[[[],[[[[],[]]]]]] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,7,6,4,5,3,1] => [3,2,1,1] => 3
[[[],[[[[[]]]]]]] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7,6,5,4,3,1] => [3,2,2] => 3
[[[[]],[],[],[],[]]] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,1] => [6,1] => 6
[[[[]],[],[],[[]]]] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,7,6,1] => [5,1,1] => 5
[[[[]],[],[[]],[]]] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,2,4,6,5,7,1] => [5,1,1] => 5
[[[[]],[],[[],[]]]] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,2,4,7,5,6,1] => [4,1,1,1] => 4
[[[[]],[],[[[]]]]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,2,4,7,6,5,1] => [4,2,1] => 4
[[[[]],[[]],[],[]]] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,2,5,4,6,7,1] => [5,1,1] => 5
[[[[]],[[]],[[]]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,5,4,7,6,1] => [4,1,1,1] => 4
[[[[]],[[],[]],[]]] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,2,6,4,5,7,1] => [4,1,1,1] => 4
[[[[]],[[[]]],[]]] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,2,6,5,4,7,1] => [4,2,1] => 4
[[[[]],[[],[],[]]]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,2,7,4,5,6,1] => [3,1,1,1,1] => 3
[[[[]],[[],[[]]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,2,7,4,6,5,1] => [3,2,1,1] => 3
[[[[]],[[[]],[]]]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,2,7,5,4,6,1] => [3,2,1,1] => 3
[[[[]],[[[],[]]]]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,7,5,6,4,1] => [3,3,1] => 3
[[[[]],[[[[]]]]]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,2,7,6,5,4,1] => [3,2,1,1] => 3
[[[[],[]],[],[],[]]] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [4,2,3,5,6,7,1] => [5,1,1] => 5
[[[[[]]],[],[],[]]] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,1] => [5,2] => 5
[[[[],[]],[],[[]]]] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,2,3,5,7,6,1] => [4,1,1,1] => 4
[[[[[]]],[],[[]]]] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,3,2,5,7,6,1] => [4,2,1] => 4
[[[[],[]],[[]],[]]] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [4,2,3,6,5,7,1] => [4,1,1,1] => 4
[[[[[]]],[[]],[]]] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,3,2,6,5,7,1] => [4,2,1] => 4
[[[[],[]],[[],[]]]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,2,3,7,5,6,1] => [3,1,1,1,1] => 3
[[[[],[]],[[[]]]]] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,2,3,7,6,5,1] => [3,2,1,1] => 3
[[[[[]]],[[],[]]]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,2,7,5,6,1] => [3,2,1,1] => 3
[[[[[]]],[[[]]]]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,3,2,7,6,5,1] => [3,2,2] => 3
[[[[],[],[]],[],[]]] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [5,2,3,4,6,7,1] => [4,1,1,1] => 4
[[[[],[[]]],[],[]]] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,2,4,3,6,7,1] => [4,2,1] => 4
[[[[[]],[]],[],[]]] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [5,3,2,4,6,7,1] => [4,2,1] => 4
[[[[[],[]]],[],[]]] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,3,4,2,6,7,1] => [4,3] => 4
[[[[[[]]]],[],[]]] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4,3,2,6,7,1] => [4,2,1] => 4
[[[[],[],[]],[[]]]] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,2,3,4,7,6,1] => [3,1,1,1,1] => 3
[[[[],[[]]],[[]]]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,2,4,3,7,6,1] => [3,2,1,1] => 3
[[[[[]],[]],[[]]]] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,3,2,4,7,6,1] => [3,2,1,1] => 3
[[[[[],[]]],[[]]]] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,3,4,2,7,6,1] => [3,3,1] => 3
[[[[[[]]]],[[]]]] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,4,3,2,7,6,1] => [3,2,1,1] => 3
[[[[],[],[],[]],[]]] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,2,3,4,5,7,1] => [3,1,1,1,1] => 3
[[[[],[],[[]]],[]]] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,2,3,5,4,7,1] => [3,2,1,1] => 3
[[[[],[[]],[]],[]]] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,2,4,3,5,7,1] => [3,2,1,1] => 3
[[[[],[[],[]]],[]]] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,2,4,5,3,7,1] => [3,3,1] => 3
[[[[],[[[]]]],[]]] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,5,4,3,7,1] => [3,2,1,1] => 3
[[[[[]],[],[]],[]]] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,3,2,4,5,7,1] => [3,2,1,1] => 3
[[[[[]],[[]]],[]]] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,2,5,4,7,1] => [3,2,2] => 3
[[[[[],[]],[]],[]]] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,3,4,2,5,7,1] => [3,3,1] => 3
[[[[[[]]],[]],[]]] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,3,2,5,7,1] => [3,2,1,1] => 3
[[[[[],[],[]]],[]]] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,4,5,2,7,1] => [4,3] => 4
[[[[[],[[]]]],[]]] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,3,5,4,2,7,1] => [3,3,1] => 3
[[[[[[]],[]]],[]]] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,4,3,5,2,7,1] => [3,3,1] => 3
[[[[[[],[]]]],[]]] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,5,3,4,2,7,1] => [3,2,1,1] => 3
[[[[[[[]]]]],[]]] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,5,4,3,2,7,1] => [3,2,2] => 3
[[[[],[],[],[],[]]]] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [7,2,3,4,5,6,1] => [2,1,1,1,1,1] => 2
[[[[],[],[],[[]]]]] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [7,2,3,4,6,5,1] => [2,2,1,1,1] => 2
[[[[],[],[[]],[]]]] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [7,2,3,5,4,6,1] => [2,2,1,1,1] => 2
[[[[],[],[[],[]]]]] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [7,2,3,5,6,4,1] => [3,2,1,1] => 3
[[[[],[],[[[]]]]]] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [7,2,3,6,5,4,1] => [2,2,1,1,1] => 2
[[[[],[[]],[],[]]]] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [7,2,4,3,5,6,1] => [2,2,1,1,1] => 2
[[[[],[[]],[[]]]]] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [7,2,4,3,6,5,1] => [2,2,2,1] => 2
[[[[],[[],[]],[]]]] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [7,2,4,5,3,6,1] => [3,2,1,1] => 3
[[[[],[[[]]],[]]]] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [7,2,5,4,3,6,1] => [2,2,1,1,1] => 2
[[[[],[[],[],[]]]]] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [7,2,4,5,6,3,1] => [4,2,1] => 4
[[[[],[[],[[]]]]]] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [7,2,4,6,5,3,1] => [3,2,1,1] => 3
[[[[],[[[]],[]]]]] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [7,2,5,4,6,3,1] => [3,2,1,1] => 3
[[[[],[[[],[]]]]]] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [7,2,6,4,5,3,1] => [2,2,1,1,1] => 2
[[[[],[[[[]]]]]]] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [7,2,6,5,4,3,1] => [2,2,2,1] => 2
[[[[[]],[],[],[]]]] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [7,3,2,4,5,6,1] => [2,2,1,1,1] => 2
[[[[[]],[],[[]]]]] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [7,3,2,4,6,5,1] => [2,2,2,1] => 2
[[[[[]],[[]],[]]]] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [7,3,2,5,4,6,1] => [2,2,2,1] => 2
[[[[[]],[[],[]]]]] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [7,3,2,5,6,4,1] => [3,2,2] => 3
[[[[[]],[[[]]]]]] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [7,3,2,6,5,4,1] => [2,2,2,1] => 2
[[[[[],[]],[],[]]]] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [7,3,4,2,5,6,1] => [3,2,1,1] => 3
[[[[[[]]],[],[]]]] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [7,4,3,2,5,6,1] => [2,2,1,1,1] => 2
[[[[[],[]],[[]]]]] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [7,3,4,2,6,5,1] => [3,2,2] => 3
[[[[[[]]],[[]]]]] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [7,4,3,2,6,5,1] => [2,2,2,1] => 2
[[[[[],[],[]],[]]]] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [7,3,4,5,2,6,1] => [4,2,1] => 4
[[[[[],[[]]],[]]]] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [7,3,5,4,2,6,1] => [3,2,1,1] => 3
[[[[[[]],[]],[]]]] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [7,4,3,5,2,6,1] => [3,2,1,1] => 3
[[[[[[],[]]],[]]]] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [7,5,3,4,2,6,1] => [2,2,1,1,1] => 2
[[[[[[[]]]],[]]]] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [7,5,4,3,2,6,1] => [2,2,2,1] => 2
[[[[[],[],[],[]]]]] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [7,3,4,5,6,2,1] => [5,2] => 5
[[[[[],[],[[]]]]]] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [7,3,4,6,5,2,1] => [4,2,1] => 4
[[[[[],[[]],[]]]]] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [7,3,5,4,6,2,1] => [4,2,1] => 4
[[[[[],[[],[]]]]]] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [7,3,6,4,5,2,1] => [3,2,1,1] => 3
[[[[[],[[[]]]]]]] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [7,3,6,5,4,2,1] => [3,2,2] => 3
[[[[[[]],[],[]]]]] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [7,4,3,5,6,2,1] => [4,2,1] => 4
[[[[[[]],[[]]]]]] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [7,4,3,6,5,2,1] => [3,2,1,1] => 3
[[[[[[],[]],[]]]]] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [7,5,3,4,6,2,1] => [3,2,1,1] => 3
[[[[[[[]]],[]]]]] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [7,5,4,3,6,2,1] => [3,2,2] => 3
[[[[[[],[],[]]]]]] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [7,6,3,4,5,2,1] => [2,2,1,1,1] => 2
[[[[[[],[[]]]]]]] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [7,6,3,5,4,2,1] => [2,2,2,1] => 2
[[[[[[[]],[]]]]]] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [7,6,4,3,5,2,1] => [2,2,2,1] => 2
[[[[[[[],[]]]]]]] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [7,6,4,5,3,2,1] => [3,2,2] => 3
[[[[[[[[]]]]]]]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,6,5,4,3,2,1] => [2,2,2,1] => 2
[[],[],[],[],[],[],[],[]] => [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] => [1,2,3,4,5,6,8,7] => [2,1,1,1,1,1,1] => 2
[[],[],[],[],[],[[]],[]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,7,6,8] => [2,1,1,1,1,1,1] => 2
[[],[],[],[],[],[[],[]]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,7,8,6] => [3,1,1,1,1,1] => 3
[[],[],[],[],[],[[[]]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,8,7,6] => [2,1,1,1,1,1,1] => 2
[[],[],[],[],[[]],[],[]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,6,5,7,8] => [2,1,1,1,1,1,1] => 2
[[],[],[],[],[[]],[[]]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,6,5,8,7] => [2,2,1,1,1,1] => 2
[[],[],[],[],[[],[]],[]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,6,7,5,8] => [3,1,1,1,1,1] => 3
[[],[],[],[],[[[]]],[]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,4,7,6,5,8] => [2,1,1,1,1,1,1] => 2
[[],[],[],[],[[],[],[]]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,5] => [4,1,1,1,1] => 4
[[],[],[],[],[[],[[]]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,6,8,7,5] => [3,1,1,1,1,1] => 3
[[],[],[],[],[[[]],[]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,4,7,6,8,5] => [3,1,1,1,1,1] => 3
[[],[],[],[],[[[],[]]]] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,8,6,7,5] => [2,1,1,1,1,1,1] => 2
[[],[],[],[],[[[[]]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,8,7,6,5] => [2,2,1,1,1,1] => 2
[[],[],[],[[]],[],[],[]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8] => [2,1,1,1,1,1,1] => 2
[[],[],[],[[]],[],[[]]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,3,5,4,6,8,7] => [2,2,1,1,1,1] => 2
[[],[],[],[[]],[[]],[]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,8] => [2,2,1,1,1,1] => 2
[[],[],[],[[]],[[],[]]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,3,5,4,7,8,6] => [3,2,1,1,1] => 3
[[],[],[],[[]],[[[]]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,5,4,8,7,6] => [2,2,1,1,1,1] => 2
[[],[],[],[[],[]],[],[]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,3,5,6,4,7,8] => [3,1,1,1,1,1] => 3
[[],[],[],[[[]]],[],[]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,3,6,5,4,7,8] => [2,1,1,1,1,1,1] => 2
[[],[],[],[[],[]],[[]]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,3,5,6,4,8,7] => [3,2,1,1,1] => 3
[[],[],[],[[[]]],[[]]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,6,5,4,8,7] => [2,2,1,1,1,1] => 2
[[],[],[],[[],[],[]],[]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,3,5,6,7,4,8] => [4,1,1,1,1] => 4
[[],[],[],[[],[[]]],[]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,3,5,7,6,4,8] => [3,1,1,1,1,1] => 3
[[],[],[],[[[]],[]],[]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,3,6,5,7,4,8] => [3,1,1,1,1,1] => 3
[[],[],[],[[[],[]]],[]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,3,7,5,6,4,8] => [2,1,1,1,1,1,1] => 2
[[],[],[],[[[[]]]],[]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,3,7,6,5,4,8] => [2,2,1,1,1,1] => 2
[[],[],[],[[],[],[],[]]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,4] => [5,1,1,1] => 5
[[],[],[],[[],[],[[]]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,3,5,6,8,7,4] => [4,1,1,1,1] => 4
[[],[],[],[[],[[]],[]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,3,5,7,6,8,4] => [4,1,1,1,1] => 4
[[],[],[],[[],[[],[]]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,3,5,8,6,7,4] => [3,1,1,1,1,1] => 3
[[],[],[],[[],[[[]]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3,5,8,7,6,4] => [3,2,1,1,1] => 3
[[],[],[],[[[]],[],[]]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,6,5,7,8,4] => [4,1,1,1,1] => 4
[[],[],[],[[[]],[[]]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,3,6,5,8,7,4] => [3,1,1,1,1,1] => 3
[[],[],[],[[[],[]],[]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,3,7,5,6,8,4] => [3,1,1,1,1,1] => 3
[[],[],[],[[[[]]],[]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,3,7,6,5,8,4] => [3,2,1,1,1] => 3
[[],[],[],[[[],[],[]]]] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,8,5,6,7,4] => [2,1,1,1,1,1,1] => 2
[[],[],[],[[[],[[]]]]] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,3,8,5,7,6,4] => [2,2,1,1,1,1] => 2
[[],[],[],[[[[]],[]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,3,8,6,5,7,4] => [2,2,1,1,1,1] => 2
[[],[],[],[[[[],[]]]]] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,3,8,6,7,5,4] => [3,2,1,1,1] => 3
[[],[],[],[[[[[]]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,8,7,6,5,4] => [2,2,1,1,1,1] => 2
[[],[],[[]],[],[],[],[]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8] => [2,1,1,1,1,1,1] => 2
[[],[],[[]],[],[],[[]]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,4,3,5,6,8,7] => [2,2,1,1,1,1] => 2
[[],[],[[]],[],[[]],[]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5,7,6,8] => [2,2,1,1,1,1] => 2
[[],[],[[]],[],[[],[]]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,2,4,3,5,7,8,6] => [3,2,1,1,1] => 3
[[],[],[[]],[],[[[]]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,4,3,5,8,7,6] => [2,2,1,1,1,1] => 2
[[],[],[[]],[[]],[],[]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,5,7,8] => [2,2,1,1,1,1] => 2
[[],[],[[]],[[]],[[]]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7] => [2,2,2,1,1] => 2
[[],[],[[]],[[],[]],[]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,2,4,3,6,7,5,8] => [3,2,1,1,1] => 3
[[],[],[[]],[[],[],[]]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,2,4,3,6,7,8,5] => [4,2,1,1] => 4
[[],[],[[]],[[],[[]]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,2,4,3,6,8,7,5] => [3,2,1,1,1] => 3
[[],[],[[]],[[[]],[]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,2,4,3,7,6,8,5] => [3,2,1,1,1] => 3
[[],[],[[]],[[[],[]]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,2,4,3,8,6,7,5] => [2,2,1,1,1,1] => 2
[[],[],[[]],[[[[]]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,8,7,6,5] => [2,2,2,1,1] => 2
[[],[],[[[]]],[],[],[]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,5,4,3,6,7,8] => [2,1,1,1,1,1,1] => 2
[[],[],[[[]]],[],[[]]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,2,5,4,3,6,8,7] => [2,2,1,1,1,1] => 2
[[],[],[[],[]],[[]],[]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,2,4,5,3,7,6,8] => [3,2,1,1,1] => 3
[[],[],[[],[]],[[],[]]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,2,4,5,3,7,8,6] => [3,3,1,1] => 3
[[],[],[[],[]],[[[]]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,2,4,5,3,8,7,6] => [3,2,1,1,1] => 3
[[],[],[[[]]],[[],[]]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,5,4,3,7,8,6] => [3,2,1,1,1] => 3
[[],[],[[[]]],[[[]]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,4,3,8,7,6] => [2,2,1,1,1,1] => 2
[[],[],[[],[],[]],[],[]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,2,4,5,6,3,7,8] => [4,1,1,1,1] => 4
[[],[],[[],[[]]],[],[]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,2,4,6,5,3,7,8] => [3,1,1,1,1,1] => 3
[[],[],[[[],[]]],[],[]] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,2,6,4,5,3,7,8] => [2,1,1,1,1,1,1] => 2
[[],[],[[[[]]]],[],[]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,6,5,4,3,7,8] => [2,2,1,1,1,1] => 2
[[],[],[[],[],[]],[[]]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,2,4,5,6,3,8,7] => [4,2,1,1] => 4
[[],[],[[],[],[],[]],[]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,7,3,8] => [5,1,1,1] => 5
[[],[],[[[]],[],[]],[]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,2,5,4,6,7,3,8] => [4,1,1,1,1] => 4
[[],[],[[[[[]]]]],[]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,7,6,5,4,3,8] => [2,2,1,1,1,1] => 2
[[],[],[[],[],[],[],[]]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,3] => [6,1,1] => 6
[[],[],[[],[],[],[[]]]] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,4,5,6,8,7,3] => [5,1,1,1] => 5
[[],[],[[],[],[[],[]]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,2,4,5,8,6,7,3] => [4,1,1,1,1] => 4
[[],[],[[],[],[[[]]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,2,4,5,8,7,6,3] => [4,2,1,1] => 4
[[],[],[[],[[]],[[]]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,2,4,6,5,8,7,3] => [4,1,1,1,1] => 4
[[],[],[[],[[],[]],[]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,2,4,7,5,6,8,3] => [4,1,1,1,1] => 4
[[],[],[[],[[[]]],[]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,2,4,7,6,5,8,3] => [4,2,1,1] => 4
[[],[],[[],[[],[],[]]]] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,2,4,8,5,6,7,3] => [3,1,1,1,1,1] => 3
[[],[],[[],[[[]],[]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,2,4,8,6,5,7,3] => [3,2,1,1,1] => 3
[[],[],[[],[[[[]]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,4,8,7,6,5,3] => [3,2,1,1,1] => 3
[[],[],[[[]],[],[],[]]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,2,5,4,6,7,8,3] => [5,1,1,1] => 5
[[],[],[[[]],[],[[]]]] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,2,5,4,6,8,7,3] => [4,1,1,1,1] => 4
[[],[],[[[]],[[],[]]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,2,5,4,8,6,7,3] => [3,1,1,1,1,1] => 3
[[],[],[[[]],[[[]]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,2,5,4,8,7,6,3] => [3,2,1,1,1] => 3
[[],[],[[[],[]],[],[]]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,2,6,4,5,7,8,3] => [4,1,1,1,1] => 4
[[],[],[[[[]]],[],[]]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,2,6,5,4,7,8,3] => [4,2,1,1] => 4
[[],[],[[[[]]],[[]]]] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,2,6,5,4,8,7,3] => [3,2,1,1,1] => 3
[[],[],[[[],[],[]],[]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,2,7,4,5,6,8,3] => [3,1,1,1,1,1] => 3
[[],[],[[[[[]]]],[]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,2,7,6,5,4,8,3] => [3,2,1,1,1] => 3
[[],[],[[[],[],[],[]]]] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,8,4,5,6,7,3] => [2,1,1,1,1,1,1] => 2
[[],[],[[[],[[],[]]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,2,8,4,6,7,5,3] => [3,2,1,1,1] => 3
[[],[],[[[],[[[]]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,2,8,4,7,6,5,3] => [2,2,1,1,1,1] => 2
[[],[],[[[[]],[],[]]]] => [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,2,8,5,4,6,7,3] => [2,2,1,1,1,1] => 2
[[],[],[[[[]],[[]]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,2,8,5,4,7,6,3] => [2,2,2,1,1] => 2
[[],[],[[[[],[]],[]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,2,8,5,6,4,7,3] => [3,2,1,1,1] => 3
[[],[],[[[[[]]],[]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,8,6,5,4,7,3] => [2,2,1,1,1,1] => 2
[[],[],[[[[],[],[]]]]] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,2,8,5,6,7,4,3] => [4,2,1,1] => 4
[[],[],[[[[[]],[]]]]] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,2,8,6,5,7,4,3] => [3,2,1,1,1] => 3
[[],[],[[[[[],[]]]]]] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,8,7,5,6,4,3] => [2,2,1,1,1,1] => 2
[[],[],[[[[[[]]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,8,7,6,5,4,3] => [2,2,2,1,1] => 2
[[],[[]],[],[],[],[],[]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8] => [2,1,1,1,1,1,1] => 2
[[],[[]],[],[],[],[[]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,8,7] => [2,2,1,1,1,1] => 2
[[],[[]],[],[],[[]],[]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,2,4,5,7,6,8] => [2,2,1,1,1,1] => 2
[[],[[]],[],[],[[],[]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,3,2,4,5,7,8,6] => [3,2,1,1,1] => 3
[[],[[]],[],[],[[[]]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,2,4,5,8,7,6] => [2,2,1,1,1,1] => 2
[[],[[]],[],[[]],[],[]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,6,5,7,8] => [2,2,1,1,1,1] => 2
[[],[[]],[],[[]],[[]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,2,4,6,5,8,7] => [2,2,2,1,1] => 2
[[],[[]],[],[[[]]],[]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,3,2,4,7,6,5,8] => [2,2,1,1,1,1] => 2
[[],[[]],[],[[],[],[]]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,3,2,4,6,7,8,5] => [4,2,1,1] => 4
[[],[[]],[],[[],[[]]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,2,4,6,8,7,5] => [3,2,1,1,1] => 3
[[],[[]],[],[[[]],[]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,3,2,4,7,6,8,5] => [3,2,1,1,1] => 3
[[],[[]],[],[[[],[]]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,3,2,4,8,6,7,5] => [2,2,1,1,1,1] => 2
[[],[[]],[],[[[[]]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,2,4,8,7,6,5] => [2,2,2,1,1] => 2
[[],[[]],[[]],[],[],[]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8] => [2,2,1,1,1,1] => 2
[[],[[]],[[]],[[]],[]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => [2,2,2,1,1] => 2
[[],[[]],[[]],[[],[]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,8,6] => [3,2,2,1] => 3
[[],[[]],[[]],[[[]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,7,6] => [2,2,2,1,1] => 2
[[],[[]],[[],[]],[],[]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,3,2,5,6,4,7,8] => [3,2,1,1,1] => 3
[[],[[]],[[[]]],[],[]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,6,5,4,7,8] => [2,2,1,1,1,1] => 2
[[],[[]],[[],[]],[[]]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,3,2,5,6,4,8,7] => [3,2,2,1] => 3
[[],[[]],[[[]]],[[]]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2,6,5,4,8,7] => [2,2,2,1,1] => 2
[[],[[]],[[],[],[]],[]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,3,2,5,6,7,4,8] => [4,2,1,1] => 4
[[],[[]],[[],[[]]],[]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,3,2,5,7,6,4,8] => [3,2,1,1,1] => 3
[[],[[]],[[[]],[]],[]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,3,2,6,5,7,4,8] => [3,2,1,1,1] => 3
[[],[[]],[[[[]]]],[]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,7,6,5,4,8] => [2,2,2,1,1] => 2
[[],[[]],[[],[],[],[]]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,3,2,5,6,7,8,4] => [5,2,1] => 5
[[],[[]],[[],[[[]]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,3,2,5,8,7,6,4] => [3,2,2,1] => 3
[[],[[]],[[[]],[],[]]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,3,2,6,5,7,8,4] => [4,2,1,1] => 4
[[],[[]],[[[],[]],[]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,3,2,7,5,6,8,4] => [3,2,1,1,1] => 3
[[],[[]],[[[[]]],[]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,3,2,7,6,5,8,4] => [3,2,2,1] => 3
[[],[[]],[[[],[[]]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,3,2,8,5,7,6,4] => [2,2,2,1,1] => 2
[[],[[]],[[[[]],[]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,3,2,8,6,5,7,4] => [2,2,2,1,1] => 2
[[],[[]],[[[[],[]]]]] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,3,2,8,6,7,5,4] => [3,2,2,1] => 3
[[],[[]],[[[[[]]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,7,6,5,4] => [2,2,2,1,1] => 2
[[],[[],[]],[],[],[],[]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8] => [3,1,1,1,1,1] => 3
[[],[[[]]],[],[],[],[]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7,8] => [2,1,1,1,1,1,1] => 2
[[],[[],[]],[],[],[[]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,3,4,2,5,6,8,7] => [3,2,1,1,1] => 3
[[],[[[]]],[],[],[[]]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,4,3,2,5,6,8,7] => [2,2,1,1,1,1] => 2
[[],[[],[]],[],[[]],[]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,3,4,2,5,7,6,8] => [3,2,1,1,1] => 3
[[],[[[]]],[],[[]],[]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,4,3,2,5,7,6,8] => [2,2,1,1,1,1] => 2
[[],[[],[]],[],[[],[]]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,3,4,2,5,7,8,6] => [3,3,1,1] => 3
[[],[[[]]],[],[[],[]]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,4,3,2,5,7,8,6] => [3,2,1,1,1] => 3
[[],[[[]]],[],[[[]]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,4,3,2,5,8,7,6] => [2,2,1,1,1,1] => 2
[[],[[],[]],[[]],[[]]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,8,7] => [3,2,2,1] => 3
[[],[[],[]],[[],[]],[]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,3,4,2,6,7,5,8] => [3,3,1,1] => 3
[[],[[[]]],[[],[]],[]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,4,3,2,6,7,5,8] => [3,2,1,1,1] => 3
[[],[[[]]],[[[]]],[]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => [2,2,1,1,1,1] => 2
[[],[[],[]],[[],[],[]]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,3,4,2,6,7,8,5] => [4,3,1] => 4
[[],[[],[]],[[],[[]]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,3,4,2,6,8,7,5] => [3,3,1,1] => 3
[[],[[],[]],[[[]],[]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,3,4,2,7,6,8,5] => [3,3,1,1] => 3
[[],[[],[]],[[[],[]]]] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,3,4,2,8,6,7,5] => [3,2,1,1,1] => 3
[[],[[],[]],[[[[]]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,3,4,2,8,7,6,5] => [3,2,2,1] => 3
[[],[[[]]],[[],[],[]]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,4,3,2,6,7,8,5] => [4,2,1,1] => 4
[[],[[[]]],[[],[[]]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,4,3,2,6,8,7,5] => [3,2,1,1,1] => 3
[[],[[[]]],[[[]],[]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,4,3,2,7,6,8,5] => [3,2,1,1,1] => 3
[[],[[[]]],[[[],[]]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,4,3,2,8,6,7,5] => [2,2,1,1,1,1] => 2
[[],[[[]]],[[[[]]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,3,2,8,7,6,5] => [2,2,2,1,1] => 2
[[],[[],[],[]],[],[],[]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2,6,7,8] => [4,1,1,1,1] => 4
[[],[[[],[]]],[],[],[]] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,5,3,4,2,6,7,8] => [2,1,1,1,1,1,1] => 2
[[],[[[[]]]],[],[],[]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,5,4,3,2,6,7,8] => [2,2,1,1,1,1] => 2
[[],[[],[[]]],[],[[]]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,3,5,4,2,6,8,7] => [3,2,1,1,1] => 3
[[],[[],[],[]],[[]],[]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,5,2,7,6,8] => [4,2,1,1] => 4
[[],[[],[[]]],[[]],[]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,3,5,4,2,7,6,8] => [3,2,1,1,1] => 3
[[],[[[]],[]],[[]],[]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,4,3,5,2,7,6,8] => [3,2,1,1,1] => 3
[[],[[[[]]]],[[]],[]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,5,4,3,2,7,6,8] => [2,2,2,1,1] => 2
[[],[[],[],[]],[[],[]]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,5,2,7,8,6] => [4,3,1] => 4
[[],[[],[],[]],[[[]]]] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,5,2,8,7,6] => [4,2,1,1] => 4
[[],[[],[[]]],[[],[]]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,3,5,4,2,7,8,6] => [3,3,1,1] => 3
[[],[[[],[]]],[[],[]]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,5,3,4,2,7,8,6] => [3,2,1,1,1] => 3
[[],[[[],[]]],[[[]]]] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,5,3,4,2,8,7,6] => [2,2,1,1,1,1] => 2
[[],[[[[]]]],[[],[]]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,5,4,3,2,7,8,6] => [3,2,2,1] => 3
[[],[[[[]]]],[[[]]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,4,3,2,8,7,6] => [2,2,2,1,1] => 2
[[],[[],[],[],[]],[],[]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,6,2,7,8] => [5,1,1,1] => 5
[[],[[[]],[],[]],[],[]] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,4,3,5,6,2,7,8] => [4,1,1,1,1] => 4
[[],[[[]],[[]]],[],[]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,4,3,6,5,2,7,8] => [3,1,1,1,1,1] => 3
[[],[[[[]]],[]],[],[]] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,5,4,3,6,2,7,8] => [3,2,1,1,1] => 3
[[],[[[],[],[]]],[],[]] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,6,3,4,5,2,7,8] => [2,1,1,1,1,1,1] => 2
[[],[[[],[[]]]],[],[]] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,6,3,5,4,2,7,8] => [2,2,1,1,1,1] => 2
[[],[[[[]],[]]],[],[]] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,6,4,3,5,2,7,8] => [2,2,1,1,1,1] => 2
[[],[[[[],[]]]],[],[]] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,6,4,5,3,2,7,8] => [3,2,1,1,1] => 3
[[],[[[[[]]]]],[],[]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,6,5,4,3,2,7,8] => [2,2,1,1,1,1] => 2
[[],[[],[],[],[]],[[]]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,6,2,8,7] => [5,2,1] => 5
[[],[[],[[],[]]],[[]]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,3,6,4,5,2,8,7] => [3,2,1,1,1] => 3
[[],[[],[[[]]]],[[]]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,3,6,5,4,2,8,7] => [3,2,2,1] => 3
[[],[[[],[]],[]],[[]]] => [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,5,3,4,6,2,8,7] => [3,2,1,1,1] => 3
[[],[[[[],[]]]],[[]]] => [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,6,4,5,3,2,8,7] => [3,2,2,1] => 3
[[],[[[[[]]]]],[[]]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,5,4,3,2,8,7] => [2,2,2,1,1] => 2
[[],[[],[],[],[],[]],[]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,2,8] => [6,1,1] => 6
[[],[[],[],[],[[]]],[]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,5,7,6,2,8] => [5,1,1,1] => 5
[[],[[],[[]],[[]]],[]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,3,5,4,7,6,2,8] => [4,1,1,1,1] => 4
[[],[[],[[],[]],[]],[]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,3,6,4,5,7,2,8] => [4,1,1,1,1] => 4
[[],[[],[[[]]],[]],[]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,3,6,5,4,7,2,8] => [4,2,1,1] => 4
[[],[[],[[],[],[]]],[]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,3,7,4,5,6,2,8] => [3,1,1,1,1,1] => 3
[[],[[[]],[],[[]]],[]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,4,3,5,7,6,2,8] => [4,1,1,1,1] => 4
[[],[[[]],[[]],[]],[]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,4,3,6,5,7,2,8] => [4,1,1,1,1] => 4
[[],[[[],[]],[],[]],[]] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,5,3,4,6,7,2,8] => [4,1,1,1,1] => 4
[[],[[[[]]],[],[]],[]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,5,4,3,6,7,2,8] => [4,2,1,1] => 4
[[],[[[],[],[],[]]],[]] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,7,3,4,5,6,2,8] => [2,1,1,1,1,1,1] => 2
[[],[[[],[[]],[]]],[]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,7,3,5,4,6,2,8] => [2,2,1,1,1,1] => 2
[[],[[[[[]]],[]]],[]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,7,5,4,3,6,2,8] => [2,2,1,1,1,1] => 2
[[],[[[[],[[]]]]],[]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,7,4,6,5,3,2,8] => [3,2,1,1,1] => 3
[[],[[[[[],[]]]]],[]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,7,6,4,5,3,2,8] => [2,2,1,1,1,1] => 2
[[],[[[[[[]]]]]],[]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,7,6,5,4,3,2,8] => [2,2,2,1,1] => 2
[[],[[],[],[],[],[],[]]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,2] => [7,1] => 7
[[],[[],[],[],[],[[]]]] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,8,7,2] => [6,1,1] => 6
[[],[[],[],[],[[],[]]]] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,5,8,6,7,2] => [5,1,1,1] => 5
[[],[[],[],[],[[[]]]]] => [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,5,8,7,6,2] => [5,2,1] => 5
[[],[[],[],[[]],[],[]]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,3,4,6,5,7,8,2] => [6,1,1] => 6
[[],[[],[],[[[]]],[]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,3,4,7,6,5,8,2] => [5,2,1] => 5
[[],[[],[],[[],[],[]]]] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,3,4,8,5,6,7,2] => [4,1,1,1,1] => 4
[[],[[],[],[[[[]]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,3,4,8,7,6,5,2] => [4,2,1,1] => 4
[[],[[],[[]],[[]],[]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,3,5,4,7,6,8,2] => [5,1,1,1] => 5
[[],[[],[[],[]],[],[]]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,3,6,4,5,7,8,2] => [5,1,1,1] => 5
[[],[[],[[],[]],[[]]]] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,3,6,4,5,8,7,2] => [4,1,1,1,1] => 4
[[],[[],[[[]]],[[]]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,3,6,5,4,8,7,2] => [4,2,1,1] => 4
[[],[[],[[],[],[]],[]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,3,7,4,5,6,8,2] => [4,1,1,1,1] => 4
[[],[[],[[],[],[],[]]]] => [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,3,8,4,5,6,7,2] => [3,1,1,1,1,1] => 3
[[],[[],[[],[[]],[]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,3,8,4,6,5,7,2] => [3,2,1,1,1] => 3
[[],[[],[[],[[],[]]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,3,8,4,6,7,5,2] => [3,3,1,1] => 3
[[],[[],[[[]],[],[]]]] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,3,8,5,4,6,7,2] => [3,2,1,1,1] => 3
[[],[[],[[[]],[[]]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,3,8,5,4,7,6,2] => [3,2,2,1] => 3
[[],[[],[[[],[],[]]]]] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,3,8,5,6,7,4,2] => [4,3,1] => 4
[[],[[],[[[],[[]]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,3,8,5,7,6,4,2] => [3,3,1,1] => 3
[[],[[],[[[[]],[]]]]] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,3,8,6,5,7,4,2] => [3,3,1,1] => 3
[[],[[],[[[[],[]]]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,3,8,7,5,6,4,2] => [3,2,1,1,1] => 3
[[],[[],[[[[[]]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,8,7,6,5,4,2] => [3,2,2,1] => 3
[[],[[[]],[],[],[],[]]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,8,2] => [6,1,1] => 6
[[],[[[]],[],[[],[]]]] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,3,5,8,6,7,2] => [4,1,1,1,1] => 4
[[],[[[]],[],[[[]]]]] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,4,3,5,8,7,6,2] => [4,2,1,1] => 4
[[],[[[]],[[]],[],[]]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,3,6,5,7,8,2] => [5,1,1,1] => 5
[[],[[[]],[[]],[[]]]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,8,7,2] => [4,1,1,1,1] => 4
[[],[[[]],[[],[],[]]]] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,3,8,5,6,7,2] => [3,1,1,1,1,1] => 3
[[],[[[]],[[],[[]]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,3,8,5,7,6,2] => [3,2,1,1,1] => 3
[[],[[[]],[[[[]]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,3,8,7,6,5,2] => [3,2,1,1,1] => 3
[[],[[[],[]],[],[],[]]] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,5,3,4,6,7,8,2] => [5,1,1,1] => 5
[[],[[[[]]],[],[],[]]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,5,4,3,6,7,8,2] => [5,2,1] => 5
[[],[[[],[]],[[],[]]]] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,5,3,4,8,6,7,2] => [3,1,1,1,1,1] => 3
[[],[[[[]]],[[[]]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,5,4,3,8,7,6,2] => [3,2,2,1] => 3
[[],[[[],[[]]],[[]]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,6,3,5,4,8,7,2] => [3,2,1,1,1] => 3
[[],[[[[]],[]],[[]]]] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,6,4,3,5,8,7,2] => [3,2,1,1,1] => 3
[[],[[[[[]]]],[[]]]] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,6,5,4,3,8,7,2] => [3,2,1,1,1] => 3
[[],[[[],[],[],[]],[]]] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,7,3,4,5,6,8,2] => [3,1,1,1,1,1] => 3
[[],[[[],[[[]]]],[]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,7,3,6,5,4,8,2] => [3,2,1,1,1] => 3
[[],[[[[]],[[]]],[]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,7,4,3,6,5,8,2] => [3,2,2,1] => 3
[[],[[[[],[]],[]],[]]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,7,4,5,3,6,8,2] => [3,3,1,1] => 3
[[],[[[[],[],[]]],[]]] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,7,4,5,6,3,8,2] => [4,3,1] => 4
[[],[[[[[[]]]]],[]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,7,6,5,4,3,8,2] => [3,2,2,1] => 3
[[],[[[],[],[],[],[]]]] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,8,3,4,5,6,7,2] => [2,1,1,1,1,1,1] => 2
[[],[[[],[],[[],[]]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,8,3,4,6,7,5,2] => [3,2,1,1,1] => 3
[[],[[[],[],[[[]]]]]] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,8,3,4,7,6,5,2] => [2,2,1,1,1,1] => 2
[[],[[[],[[]],[],[]]]] => [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,8,3,5,4,6,7,2] => [2,2,1,1,1,1] => 2
[[],[[[],[[]],[[]]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,8,3,5,4,7,6,2] => [2,2,2,1,1] => 2
[[],[[[],[[],[]],[]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,8,3,5,6,4,7,2] => [3,2,1,1,1] => 3
[[],[[[],[[[]]],[]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,8,3,6,5,4,7,2] => [2,2,1,1,1,1] => 2
[[],[[[],[[],[],[]]]]] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,8,3,5,6,7,4,2] => [4,2,1,1] => 4
[[],[[[],[[],[[]]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,8,3,5,7,6,4,2] => [3,2,1,1,1] => 3
[[],[[[],[[[],[]]]]]] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,8,3,7,5,6,4,2] => [2,2,1,1,1,1] => 2
[[],[[[],[[[[]]]]]]] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,8,3,7,6,5,4,2] => [2,2,2,1,1] => 2
[[],[[[[]],[],[],[]]]] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,8,4,3,5,6,7,2] => [2,2,1,1,1,1] => 2
[[],[[[[]],[],[[]]]]] => [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,8,4,3,5,7,6,2] => [2,2,2,1,1] => 2
[[],[[[[]],[[]],[]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,8,4,3,6,5,7,2] => [2,2,2,1,1] => 2
[[],[[[[],[]],[],[]]]] => [1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,8,4,5,3,6,7,2] => [3,2,1,1,1] => 3
[[],[[[[[]]],[],[]]]] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,8,5,4,3,6,7,2] => [2,2,1,1,1,1] => 2
[[],[[[[[]]],[[]]]]] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,8,5,4,3,7,6,2] => [2,2,2,1,1] => 2
[[],[[[[[]],[]],[]]]] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,8,5,4,6,3,7,2] => [3,2,1,1,1] => 3
[[],[[[[[],[]]],[]]]] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,8,6,4,5,3,7,2] => [2,2,1,1,1,1] => 2
[[],[[[[[[]]]],[]]]] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,8,6,5,4,3,7,2] => [2,2,2,1,1] => 2
[[],[[[[],[],[],[]]]]] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,8,4,5,6,7,3,2] => [5,2,1] => 5
[[],[[[[],[[]],[]]]]] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,8,4,6,5,7,3,2] => [4,2,1,1] => 4
[[],[[[[],[[[]]]]]]] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,8,4,7,6,5,3,2] => [3,2,2,1] => 3
[[],[[[[[]],[],[]]]]] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,8,5,4,6,7,3,2] => [4,2,1,1] => 4
[[],[[[[[]],[[]]]]]] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,8,5,4,7,6,3,2] => [3,2,1,1,1] => 3
[[],[[[[[],[]],[]]]]] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,8,6,4,5,7,3,2] => [3,2,1,1,1] => 3
[[],[[[[[[]]],[]]]]] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,8,6,5,4,7,3,2] => [3,2,2,1] => 3
[[],[[[[[],[],[]]]]]] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,8,7,4,5,6,3,2] => [2,2,1,1,1,1] => 2
[[],[[[[[],[[]]]]]]] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,8,7,4,6,5,3,2] => [2,2,2,1,1] => 2
[[],[[[[[[]],[]]]]]] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,8,7,5,4,6,3,2] => [2,2,2,1,1] => 2
[[],[[[[[[],[]]]]]]] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,8,7,5,6,4,3,2] => [3,2,2,1] => 3
[[],[[[[[[[]]]]]]]] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,7,6,5,4,3,2] => [2,2,2,1,1] => 2
[[[]],[],[],[],[],[],[]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8] => [2,1,1,1,1,1,1] => 2
[[[]],[],[],[],[],[[]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,8,7] => [2,2,1,1,1,1] => 2
[[[]],[],[],[],[[]],[]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,7,6,8] => [2,2,1,1,1,1] => 2
[[[]],[],[],[],[[],[]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,7,8,6] => [3,2,1,1,1] => 3
[[[]],[],[],[],[[[]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,5,8,7,6] => [2,2,1,1,1,1] => 2
[[[]],[],[],[[]],[],[]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,4,6,5,7,8] => [2,2,1,1,1,1] => 2
[[[]],[],[],[[]],[[]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,4,6,5,8,7] => [2,2,2,1,1] => 2
[[[]],[],[],[[],[],[]]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,4,6,7,8,5] => [4,2,1,1] => 4
[[[]],[],[],[[[]],[]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,4,7,6,8,5] => [3,2,1,1,1] => 3
[[[]],[],[],[[[],[]]]] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,4,8,6,7,5] => [2,2,1,1,1,1] => 2
[[[]],[],[],[[[[]]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,8,7,6,5] => [2,2,2,1,1] => 2
[[[]],[],[[]],[],[],[]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,3,5,4,6,7,8] => [2,2,1,1,1,1] => 2
[[[]],[],[[]],[],[[]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4,6,8,7] => [2,2,2,1,1] => 2
[[[]],[],[[]],[[],[]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,3,5,4,7,8,6] => [3,2,2,1] => 3
[[[]],[],[[]],[[[]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,3,5,4,8,7,6] => [2,2,2,1,1] => 2
[[[]],[],[[],[]],[[]]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,1,3,5,6,4,8,7] => [3,2,2,1] => 3
[[[]],[],[[],[],[],[]]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,3,5,6,7,8,4] => [5,2,1] => 5
[[[]],[],[[],[[],[]]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,1,3,5,8,6,7,4] => [3,2,1,1,1] => 3
[[[]],[],[[[],[],[]]]] => [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,1,3,8,5,6,7,4] => [2,2,1,1,1,1] => 2
[[[]],[],[[[],[[]]]]] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,1,3,8,5,7,6,4] => [2,2,2,1,1] => 2
[[[]],[],[[[[],[]]]]] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,3,8,6,7,5,4] => [3,2,2,1] => 3
[[[]],[],[[[[[]]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,8,7,6,5,4] => [2,2,2,1,1] => 2
[[[]],[[]],[],[],[],[]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8] => [2,2,1,1,1,1] => 2
[[[]],[[]],[],[],[[]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,4,3,5,6,8,7] => [2,2,2,1,1] => 2
[[[]],[[]],[],[[],[]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,4,3,5,7,8,6] => [3,2,2,1] => 3
[[[]],[[]],[[]],[],[]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,5,7,8] => [2,2,2,1,1] => 2
[[[]],[[]],[[]],[[]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => [2,2,2,2] => 2
[[[]],[[]],[[],[]],[]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,3,6,7,5,8] => [3,2,2,1] => 3
[[[]],[[]],[[],[],[]]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,5] => [4,2,2] => 4
[[[]],[[]],[[],[[]]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,8,7,5] => [3,2,2,1] => 3
[[[]],[[]],[[[]],[]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,6,8,5] => [3,2,2,1] => 3
[[[]],[[]],[[[],[]]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,3,8,6,7,5] => [2,2,2,1,1] => 2
[[[]],[[]],[[[[]]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => [2,2,2,2] => 2
[[[]],[[],[]],[],[],[]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,4,5,3,6,7,8] => [3,2,1,1,1] => 3
[[[]],[[[]]],[],[],[]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,5,4,3,6,7,8] => [2,2,1,1,1,1] => 2
[[[]],[[],[]],[],[[]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,1,4,5,3,6,8,7] => [3,2,2,1] => 3
[[[]],[[[]]],[],[[]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,1,5,4,3,6,8,7] => [2,2,2,1,1] => 2
[[[]],[[],[]],[[[]]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,1,4,5,3,8,7,6] => [3,2,2,1] => 3
[[[]],[[],[[]]],[],[]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,1,4,6,5,3,7,8] => [3,2,1,1,1] => 3
[[[]],[[],[],[]],[[]]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,1,4,5,6,3,8,7] => [4,2,2] => 4
[[[]],[[],[[]]],[[]]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,6,5,3,8,7] => [3,2,2,1] => 3
[[[]],[[[]],[]],[[]]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,4,6,3,8,7] => [3,2,2,1] => 3
[[[]],[[[],[]]],[[]]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,1,6,4,5,3,8,7] => [2,2,2,1,1] => 2
[[[]],[[[[]]]],[[]]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => [2,2,2,2] => 2
[[[]],[[],[],[],[]],[]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,7,3,8] => [5,2,1] => 5
[[[]],[[[]],[],[]],[]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,1,5,4,6,7,3,8] => [4,2,1,1] => 4
[[[]],[[[[[]]]]],[]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,7,6,5,4,3,8] => [2,2,2,1,1] => 2
[[[]],[[],[],[],[],[]]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,3] => [6,2] => 6
[[[]],[[],[],[],[[]]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,1,4,5,6,8,7,3] => [5,2,1] => 5
[[[]],[[],[],[[],[]]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,1,4,5,8,6,7,3] => [4,2,1,1] => 4
[[[]],[[],[],[[[]]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,1,4,5,8,7,6,3] => [4,2,2] => 4
[[[]],[[],[[]],[[]]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,1,4,6,5,8,7,3] => [4,2,1,1] => 4
[[[]],[[],[[[]]],[]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,1,4,7,6,5,8,3] => [4,2,2] => 4
[[[]],[[],[[],[],[]]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,1,4,8,5,6,7,3] => [3,2,1,1,1] => 3
[[[]],[[],[[],[[]]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,1,4,8,5,7,6,3] => [3,2,2,1] => 3
[[[]],[[],[[[]],[]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,1,4,8,6,5,7,3] => [3,2,2,1] => 3
[[[]],[[],[[[],[]]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,4,8,6,7,5,3] => [3,3,2] => 3
[[[]],[[],[[[[]]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,1,4,8,7,6,5,3] => [3,2,2,1] => 3
[[[]],[[[]],[],[],[]]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,1,5,4,6,7,8,3] => [5,2,1] => 5
[[[]],[[[]],[[]],[]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,4,7,6,8,3] => [4,2,1,1] => 4
[[[]],[[[]],[[],[]]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,1,5,4,8,6,7,3] => [3,2,1,1,1] => 3
[[[]],[[[]],[[[]]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,1,5,4,8,7,6,3] => [3,2,2,1] => 3
[[[]],[[[],[]],[],[]]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,1,6,4,5,7,8,3] => [4,2,1,1] => 4
[[[]],[[[],[]],[[]]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,1,6,4,5,8,7,3] => [3,2,1,1,1] => 3
[[[]],[[[],[[]]],[]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,1,7,4,6,5,8,3] => [3,2,2,1] => 3
[[[]],[[[[],[]]],[]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,1,7,5,6,4,8,3] => [3,3,2] => 3
[[[]],[[[[[]]]],[]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,1,7,6,5,4,8,3] => [3,2,2,1] => 3
[[[]],[[[],[],[],[]]]] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,1,8,4,5,6,7,3] => [2,2,1,1,1,1] => 2
[[[]],[[[],[],[[]]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,1,8,4,5,7,6,3] => [2,2,2,1,1] => 2
[[[]],[[[],[[]],[]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,1,8,4,6,5,7,3] => [2,2,2,1,1] => 2
[[[]],[[[],[[],[]]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,8,4,6,7,5,3] => [3,2,2,1] => 3
[[[]],[[[],[[[]]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,1,8,4,7,6,5,3] => [2,2,2,1,1] => 2
[[[]],[[[[]],[[]]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,1,8,5,4,7,6,3] => [2,2,2,2] => 2
[[[]],[[[[],[]],[]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,1,8,5,6,4,7,3] => [3,2,2,1] => 3
[[[]],[[[[[]]],[]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,1,8,6,5,4,7,3] => [2,2,2,1,1] => 2
[[[]],[[[[],[],[]]]]] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,1,8,5,6,7,4,3] => [4,2,2] => 4
[[[]],[[[[],[[]]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,1,8,5,7,6,4,3] => [3,2,2,1] => 3
[[[]],[[[[[]],[]]]]] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,1,8,6,5,7,4,3] => [3,2,2,1] => 3
[[[]],[[[[[],[]]]]]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,8,7,5,6,4,3] => [2,2,2,1,1] => 2
[[[]],[[[[[[]]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => [2,2,2,2] => 2
[[[],[]],[],[],[],[],[]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8] => [3,1,1,1,1,1] => 3
[[[[]]],[],[],[],[],[]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8] => [2,1,1,1,1,1,1] => 2
[[[],[]],[],[],[],[[]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,8,7] => [3,2,1,1,1] => 3
[[[[]]],[],[],[],[[]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,6,8,7] => [2,2,1,1,1,1] => 2
[[[],[]],[],[],[[]],[]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,3,1,4,5,7,6,8] => [3,2,1,1,1] => 3
[[[[]]],[],[],[[]],[]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [3,2,1,4,5,7,6,8] => [2,2,1,1,1,1] => 2
[[[],[]],[],[],[[],[]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,3,1,4,5,7,8,6] => [3,3,1,1] => 3
[[[[]]],[],[],[[],[]]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [3,2,1,4,5,7,8,6] => [3,2,1,1,1] => 3
[[[[]]],[],[],[[[]]]] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,2,1,4,5,8,7,6] => [2,2,1,1,1,1] => 2
[[[],[]],[],[[]],[[]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,3,1,4,6,5,8,7] => [3,2,2,1] => 3
[[[],[]],[],[[],[]],[]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,3,1,4,6,7,5,8] => [3,3,1,1] => 3
[[[[]]],[],[[[]]],[]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [3,2,1,4,7,6,5,8] => [2,2,1,1,1,1] => 2
[[[],[]],[],[[],[],[]]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,3,1,4,6,7,8,5] => [4,3,1] => 4
[[[],[]],[],[[[]],[]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,3,1,4,7,6,8,5] => [3,3,1,1] => 3
[[[],[]],[],[[[[]]]]] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,8,7,6,5] => [3,2,2,1] => 3
[[[[]]],[],[[],[],[]]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [3,2,1,4,6,7,8,5] => [4,2,1,1] => 4
[[[[]]],[],[[],[[]]]] => [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [3,2,1,4,6,8,7,5] => [3,2,1,1,1] => 3
[[[[]]],[],[[[]],[]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [3,2,1,4,7,6,8,5] => [3,2,1,1,1] => 3
[[[[]]],[],[[[],[]]]] => [1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [3,2,1,4,8,6,7,5] => [2,2,1,1,1,1] => 2
[[[[]]],[],[[[[]]]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [3,2,1,4,8,7,6,5] => [2,2,2,1,1] => 2
[[[],[]],[[]],[],[],[]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,3,1,5,4,6,7,8] => [3,2,1,1,1] => 3
[[[[]]],[[]],[],[],[]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [3,2,1,5,4,6,7,8] => [2,2,1,1,1,1] => 2
[[[],[]],[[]],[[]],[]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,8] => [3,2,2,1] => 3
[[[[]]],[[]],[[]],[]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,1,5,4,7,6,8] => [2,2,2,1,1] => 2
[[[],[]],[[],[]],[],[]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,3,1,5,6,4,7,8] => [3,3,1,1] => 3
[[[],[]],[[[]]],[],[]] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,6,5,4,7,8] => [3,2,1,1,1] => 3
[[[[]]],[[[]]],[],[]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [3,2,1,6,5,4,7,8] => [2,2,1,1,1,1] => 2
[[[],[]],[[[]]],[[]]] => [1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,3,1,6,5,4,8,7] => [3,2,2,1] => 3
[[[[]]],[[[]]],[[]]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,2,1,6,5,4,8,7] => [2,2,2,1,1] => 2
[[[],[]],[[],[],[]],[]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,3,1,5,6,7,4,8] => [4,3,1] => 4
[[[],[]],[[[]],[]],[]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,3,1,6,5,7,4,8] => [3,3,1,1] => 3
[[[],[]],[[[],[]]],[]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,3,1,7,5,6,4,8] => [3,2,1,1,1] => 3
[[[[]]],[[],[[]]],[]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [3,2,1,5,7,6,4,8] => [3,2,1,1,1] => 3
[[[[]]],[[[]],[]],[]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [3,2,1,6,5,7,4,8] => [3,2,1,1,1] => 3
[[[[]]],[[[],[]]],[]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [3,2,1,7,5,6,4,8] => [2,2,1,1,1,1] => 2
[[[[]]],[[[[]]]],[]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,2,1,7,6,5,4,8] => [2,2,2,1,1] => 2
[[[],[]],[[],[],[],[]]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,3,1,5,6,7,8,4] => [5,3] => 5
[[[],[]],[[],[[]],[]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,3,1,5,7,6,8,4] => [4,3,1] => 4
[[[],[]],[[[]],[[]]]] => [1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,3,1,6,5,8,7,4] => [3,3,1,1] => 3
[[[],[]],[[[[]]],[]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,3,1,7,6,5,8,4] => [3,3,2] => 3
[[[],[]],[[[],[],[]]]] => [1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,3,1,8,5,6,7,4] => [3,2,1,1,1] => 3
[[[],[]],[[[[],[]]]]] => [1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,3,1,8,6,7,5,4] => [3,3,2] => 3
[[[],[]],[[[[[]]]]]] => [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,1,8,7,6,5,4] => [3,2,2,1] => 3
[[[[]]],[[],[],[],[]]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [3,2,1,5,6,7,8,4] => [5,2,1] => 5
[[[[]]],[[],[[],[]]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [3,2,1,5,8,6,7,4] => [3,2,1,1,1] => 3
[[[[]]],[[[]],[[]]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [3,2,1,6,5,8,7,4] => [3,2,1,1,1] => 3
[[[[]]],[[[[]]],[]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [3,2,1,7,6,5,8,4] => [3,2,2,1] => 3
[[[[]]],[[[],[],[]]]] => [1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,8,5,6,7,4] => [2,2,1,1,1,1] => 2
[[[[]]],[[[],[[]]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [3,2,1,8,5,7,6,4] => [2,2,2,1,1] => 2
[[[[]]],[[[[]],[]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [3,2,1,8,6,5,7,4] => [2,2,2,1,1] => 2
[[[[]]],[[[[],[]]]]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,1,8,6,7,5,4] => [3,2,2,1] => 3
[[[[]]],[[[[[]]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => [2,2,2,1,1] => 2
[[[],[],[]],[],[],[],[]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8] => [4,1,1,1,1] => 4
[[[],[[]]],[],[],[],[]] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7,8] => [3,1,1,1,1,1] => 3
[[[[]],[]],[],[],[],[]] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8] => [3,1,1,1,1,1] => 3
[[[[],[]]],[],[],[],[]] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [4,2,3,1,5,6,7,8] => [2,1,1,1,1,1,1] => 2
[[[[[]]]],[],[],[],[]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8] => [2,2,1,1,1,1] => 2
[[[],[],[]],[],[],[[]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5,6,8,7] => [4,2,1,1] => 4
[[[[]],[]],[],[],[[]]] => [1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [3,2,4,1,5,6,8,7] => [3,2,1,1,1] => 3
[[[[[]]]],[],[],[[]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [4,3,2,1,5,6,8,7] => [2,2,2,1,1] => 2
[[[],[],[]],[],[[]],[]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,4,1,5,7,6,8] => [4,2,1,1] => 4
[[[[]],[]],[],[[]],[]] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [3,2,4,1,5,7,6,8] => [3,2,1,1,1] => 3
[[[],[],[]],[],[[],[]]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,4,1,5,7,8,6] => [4,3,1] => 4
[[[],[],[]],[],[[[]]]] => [1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,4,1,5,8,7,6] => [4,2,1,1] => 4
[[[[]],[]],[],[[],[]]] => [1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [3,2,4,1,5,7,8,6] => [3,3,1,1] => 3
[[[[]],[]],[],[[[]]]] => [1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [3,2,4,1,5,8,7,6] => [3,2,1,1,1] => 3
[[[[],[]]],[],[[],[]]] => [1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [4,2,3,1,5,7,8,6] => [3,2,1,1,1] => 3
[[[[],[]]],[],[[[]]]] => [1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [4,2,3,1,5,8,7,6] => [2,2,1,1,1,1] => 2
[[[[[]]]],[],[[],[]]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [4,3,2,1,5,7,8,6] => [3,2,2,1] => 3
[[[],[],[]],[[]],[],[]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,4,1,6,5,7,8] => [4,2,1,1] => 4
[[[[]],[]],[[]],[],[]] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [3,2,4,1,6,5,7,8] => [3,2,1,1,1] => 3
[[[[],[]]],[[]],[],[]] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [4,2,3,1,6,5,7,8] => [2,2,1,1,1,1] => 2
[[[[[]]]],[[]],[],[]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [4,3,2,1,6,5,7,8] => [2,2,2,1,1] => 2
[[[],[],[]],[[]],[[]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,8,7] => [4,2,2] => 4
[[[],[[]]],[[]],[[]]] => [1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,4,3,1,6,5,8,7] => [3,2,2,1] => 3
[[[[]],[]],[[]],[[]]] => [1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,2,4,1,6,5,8,7] => [3,2,2,1] => 3
[[[[],[]]],[[]],[[]]] => [1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [4,2,3,1,6,5,8,7] => [2,2,2,1,1] => 2
[[[[[]]]],[[]],[[]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7] => [2,2,2,2] => 2
[[[],[],[]],[[],[]],[]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,4,1,6,7,5,8] => [4,3,1] => 4
[[[],[],[]],[[[]]],[]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,4,1,7,6,5,8] => [4,2,1,1] => 4
[[[[]],[]],[[],[]],[]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [3,2,4,1,6,7,5,8] => [3,3,1,1] => 3
[[[[]],[]],[[[]]],[]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [3,2,4,1,7,6,5,8] => [3,2,1,1,1] => 3
[[[[],[]]],[[[]]],[]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [4,2,3,1,7,6,5,8] => [2,2,1,1,1,1] => 2
[[[[[]]]],[[[]]],[]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,3,2,1,7,6,5,8] => [2,2,2,1,1] => 2
[[[],[],[]],[[],[],[]]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,5] => [4,4] => 4
[[[],[],[]],[[],[[]]]] => [1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,4,1,6,8,7,5] => [4,3,1] => 4
[[[],[],[]],[[[]],[]]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,4,1,7,6,8,5] => [4,3,1] => 4
[[[],[],[]],[[[],[]]]] => [1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,4,1,8,6,7,5] => [4,2,1,1] => 4
[[[],[],[]],[[[[]]]]] => [1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,4,1,8,7,6,5] => [4,2,2] => 4
[[[],[[]]],[[],[],[]]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [2,4,3,1,6,7,8,5] => [4,3,1] => 4
[[[],[[]]],[[],[[]]]] => [1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,4,3,1,6,8,7,5] => [3,3,1,1] => 3
[[[],[[]]],[[[]],[]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,4,3,1,7,6,8,5] => [3,3,1,1] => 3
[[[],[[]]],[[[[]]]]] => [1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,4,3,1,8,7,6,5] => [3,2,2,1] => 3
[[[[]],[]],[[],[],[]]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [3,2,4,1,6,7,8,5] => [4,3,1] => 4
[[[[]],[]],[[],[[]]]] => [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [3,2,4,1,6,8,7,5] => [3,3,1,1] => 3
[[[[]],[]],[[[]],[]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,2,4,1,7,6,8,5] => [3,3,1,1] => 3
[[[[]],[]],[[[],[]]]] => [1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [3,2,4,1,8,6,7,5] => [3,2,1,1,1] => 3
[[[[]],[]],[[[[]]]]] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [3,2,4,1,8,7,6,5] => [3,2,2,1] => 3
[[[[],[]]],[[],[],[]]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [4,2,3,1,6,7,8,5] => [4,2,1,1] => 4
[[[[],[]]],[[],[[]]]] => [1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [4,2,3,1,6,8,7,5] => [3,2,1,1,1] => 3
[[[[],[]]],[[[]],[]]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [4,2,3,1,7,6,8,5] => [3,2,1,1,1] => 3
[[[[],[]]],[[[],[]]]] => [1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [4,2,3,1,8,6,7,5] => [2,2,1,1,1,1] => 2
[[[[],[]]],[[[[]]]]] => [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,2,3,1,8,7,6,5] => [2,2,2,1,1] => 2
[[[[[]]]],[[],[],[]]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [4,3,2,1,6,7,8,5] => [4,2,2] => 4
[[[[[]]]],[[[]],[]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [4,3,2,1,7,6,8,5] => [3,2,2,1] => 3
[[[[[]]]],[[[],[]]]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [4,3,2,1,8,6,7,5] => [2,2,2,1,1] => 2
[[[[[]]]],[[[[]]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => [2,2,2,2] => 2
[[[],[],[],[]],[],[],[]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8] => [5,1,1,1] => 5
[[[],[],[[]]],[],[],[]] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,3,5,4,1,6,7,8] => [4,1,1,1,1] => 4
[[[],[[]],[]],[],[],[]] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,4,3,5,1,6,7,8] => [4,1,1,1,1] => 4
[[[],[[],[]]],[],[],[]] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [2,5,3,4,1,6,7,8] => [3,1,1,1,1,1] => 3
[[[],[[[]]]],[],[],[]] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,5,4,3,1,6,7,8] => [3,2,1,1,1] => 3
[[[[]],[],[]],[],[],[]] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [3,2,4,5,1,6,7,8] => [4,1,1,1,1] => 4
[[[[]],[[]]],[],[],[]] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [3,2,5,4,1,6,7,8] => [3,1,1,1,1,1] => 3
[[[[],[]],[]],[],[],[]] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [4,2,3,5,1,6,7,8] => [3,1,1,1,1,1] => 3
[[[[[]]],[]],[],[],[]] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [4,3,2,5,1,6,7,8] => [3,2,1,1,1] => 3
[[[[],[],[]]],[],[],[]] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [5,2,3,4,1,6,7,8] => [2,1,1,1,1,1,1] => 2
[[[[],[[]]]],[],[],[]] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [5,2,4,3,1,6,7,8] => [2,2,1,1,1,1] => 2
[[[[[]],[]]],[],[],[]] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [5,3,2,4,1,6,7,8] => [2,2,1,1,1,1] => 2
[[[[[],[]]]],[],[],[]] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [5,3,4,2,1,6,7,8] => [3,2,1,1,1] => 3
[[[[[[]]]]],[],[],[]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8] => [2,2,1,1,1,1] => 2
[[[],[],[],[]],[],[[]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,5,1,6,8,7] => [5,2,1] => 5
[[[],[],[[]]],[],[[]]] => [1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,3,5,4,1,6,8,7] => [4,2,1,1] => 4
[[[],[[]],[]],[],[[]]] => [1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [2,4,3,5,1,6,8,7] => [4,2,1,1] => 4
[[[],[[[]]]],[],[[]]] => [1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [2,5,4,3,1,6,8,7] => [3,2,2,1] => 3
[[[[]],[[]]],[],[[]]] => [1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [3,2,5,4,1,6,8,7] => [3,2,1,1,1] => 3
[[[[],[]],[]],[],[[]]] => [1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [4,2,3,5,1,6,8,7] => [3,2,1,1,1] => 3
[[[[],[],[]]],[],[[]]] => [1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [5,2,3,4,1,6,8,7] => [2,2,1,1,1,1] => 2
[[[[],[[]]]],[],[[]]] => [1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [5,2,4,3,1,6,8,7] => [2,2,2,1,1] => 2
[[[[[]],[]]],[],[[]]] => [1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [5,3,2,4,1,6,8,7] => [2,2,2,1,1] => 2
[[[[[],[]]]],[],[[]]] => [1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [5,3,4,2,1,6,8,7] => [3,2,2,1] => 3
[[[[[[]]]]],[],[[]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [5,4,3,2,1,6,8,7] => [2,2,2,1,1] => 2
[[[],[],[],[]],[[]],[]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,5,1,7,6,8] => [5,2,1] => 5
[[[],[],[[]]],[[]],[]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,3,5,4,1,7,6,8] => [4,2,1,1] => 4
[[[],[[]],[]],[[]],[]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,4,3,5,1,7,6,8] => [4,2,1,1] => 4
[[[],[[[]]]],[[]],[]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [2,5,4,3,1,7,6,8] => [3,2,2,1] => 3
[[[[]],[[]]],[[]],[]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [3,2,5,4,1,7,6,8] => [3,2,1,1,1] => 3
[[[[],[[]]]],[[]],[]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [5,2,4,3,1,7,6,8] => [2,2,2,1,1] => 2
[[[[[]],[]]],[[]],[]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [5,3,2,4,1,7,6,8] => [2,2,2,1,1] => 2
[[[[[[]]]]],[[]],[]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [5,4,3,2,1,7,6,8] => [2,2,2,1,1] => 2
[[[],[],[],[]],[[],[]]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,1,7,8,6] => [5,3] => 5
[[[],[],[],[]],[[[]]]] => [1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,1,8,7,6] => [5,2,1] => 5
[[[],[],[[]]],[[[]]]] => [1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,4,1,8,7,6] => [4,2,1,1] => 4
[[[],[[]],[]],[[],[]]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,4,3,5,1,7,8,6] => [4,3,1] => 4
[[[],[[]],[]],[[[]]]] => [1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [2,4,3,5,1,8,7,6] => [4,2,1,1] => 4
[[[],[[],[]]],[[[]]]] => [1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [2,5,3,4,1,8,7,6] => [3,2,1,1,1] => 3
[[[],[[[]]]],[[],[]]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [2,5,4,3,1,7,8,6] => [3,3,2] => 3
[[[],[[[]]]],[[[]]]] => [1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,5,4,3,1,8,7,6] => [3,2,2,1] => 3
[[[[]],[],[]],[[[]]]] => [1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [3,2,4,5,1,8,7,6] => [4,2,1,1] => 4
[[[[]],[[]]],[[],[]]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [3,2,5,4,1,7,8,6] => [3,3,1,1] => 3
[[[[]],[[]]],[[[]]]] => [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [3,2,5,4,1,8,7,6] => [3,2,1,1,1] => 3
[[[[],[]],[]],[[],[]]] => [1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [4,2,3,5,1,7,8,6] => [3,3,1,1] => 3
[[[[],[]],[]],[[[]]]] => [1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [4,2,3,5,1,8,7,6] => [3,2,1,1,1] => 3
[[[[[]]],[]],[[],[]]] => [1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [4,3,2,5,1,7,8,6] => [3,3,2] => 3
[[[[[]]],[]],[[[]]]] => [1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [4,3,2,5,1,8,7,6] => [3,2,2,1] => 3
[[[[],[],[]]],[[],[]]] => [1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [5,2,3,4,1,7,8,6] => [3,2,1,1,1] => 3
[[[[],[],[]]],[[[]]]] => [1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [5,2,3,4,1,8,7,6] => [2,2,1,1,1,1] => 2
[[[[],[[]]]],[[[]]]] => [1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [5,2,4,3,1,8,7,6] => [2,2,2,1,1] => 2
[[[[[]],[]]],[[[]]]] => [1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [5,3,2,4,1,8,7,6] => [2,2,2,1,1] => 2
[[[[[],[]]]],[[],[]]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [5,3,4,2,1,7,8,6] => [3,3,2] => 3
[[[[[],[]]]],[[[]]]] => [1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,3,4,2,1,8,7,6] => [3,2,2,1] => 3
[[[[[[]]]]],[[],[]]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [5,4,3,2,1,7,8,6] => [3,2,2,1] => 3
[[[[[[]]]]],[[[]]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,4,3,2,1,8,7,6] => [2,2,2,1,1] => 2
[[[],[],[],[],[]],[],[]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,1,7,8] => [6,1,1] => 6
[[[],[],[],[[]]],[],[]] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,4,6,5,1,7,8] => [5,1,1,1] => 5
[[[],[],[[]],[]],[],[]] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,3,5,4,6,1,7,8] => [5,1,1,1] => 5
[[[],[],[[],[]]],[],[]] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,3,6,4,5,1,7,8] => [4,1,1,1,1] => 4
[[[],[[],[],[]]],[],[]] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [2,6,3,4,5,1,7,8] => [3,1,1,1,1,1] => 3
[[[[]],[],[],[]],[],[]] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,6,1,7,8] => [5,1,1,1] => 5
[[[[],[]],[],[]],[],[]] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [4,2,3,5,6,1,7,8] => [4,1,1,1,1] => 4
[[[[[]]],[],[]],[],[]] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [4,3,2,5,6,1,7,8] => [4,2,1,1] => 4
[[[[[]]],[[]]],[],[]] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [4,3,2,6,5,1,7,8] => [3,2,1,1,1] => 3
[[[[],[],[]],[]],[],[]] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [5,2,3,4,6,1,7,8] => [3,1,1,1,1,1] => 3
[[[[],[[]]],[]],[],[]] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [5,2,4,3,6,1,7,8] => [3,2,1,1,1] => 3
[[[[[]],[]],[]],[],[]] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [5,3,2,4,6,1,7,8] => [3,2,1,1,1] => 3
[[[[[[]]]],[]],[],[]] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [5,4,3,2,6,1,7,8] => [3,2,1,1,1] => 3
[[[[],[],[],[]]],[],[]] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [6,2,3,4,5,1,7,8] => [2,1,1,1,1,1,1] => 2
[[[[],[],[[]]]],[],[]] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [6,2,3,5,4,1,7,8] => [2,2,1,1,1,1] => 2
[[[[],[[[]]]]],[],[]] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [6,2,5,4,3,1,7,8] => [2,2,1,1,1,1] => 2
[[[[[[]]],[]]],[],[]] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [6,4,3,2,5,1,7,8] => [2,2,1,1,1,1] => 2
[[[[[[],[]]]]],[],[]] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [6,5,3,4,2,1,7,8] => [2,2,1,1,1,1] => 2
[[[[[[[]]]]]],[],[]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,5,4,3,2,1,7,8] => [2,2,2,1,1] => 2
[[[],[],[],[],[]],[[]]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,1,8,7] => [6,2] => 6
[[[],[],[[],[]]],[[]]] => [1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,3,6,4,5,1,8,7] => [4,2,1,1] => 4
[[[],[],[[[]]]],[[]]] => [1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,3,6,5,4,1,8,7] => [4,2,2] => 4
[[[],[[]],[],[]],[[]]] => [1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [2,4,3,5,6,1,8,7] => [5,2,1] => 5
[[[],[[]],[[]]],[[]]] => [1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,4,3,6,5,1,8,7] => [4,2,1,1] => 4
[[[],[[[]]],[]],[[]]] => [1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [2,5,4,3,6,1,8,7] => [4,2,2] => 4
[[[],[[],[[]]]],[[]]] => [1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,6,3,5,4,1,8,7] => [3,2,2,1] => 3
[[[],[[[]],[]]],[[]]] => [1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [2,6,4,3,5,1,8,7] => [3,2,2,1] => 3
[[[],[[[[]]]]],[[]]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,6,5,4,3,1,8,7] => [3,2,2,1] => 3
[[[[]],[[]],[]],[[]]] => [1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,2,5,4,6,1,8,7] => [4,2,1,1] => 4
[[[[]],[[],[]]],[[]]] => [1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [3,2,6,4,5,1,8,7] => [3,2,1,1,1] => 3
[[[[],[]],[],[]],[[]]] => [1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [4,2,3,5,6,1,8,7] => [4,2,1,1] => 4
[[[[[]]],[],[]],[[]]] => [1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [4,3,2,5,6,1,8,7] => [4,2,2] => 4
[[[[[]]],[[]]],[[]]] => [1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [4,3,2,6,5,1,8,7] => [3,2,2,1] => 3
[[[[],[],[]],[]],[[]]] => [1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [5,2,3,4,6,1,8,7] => [3,2,1,1,1] => 3
[[[[],[[]]],[]],[[]]] => [1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [5,2,4,3,6,1,8,7] => [3,2,2,1] => 3
[[[[[]],[]],[]],[[]]] => [1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [5,3,2,4,6,1,8,7] => [3,2,2,1] => 3
[[[[[],[]]],[]],[[]]] => [1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [5,3,4,2,6,1,8,7] => [3,3,2] => 3
[[[[[[]]]],[]],[[]]] => [1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [5,4,3,2,6,1,8,7] => [3,2,2,1] => 3
[[[[],[],[],[]]],[[]]] => [1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [6,2,3,4,5,1,8,7] => [2,2,1,1,1,1] => 2
[[[[],[],[[]]]],[[]]] => [1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [6,2,3,5,4,1,8,7] => [2,2,2,1,1] => 2
[[[[],[[]],[]]],[[]]] => [1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [6,2,4,3,5,1,8,7] => [2,2,2,1,1] => 2
[[[[],[[[]]]]],[[]]] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [6,2,5,4,3,1,8,7] => [2,2,2,1,1] => 2
[[[[[]],[[]]]],[[]]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [6,3,2,5,4,1,8,7] => [2,2,2,2] => 2
[[[[[],[]],[]]],[[]]] => [1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [6,3,4,2,5,1,8,7] => [3,2,2,1] => 3
[[[[[[]]],[]]],[[]]] => [1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [6,4,3,2,5,1,8,7] => [2,2,2,1,1] => 2
[[[[[],[],[]]]],[[]]] => [1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [6,3,4,5,2,1,8,7] => [4,2,2] => 4
[[[[[],[[]]]]],[[]]] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [6,3,5,4,2,1,8,7] => [3,2,2,1] => 3
[[[[[[]],[]]]],[[]]] => [1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [6,4,3,5,2,1,8,7] => [3,2,2,1] => 3
[[[[[[],[]]]]],[[]]] => [1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [6,5,3,4,2,1,8,7] => [2,2,2,1,1] => 2
[[[[[[[]]]]]],[[]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,5,4,3,2,1,8,7] => [2,2,2,2] => 2
[[[],[],[],[],[],[]],[]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,1,8] => [7,1] => 7
[[[],[],[],[],[[]]],[]] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,7,6,1,8] => [6,1,1] => 6
[[[],[],[],[[]],[]],[]] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,4,6,5,7,1,8] => [6,1,1] => 6
[[[],[],[],[[],[]]],[]] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,4,7,5,6,1,8] => [5,1,1,1] => 5
[[[],[],[],[[[]]]],[]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,4,7,6,5,1,8] => [5,2,1] => 5
[[[],[],[[[]],[]]],[]] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,3,7,5,4,6,1,8] => [4,2,1,1] => 4
[[[],[],[[[],[]]]],[]] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,3,7,5,6,4,1,8] => [4,3,1] => 4
[[[],[],[[[[]]]]],[]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,3,7,6,5,4,1,8] => [4,2,1,1] => 4
[[[],[[]],[[]],[]],[]] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,4,3,6,5,7,1,8] => [5,1,1,1] => 5
[[[],[[],[]],[],[]],[]] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [2,5,3,4,6,7,1,8] => [5,1,1,1] => 5
[[[],[[[]]],[],[]],[]] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [2,5,4,3,6,7,1,8] => [5,2,1] => 5
[[[],[[],[],[],[]]],[]] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [2,7,3,4,5,6,1,8] => [3,1,1,1,1,1] => 3
[[[],[[],[[[]]]]],[]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [2,7,3,6,5,4,1,8] => [3,2,1,1,1] => 3
[[[],[[[],[],[]]]],[]] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [2,7,4,5,6,3,1,8] => [4,3,1] => 4
[[[],[[[[[]]]]]],[]] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,7,6,5,4,3,1,8] => [3,2,2,1] => 3
[[[[]],[],[],[],[]],[]] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,7,1,8] => [6,1,1] => 6
[[[[]],[[]],[[]]],[]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,7,6,1,8] => [4,1,1,1,1] => 4
[[[[]],[[[]]],[]],[]] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [3,2,6,5,4,7,1,8] => [4,2,1,1] => 4
[[[[]],[[],[],[]]],[]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [3,2,7,4,5,6,1,8] => [3,1,1,1,1,1] => 3
[[[[]],[[],[[]]]],[]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [3,2,7,4,6,5,1,8] => [3,2,1,1,1] => 3
[[[[]],[[[]],[]]],[]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [3,2,7,5,4,6,1,8] => [3,2,1,1,1] => 3
[[[[]],[[[],[]]]],[]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [3,2,7,5,6,4,1,8] => [3,3,1,1] => 3
[[[[]],[[[[]]]]],[]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [3,2,7,6,5,4,1,8] => [3,2,1,1,1] => 3
[[[[],[]],[],[],[]],[]] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [4,2,3,5,6,7,1,8] => [5,1,1,1] => 5
[[[[[]]],[],[],[]],[]] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [4,3,2,5,6,7,1,8] => [5,2,1] => 5
[[[[[]]],[],[[]]],[]] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [4,3,2,5,7,6,1,8] => [4,2,1,1] => 4
[[[[[]]],[[]],[]],[]] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [4,3,2,6,5,7,1,8] => [4,2,1,1] => 4
[[[[],[]],[[],[]]],[]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [4,2,3,7,5,6,1,8] => [3,1,1,1,1,1] => 3
[[[[],[],[]],[],[]],[]] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [5,2,3,4,6,7,1,8] => [4,1,1,1,1] => 4
[[[[[[]]]],[],[]],[]] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [5,4,3,2,6,7,1,8] => [4,2,1,1] => 4
[[[[],[],[]],[[]]],[]] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [5,2,3,4,7,6,1,8] => [3,1,1,1,1,1] => 3
[[[[],[[]]],[[]]],[]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [5,2,4,3,7,6,1,8] => [3,2,1,1,1] => 3
[[[[[]],[]],[[]]],[]] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [5,3,2,4,7,6,1,8] => [3,2,1,1,1] => 3
[[[[[],[]]],[[]]],[]] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [5,3,4,2,7,6,1,8] => [3,3,1,1] => 3
[[[[[[]]]],[[]]],[]] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [5,4,3,2,7,6,1,8] => [3,2,1,1,1] => 3
[[[[],[],[],[]],[]],[]] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [6,2,3,4,5,7,1,8] => [3,1,1,1,1,1] => 3
[[[[],[],[[]]],[]],[]] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [6,2,3,5,4,7,1,8] => [3,2,1,1,1] => 3
[[[[],[[[]]]],[]],[]] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [6,2,5,4,3,7,1,8] => [3,2,1,1,1] => 3
[[[[[]],[],[]],[]],[]] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [6,3,2,4,5,7,1,8] => [3,2,1,1,1] => 3
[[[[[]],[[]]],[]],[]] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [6,3,2,5,4,7,1,8] => [3,2,2,1] => 3
[[[[[],[],[]]],[]],[]] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [6,3,4,5,2,7,1,8] => [4,3,1] => 4
[[[[[],[[]]]],[]],[]] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [6,3,5,4,2,7,1,8] => [3,3,1,1] => 3
[[[[[[[]]]]],[]],[]] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [6,5,4,3,2,7,1,8] => [3,2,2,1] => 3
[[[[],[],[],[],[]]],[]] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [7,2,3,4,5,6,1,8] => [2,1,1,1,1,1,1] => 2
[[[[],[],[],[[]]]],[]] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [7,2,3,4,6,5,1,8] => [2,2,1,1,1,1] => 2
[[[[],[],[[]],[]]],[]] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [7,2,3,5,4,6,1,8] => [2,2,1,1,1,1] => 2
[[[[],[],[[],[]]]],[]] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [7,2,3,5,6,4,1,8] => [3,2,1,1,1] => 3
[[[[],[],[[[]]]]],[]] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,3,6,5,4,1,8] => [2,2,1,1,1,1] => 2
[[[[],[[]],[[]]]],[]] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [7,2,4,3,6,5,1,8] => [2,2,2,1,1] => 2
[[[[],[[],[]],[]]],[]] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [7,2,4,5,3,6,1,8] => [3,2,1,1,1] => 3
[[[[],[[[]]],[]]],[]] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [7,2,5,4,3,6,1,8] => [2,2,1,1,1,1] => 2
[[[[],[[[],[]]]]],[]] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,6,4,5,3,1,8] => [2,2,1,1,1,1] => 2
[[[[],[[[[]]]]]],[]] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [7,2,6,5,4,3,1,8] => [2,2,2,1,1] => 2
[[[[[]],[[]],[]]],[]] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [7,3,2,5,4,6,1,8] => [2,2,2,1,1] => 2
[[[[[[]]],[[]]]],[]] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [7,4,3,2,6,5,1,8] => [2,2,2,1,1] => 2
[[[[[],[[]]],[]]],[]] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [7,3,5,4,2,6,1,8] => [3,2,1,1,1] => 3
[[[[[[]],[]],[]]],[]] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [7,4,3,5,2,6,1,8] => [3,2,1,1,1] => 3
[[[[[[],[]]],[]]],[]] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [7,5,3,4,2,6,1,8] => [2,2,1,1,1,1] => 2
[[[[[[[]]]],[]]],[]] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [7,5,4,3,2,6,1,8] => [2,2,2,1,1] => 2
[[[[[],[],[],[]]]],[]] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [7,3,4,5,6,2,1,8] => [5,2,1] => 5
[[[[[],[[],[]]]]],[]] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [7,3,6,4,5,2,1,8] => [3,2,1,1,1] => 3
[[[[[],[[[]]]]]],[]] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [7,3,6,5,4,2,1,8] => [3,2,2,1] => 3
[[[[[[]],[[]]]]],[]] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [7,4,3,6,5,2,1,8] => [3,2,1,1,1] => 3
[[[[[[[]]],[]]]],[]] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,5,4,3,6,2,1,8] => [3,2,2,1] => 3
[[[[[[],[],[]]]]],[]] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [7,6,3,4,5,2,1,8] => [2,2,1,1,1,1] => 2
[[[[[[],[[]]]]]],[]] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [7,6,3,5,4,2,1,8] => [2,2,2,1,1] => 2
[[[[[[[]],[]]]]],[]] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,6,4,3,5,2,1,8] => [2,2,2,1,1] => 2
[[[[[[[],[]]]]]],[]] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,6,4,5,3,2,1,8] => [3,2,2,1] => 3
[[[[[[[[]]]]]]],[]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,6,5,4,3,2,1,8] => [2,2,2,1,1] => 2
[[[],[],[],[],[],[],[]]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,1] => [8] => 8
[[[],[],[],[],[],[[]]]] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,8,7,1] => [7,1] => 7
[[[],[],[],[],[[]],[]]] => [1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,7,6,8,1] => [7,1] => 7
[[[],[],[],[],[[],[]]]] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,8,6,7,1] => [6,1,1] => 6
[[[],[],[],[],[[[]]]]] => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,8,7,6,1] => [6,2] => 6
[[[],[],[],[[]],[],[]]] => [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,4,6,5,7,8,1] => [7,1] => 7
[[[],[],[],[[]],[[]]]] => [1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,4,6,5,8,7,1] => [6,1,1] => 6
[[[],[],[],[[],[]],[]]] => [1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,4,7,5,6,8,1] => [6,1,1] => 6
[[[],[],[],[[[]]],[]]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,4,7,6,5,8,1] => [6,2] => 6
[[[],[],[],[[],[],[]]]] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,8,5,6,7,1] => [5,1,1,1] => 5
[[[],[],[],[[],[[]]]]] => [1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,4,8,5,7,6,1] => [5,2,1] => 5
[[[],[],[],[[[]],[]]]] => [1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,4,8,6,5,7,1] => [5,2,1] => 5
[[[],[],[],[[[],[]]]]] => [1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,4,8,6,7,5,1] => [5,3] => 5
[[[],[],[],[[[[]]]]]] => [1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,8,7,6,5,1] => [5,2,1] => 5
[[[],[],[[]],[],[],[]]] => [1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,3,5,4,6,7,8,1] => [7,1] => 7
[[[],[],[[]],[[]],[]]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,3,5,4,7,6,8,1] => [6,1,1] => 6
[[[],[],[[]],[[],[]]]] => [1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,3,5,4,8,6,7,1] => [5,1,1,1] => 5
[[[],[],[[]],[[[]]]]] => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,3,5,4,8,7,6,1] => [5,2,1] => 5
[[[],[],[[],[]],[],[]]] => [1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,3,6,4,5,7,8,1] => [6,1,1] => 6
[[[],[],[[[]]],[],[]]] => [1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,3,6,5,4,7,8,1] => [6,2] => 6
[[[],[],[[],[]],[[]]]] => [1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,3,6,4,5,8,7,1] => [5,1,1,1] => 5
[[[],[],[[],[],[]],[]]] => [1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,3,7,4,5,6,8,1] => [5,1,1,1] => 5
[[[],[],[[],[[]]],[]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,3,7,4,6,5,8,1] => [5,2,1] => 5
[[[],[],[[[]],[]],[]]] => [1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,3,7,5,4,6,8,1] => [5,2,1] => 5
[[[],[],[[[],[]]],[]]] => [1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,3,7,5,6,4,8,1] => [5,3] => 5
[[[],[],[[[[]]]],[]]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,3,7,6,5,4,8,1] => [5,2,1] => 5
[[[],[],[[],[],[],[]]]] => [1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,8,4,5,6,7,1] => [4,1,1,1,1] => 4
[[[],[],[[],[[],[]]]]] => [1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,3,8,4,6,7,5,1] => [4,3,1] => 4
[[[],[],[[[],[],[]]]]] => [1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,3,8,5,6,7,4,1] => [4,4] => 4
[[[],[],[[[],[[]]]]]] => [1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,3,8,5,7,6,4,1] => [4,3,1] => 4
[[[],[],[[[[[]]]]]]] => [1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,8,7,6,5,4,1] => [4,2,2] => 4
[[[],[[]],[],[],[],[]]] => [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,8,1] => [7,1] => 7
[[[],[[]],[],[],[[]]]] => [1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,4,3,5,6,8,7,1] => [6,1,1] => 6
[[[],[[]],[],[[]],[]]] => [1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [2,4,3,5,7,6,8,1] => [6,1,1] => 6
[[[],[[]],[],[[],[]]]] => [1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [2,4,3,5,8,6,7,1] => [5,1,1,1] => 5
[[[],[[]],[[]],[],[]]] => [1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,4,3,6,5,7,8,1] => [6,1,1] => 6
[[[],[[]],[[]],[[]]]] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,8,7,1] => [5,1,1,1] => 5
[[[],[[]],[[],[]],[]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,4,3,7,5,6,8,1] => [5,1,1,1] => 5
[[[],[[]],[[],[],[]]]] => [1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,4,3,8,5,6,7,1] => [4,1,1,1,1] => 4
[[[],[[]],[[[]],[]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [2,4,3,8,6,5,7,1] => [4,2,1,1] => 4
[[[],[[],[]],[],[],[]]] => [1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,5,3,4,6,7,8,1] => [6,1,1] => 6
[[[],[[],[]],[],[[]]]] => [1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [2,5,3,4,6,8,7,1] => [5,1,1,1] => 5
[[[],[[],[]],[[]],[]]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [2,5,3,4,7,6,8,1] => [5,1,1,1] => 5
[[[],[[],[]],[[],[]]]] => [1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [2,5,3,4,8,6,7,1] => [4,1,1,1,1] => 4
[[[],[[],[]],[[[]]]]] => [1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [2,5,3,4,8,7,6,1] => [4,2,1,1] => 4
[[[],[[[]]],[[],[]]]] => [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [2,5,4,3,8,6,7,1] => [4,2,1,1] => 4
[[[],[[[]]],[[[]]]]] => [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,5,4,3,8,7,6,1] => [4,2,2] => 4
[[[],[[],[],[]],[],[]]] => [1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [2,6,3,4,5,7,8,1] => [5,1,1,1] => 5
[[[],[[],[[]]],[],[]]] => [1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [2,6,3,5,4,7,8,1] => [5,2,1] => 5
[[[],[[[]],[]],[],[]]] => [1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [2,6,4,3,5,7,8,1] => [5,2,1] => 5
[[[],[[[],[]]],[],[]]] => [1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [2,6,4,5,3,7,8,1] => [5,3] => 5
[[[],[[[[]]]],[],[]]] => [1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,6,5,4,3,7,8,1] => [5,2,1] => 5
[[[],[[],[],[]],[[]]]] => [1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [2,6,3,4,5,8,7,1] => [4,1,1,1,1] => 4
[[[],[[[]],[]],[[]]]] => [1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [2,6,4,3,5,8,7,1] => [4,2,1,1] => 4
[[[],[[[[]]]],[[]]]] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,6,5,4,3,8,7,1] => [4,2,1,1] => 4
[[[],[[],[[]],[]],[]]] => [1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [2,7,3,5,4,6,8,1] => [4,2,1,1] => 4
[[[],[[],[[],[]]],[]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [2,7,3,5,6,4,8,1] => [4,3,1] => 4
[[[],[[[]],[],[]],[]]] => [1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [2,7,4,3,5,6,8,1] => [4,2,1,1] => 4
[[[],[[[]],[[]]],[]]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,7,4,3,6,5,8,1] => [4,2,2] => 4
[[[],[[[[]]],[]],[]]] => [1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [2,7,5,4,3,6,8,1] => [4,2,1,1] => 4
[[[],[[[],[],[]]],[]]] => [1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [2,7,4,5,6,3,8,1] => [4,4] => 4
[[[],[[[],[[]]]],[]]] => [1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [2,7,4,6,5,3,8,1] => [4,3,1] => 4
[[[],[[[[]],[]]],[]]] => [1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,7,5,4,6,3,8,1] => [4,3,1] => 4
[[[],[[[[],[]]]],[]]] => [1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [2,7,6,4,5,3,8,1] => [4,2,1,1] => 4
[[[],[[[[[]]]]],[]]] => [1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,7,6,5,4,3,8,1] => [4,2,2] => 4
[[[],[[],[],[],[],[]]]] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,8,3,4,5,6,7,1] => [3,1,1,1,1,1] => 3
[[[],[[],[],[],[[]]]]] => [1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [2,8,3,4,5,7,6,1] => [3,2,1,1,1] => 3
[[[],[[],[[]],[[]]]]] => [1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,8,3,5,4,7,6,1] => [3,2,2,1] => 3
[[[],[[],[[],[],[]]]]] => [1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,8,3,5,6,7,4,1] => [4,3,1] => 4
[[[],[[],[[],[[]]]]]] => [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,8,3,5,7,6,4,1] => [3,3,1,1] => 3
[[[],[[],[[[],[]]]]]] => [1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,8,3,7,5,6,4,1] => [3,2,1,1,1] => 3
[[[],[[],[[[[]]]]]]] => [1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,8,3,7,6,5,4,1] => [3,2,2,1] => 3
[[[],[[[]],[],[],[]]]] => [1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,8,4,3,5,6,7,1] => [3,2,1,1,1] => 3
[[[],[[[]],[],[[]]]]] => [1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [2,8,4,3,5,7,6,1] => [3,2,2,1] => 3
[[[],[[[]],[[]],[]]]] => [1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,8,4,3,6,5,7,1] => [3,2,2,1] => 3
[[[],[[[]],[[],[]]]]] => [1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,8,4,3,6,7,5,1] => [3,3,2] => 3
[[[],[[[]],[[[]]]]]] => [1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,8,4,3,7,6,5,1] => [3,2,2,1] => 3
[[[],[[[[]]],[],[]]]] => [1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,8,5,4,3,6,7,1] => [3,2,1,1,1] => 3
[[[],[[[[]]],[[]]]]] => [1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [2,8,5,4,3,7,6,1] => [3,2,2,1] => 3
[[[],[[[],[],[]],[]]]] => [1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [2,8,4,5,6,3,7,1] => [4,3,1] => 4
[[[],[[[],[[]]],[]]]] => [1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [2,8,4,6,5,3,7,1] => [3,3,1,1] => 3
[[[],[[[],[],[],[]]]]] => [1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,8,4,5,6,7,3,1] => [5,3] => 5
[[[],[[[],[[[]]]]]]] => [1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,8,4,7,6,5,3,1] => [3,3,2] => 3
[[[],[[[[]],[],[]]]]] => [1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,8,5,4,6,7,3,1] => [4,3,1] => 4
[[[],[[[[]],[[]]]]]] => [1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,8,5,4,7,6,3,1] => [3,3,1,1] => 3
[[[],[[[[],[],[]]]]]] => [1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,8,7,4,5,6,3,1] => [3,2,1,1,1] => 3
[[[],[[[[],[[]]]]]]] => [1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,8,7,4,6,5,3,1] => [3,2,2,1] => 3
[[[],[[[[[]],[]]]]]] => [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,8,7,5,4,6,3,1] => [3,2,2,1] => 3
[[[],[[[[[],[]]]]]]] => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,8,7,5,6,4,3,1] => [3,3,2] => 3
[[[],[[[[[[]]]]]]]] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,8,7,6,5,4,3,1] => [3,2,2,1] => 3
[[[[]],[],[],[],[],[]]] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,1] => [7,1] => 7
[[[[]],[],[],[],[[]]]] => [1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,6,8,7,1] => [6,1,1] => 6
[[[[]],[],[],[[]],[]]] => [1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [3,2,4,5,7,6,8,1] => [6,1,1] => 6
[[[[]],[],[],[[],[]]]] => [1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [3,2,4,5,8,6,7,1] => [5,1,1,1] => 5
[[[[]],[],[[]],[[]]]] => [1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [3,2,4,6,5,8,7,1] => [5,1,1,1] => 5
[[[[]],[],[[],[]],[]]] => [1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [3,2,4,7,5,6,8,1] => [5,1,1,1] => 5
[[[[]],[],[[],[],[]]]] => [1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [3,2,4,8,5,6,7,1] => [4,1,1,1,1] => 4
[[[[]],[],[[[],[]]]]] => [1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,8,6,7,5,1] => [4,3,1] => 4
[[[[]],[],[[[[]]]]]] => [1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,2,4,8,7,6,5,1] => [4,2,1,1] => 4
[[[[]],[[]],[],[],[]]] => [1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [3,2,5,4,6,7,8,1] => [6,1,1] => 6
[[[[]],[[]],[],[[]]]] => [1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [3,2,5,4,6,8,7,1] => [5,1,1,1] => 5
[[[[]],[[]],[[]],[]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,7,6,8,1] => [5,1,1,1] => 5
[[[[]],[[]],[[],[]]]] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [3,2,5,4,8,6,7,1] => [4,1,1,1,1] => 4
[[[[]],[[[]]],[[]]]] => [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [3,2,6,5,4,8,7,1] => [4,2,1,1] => 4
[[[[]],[[],[[]]],[]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [3,2,7,4,6,5,8,1] => [4,2,1,1] => 4
[[[[]],[[[],[]]],[]]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [3,2,7,5,6,4,8,1] => [4,3,1] => 4
[[[[]],[[[[]]]],[]]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [3,2,7,6,5,4,8,1] => [4,2,1,1] => 4
[[[[]],[[],[],[],[]]]] => [1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [3,2,8,4,5,6,7,1] => [3,1,1,1,1,1] => 3
[[[[]],[[],[[]],[]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [3,2,8,4,6,5,7,1] => [3,2,1,1,1] => 3
[[[[]],[[[]],[],[]]]] => [1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [3,2,8,5,4,6,7,1] => [3,2,1,1,1] => 3
[[[[]],[[[]],[[]]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [3,2,8,5,4,7,6,1] => [3,2,2,1] => 3
[[[[]],[[[],[]],[]]]] => [1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [3,2,8,5,6,4,7,1] => [3,3,1,1] => 3
[[[[]],[[[],[[]]]]]] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,2,8,5,7,6,4,1] => [3,3,1,1] => 3
[[[[]],[[[[],[]]]]]] => [1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,8,7,5,6,4,1] => [3,2,1,1,1] => 3
[[[[]],[[[[[]]]]]]] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,2,8,7,6,5,4,1] => [3,2,2,1] => 3
[[[[],[]],[],[],[],[]]] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [4,2,3,5,6,7,8,1] => [6,1,1] => 6
[[[[[]]],[],[],[],[]]] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,1] => [6,2] => 6
[[[[],[]],[],[],[[]]]] => [1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [4,2,3,5,6,8,7,1] => [5,1,1,1] => 5
[[[[[]]],[],[],[[]]]] => [1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [4,3,2,5,6,8,7,1] => [5,2,1] => 5
[[[[[]]],[],[[]],[]]] => [1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [4,3,2,5,7,6,8,1] => [5,2,1] => 5
[[[[[]]],[],[[[]]]]] => [1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,3,2,5,8,7,6,1] => [4,2,2] => 4
[[[[[]]],[[]],[],[]]] => [1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [4,3,2,6,5,7,8,1] => [5,2,1] => 5
[[[[],[]],[[]],[[]]]] => [1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [4,2,3,6,5,8,7,1] => [4,1,1,1,1] => 4
[[[[[]]],[[]],[[]]]] => [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [4,3,2,6,5,8,7,1] => [4,2,1,1] => 4
[[[[],[]],[[],[]],[]]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [4,2,3,7,5,6,8,1] => [4,1,1,1,1] => 4
[[[[[]]],[[],[]],[]]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [4,3,2,7,5,6,8,1] => [4,2,1,1] => 4
[[[[],[]],[[],[],[]]]] => [1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [4,2,3,8,5,6,7,1] => [3,1,1,1,1,1] => 3
[[[[],[]],[[],[[]]]]] => [1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [4,2,3,8,5,7,6,1] => [3,2,1,1,1] => 3
[[[[[]]],[[],[],[]]]] => [1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [4,3,2,8,5,6,7,1] => [3,2,1,1,1] => 3
[[[[[]]],[[],[[]]]]] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,3,2,8,5,7,6,1] => [3,2,2,1] => 3
[[[[[]]],[[[],[]]]]] => [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,2,8,6,7,5,1] => [3,3,2] => 3
[[[[[]]],[[[[]]]]]] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,3,2,8,7,6,5,1] => [3,2,2,1] => 3
[[[[],[],[]],[],[],[]]] => [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [5,2,3,4,6,7,8,1] => [5,1,1,1] => 5
[[[[[]],[]],[],[],[]]] => [1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [5,3,2,4,6,7,8,1] => [5,2,1] => 5
[[[[[],[]]],[],[],[]]] => [1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [5,3,4,2,6,7,8,1] => [5,3] => 5
[[[[[[]]]],[],[],[]]] => [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [5,4,3,2,6,7,8,1] => [5,2,1] => 5
[[[[[[]]]],[],[[]]]] => [1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,4,3,2,6,8,7,1] => [4,2,1,1] => 4
[[[[],[[]]],[[]],[]]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [5,2,4,3,7,6,8,1] => [4,2,1,1] => 4
[[[[[],[]]],[[]],[]]] => [1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [5,3,4,2,7,6,8,1] => [4,3,1] => 4
[[[[[[]]]],[[]],[]]] => [1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [5,4,3,2,7,6,8,1] => [4,2,1,1] => 4
[[[[],[],[]],[[],[]]]] => [1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [5,2,3,4,8,6,7,1] => [3,1,1,1,1,1] => 3
[[[[],[],[]],[[[]]]]] => [1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [5,2,3,4,8,7,6,1] => [3,2,1,1,1] => 3
[[[[[],[]]],[[],[]]]] => [1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [5,3,4,2,8,6,7,1] => [3,3,1,1] => 3
[[[[[[]]]],[[],[]]]] => [1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,4,3,2,8,6,7,1] => [3,2,1,1,1] => 3
[[[[[[]]]],[[[]]]]] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,4,3,2,8,7,6,1] => [3,2,2,1] => 3
[[[[],[],[],[]],[],[]]] => [1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [6,2,3,4,5,7,8,1] => [4,1,1,1,1] => 4
[[[[[]],[[]]],[],[]]] => [1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [6,3,2,5,4,7,8,1] => [4,2,2] => 4
[[[[[],[],[]]],[],[]]] => [1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [6,3,4,5,2,7,8,1] => [4,4] => 4
[[[[[],[[]]]],[],[]]] => [1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [6,3,5,4,2,7,8,1] => [4,3,1] => 4
[[[[[[[]]]]],[],[]]] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5,4,3,2,7,8,1] => [4,2,2] => 4
[[[[],[],[],[]],[[]]]] => [1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [6,2,3,4,5,8,7,1] => [3,1,1,1,1,1] => 3
[[[[[[]]],[]],[[]]]] => [1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [6,4,3,2,5,8,7,1] => [3,2,1,1,1] => 3
[[[[[],[],[]]],[[]]]] => [1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [6,3,4,5,2,8,7,1] => [4,3,1] => 4
[[[[[[[]]]]],[[]]]] => [1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,5,4,3,2,8,7,1] => [3,2,2,1] => 3
[[[[],[],[],[],[]],[]]] => [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [7,2,3,4,5,6,8,1] => [3,1,1,1,1,1] => 3
[[[[],[[]],[[]]],[]]] => [1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [7,2,4,3,6,5,8,1] => [3,2,2,1] => 3
[[[[],[[],[]],[]],[]]] => [1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [7,2,4,5,3,6,8,1] => [3,3,1,1] => 3
[[[[],[[],[[]]]],[]]] => [1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [7,2,4,6,5,3,8,1] => [3,3,1,1] => 3
[[[[],[[[],[]]]],[]]] => [1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [7,2,6,4,5,3,8,1] => [3,2,1,1,1] => 3
[[[[[]],[],[],[]],[]]] => [1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [7,3,2,4,5,6,8,1] => [3,2,1,1,1] => 3
[[[[[]],[[],[]]],[]]] => [1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [7,3,2,5,6,4,8,1] => [3,3,2] => 3
[[[[[[]]],[],[]],[]]] => [1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [7,4,3,2,5,6,8,1] => [3,2,1,1,1] => 3
[[[[[],[]],[[]]],[]]] => [1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [7,3,4,2,6,5,8,1] => [3,3,2] => 3
[[[[[[]]],[[]]],[]]] => [1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [7,4,3,2,6,5,8,1] => [3,2,2,1] => 3
[[[[[[]],[]],[]],[]]] => [1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [7,4,3,5,2,6,8,1] => [3,3,1,1] => 3
[[[[[[[]]]],[]],[]]] => [1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [7,5,4,3,2,6,8,1] => [3,2,2,1] => 3
[[[[[],[],[],[]]],[]]] => [1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [7,3,4,5,6,2,8,1] => [5,3] => 5
[[[[[],[[]],[]]],[]]] => [1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [7,3,5,4,6,2,8,1] => [4,3,1] => 4
[[[[[],[[],[]]]],[]]] => [1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [7,3,6,4,5,2,8,1] => [3,3,1,1] => 3
[[[[[],[[[]]]]],[]]] => [1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [7,3,6,5,4,2,8,1] => [3,3,2] => 3
[[[[[[]],[[]]]],[]]] => [1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [7,4,3,6,5,2,8,1] => [3,3,1,1] => 3
[[[[[[[]]],[]]],[]]] => [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [7,5,4,3,6,2,8,1] => [3,3,2] => 3
[[[[[[],[],[]]]],[]]] => [1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [7,6,3,4,5,2,8,1] => [3,2,1,1,1] => 3
[[[[[[],[[]]]]],[]]] => [1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [7,6,3,5,4,2,8,1] => [3,2,2,1] => 3
[[[[[[[]],[]]]],[]]] => [1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [7,6,4,3,5,2,8,1] => [3,2,2,1] => 3
[[[[[[[],[]]]]],[]]] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,6,4,5,3,2,8,1] => [3,3,2] => 3
[[[[[[[[]]]]]],[]]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,6,5,4,3,2,8,1] => [3,2,2,1] => 3
[[[[],[],[],[],[],[]]]] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8,2,3,4,5,6,7,1] => [2,1,1,1,1,1,1] => 2
[[[[],[],[],[],[[]]]]] => [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [8,2,3,4,5,7,6,1] => [2,2,1,1,1,1] => 2
[[[[],[],[],[[[]]]]]] => [1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [8,2,3,4,7,6,5,1] => [2,2,1,1,1,1] => 2
[[[[],[],[[]],[],[]]]] => [1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [8,2,3,5,4,6,7,1] => [2,2,1,1,1,1] => 2
[[[[],[],[[]],[[]]]]] => [1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [8,2,3,5,4,7,6,1] => [2,2,2,1,1] => 2
[[[[],[],[[],[],[]]]]] => [1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [8,2,3,5,6,7,4,1] => [4,2,1,1] => 4
[[[[],[],[[],[[]]]]]] => [1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [8,2,3,5,7,6,4,1] => [3,2,1,1,1] => 3
[[[[],[],[[[],[]]]]]] => [1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [8,2,3,7,5,6,4,1] => [2,2,1,1,1,1] => 2
[[[[],[],[[[[]]]]]]] => [1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [8,2,3,7,6,5,4,1] => [2,2,2,1,1] => 2
[[[[],[[]],[[]],[]]]] => [1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [8,2,4,3,6,5,7,1] => [2,2,2,1,1] => 2
[[[[],[[]],[[],[]]]]] => [1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [8,2,4,3,6,7,5,1] => [3,2,2,1] => 3
[[[[],[[]],[[[]]]]]] => [1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [8,2,4,3,7,6,5,1] => [2,2,2,1,1] => 2
[[[[],[[[]]],[],[]]]] => [1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [8,2,5,4,3,6,7,1] => [2,2,1,1,1,1] => 2
[[[[],[[],[]],[[]]]]] => [1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [8,2,4,5,3,7,6,1] => [3,2,2,1] => 3
[[[[],[[[]]],[[]]]]] => [1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [8,2,5,4,3,7,6,1] => [2,2,2,1,1] => 2
[[[[],[[[],[]]],[]]]] => [1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [8,2,6,4,5,3,7,1] => [2,2,1,1,1,1] => 2
[[[[],[[[[]]]],[]]]] => [1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [8,2,6,5,4,3,7,1] => [2,2,2,1,1] => 2
[[[[],[[],[],[],[]]]]] => [1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [8,2,4,5,6,7,3,1] => [5,2,1] => 5
[[[[],[[],[],[[]]]]]] => [1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [8,2,4,5,7,6,3,1] => [4,2,1,1] => 4
[[[[],[[],[[],[]]]]]] => [1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [8,2,4,7,5,6,3,1] => [3,2,1,1,1] => 3
[[[[],[[],[[[]]]]]]] => [1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [8,2,4,7,6,5,3,1] => [3,2,2,1] => 3
[[[[],[[[],[]],[]]]]] => [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [8,2,6,4,5,7,3,1] => [3,2,1,1,1] => 3
[[[[],[[[[]]],[]]]]] => [1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [8,2,6,5,4,7,3,1] => [3,2,2,1] => 3
[[[[],[[[],[],[]]]]]] => [1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [8,2,7,4,5,6,3,1] => [2,2,1,1,1,1] => 2
[[[[],[[[],[[]]]]]]] => [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [8,2,7,4,6,5,3,1] => [2,2,2,1,1] => 2
[[[[],[[[[]],[]]]]]] => [1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [8,2,7,5,4,6,3,1] => [2,2,2,1,1] => 2
[[[[],[[[[],[]]]]]]] => [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [8,2,7,5,6,4,3,1] => [3,2,2,1] => 3
[[[[],[[[[[]]]]]]]] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [8,2,7,6,5,4,3,1] => [2,2,2,1,1] => 2
[[[[[]],[],[],[],[]]]] => [1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [8,3,2,4,5,6,7,1] => [2,2,1,1,1,1] => 2
[[[[[]],[],[[]],[]]]] => [1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [8,3,2,4,6,5,7,1] => [2,2,2,1,1] => 2
[[[[[]],[],[[[]]]]]] => [1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [8,3,2,4,7,6,5,1] => [2,2,2,1,1] => 2
[[[[[]],[[]],[[]]]]] => [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [8,3,2,5,4,7,6,1] => [2,2,2,2] => 2
[[[[[]],[[],[],[]]]]] => [1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [8,3,2,5,6,7,4,1] => [4,2,2] => 4
[[[[[]],[[],[[]]]]]] => [1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [8,3,2,5,7,6,4,1] => [3,2,2,1] => 3
[[[[[]],[[[]],[]]]]] => [1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [8,3,2,6,5,7,4,1] => [3,2,2,1] => 3
[[[[[]],[[[],[]]]]]] => [1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [8,3,2,7,5,6,4,1] => [2,2,2,1,1] => 2
[[[[[]],[[[[]]]]]]] => [1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [8,3,2,7,6,5,4,1] => [2,2,2,2] => 2
[[[[[],[]],[],[],[]]]] => [1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [8,3,4,2,5,6,7,1] => [3,2,1,1,1] => 3
[[[[[[]]],[],[],[]]]] => [1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [8,4,3,2,5,6,7,1] => [2,2,1,1,1,1] => 2
[[[[[[]]],[],[[]]]]] => [1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [8,4,3,2,5,7,6,1] => [2,2,2,1,1] => 2
[[[[[[]]],[[]],[]]]] => [1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [8,4,3,2,6,5,7,1] => [2,2,2,1,1] => 2
[[[[[[]]],[[],[]]]]] => [1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [8,4,3,2,6,7,5,1] => [3,2,2,1] => 3
[[[[[[]]],[[[]]]]]] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [8,4,3,2,7,6,5,1] => [2,2,2,1,1] => 2
[[[[[],[],[]],[],[]]]] => [1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [8,3,4,5,2,6,7,1] => [4,2,1,1] => 4
[[[[[],[[]]],[],[]]]] => [1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [8,3,5,4,2,6,7,1] => [3,2,1,1,1] => 3
[[[[[[],[]]],[],[]]]] => [1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [8,5,3,4,2,6,7,1] => [2,2,1,1,1,1] => 2
[[[[[[[]]]],[],[]]]] => [1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [8,5,4,3,2,6,7,1] => [2,2,2,1,1] => 2
[[[[[],[],[]],[[]]]]] => [1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [8,3,4,5,2,7,6,1] => [4,2,2] => 4
[[[[[[],[]]],[[]]]]] => [1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [8,5,3,4,2,7,6,1] => [2,2,2,1,1] => 2
[[[[[[[]]]],[[]]]]] => [1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [8,5,4,3,2,7,6,1] => [2,2,2,2] => 2
[[[[[],[],[],[]],[]]]] => [1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [8,3,4,5,6,2,7,1] => [5,2,1] => 5
[[[[[],[[],[]]],[]]]] => [1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [8,3,6,4,5,2,7,1] => [3,2,1,1,1] => 3
[[[[[],[[[]]]],[]]]] => [1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [8,3,6,5,4,2,7,1] => [3,2,2,1] => 3
[[[[[[]],[],[]],[]]]] => [1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [8,4,3,5,6,2,7,1] => [4,2,1,1] => 4
[[[[[[[]]],[]],[]]]] => [1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [8,5,4,3,6,2,7,1] => [3,2,2,1] => 3
[[[[[[],[],[]]],[]]]] => [1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [8,6,3,4,5,2,7,1] => [2,2,1,1,1,1] => 2
[[[[[[],[[]]]],[]]]] => [1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [8,6,3,5,4,2,7,1] => [2,2,2,1,1] => 2
[[[[[[[]],[]]],[]]]] => [1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [8,6,4,3,5,2,7,1] => [2,2,2,1,1] => 2
[[[[[[[],[]]]],[]]]] => [1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [8,6,4,5,3,2,7,1] => [3,2,2,1] => 3
[[[[[[[[]]]]],[]]]] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [8,6,5,4,3,2,7,1] => [2,2,2,1,1] => 2
[[[[[],[],[],[],[]]]]] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [8,3,4,5,6,7,2,1] => [6,2] => 6
[[[[[],[],[],[[]]]]]] => [1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [8,3,4,5,7,6,2,1] => [5,2,1] => 5
[[[[[],[],[[[]]]]]]] => [1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [8,3,4,7,6,5,2,1] => [4,2,2] => 4
[[[[[],[[]],[],[]]]]] => [1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [8,3,5,4,6,7,2,1] => [5,2,1] => 5
[[[[[],[[]],[[]]]]]] => [1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [8,3,5,4,7,6,2,1] => [4,2,1,1] => 4
[[[[[],[[[]]],[]]]]] => [1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [8,3,6,5,4,7,2,1] => [4,2,2] => 4
[[[[[],[[],[],[]]]]]] => [1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [8,3,7,4,5,6,2,1] => [3,2,1,1,1] => 3
[[[[[],[[],[[]]]]]]] => [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [8,3,7,4,6,5,2,1] => [3,2,2,1] => 3
[[[[[],[[[],[]]]]]]] => [1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [8,3,7,5,6,4,2,1] => [3,3,2] => 3
[[[[[],[[[[]]]]]]]] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [8,3,7,6,5,4,2,1] => [3,2,2,1] => 3
[[[[[[]],[],[],[]]]]] => [1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [8,4,3,5,6,7,2,1] => [5,2,1] => 5
[[[[[[]],[],[[]]]]]] => [1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [8,4,3,5,7,6,2,1] => [4,2,1,1] => 4
[[[[[[]],[[],[]]]]]] => [1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [8,4,3,7,5,6,2,1] => [3,2,1,1,1] => 3
[[[[[[],[]],[],[]]]]] => [1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [8,5,3,4,6,7,2,1] => [4,2,1,1] => 4
[[[[[[[]]],[],[]]]]] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [8,5,4,3,6,7,2,1] => [4,2,2] => 4
[[[[[[],[]],[[]]]]]] => [1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [8,5,3,4,7,6,2,1] => [3,2,1,1,1] => 3
[[[[[[[]]],[[]]]]]] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [8,5,4,3,7,6,2,1] => [3,2,2,1] => 3
[[[[[[[]],[]],[]]]]] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [8,6,4,3,5,7,2,1] => [3,2,2,1] => 3
[[[[[[[[]]]],[]]]]] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [8,6,5,4,3,7,2,1] => [3,2,2,1] => 3
[[[[[[],[],[],[]]]]]] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [8,7,3,4,5,6,2,1] => [2,2,1,1,1,1] => 2
[[[[[[],[],[[]]]]]]] => [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [8,7,3,4,6,5,2,1] => [2,2,2,1,1] => 2
[[[[[[],[[]],[]]]]]] => [1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [8,7,3,5,4,6,2,1] => [2,2,2,1,1] => 2
[[[[[[],[[],[]]]]]]] => [1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [8,7,3,5,6,4,2,1] => [3,2,2,1] => 3
[[[[[[],[[[]]]]]]]] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [8,7,3,6,5,4,2,1] => [2,2,2,1,1] => 2
[[[[[[[]],[],[]]]]]] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [8,7,4,3,5,6,2,1] => [2,2,2,1,1] => 2
[[[[[[[]],[[]]]]]]] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [8,7,4,3,6,5,2,1] => [2,2,2,2] => 2
[[[[[[[],[]],[]]]]]] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [8,7,4,5,3,6,2,1] => [3,2,2,1] => 3
[[[[[[[[]]],[]]]]]] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [8,7,5,4,3,6,2,1] => [2,2,2,1,1] => 2
[[[[[[[],[],[]]]]]]] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [8,7,4,5,6,3,2,1] => [4,2,2] => 4
[[[[[[[],[[]]]]]]]] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [8,7,4,6,5,3,2,1] => [3,2,2,1] => 3
[[[[[[[[]],[]]]]]]] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [8,7,5,4,6,3,2,1] => [3,2,2,1] => 3
[[[[[[[[],[]]]]]]]] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [8,7,6,4,5,3,2,1] => [2,2,2,1,1] => 2
[[[[[[[[[]]]]]]]]] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8,7,6,5,4,3,2,1] => [2,2,2,2] => 2
search for individual values
searching the database for the individual values of this statistic
/
search for generating function
searching the database for statistics with the same generating function
Generating function
click to show known generating functions
Search the OEIS for these generating functions
Search the Online Encyclopedia of Integer
Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 1,3,1 1,8,4,1 1,20,15,5,1 1,50,53,21,6,1 1,126,182,84,28,7,1
F1=1
F2=q
F3=q+q2
F4=q+3 q2+q3
F5=q+8 q2+4 q3+q4
F6=q+20 q2+15 q3+5 q4+q5
F7=q+50 q2+53 q3+21 q4+6 q5+q6
F8=q+126 q2+182 q3+84 q4+28 q5+7 q6+q7
Description
The largest part of an integer partition.
Map
to non-crossing permutation
Description
Sends a Dyck path D with valley at positions {(i1,j1),…,(ik,jk)} to the unique non-crossing permutation π having descents {i1,…,ik} and whose inverse has descents {j1,…,jk}.
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to n(n−1) minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to n(n−1) minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
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
cycle type
Description
The cycle type of a permutation as a partition.
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