Identifier
Mp00051:
Ordered trees
—to Dyck path⟶
Dyck paths
Mp00023: Dyck paths —to non-crossing permutation⟶ Permutations
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Mp00023: Dyck paths —to non-crossing permutation⟶ Permutations
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Images
[] => [] => [] => []
[[]] => [1,0] => [1] => [1]
[[],[]] => [1,0,1,0] => [1,2] => [2]
[[[]]] => [1,1,0,0] => [2,1] => [1,1]
[[],[],[]] => [1,0,1,0,1,0] => [1,2,3] => [3]
[[],[[]]] => [1,0,1,1,0,0] => [1,3,2] => [2,1]
[[[]],[]] => [1,1,0,0,1,0] => [2,1,3] => [2,1]
[[[],[]]] => [1,1,0,1,0,0] => [2,3,1] => [2,1]
[[[[]]]] => [1,1,1,0,0,0] => [3,2,1] => [1,1,1]
[[],[],[],[]] => [1,0,1,0,1,0,1,0] => [1,2,3,4] => [4]
[[],[],[[]]] => [1,0,1,0,1,1,0,0] => [1,2,4,3] => [3,1]
[[],[[]],[]] => [1,0,1,1,0,0,1,0] => [1,3,2,4] => [3,1]
[[],[[],[]]] => [1,0,1,1,0,1,0,0] => [1,3,4,2] => [3,1]
[[],[[[]]]] => [1,0,1,1,1,0,0,0] => [1,4,3,2] => [2,1,1]
[[[]],[],[]] => [1,1,0,0,1,0,1,0] => [2,1,3,4] => [3,1]
[[[]],[[]]] => [1,1,0,0,1,1,0,0] => [2,1,4,3] => [2,2]
[[[],[]],[]] => [1,1,0,1,0,0,1,0] => [2,3,1,4] => [3,1]
[[[[]]],[]] => [1,1,1,0,0,0,1,0] => [3,2,1,4] => [2,1,1]
[[[],[],[]]] => [1,1,0,1,0,1,0,0] => [2,3,4,1] => [3,1]
[[[],[[]]]] => [1,1,0,1,1,0,0,0] => [2,4,3,1] => [2,1,1]
[[[[]],[]]] => [1,1,1,0,0,1,0,0] => [3,2,4,1] => [2,1,1]
[[[[],[]]]] => [1,1,1,0,1,0,0,0] => [4,2,3,1] => [2,1,1]
[[[[[]]]]] => [1,1,1,1,0,0,0,0] => [4,3,2,1] => [1,1,1,1]
[[],[],[],[],[]] => [1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => [5]
[[],[],[],[[]]] => [1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => [4,1]
[[],[],[[]],[]] => [1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [4,1]
[[],[],[[],[]]] => [1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [4,1]
[[],[],[[[]]]] => [1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => [3,1,1]
[[],[[]],[],[]] => [1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [4,1]
[[],[[]],[[]]] => [1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [3,2]
[[],[[],[]],[]] => [1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [4,1]
[[],[[[]]],[]] => [1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => [3,1,1]
[[],[[],[],[]]] => [1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [4,1]
[[],[[],[[]]]] => [1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => [3,1,1]
[[],[[[]],[]]] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => [3,1,1]
[[],[[[],[]]]] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => [3,1,1]
[[],[[[[]]]]] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => [2,1,1,1]
[[[]],[],[],[]] => [1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [4,1]
[[[]],[],[[]]] => [1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [3,2]
[[[]],[[]],[]] => [1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [3,2]
[[[]],[[],[]]] => [1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [3,2]
[[[]],[[[]]]] => [1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => [2,2,1]
[[[],[]],[],[]] => [1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [4,1]
[[[[]]],[],[]] => [1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => [3,1,1]
[[[],[]],[[]]] => [1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [3,2]
[[[[]]],[[]]] => [1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => [2,2,1]
[[[],[],[]],[]] => [1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [4,1]
[[[],[[]]],[]] => [1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => [3,1,1]
[[[[]],[]],[]] => [1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => [3,1,1]
[[[[],[]]],[]] => [1,1,1,0,1,0,0,0,1,0] => [4,2,3,1,5] => [3,1,1]
[[[[[]]]],[]] => [1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => [2,1,1,1]
[[[],[],[],[]]] => [1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [4,1]
[[[],[],[[]]]] => [1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1] => [3,1,1]
[[[],[[]],[]]] => [1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => [3,1,1]
[[[],[[],[]]]] => [1,1,0,1,1,0,1,0,0,0] => [2,5,3,4,1] => [3,1,1]
[[[],[[[]]]]] => [1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => [2,1,1,1]
[[[[]],[],[]]] => [1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => [3,1,1]
[[[[]],[[]]]] => [1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => [2,2,1]
[[[[],[]],[]]] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => [3,1,1]
[[[[[]]],[]]] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => [2,1,1,1]
[[[[],[],[]]]] => [1,1,1,0,1,0,1,0,0,0] => [5,2,3,4,1] => [3,1,1]
[[[[],[[]]]]] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => [2,1,1,1]
[[[[[]],[]]]] => [1,1,1,1,0,0,1,0,0,0] => [5,3,2,4,1] => [2,1,1,1]
[[[[[],[]]]]] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => [2,1,1,1]
[[[[[[]]]]]] => [1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => [1,1,1,1,1]
[[],[],[],[],[],[]] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => [6]
[[],[],[],[],[[]]] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => [5,1]
[[],[],[],[[]],[]] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => [5,1]
[[],[],[],[[],[]]] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [5,1]
[[],[],[],[[[]]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => [4,1,1]
[[],[],[[]],[],[]] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [5,1]
[[],[],[[]],[[]]] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [4,2]
[[],[],[[],[]],[]] => [1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [5,1]
[[],[],[[[]]],[]] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => [4,1,1]
[[],[],[[],[],[]]] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [5,1]
[[],[],[[],[[]]]] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => [4,1,1]
[[],[],[[[]],[]]] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => [4,1,1]
[[],[],[[[],[]]]] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => [4,1,1]
[[],[],[[[[]]]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => [3,1,1,1]
[[],[[]],[],[],[]] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [5,1]
[[],[[]],[],[[]]] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [4,2]
[[],[[]],[[]],[]] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [4,2]
[[],[[]],[[],[]]] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [4,2]
[[],[[]],[[[]]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => [3,2,1]
[[],[[],[]],[],[]] => [1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [5,1]
[[],[[[]]],[],[]] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => [4,1,1]
[[],[[],[]],[[]]] => [1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [4,2]
[[],[[[]]],[[]]] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => [3,2,1]
[[],[[],[],[]],[]] => [1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [5,1]
[[],[[],[[]]],[]] => [1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => [4,1,1]
[[],[[[]],[]],[]] => [1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => [4,1,1]
[[],[[[],[]]],[]] => [1,0,1,1,1,0,1,0,0,0,1,0] => [1,5,3,4,2,6] => [4,1,1]
[[],[[[[]]]],[]] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => [3,1,1,1]
[[],[[],[],[],[]]] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [5,1]
[[],[[],[],[[]]]] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => [4,1,1]
[[],[[],[[]],[]]] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => [4,1,1]
[[],[[],[[],[]]]] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,6,4,5,2] => [4,1,1]
[[],[[],[[[]]]]] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => [3,1,1,1]
[[],[[[]],[],[]]] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => [4,1,1]
[[],[[[]],[[]]]] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => [3,2,1]
[[],[[[],[]],[]]] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => [4,1,1]
>>> Load all 1498 entries. <<<
[[],[[[[]]],[]]] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => [3,1,1,1]
[[],[[[],[],[]]]] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,6,3,4,5,2] => [4,1,1]
[[],[[[],[[]]]]] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,6,3,5,4,2] => [3,1,1,1]
[[],[[[[]],[]]]] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,6,4,3,5,2] => [3,1,1,1]
[[],[[[[],[]]]]] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,6,4,5,3,2] => [3,1,1,1]
[[],[[[[[]]]]]] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => [2,1,1,1,1]
[[[]],[],[],[],[]] => [1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [5,1]
[[[]],[],[],[[]]] => [1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => [4,2]
[[[]],[],[[]],[]] => [1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [4,2]
[[[]],[],[[],[]]] => [1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [4,2]
[[[]],[],[[[]]]] => [1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => [3,2,1]
[[[]],[[]],[],[]] => [1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [4,2]
[[[]],[[]],[[]]] => [1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [3,3]
[[[]],[[],[]],[]] => [1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [4,2]
[[[]],[[[]]],[]] => [1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => [3,2,1]
[[[]],[[],[],[]]] => [1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [4,2]
[[[]],[[],[[]]]] => [1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => [3,2,1]
[[[]],[[[]],[]]] => [1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => [3,2,1]
[[[]],[[[],[]]]] => [1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,6,4,5,3] => [3,2,1]
[[[]],[[[[]]]]] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => [2,2,1,1]
[[[],[]],[],[],[]] => [1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [5,1]
[[[[]]],[],[],[]] => [1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => [4,1,1]
[[[],[]],[],[[]]] => [1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [4,2]
[[[[]]],[],[[]]] => [1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => [3,2,1]
[[[],[]],[[]],[]] => [1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [4,2]
[[[[]]],[[]],[]] => [1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => [3,2,1]
[[[],[]],[[],[]]] => [1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [4,2]
[[[],[]],[[[]]]] => [1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => [3,2,1]
[[[[]]],[[],[]]] => [1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => [3,2,1]
[[[[]]],[[[]]]] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => [2,2,2]
[[[],[],[]],[],[]] => [1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [5,1]
[[[],[[]]],[],[]] => [1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => [4,1,1]
[[[[]],[]],[],[]] => [1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => [4,1,1]
[[[[],[]]],[],[]] => [1,1,1,0,1,0,0,0,1,0,1,0] => [4,2,3,1,5,6] => [4,1,1]
[[[[[]]]],[],[]] => [1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => [3,1,1,1]
[[[],[],[]],[[]]] => [1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [4,2]
[[[],[[]]],[[]]] => [1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => [3,2,1]
[[[[]],[]],[[]]] => [1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => [3,2,1]
[[[[],[]]],[[]]] => [1,1,1,0,1,0,0,0,1,1,0,0] => [4,2,3,1,6,5] => [3,2,1]
[[[[[]]]],[[]]] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => [2,2,1,1]
[[[],[],[],[]],[]] => [1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [5,1]
[[[],[],[[]]],[]] => [1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => [4,1,1]
[[[],[[]],[]],[]] => [1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => [4,1,1]
[[[],[[],[]]],[]] => [1,1,0,1,1,0,1,0,0,0,1,0] => [2,5,3,4,1,6] => [4,1,1]
[[[],[[[]]]],[]] => [1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => [3,1,1,1]
[[[[]],[],[]],[]] => [1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => [4,1,1]
[[[[]],[[]]],[]] => [1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => [3,2,1]
[[[[],[]],[]],[]] => [1,1,1,0,1,0,0,1,0,0,1,0] => [4,2,3,5,1,6] => [4,1,1]
[[[[[]]],[]],[]] => [1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => [3,1,1,1]
[[[[],[],[]]],[]] => [1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,3,4,1,6] => [4,1,1]
[[[[],[[]]]],[]] => [1,1,1,0,1,1,0,0,0,0,1,0] => [5,2,4,3,1,6] => [3,1,1,1]
[[[[[]],[]]],[]] => [1,1,1,1,0,0,1,0,0,0,1,0] => [5,3,2,4,1,6] => [3,1,1,1]
[[[[[],[]]]],[]] => [1,1,1,1,0,1,0,0,0,0,1,0] => [5,3,4,2,1,6] => [3,1,1,1]
[[[[[[]]]]],[]] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => [2,1,1,1,1]
[[[],[],[],[],[]]] => [1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [5,1]
[[[],[],[],[[]]]] => [1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,5,1] => [4,1,1]
[[[],[],[[]],[]]] => [1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,4,6,1] => [4,1,1]
[[[],[],[[],[]]]] => [1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,6,4,5,1] => [4,1,1]
[[[],[],[[[]]]]] => [1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => [3,1,1,1]
[[[],[[]],[],[]]] => [1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,3,5,6,1] => [4,1,1]
[[[],[[]],[[]]]] => [1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => [3,2,1]
[[[],[[],[]],[]]] => [1,1,0,1,1,0,1,0,0,1,0,0] => [2,5,3,4,6,1] => [4,1,1]
[[[],[[[]]],[]]] => [1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => [3,1,1,1]
[[[],[[],[],[]]]] => [1,1,0,1,1,0,1,0,1,0,0,0] => [2,6,3,4,5,1] => [4,1,1]
[[[],[[],[[]]]]] => [1,1,0,1,1,0,1,1,0,0,0,0] => [2,6,3,5,4,1] => [3,1,1,1]
[[[],[[[]],[]]]] => [1,1,0,1,1,1,0,0,1,0,0,0] => [2,6,4,3,5,1] => [3,1,1,1]
[[[],[[[],[]]]]] => [1,1,0,1,1,1,0,1,0,0,0,0] => [2,6,4,5,3,1] => [3,1,1,1]
[[[],[[[[]]]]]] => [1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => [2,1,1,1,1]
[[[[]],[],[],[]]] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => [4,1,1]
[[[[]],[],[[]]]] => [1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => [3,2,1]
[[[[]],[[]],[]]] => [1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => [3,2,1]
[[[[]],[[],[]]]] => [1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,6,4,5,1] => [3,2,1]
[[[[]],[[[]]]]] => [1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => [2,2,1,1]
[[[[],[]],[],[]]] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => [4,1,1]
[[[[[]]],[],[]]] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => [3,1,1,1]
[[[[],[]],[[]]]] => [1,1,1,0,1,0,0,1,1,0,0,0] => [4,2,3,6,5,1] => [3,2,1]
[[[[[]]],[[]]]] => [1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => [2,2,1,1]
[[[[],[],[]],[]]] => [1,1,1,0,1,0,1,0,0,1,0,0] => [5,2,3,4,6,1] => [4,1,1]
[[[[],[[]]],[]]] => [1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,4,3,6,1] => [3,1,1,1]
[[[[[]],[]],[]]] => [1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => [3,1,1,1]
[[[[[],[]]],[]]] => [1,1,1,1,0,1,0,0,0,1,0,0] => [5,3,4,2,6,1] => [3,1,1,1]
[[[[[[]]]],[]]] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => [2,1,1,1,1]
[[[[],[],[],[]]]] => [1,1,1,0,1,0,1,0,1,0,0,0] => [6,2,3,4,5,1] => [4,1,1]
[[[[],[],[[]]]]] => [1,1,1,0,1,0,1,1,0,0,0,0] => [6,2,3,5,4,1] => [3,1,1,1]
[[[[],[[]],[]]]] => [1,1,1,0,1,1,0,0,1,0,0,0] => [6,2,4,3,5,1] => [3,1,1,1]
[[[[],[[],[]]]]] => [1,1,1,0,1,1,0,1,0,0,0,0] => [6,2,4,5,3,1] => [3,1,1,1]
[[[[],[[[]]]]]] => [1,1,1,0,1,1,1,0,0,0,0,0] => [6,2,5,4,3,1] => [2,1,1,1,1]
[[[[[]],[],[]]]] => [1,1,1,1,0,0,1,0,1,0,0,0] => [6,3,2,4,5,1] => [3,1,1,1]
[[[[[]],[[]]]]] => [1,1,1,1,0,0,1,1,0,0,0,0] => [6,3,2,5,4,1] => [2,2,1,1]
[[[[[],[]],[]]]] => [1,1,1,1,0,1,0,0,1,0,0,0] => [6,3,4,2,5,1] => [3,1,1,1]
[[[[[[]]],[]]]] => [1,1,1,1,1,0,0,0,1,0,0,0] => [6,4,3,2,5,1] => [2,1,1,1,1]
[[[[[],[],[]]]]] => [1,1,1,1,0,1,0,1,0,0,0,0] => [6,3,4,5,2,1] => [3,1,1,1]
[[[[[],[[]]]]]] => [1,1,1,1,0,1,1,0,0,0,0,0] => [6,3,5,4,2,1] => [2,1,1,1,1]
[[[[[[]],[]]]]] => [1,1,1,1,1,0,0,1,0,0,0,0] => [6,4,3,5,2,1] => [2,1,1,1,1]
[[[[[[],[]]]]]] => [1,1,1,1,1,0,1,0,0,0,0,0] => [6,5,3,4,2,1] => [2,1,1,1,1]
[[[[[[[]]]]]]] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => [1,1,1,1,1,1]
[[],[],[],[],[],[],[]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => [7]
[[],[],[],[],[],[[]]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => [6,1]
[[],[],[],[],[[]],[]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => [6,1]
[[],[],[],[],[[],[]]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => [6,1]
[[],[],[],[],[[[]]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => [5,1,1]
[[],[],[],[[]],[],[]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,6,7] => [6,1]
[[],[],[],[[]],[[]]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => [5,2]
[[],[],[],[[],[]],[]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,5,6,4,7] => [6,1]
[[],[],[],[[[]]],[]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,5,4,7] => [5,1,1]
[[],[],[],[[],[],[]]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => [6,1]
[[],[],[],[[],[[]]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,6,4] => [5,1,1]
[[],[],[],[[[]],[]]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => [5,1,1]
[[],[],[],[[[],[]]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,7,5,6,4] => [5,1,1]
[[],[],[],[[[[]]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,6,5,4] => [4,1,1,1]
[[],[],[[]],[],[],[]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7] => [6,1]
[[],[],[[]],[],[[]]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => [5,2]
[[],[],[[]],[[]],[]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => [5,2]
[[],[],[[]],[[],[]]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,7,5] => [5,2]
[[],[],[[]],[[[]]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,6,5] => [4,2,1]
[[],[],[[],[]],[],[]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,5,3,6,7] => [6,1]
[[],[],[[[]]],[],[]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,4,3,6,7] => [5,1,1]
[[],[],[[],[]],[[]]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6] => [5,2]
[[],[],[[[]]],[[]]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,4,3,7,6] => [4,2,1]
[[],[],[[],[],[]],[]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => [6,1]
[[],[],[[],[[]]],[]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,5,3,7] => [5,1,1]
[[],[],[[[]],[]],[]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,5,4,6,3,7] => [5,1,1]
[[],[],[[[],[]]],[]] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,6,4,5,3,7] => [5,1,1]
[[],[],[[[[]]]],[]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,5,4,3,7] => [4,1,1,1]
[[],[],[[],[],[],[]]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => [6,1]
[[],[],[[],[],[[]]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,6,3] => [5,1,1]
[[],[],[[],[[]],[]]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,5,7,3] => [5,1,1]
[[],[],[[],[[],[]]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,7,5,6,3] => [5,1,1]
[[],[],[[],[[[]]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,6,5,3] => [4,1,1,1]
[[],[],[[[]],[],[]]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => [5,1,1]
[[],[],[[[]],[[]]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,4,7,6,3] => [4,2,1]
[[],[],[[[],[]],[]]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,6,4,5,7,3] => [5,1,1]
[[],[],[[[[]]],[]]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,5,4,7,3] => [4,1,1,1]
[[],[],[[[],[],[]]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,7,4,5,6,3] => [5,1,1]
[[],[],[[[],[[]]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,7,4,6,5,3] => [4,1,1,1]
[[],[],[[[[]],[]]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,7,5,4,6,3] => [4,1,1,1]
[[],[],[[[[],[]]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,7,5,6,4,3] => [4,1,1,1]
[[],[],[[[[[]]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => [3,1,1,1,1]
[[],[[]],[],[],[],[]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => [6,1]
[[],[[]],[],[],[[]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => [5,2]
[[],[[]],[],[[]],[]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => [5,2]
[[],[[]],[],[[],[]]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,4,6,7,5] => [5,2]
[[],[[]],[],[[[]]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,6,5] => [4,2,1]
[[],[[]],[[]],[],[]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => [5,2]
[[],[[]],[[]],[[]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => [4,3]
[[],[[]],[[],[]],[]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,6,4,7] => [5,2]
[[],[[]],[[[]]],[]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,5,4,7] => [4,2,1]
[[],[[]],[[],[],[]]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,6,7,4] => [5,2]
[[],[[]],[[],[[]]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,6,4] => [4,2,1]
[[],[[]],[[[]],[]]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,5,7,4] => [4,2,1]
[[],[[]],[[[],[]]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,7,5,6,4] => [4,2,1]
[[],[[]],[[[[]]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,6,5,4] => [3,2,1,1]
[[],[[],[]],[],[],[]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7] => [6,1]
[[],[[[]]],[],[],[]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7] => [5,1,1]
[[],[[],[]],[],[[]]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => [5,2]
[[],[[[]]],[],[[]]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,3,2,5,7,6] => [4,2,1]
[[],[[],[]],[[]],[]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,7] => [5,2]
[[],[[[]]],[[]],[]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,3,2,6,5,7] => [4,2,1]
[[],[[],[]],[[],[]]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,2,6,7,5] => [5,2]
[[],[[],[]],[[[]]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,6,5] => [4,2,1]
[[],[[[]]],[[],[]]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,3,2,6,7,5] => [4,2,1]
[[],[[[]]],[[[]]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3,2,7,6,5] => [3,2,2]
[[],[[],[],[]],[],[]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,2,6,7] => [6,1]
[[],[[],[[]]],[],[]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,4,2,6,7] => [5,1,1]
[[],[[[]],[]],[],[]] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,3,5,2,6,7] => [5,1,1]
[[],[[[],[]]],[],[]] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,5,3,4,2,6,7] => [5,1,1]
[[],[[[[]]]],[],[]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,4,3,2,6,7] => [4,1,1,1]
[[],[[],[],[]],[[]]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6] => [5,2]
[[],[[],[[]]],[[]]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,4,2,7,6] => [4,2,1]
[[],[[[]],[]],[[]]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,3,5,2,7,6] => [4,2,1]
[[],[[[],[]]],[[]]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,5,3,4,2,7,6] => [4,2,1]
[[],[[[[]]]],[[]]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,4,3,2,7,6] => [3,2,1,1]
[[],[[],[],[],[]],[]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,2,7] => [6,1]
[[],[[],[],[[]]],[]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,6,5,2,7] => [5,1,1]
[[],[[],[[]],[]],[]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,4,6,2,7] => [5,1,1]
[[],[[],[[],[]]],[]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,6,4,5,2,7] => [5,1,1]
[[],[[],[[[]]]],[]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,5,4,2,7] => [4,1,1,1]
[[],[[[]],[],[]],[]] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,3,5,6,2,7] => [5,1,1]
[[],[[[]],[[]]],[]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,3,6,5,2,7] => [4,2,1]
[[],[[[],[]],[]],[]] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,5,3,4,6,2,7] => [5,1,1]
[[],[[[[]]],[]],[]] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,4,3,6,2,7] => [4,1,1,1]
[[],[[[],[],[]]],[]] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,6,3,4,5,2,7] => [5,1,1]
[[],[[[],[[]]]],[]] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,6,3,5,4,2,7] => [4,1,1,1]
[[],[[[[]],[]]],[]] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,6,4,3,5,2,7] => [4,1,1,1]
[[],[[[[],[]]]],[]] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,6,4,5,3,2,7] => [4,1,1,1]
[[],[[[[[]]]]],[]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,5,4,3,2,7] => [3,1,1,1,1]
[[],[[],[],[],[],[]]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => [6,1]
[[],[[],[],[],[[]]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,6,2] => [5,1,1]
[[],[[],[],[[]],[]]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,6,5,7,2] => [5,1,1]
[[],[[],[],[[],[]]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,7,5,6,2] => [5,1,1]
[[],[[],[],[[[]]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,6,5,2] => [4,1,1,1]
[[],[[],[[]],[],[]]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,4,6,7,2] => [5,1,1]
[[],[[],[[]],[[]]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,4,7,6,2] => [4,2,1]
[[],[[],[[],[]],[]]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,6,4,5,7,2] => [5,1,1]
[[],[[],[[[]]],[]]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,5,4,7,2] => [4,1,1,1]
[[],[[],[[],[],[]]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,7,4,5,6,2] => [5,1,1]
[[],[[],[[],[[]]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,7,4,6,5,2] => [4,1,1,1]
[[],[[],[[[]],[]]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,7,5,4,6,2] => [4,1,1,1]
[[],[[],[[[],[]]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,7,5,6,4,2] => [4,1,1,1]
[[],[[],[[[[]]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => [3,1,1,1,1]
[[],[[[]],[],[],[]]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => [5,1,1]
[[],[[[]],[],[[]]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,3,5,7,6,2] => [4,2,1]
[[],[[[]],[[]],[]]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,3,6,5,7,2] => [4,2,1]
[[],[[[]],[[],[]]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,3,7,5,6,2] => [4,2,1]
[[],[[[]],[[[]]]]] => [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]
[[],[[[],[]],[],[]]] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,5,3,4,6,7,2] => [5,1,1]
[[],[[[[]]],[],[]]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,4,3,6,7,2] => [4,1,1,1]
[[],[[[],[]],[[]]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,5,3,4,7,6,2] => [4,2,1]
[[],[[[[]]],[[]]]] => [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]
[[],[[[],[],[]],[]]] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,6,3,4,5,7,2] => [5,1,1]
[[],[[[],[[]]],[]]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,6,3,5,4,7,2] => [4,1,1,1]
[[],[[[[]],[]],[]]] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,6,4,3,5,7,2] => [4,1,1,1]
[[],[[[[],[]]],[]]] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,6,4,5,3,7,2] => [4,1,1,1]
[[],[[[[[]]]],[]]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,5,4,3,7,2] => [3,1,1,1,1]
[[],[[[],[],[],[]]]] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,7,3,4,5,6,2] => [5,1,1]
[[],[[[],[],[[]]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,7,3,4,6,5,2] => [4,1,1,1]
[[],[[[],[[]],[]]]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,7,3,5,4,6,2] => [4,1,1,1]
[[],[[[],[[],[]]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,7,3,5,6,4,2] => [4,1,1,1]
[[],[[[],[[[]]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,7,3,6,5,4,2] => [3,1,1,1,1]
[[],[[[[]],[],[]]]] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,7,4,3,5,6,2] => [4,1,1,1]
[[],[[[[]],[[]]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,7,4,3,6,5,2] => [3,2,1,1]
[[],[[[[],[]],[]]]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,7,4,5,3,6,2] => [4,1,1,1]
[[],[[[[[]]],[]]]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,7,5,4,3,6,2] => [3,1,1,1,1]
[[],[[[[],[],[]]]]] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,7,4,5,6,3,2] => [4,1,1,1]
[[],[[[[],[[]]]]]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,7,4,6,5,3,2] => [3,1,1,1,1]
[[],[[[[[]],[]]]]] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,7,5,4,6,3,2] => [3,1,1,1,1]
[[],[[[[[],[]]]]]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,7,6,4,5,3,2] => [3,1,1,1,1]
[[],[[[[[[]]]]]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => [2,1,1,1,1,1]
[[[]],[],[],[],[],[]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => [6,1]
[[[]],[],[],[],[[]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,7,6] => [5,2]
[[[]],[],[],[[]],[]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,6,5,7] => [5,2]
[[[]],[],[],[[],[]]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,6,7,5] => [5,2]
[[[]],[],[],[[[]]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,6,5] => [4,2,1]
[[[]],[],[[]],[],[]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,6,7] => [5,2]
[[[]],[],[[]],[[]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,5,4,7,6] => [4,3]
[[[]],[],[[],[]],[]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,6,4,7] => [5,2]
[[[]],[],[[[]]],[]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,6,5,4,7] => [4,2,1]
[[[]],[],[[],[],[]]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,5,6,7,4] => [5,2]
[[[]],[],[[],[[]]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,5,7,6,4] => [4,2,1]
[[[]],[],[[[]],[]]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,6,5,7,4] => [4,2,1]
[[[]],[],[[[],[]]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,7,5,6,4] => [4,2,1]
[[[]],[],[[[[]]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,6,5,4] => [3,2,1,1]
[[[]],[[]],[],[],[]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7] => [5,2]
[[[]],[[]],[],[[]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,5,7,6] => [4,3]
[[[]],[[]],[[]],[]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => [4,3]
[[[]],[[]],[[],[]]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,7,5] => [4,3]
[[[]],[[]],[[[]]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,6,5] => [3,3,1]
[[[]],[[],[]],[],[]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,5,3,6,7] => [5,2]
[[[]],[[[]]],[],[]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,4,3,6,7] => [4,2,1]
[[[]],[[],[]],[[]]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,4,5,3,7,6] => [4,3]
[[[]],[[[]]],[[]]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,4,3,7,6] => [3,3,1]
[[[]],[[],[],[]],[]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,3,7] => [5,2]
[[[]],[[],[[]]],[]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,5,3,7] => [4,2,1]
[[[]],[[[]],[]],[]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,4,6,3,7] => [4,2,1]
[[[]],[[[],[]]],[]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,6,4,5,3,7] => [4,2,1]
[[[]],[[[[]]]],[]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,5,4,3,7] => [3,2,1,1]
[[[]],[[],[],[],[]]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,3] => [5,2]
[[[]],[[],[],[[]]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,5,7,6,3] => [4,2,1]
[[[]],[[],[[]],[]]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,5,7,3] => [4,2,1]
[[[]],[[],[[],[]]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,7,5,6,3] => [4,2,1]
[[[]],[[],[[[]]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,7,6,5,3] => [3,2,1,1]
[[[]],[[[]],[],[]]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,4,6,7,3] => [4,2,1]
[[[]],[[[]],[[]]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,4,7,6,3] => [3,3,1]
[[[]],[[[],[]],[]]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,6,4,5,7,3] => [4,2,1]
[[[]],[[[[]]],[]]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,6,5,4,7,3] => [3,2,1,1]
[[[]],[[[],[],[]]]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,7,4,5,6,3] => [4,2,1]
[[[]],[[[],[[]]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,7,4,6,5,3] => [3,2,1,1]
[[[]],[[[[]],[]]]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,7,5,4,6,3] => [3,2,1,1]
[[[]],[[[[],[]]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,7,5,6,4,3] => [3,2,1,1]
[[[]],[[[[[]]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => [2,2,1,1,1]
[[[],[]],[],[],[],[]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7] => [6,1]
[[[[]]],[],[],[],[]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7] => [5,1,1]
[[[],[]],[],[],[[]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,7,6] => [5,2]
[[[[]]],[],[],[[]]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,7,6] => [4,2,1]
[[[],[]],[],[[]],[]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,1,4,6,5,7] => [5,2]
[[[[]]],[],[[]],[]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,2,1,4,6,5,7] => [4,2,1]
[[[],[]],[],[[],[]]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,4,6,7,5] => [5,2]
[[[],[]],[],[[[]]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,4,7,6,5] => [4,2,1]
[[[[]]],[],[[],[]]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,2,1,4,6,7,5] => [4,2,1]
[[[[]]],[],[[[]]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,2,1,4,7,6,5] => [3,2,2]
[[[],[]],[[]],[],[]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,1,5,4,6,7] => [5,2]
[[[[]]],[[]],[],[]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,5,4,6,7] => [4,2,1]
[[[],[]],[[]],[[]]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6] => [4,3]
[[[[]]],[[]],[[]]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,1,5,4,7,6] => [3,3,1]
[[[],[]],[[],[]],[]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1,5,6,4,7] => [5,2]
[[[],[]],[[[]]],[]] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1,6,5,4,7] => [4,2,1]
[[[[]]],[[],[]],[]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,2,1,5,6,4,7] => [4,2,1]
[[[[]]],[[[]]],[]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,2,1,6,5,4,7] => [3,2,2]
[[[],[]],[[],[],[]]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,6,7,4] => [5,2]
[[[],[]],[[],[[]]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,1,5,7,6,4] => [4,2,1]
[[[],[]],[[[]],[]]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1,6,5,7,4] => [4,2,1]
[[[],[]],[[[],[]]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,7,5,6,4] => [4,2,1]
[[[],[]],[[[[]]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,7,6,5,4] => [3,2,1,1]
[[[[]]],[[],[],[]]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,2,1,5,6,7,4] => [4,2,1]
[[[[]]],[[],[[]]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,2,1,5,7,6,4] => [3,2,2]
[[[[]]],[[[]],[]]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,2,1,6,5,7,4] => [3,2,2]
[[[[]]],[[[],[]]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,2,1,7,5,6,4] => [3,2,2]
[[[[]]],[[[[]]]]] => [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]
[[[],[],[]],[],[],[]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => [6,1]
[[[],[[]]],[],[],[]] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7] => [5,1,1]
[[[[]],[]],[],[],[]] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7] => [5,1,1]
[[[[],[]]],[],[],[]] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [4,2,3,1,5,6,7] => [5,1,1]
[[[[[]]]],[],[],[]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7] => [4,1,1,1]
[[[],[],[]],[],[[]]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,1,5,7,6] => [5,2]
[[[],[[]]],[],[[]]] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,4,3,1,5,7,6] => [4,2,1]
[[[[]],[]],[],[[]]] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,2,4,1,5,7,6] => [4,2,1]
[[[[],[]]],[],[[]]] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [4,2,3,1,5,7,6] => [4,2,1]
[[[[[]]]],[],[[]]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,3,2,1,5,7,6] => [3,2,1,1]
[[[],[],[]],[[]],[]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,7] => [5,2]
[[[],[[]]],[[]],[]] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,3,1,6,5,7] => [4,2,1]
[[[[]],[]],[[]],[]] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,2,4,1,6,5,7] => [4,2,1]
[[[[],[]]],[[]],[]] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [4,2,3,1,6,5,7] => [4,2,1]
[[[[[]]]],[[]],[]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,3,2,1,6,5,7] => [3,2,1,1]
[[[],[],[]],[[],[]]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,7,5] => [5,2]
[[[],[],[]],[[[]]]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,1,7,6,5] => [4,2,1]
[[[],[[]]],[[],[]]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,3,1,6,7,5] => [4,2,1]
[[[],[[]]],[[[]]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,3,1,7,6,5] => [3,2,2]
[[[[]],[]],[[],[]]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,2,4,1,6,7,5] => [4,2,1]
[[[[]],[]],[[[]]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,2,4,1,7,6,5] => [3,2,2]
[[[[],[]]],[[],[]]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [4,2,3,1,6,7,5] => [4,2,1]
[[[[],[]]],[[[]]]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,2,3,1,7,6,5] => [3,2,2]
[[[[[]]]],[[],[]]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,3,2,1,6,7,5] => [3,2,1,1]
[[[[[]]]],[[[]]]] => [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]
[[[],[],[],[]],[],[]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => [6,1]
[[[],[],[[]]],[],[]] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,5,4,1,6,7] => [5,1,1]
[[[],[[]],[]],[],[]] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,3,5,1,6,7] => [5,1,1]
[[[],[[],[]]],[],[]] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,5,3,4,1,6,7] => [5,1,1]
[[[],[[[]]]],[],[]] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,5,4,3,1,6,7] => [4,1,1,1]
[[[[]],[],[]],[],[]] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,1,6,7] => [5,1,1]
[[[[]],[[]]],[],[]] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,2,5,4,1,6,7] => [4,2,1]
[[[[],[]],[]],[],[]] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [4,2,3,5,1,6,7] => [5,1,1]
[[[[[]]],[]],[],[]] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,3,2,5,1,6,7] => [4,1,1,1]
[[[[],[],[]]],[],[]] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [5,2,3,4,1,6,7] => [5,1,1]
[[[[],[[]]]],[],[]] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [5,2,4,3,1,6,7] => [4,1,1,1]
[[[[[]],[]]],[],[]] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [5,3,2,4,1,6,7] => [4,1,1,1]
[[[[[],[]]]],[],[]] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [5,3,4,2,1,6,7] => [4,1,1,1]
[[[[[[]]]]],[],[]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,4,3,2,1,6,7] => [3,1,1,1,1]
[[[],[],[],[]],[[]]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => [5,2]
[[[],[],[[]]],[[]]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,4,1,7,6] => [4,2,1]
[[[],[[]],[]],[[]]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,3,5,1,7,6] => [4,2,1]
[[[],[[],[]]],[[]]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,5,3,4,1,7,6] => [4,2,1]
[[[],[[[]]]],[[]]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,4,3,1,7,6] => [3,2,1,1]
[[[[]],[],[]],[[]]] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,2,4,5,1,7,6] => [4,2,1]
[[[[]],[[]]],[[]]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,2,5,4,1,7,6] => [3,3,1]
[[[[],[]],[]],[[]]] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [4,2,3,5,1,7,6] => [4,2,1]
[[[[[]]],[]],[[]]] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,3,2,5,1,7,6] => [3,2,1,1]
[[[[],[],[]]],[[]]] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [5,2,3,4,1,7,6] => [4,2,1]
[[[[],[[]]]],[[]]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,2,4,3,1,7,6] => [3,2,1,1]
[[[[[]],[]]],[[]]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,3,2,4,1,7,6] => [3,2,1,1]
[[[[[],[]]]],[[]]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,3,4,2,1,7,6] => [3,2,1,1]
[[[[[[]]]]],[[]]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,4,3,2,1,7,6] => [2,2,1,1,1]
[[[],[],[],[],[]],[]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,1,7] => [6,1]
[[[],[],[],[[]]],[]] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,6,5,1,7] => [5,1,1]
[[[],[],[[]],[]],[]] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,4,6,1,7] => [5,1,1]
[[[],[],[[],[]]],[]] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,6,4,5,1,7] => [5,1,1]
[[[],[],[[[]]]],[]] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,6,5,4,1,7] => [4,1,1,1]
[[[],[[]],[],[]],[]] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,3,5,6,1,7] => [5,1,1]
[[[],[[]],[[]]],[]] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,3,6,5,1,7] => [4,2,1]
[[[],[[],[]],[]],[]] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,5,3,4,6,1,7] => [5,1,1]
[[[],[[[]]],[]],[]] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,5,4,3,6,1,7] => [4,1,1,1]
[[[],[[],[],[]]],[]] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,6,3,4,5,1,7] => [5,1,1]
[[[],[[],[[]]]],[]] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,6,3,5,4,1,7] => [4,1,1,1]
[[[],[[[]],[]]],[]] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,6,4,3,5,1,7] => [4,1,1,1]
[[[],[[[],[]]]],[]] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,6,4,5,3,1,7] => [4,1,1,1]
[[[],[[[[]]]]],[]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,5,4,3,1,7] => [3,1,1,1,1]
[[[[]],[],[],[]],[]] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,1,7] => [5,1,1]
[[[[]],[],[[]]],[]] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,2,4,6,5,1,7] => [4,2,1]
[[[[]],[[]],[]],[]] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,2,5,4,6,1,7] => [4,2,1]
[[[[]],[[],[]]],[]] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,2,6,4,5,1,7] => [4,2,1]
[[[[]],[[[]]]],[]] => [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]
[[[[],[]],[],[]],[]] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [4,2,3,5,6,1,7] => [5,1,1]
[[[[[]]],[],[]],[]] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,3,2,5,6,1,7] => [4,1,1,1]
[[[[],[]],[[]]],[]] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [4,2,3,6,5,1,7] => [4,2,1]
[[[[[]]],[[]]],[]] => [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]
[[[[],[],[]],[]],[]] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [5,2,3,4,6,1,7] => [5,1,1]
[[[[],[[]]],[]],[]] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [5,2,4,3,6,1,7] => [4,1,1,1]
[[[[[]],[]],[]],[]] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [5,3,2,4,6,1,7] => [4,1,1,1]
[[[[[],[]]],[]],[]] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [5,3,4,2,6,1,7] => [4,1,1,1]
[[[[[[]]]],[]],[]] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,4,3,2,6,1,7] => [3,1,1,1,1]
[[[[],[],[],[]]],[]] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,2,3,4,5,1,7] => [5,1,1]
[[[[],[],[[]]]],[]] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,2,3,5,4,1,7] => [4,1,1,1]
[[[[],[[]],[]]],[]] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [6,2,4,3,5,1,7] => [4,1,1,1]
[[[[],[[],[]]]],[]] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,2,4,5,3,1,7] => [4,1,1,1]
[[[[],[[[]]]]],[]] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,2,5,4,3,1,7] => [3,1,1,1,1]
[[[[[]],[],[]]],[]] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1,7] => [4,1,1,1]
[[[[[]],[[]]]],[]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,3,2,5,4,1,7] => [3,2,1,1]
[[[[[],[]],[]]],[]] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,4,2,5,1,7] => [4,1,1,1]
[[[[[[]]],[]]],[]] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,4,3,2,5,1,7] => [3,1,1,1,1]
[[[[[],[],[]]]],[]] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,3,4,5,2,1,7] => [4,1,1,1]
[[[[[],[[]]]]],[]] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,3,5,4,2,1,7] => [3,1,1,1,1]
[[[[[[]],[]]]],[]] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,4,3,5,2,1,7] => [3,1,1,1,1]
[[[[[[],[]]]]],[]] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,5,3,4,2,1,7] => [3,1,1,1,1]
[[[[[[[]]]]]],[]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,5,4,3,2,1,7] => [2,1,1,1,1,1]
[[[],[],[],[],[],[]]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => [6,1]
[[[],[],[],[],[[]]]] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,7,6,1] => [5,1,1]
[[[],[],[],[[]],[]]] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,6,5,7,1] => [5,1,1]
[[[],[],[],[[],[]]]] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,7,5,6,1] => [5,1,1]
[[[],[],[],[[[]]]]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,7,6,5,1] => [4,1,1,1]
[[[],[],[[]],[],[]]] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,5,4,6,7,1] => [5,1,1]
[[[],[],[[]],[[]]]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,4,7,6,1] => [4,2,1]
[[[],[],[[],[]],[]]] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,6,4,5,7,1] => [5,1,1]
[[[],[],[[[]]],[]]] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,6,5,4,7,1] => [4,1,1,1]
[[[],[],[[],[],[]]]] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,7,4,5,6,1] => [5,1,1]
[[[],[],[[],[[]]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,7,4,6,5,1] => [4,1,1,1]
[[[],[],[[[]],[]]]] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,7,5,4,6,1] => [4,1,1,1]
[[[],[],[[[],[]]]]] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,7,5,6,4,1] => [4,1,1,1]
[[[],[],[[[[]]]]]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,7,6,5,4,1] => [3,1,1,1,1]
[[[],[[]],[],[],[]]] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,1] => [5,1,1]
[[[],[[]],[],[[]]]] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,4,3,5,7,6,1] => [4,2,1]
[[[],[[]],[[]],[]]] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,3,6,5,7,1] => [4,2,1]
[[[],[[]],[[],[]]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,3,7,5,6,1] => [4,2,1]
[[[],[[]],[[[]]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,3,7,6,5,1] => [3,2,1,1]
[[[],[[],[]],[],[]]] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,5,3,4,6,7,1] => [5,1,1]
[[[],[[[]]],[],[]]] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,5,4,3,6,7,1] => [4,1,1,1]
[[[],[[],[]],[[]]]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,5,3,4,7,6,1] => [4,2,1]
[[[],[[[]]],[[]]]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,5,4,3,7,6,1] => [3,2,1,1]
[[[],[[],[],[]],[]]] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,6,3,4,5,7,1] => [5,1,1]
[[[],[[],[[]]],[]]] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,6,3,5,4,7,1] => [4,1,1,1]
[[[],[[[]],[]],[]]] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,6,4,3,5,7,1] => [4,1,1,1]
[[[],[[[],[]]],[]]] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,6,4,5,3,7,1] => [4,1,1,1]
[[[],[[[[]]]],[]]] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,6,5,4,3,7,1] => [3,1,1,1,1]
[[[],[[],[],[],[]]]] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,7,3,4,5,6,1] => [5,1,1]
[[[],[[],[],[[]]]]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,7,3,4,6,5,1] => [4,1,1,1]
[[[],[[],[[]],[]]]] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,7,3,5,4,6,1] => [4,1,1,1]
[[[],[[],[[],[]]]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,7,3,5,6,4,1] => [4,1,1,1]
[[[],[[],[[[]]]]]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,7,3,6,5,4,1] => [3,1,1,1,1]
[[[],[[[]],[],[]]]] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,7,4,3,5,6,1] => [4,1,1,1]
[[[],[[[]],[[]]]]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,7,4,3,6,5,1] => [3,2,1,1]
[[[],[[[],[]],[]]]] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,7,4,5,3,6,1] => [4,1,1,1]
[[[],[[[[]]],[]]]] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,7,5,4,3,6,1] => [3,1,1,1,1]
[[[],[[[],[],[]]]]] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,7,4,5,6,3,1] => [4,1,1,1]
[[[],[[[],[[]]]]]] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,7,4,6,5,3,1] => [3,1,1,1,1]
[[[],[[[[]],[]]]]] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,7,5,4,6,3,1] => [3,1,1,1,1]
[[[],[[[[],[]]]]]] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,7,6,4,5,3,1] => [3,1,1,1,1]
[[[],[[[[[]]]]]]] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7,6,5,4,3,1] => [2,1,1,1,1,1]
[[[[]],[],[],[],[]]] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,1] => [5,1,1]
[[[[]],[],[],[[]]]] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,7,6,1] => [4,2,1]
[[[[]],[],[[]],[]]] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,2,4,6,5,7,1] => [4,2,1]
[[[[]],[],[[],[]]]] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,2,4,7,5,6,1] => [4,2,1]
[[[[]],[],[[[]]]]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,2,4,7,6,5,1] => [3,2,1,1]
[[[[]],[[]],[],[]]] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,2,5,4,6,7,1] => [4,2,1]
[[[[]],[[]],[[]]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,5,4,7,6,1] => [3,3,1]
[[[[]],[[],[]],[]]] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,2,6,4,5,7,1] => [4,2,1]
[[[[]],[[[]]],[]]] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,2,6,5,4,7,1] => [3,2,1,1]
[[[[]],[[],[],[]]]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,2,7,4,5,6,1] => [4,2,1]
[[[[]],[[],[[]]]]] => [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]
[[[[]],[[[]],[]]]] => [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]
[[[[]],[[[],[]]]]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,7,5,6,4,1] => [3,2,1,1]
[[[[]],[[[[]]]]]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,2,7,6,5,4,1] => [2,2,1,1,1]
[[[[],[]],[],[],[]]] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [4,2,3,5,6,7,1] => [5,1,1]
[[[[[]]],[],[],[]]] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,1] => [4,1,1,1]
[[[[],[]],[],[[]]]] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,2,3,5,7,6,1] => [4,2,1]
[[[[[]]],[],[[]]]] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,3,2,5,7,6,1] => [3,2,1,1]
[[[[],[]],[[]],[]]] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [4,2,3,6,5,7,1] => [4,2,1]
[[[[[]]],[[]],[]]] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,3,2,6,5,7,1] => [3,2,1,1]
[[[[],[]],[[],[]]]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,2,3,7,5,6,1] => [4,2,1]
[[[[],[]],[[[]]]]] => [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]
[[[[[]]],[[],[]]]] => [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]
[[[[[]]],[[[]]]]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,3,2,7,6,5,1] => [2,2,2,1]
[[[[],[],[]],[],[]]] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [5,2,3,4,6,7,1] => [5,1,1]
[[[[],[[]]],[],[]]] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,2,4,3,6,7,1] => [4,1,1,1]
[[[[[]],[]],[],[]]] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [5,3,2,4,6,7,1] => [4,1,1,1]
[[[[[],[]]],[],[]]] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,3,4,2,6,7,1] => [4,1,1,1]
[[[[[[]]]],[],[]]] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4,3,2,6,7,1] => [3,1,1,1,1]
[[[[],[],[]],[[]]]] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,2,3,4,7,6,1] => [4,2,1]
[[[[],[[]]],[[]]]] => [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]
[[[[[]],[]],[[]]]] => [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]
[[[[[],[]]],[[]]]] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,3,4,2,7,6,1] => [3,2,1,1]
[[[[[[]]]],[[]]]] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,4,3,2,7,6,1] => [2,2,1,1,1]
[[[[],[],[],[]],[]]] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,2,3,4,5,7,1] => [5,1,1]
[[[[],[],[[]]],[]]] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,2,3,5,4,7,1] => [4,1,1,1]
[[[[],[[]],[]],[]]] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,2,4,3,5,7,1] => [4,1,1,1]
[[[[],[[],[]]],[]]] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,2,4,5,3,7,1] => [4,1,1,1]
[[[[],[[[]]]],[]]] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,5,4,3,7,1] => [3,1,1,1,1]
[[[[[]],[],[]],[]]] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,3,2,4,5,7,1] => [4,1,1,1]
[[[[[]],[[]]],[]]] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,2,5,4,7,1] => [3,2,1,1]
[[[[[],[]],[]],[]]] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,3,4,2,5,7,1] => [4,1,1,1]
[[[[[[]]],[]],[]]] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,3,2,5,7,1] => [3,1,1,1,1]
[[[[[],[],[]]],[]]] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,4,5,2,7,1] => [4,1,1,1]
[[[[[],[[]]]],[]]] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,3,5,4,2,7,1] => [3,1,1,1,1]
[[[[[[]],[]]],[]]] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,4,3,5,2,7,1] => [3,1,1,1,1]
[[[[[[],[]]]],[]]] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,5,3,4,2,7,1] => [3,1,1,1,1]
[[[[[[[]]]]],[]]] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,5,4,3,2,7,1] => [2,1,1,1,1,1]
[[[[],[],[],[],[]]]] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [7,2,3,4,5,6,1] => [5,1,1]
[[[[],[],[],[[]]]]] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [7,2,3,4,6,5,1] => [4,1,1,1]
[[[[],[],[[]],[]]]] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [7,2,3,5,4,6,1] => [4,1,1,1]
[[[[],[],[[],[]]]]] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [7,2,3,5,6,4,1] => [4,1,1,1]
[[[[],[],[[[]]]]]] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [7,2,3,6,5,4,1] => [3,1,1,1,1]
[[[[],[[]],[],[]]]] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [7,2,4,3,5,6,1] => [4,1,1,1]
[[[[],[[]],[[]]]]] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [7,2,4,3,6,5,1] => [3,2,1,1]
[[[[],[[],[]],[]]]] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [7,2,4,5,3,6,1] => [4,1,1,1]
[[[[],[[[]]],[]]]] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [7,2,5,4,3,6,1] => [3,1,1,1,1]
[[[[],[[],[],[]]]]] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [7,2,4,5,6,3,1] => [4,1,1,1]
[[[[],[[],[[]]]]]] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [7,2,4,6,5,3,1] => [3,1,1,1,1]
[[[[],[[[]],[]]]]] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [7,2,5,4,6,3,1] => [3,1,1,1,1]
[[[[],[[[],[]]]]]] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [7,2,6,4,5,3,1] => [3,1,1,1,1]
[[[[],[[[[]]]]]]] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [7,2,6,5,4,3,1] => [2,1,1,1,1,1]
[[[[[]],[],[],[]]]] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [7,3,2,4,5,6,1] => [4,1,1,1]
[[[[[]],[],[[]]]]] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [7,3,2,4,6,5,1] => [3,2,1,1]
[[[[[]],[[]],[]]]] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [7,3,2,5,4,6,1] => [3,2,1,1]
[[[[[]],[[],[]]]]] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [7,3,2,5,6,4,1] => [3,2,1,1]
[[[[[]],[[[]]]]]] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [7,3,2,6,5,4,1] => [2,2,1,1,1]
[[[[[],[]],[],[]]]] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [7,3,4,2,5,6,1] => [4,1,1,1]
[[[[[[]]],[],[]]]] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [7,4,3,2,5,6,1] => [3,1,1,1,1]
[[[[[],[]],[[]]]]] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [7,3,4,2,6,5,1] => [3,2,1,1]
[[[[[[]]],[[]]]]] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [7,4,3,2,6,5,1] => [2,2,1,1,1]
[[[[[],[],[]],[]]]] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [7,3,4,5,2,6,1] => [4,1,1,1]
[[[[[],[[]]],[]]]] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [7,3,5,4,2,6,1] => [3,1,1,1,1]
[[[[[[]],[]],[]]]] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [7,4,3,5,2,6,1] => [3,1,1,1,1]
[[[[[[],[]]],[]]]] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [7,5,3,4,2,6,1] => [3,1,1,1,1]
[[[[[[[]]]],[]]]] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [7,5,4,3,2,6,1] => [2,1,1,1,1,1]
[[[[[],[],[],[]]]]] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [7,3,4,5,6,2,1] => [4,1,1,1]
[[[[[],[],[[]]]]]] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [7,3,4,6,5,2,1] => [3,1,1,1,1]
[[[[[],[[]],[]]]]] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [7,3,5,4,6,2,1] => [3,1,1,1,1]
[[[[[],[[],[]]]]]] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [7,3,6,4,5,2,1] => [3,1,1,1,1]
[[[[[],[[[]]]]]]] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [7,3,6,5,4,2,1] => [2,1,1,1,1,1]
[[[[[[]],[],[]]]]] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [7,4,3,5,6,2,1] => [3,1,1,1,1]
[[[[[[]],[[]]]]]] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [7,4,3,6,5,2,1] => [2,2,1,1,1]
[[[[[[],[]],[]]]]] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [7,5,3,4,6,2,1] => [3,1,1,1,1]
[[[[[[[]]],[]]]]] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [7,5,4,3,6,2,1] => [2,1,1,1,1,1]
[[[[[[],[],[]]]]]] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [7,6,3,4,5,2,1] => [3,1,1,1,1]
[[[[[[],[[]]]]]]] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [7,6,3,5,4,2,1] => [2,1,1,1,1,1]
[[[[[[[]],[]]]]]] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [7,6,4,3,5,2,1] => [2,1,1,1,1,1]
[[[[[[[],[]]]]]]] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [7,6,4,5,3,2,1] => [2,1,1,1,1,1]
[[[[[[[[]]]]]]]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,6,5,4,3,2,1] => [1,1,1,1,1,1,1]
[[],[],[],[],[],[],[],[]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8] => [8]
[[],[],[],[],[],[],[[]]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,8,7] => [7,1]
[[],[],[],[],[],[[]],[]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,7,6,8] => [7,1]
[[],[],[],[],[],[[],[]]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,7,8,6] => [7,1]
[[],[],[],[],[],[[[]]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,8,7,6] => [6,1,1]
[[],[],[],[],[[]],[],[]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,6,5,7,8] => [7,1]
[[],[],[],[],[[]],[[]]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,6,5,8,7] => [6,2]
[[],[],[],[],[[],[]],[]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,6,7,5,8] => [7,1]
[[],[],[],[],[[[]]],[]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,4,7,6,5,8] => [6,1,1]
[[],[],[],[],[[],[],[]]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,5] => [7,1]
[[],[],[],[],[[],[[]]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,6,8,7,5] => [6,1,1]
[[],[],[],[],[[[]],[]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,4,7,6,8,5] => [6,1,1]
[[],[],[],[],[[[],[]]]] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,8,6,7,5] => [6,1,1]
[[],[],[],[],[[[[]]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,8,7,6,5] => [5,1,1,1]
[[],[],[],[[]],[],[],[]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8] => [7,1]
[[],[],[],[[]],[],[[]]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,3,5,4,6,8,7] => [6,2]
[[],[],[],[[]],[[]],[]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,8] => [6,2]
[[],[],[],[[]],[[],[]]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,3,5,4,7,8,6] => [6,2]
[[],[],[],[[]],[[[]]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,5,4,8,7,6] => [5,2,1]
[[],[],[],[[],[]],[],[]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,3,5,6,4,7,8] => [7,1]
[[],[],[],[[[]]],[],[]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,3,6,5,4,7,8] => [6,1,1]
[[],[],[],[[],[]],[[]]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,3,5,6,4,8,7] => [6,2]
[[],[],[],[[[]]],[[]]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,6,5,4,8,7] => [5,2,1]
[[],[],[],[[],[],[]],[]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,3,5,6,7,4,8] => [7,1]
[[],[],[],[[],[[]]],[]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,3,5,7,6,4,8] => [6,1,1]
[[],[],[],[[[]],[]],[]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,3,6,5,7,4,8] => [6,1,1]
[[],[],[],[[[],[]]],[]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,3,7,5,6,4,8] => [6,1,1]
[[],[],[],[[[[]]]],[]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,3,7,6,5,4,8] => [5,1,1,1]
[[],[],[],[[],[],[],[]]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,4] => [7,1]
[[],[],[],[[],[],[[]]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,3,5,6,8,7,4] => [6,1,1]
[[],[],[],[[],[[]],[]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,3,5,7,6,8,4] => [6,1,1]
[[],[],[],[[],[[],[]]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,3,5,8,6,7,4] => [6,1,1]
[[],[],[],[[],[[[]]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3,5,8,7,6,4] => [5,1,1,1]
[[],[],[],[[[]],[],[]]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,6,5,7,8,4] => [6,1,1]
[[],[],[],[[[]],[[]]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,3,6,5,8,7,4] => [5,2,1]
[[],[],[],[[[],[]],[]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,3,7,5,6,8,4] => [6,1,1]
[[],[],[],[[[[]]],[]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,3,7,6,5,8,4] => [5,1,1,1]
[[],[],[],[[[],[],[]]]] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,8,5,6,7,4] => [6,1,1]
[[],[],[],[[[],[[]]]]] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,3,8,5,7,6,4] => [5,1,1,1]
[[],[],[],[[[[]],[]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,3,8,6,5,7,4] => [5,1,1,1]
[[],[],[],[[[[],[]]]]] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,3,8,6,7,5,4] => [5,1,1,1]
[[],[],[],[[[[[]]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,8,7,6,5,4] => [4,1,1,1,1]
[[],[],[[]],[],[],[],[]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8] => [7,1]
[[],[],[[]],[],[],[[]]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,4,3,5,6,8,7] => [6,2]
[[],[],[[]],[],[[]],[]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5,7,6,8] => [6,2]
[[],[],[[]],[],[[],[]]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,2,4,3,5,7,8,6] => [6,2]
[[],[],[[]],[],[[[]]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,4,3,5,8,7,6] => [5,2,1]
[[],[],[[]],[[]],[],[]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,5,7,8] => [6,2]
[[],[],[[]],[[]],[[]]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7] => [5,3]
[[],[],[[]],[[],[]],[]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,2,4,3,6,7,5,8] => [6,2]
[[],[],[[]],[[],[],[]]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,2,4,3,6,7,8,5] => [6,2]
[[],[],[[]],[[[]],[]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,2,4,3,7,6,8,5] => [5,2,1]
[[],[],[[]],[[[[]]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,8,7,6,5] => [4,2,1,1]
[[],[],[[[]]],[],[],[]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,5,4,3,6,7,8] => [6,1,1]
[[],[],[[[]]],[],[[]]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,2,5,4,3,6,8,7] => [5,2,1]
[[],[],[[],[]],[[]],[]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,2,4,5,3,7,6,8] => [6,2]
[[],[],[[],[]],[[],[]]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,2,4,5,3,7,8,6] => [6,2]
[[],[],[[],[]],[[[]]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,2,4,5,3,8,7,6] => [5,2,1]
[[],[],[[[]]],[[],[]]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,5,4,3,7,8,6] => [5,2,1]
[[],[],[[],[],[]],[],[]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,2,4,5,6,3,7,8] => [7,1]
[[],[],[[],[[]]],[],[]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,2,4,6,5,3,7,8] => [6,1,1]
[[],[],[[[[]]]],[],[]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,6,5,4,3,7,8] => [5,1,1,1]
[[],[],[[],[],[]],[[]]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,2,4,5,6,3,8,7] => [6,2]
[[],[],[[],[],[],[]],[]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,7,3,8] => [7,1]
[[],[],[[[]],[],[]],[]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,2,5,4,6,7,3,8] => [6,1,1]
[[],[],[[[[[]]]]],[]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,7,6,5,4,3,8] => [4,1,1,1,1]
[[],[],[[],[],[],[],[]]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,3] => [7,1]
[[],[],[[],[],[],[[]]]] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,4,5,6,8,7,3] => [6,1,1]
[[],[],[[],[],[[],[]]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,2,4,5,8,6,7,3] => [6,1,1]
[[],[],[[],[],[[[]]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,2,4,5,8,7,6,3] => [5,1,1,1]
[[],[],[[],[[],[]],[]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,2,4,7,5,6,8,3] => [6,1,1]
[[],[],[[],[[[]]],[]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,2,4,7,6,5,8,3] => [5,1,1,1]
[[],[],[[],[[],[],[]]]] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,2,4,8,5,6,7,3] => [6,1,1]
[[],[],[[],[[[]],[]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,2,4,8,6,5,7,3] => [5,1,1,1]
[[],[],[[],[[[[]]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,4,8,7,6,5,3] => [4,1,1,1,1]
[[],[],[[[]],[],[],[]]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,2,5,4,6,7,8,3] => [6,1,1]
[[],[],[[[]],[],[[]]]] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,2,5,4,6,8,7,3] => [5,2,1]
[[],[],[[[]],[[]],[]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,2,5,4,7,6,8,3] => [5,2,1]
[[],[],[[[]],[[[]]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,2,5,4,8,7,6,3] => [4,2,1,1]
[[],[],[[[],[]],[],[]]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,2,6,4,5,7,8,3] => [6,1,1]
[[],[],[[[[]]],[],[]]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,2,6,5,4,7,8,3] => [5,1,1,1]
[[],[],[[[],[],[]],[]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,2,7,4,5,6,8,3] => [6,1,1]
[[],[],[[[[[]]]],[]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,2,7,6,5,4,8,3] => [4,1,1,1,1]
[[],[],[[[],[],[],[]]]] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,8,4,5,6,7,3] => [6,1,1]
[[],[],[[[],[[],[]]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,2,8,4,6,7,5,3] => [5,1,1,1]
[[],[],[[[],[[[]]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,2,8,4,7,6,5,3] => [4,1,1,1,1]
[[],[],[[[[]],[],[]]]] => [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,2,8,5,4,6,7,3] => [5,1,1,1]
[[],[],[[[[],[]],[]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,2,8,5,6,4,7,3] => [5,1,1,1]
[[],[],[[[[[]]],[]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,8,6,5,4,7,3] => [4,1,1,1,1]
[[],[],[[[[],[],[]]]]] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,2,8,5,6,7,4,3] => [5,1,1,1]
[[],[],[[[[[],[]]]]]] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,8,7,5,6,4,3] => [4,1,1,1,1]
[[],[],[[[[[[]]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,8,7,6,5,4,3] => [3,1,1,1,1,1]
[[],[[]],[],[],[],[],[]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8] => [7,1]
[[],[[]],[],[],[],[[]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,8,7] => [6,2]
[[],[[]],[],[],[[]],[]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,2,4,5,7,6,8] => [6,2]
[[],[[]],[],[],[[],[]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,3,2,4,5,7,8,6] => [6,2]
[[],[[]],[],[],[[[]]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,2,4,5,8,7,6] => [5,2,1]
[[],[[]],[],[[]],[],[]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,6,5,7,8] => [6,2]
[[],[[]],[],[[]],[[]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,2,4,6,5,8,7] => [5,3]
[[],[[]],[],[[[]]],[]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,3,2,4,7,6,5,8] => [5,2,1]
[[],[[]],[],[[],[],[]]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,3,2,4,6,7,8,5] => [6,2]
[[],[[]],[],[[],[[]]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,2,4,6,8,7,5] => [5,2,1]
[[],[[]],[],[[[]],[]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,3,2,4,7,6,8,5] => [5,2,1]
[[],[[]],[],[[[[]]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,2,4,8,7,6,5] => [4,2,1,1]
[[],[[]],[[]],[],[],[]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8] => [6,2]
[[],[[]],[[]],[[]],[]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => [5,3]
[[],[[]],[[]],[[],[]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,8,6] => [5,3]
[[],[[]],[[]],[[[]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,7,6] => [4,3,1]
[[],[[]],[[],[]],[],[]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,3,2,5,6,4,7,8] => [6,2]
[[],[[]],[[[]]],[],[]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,6,5,4,7,8] => [5,2,1]
[[],[[]],[[],[]],[[]]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,3,2,5,6,4,8,7] => [5,3]
[[],[[]],[[[]]],[[]]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2,6,5,4,8,7] => [4,3,1]
[[],[[]],[[],[],[]],[]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,3,2,5,6,7,4,8] => [6,2]
[[],[[]],[[],[[]]],[]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,3,2,5,7,6,4,8] => [5,2,1]
[[],[[]],[[[[]]]],[]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,7,6,5,4,8] => [4,2,1,1]
[[],[[]],[[],[],[],[]]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,3,2,5,6,7,8,4] => [6,2]
[[],[[]],[[],[],[[]]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,3,2,5,6,8,7,4] => [5,2,1]
[[],[[]],[[],[[[]]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,3,2,5,8,7,6,4] => [4,2,1,1]
[[],[[]],[[[]],[],[]]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,3,2,6,5,7,8,4] => [5,2,1]
[[],[[]],[[[]],[[]]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2,6,5,8,7,4] => [4,3,1]
[[],[[]],[[[],[]],[]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,3,2,7,5,6,8,4] => [5,2,1]
[[],[[]],[[[[]]],[]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,3,2,7,6,5,8,4] => [4,2,1,1]
[[],[[]],[[[],[[]]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,3,2,8,5,7,6,4] => [4,2,1,1]
[[],[[]],[[[[]],[]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,3,2,8,6,5,7,4] => [4,2,1,1]
[[],[[]],[[[[],[]]]]] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,3,2,8,6,7,5,4] => [4,2,1,1]
[[],[[]],[[[[[]]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,7,6,5,4] => [3,2,1,1,1]
[[],[[],[]],[],[],[],[]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8] => [7,1]
[[],[[[]]],[],[],[],[]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7,8] => [6,1,1]
[[],[[],[]],[],[],[[]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,3,4,2,5,6,8,7] => [6,2]
[[],[[[]]],[],[],[[]]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,4,3,2,5,6,8,7] => [5,2,1]
[[],[[],[]],[],[[]],[]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,3,4,2,5,7,6,8] => [6,2]
[[],[[[]]],[],[[]],[]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,4,3,2,5,7,6,8] => [5,2,1]
[[],[[],[]],[],[[],[]]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,3,4,2,5,7,8,6] => [6,2]
[[],[[[]]],[],[[],[]]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,4,3,2,5,7,8,6] => [5,2,1]
[[],[[[]]],[],[[[]]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,4,3,2,5,8,7,6] => [4,2,2]
[[],[[],[]],[[]],[[]]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,8,7] => [5,3]
[[],[[],[]],[[],[]],[]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,3,4,2,6,7,5,8] => [6,2]
[[],[[[]]],[[],[]],[]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,4,3,2,6,7,5,8] => [5,2,1]
[[],[[[]]],[[[]]],[]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => [4,2,2]
[[],[[],[]],[[],[],[]]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,3,4,2,6,7,8,5] => [6,2]
[[],[[],[]],[[],[[]]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,3,4,2,6,8,7,5] => [5,2,1]
[[],[[],[]],[[[]],[]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,3,4,2,7,6,8,5] => [5,2,1]
[[],[[],[]],[[[],[]]]] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,3,4,2,8,6,7,5] => [5,2,1]
[[],[[],[]],[[[[]]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,3,4,2,8,7,6,5] => [4,2,1,1]
[[],[[[]]],[[],[],[]]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,4,3,2,6,7,8,5] => [5,2,1]
[[],[[[]]],[[],[[]]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,4,3,2,6,8,7,5] => [4,2,2]
[[],[[[]]],[[[]],[]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,4,3,2,7,6,8,5] => [4,2,2]
[[],[[[]]],[[[[]]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,3,2,8,7,6,5] => [3,2,2,1]
[[],[[],[],[]],[],[],[]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2,6,7,8] => [7,1]
[[],[[[],[]]],[],[],[]] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,5,3,4,2,6,7,8] => [6,1,1]
[[],[[[[]]]],[],[],[]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,5,4,3,2,6,7,8] => [5,1,1,1]
[[],[[],[[]]],[],[[]]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,3,5,4,2,6,8,7] => [5,2,1]
[[],[[],[],[]],[[]],[]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,5,2,7,6,8] => [6,2]
[[],[[],[[]]],[[]],[]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,3,5,4,2,7,6,8] => [5,2,1]
[[],[[[[]]]],[[]],[]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,5,4,3,2,7,6,8] => [4,2,1,1]
[[],[[],[],[]],[[],[]]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,5,2,7,8,6] => [6,2]
[[],[[],[],[]],[[[]]]] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,5,2,8,7,6] => [5,2,1]
[[],[[],[[]]],[[],[]]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,3,5,4,2,7,8,6] => [5,2,1]
[[],[[[],[]]],[[],[]]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,5,3,4,2,7,8,6] => [5,2,1]
[[],[[[],[]]],[[[]]]] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,5,3,4,2,8,7,6] => [4,2,2]
[[],[[[[]]]],[[],[]]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,5,4,3,2,7,8,6] => [4,2,1,1]
[[],[[[[]]]],[[[]]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,4,3,2,8,7,6] => [3,2,2,1]
[[],[[],[],[],[]],[],[]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,6,2,7,8] => [7,1]
[[],[[[]],[],[]],[],[]] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,4,3,5,6,2,7,8] => [6,1,1]
[[],[[[]],[[]]],[],[]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,4,3,6,5,2,7,8] => [5,2,1]
[[],[[[[]]],[]],[],[]] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,5,4,3,6,2,7,8] => [5,1,1,1]
[[],[[[],[[]]]],[],[]] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,6,3,5,4,2,7,8] => [5,1,1,1]
[[],[[[[]],[]]],[],[]] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,6,4,3,5,2,7,8] => [5,1,1,1]
[[],[[[[],[]]]],[],[]] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,6,4,5,3,2,7,8] => [5,1,1,1]
[[],[[[[[]]]]],[],[]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,6,5,4,3,2,7,8] => [4,1,1,1,1]
[[],[[],[],[],[]],[[]]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,6,2,8,7] => [6,2]
[[],[[],[[],[]]],[[]]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,3,6,4,5,2,8,7] => [5,2,1]
[[],[[],[[[]]]],[[]]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,3,6,5,4,2,8,7] => [4,2,1,1]
[[],[[[],[]],[]],[[]]] => [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,5,3,4,6,2,8,7] => [5,2,1]
[[],[[[[],[]]]],[[]]] => [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,6,4,5,3,2,8,7] => [4,2,1,1]
[[],[[[[[]]]]],[[]]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,5,4,3,2,8,7] => [3,2,1,1,1]
[[],[[],[],[],[],[]],[]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,2,8] => [7,1]
[[],[[],[],[],[[]]],[]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,5,7,6,2,8] => [6,1,1]
[[],[[],[[]],[[]]],[]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,3,5,4,7,6,2,8] => [5,2,1]
[[],[[],[[[]]],[]],[]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,3,6,5,4,7,2,8] => [5,1,1,1]
[[],[[],[[],[],[]]],[]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,3,7,4,5,6,2,8] => [6,1,1]
[[],[[[]],[],[[]]],[]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,4,3,5,7,6,2,8] => [5,2,1]
[[],[[[],[]],[],[]],[]] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,5,3,4,6,7,2,8] => [6,1,1]
[[],[[[[]]],[],[]],[]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,5,4,3,6,7,2,8] => [5,1,1,1]
[[],[[[],[[]],[]]],[]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,7,3,5,4,6,2,8] => [5,1,1,1]
[[],[[[[],[[]]]]],[]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,7,4,6,5,3,2,8] => [4,1,1,1,1]
[[],[[[[[],[]]]]],[]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,7,6,4,5,3,2,8] => [4,1,1,1,1]
[[],[[[[[[]]]]]],[]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,7,6,5,4,3,2,8] => [3,1,1,1,1,1]
[[],[[],[],[],[],[],[]]] => [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]
[[],[[],[],[],[],[[]]]] => [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]
[[],[[],[],[],[[]],[]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,5,7,6,8,2] => [6,1,1]
[[],[[],[],[],[[],[]]]] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,5,8,6,7,2] => [6,1,1]
[[],[[],[],[],[[[]]]]] => [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,5,8,7,6,2] => [5,1,1,1]
[[],[[],[],[[]],[],[]]] => [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]
[[],[[],[],[[],[],[]]]] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,3,4,8,5,6,7,2] => [6,1,1]
[[],[[],[],[[[[]]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,3,4,8,7,6,5,2] => [4,1,1,1,1]
[[],[[],[[]],[[]],[]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,3,5,4,7,6,8,2] => [5,2,1]
[[],[[],[[],[]],[],[]]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,3,6,4,5,7,8,2] => [6,1,1]
[[],[[],[[],[],[]],[]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,3,7,4,5,6,8,2] => [6,1,1]
[[],[[],[[],[],[],[]]]] => [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,3,8,4,5,6,7,2] => [6,1,1]
[[],[[],[[],[[]],[]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,3,8,4,6,5,7,2] => [5,1,1,1]
[[],[[],[[[]],[],[]]]] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,3,8,5,4,6,7,2] => [5,1,1,1]
[[],[[],[[[]],[[]]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,3,8,5,4,7,6,2] => [4,2,1,1]
[[],[[],[[[],[],[]]]]] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,3,8,5,6,7,4,2] => [5,1,1,1]
[[],[[],[[[],[[]]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,3,8,5,7,6,4,2] => [4,1,1,1,1]
[[],[[],[[[[]],[]]]]] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,3,8,6,5,7,4,2] => [4,1,1,1,1]
[[],[[],[[[[],[]]]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,3,8,7,5,6,4,2] => [4,1,1,1,1]
[[],[[],[[[[[]]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,8,7,6,5,4,2] => [3,1,1,1,1,1]
[[],[[[]],[],[],[],[]]] => [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]
[[],[[[]],[],[[],[]]]] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,3,5,8,6,7,2] => [5,2,1]
[[],[[[]],[[]],[],[]]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,3,6,5,7,8,2] => [5,2,1]
[[],[[[]],[[]],[[]]]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,8,7,2] => [4,3,1]
[[],[[[]],[[],[],[]]]] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,3,8,5,6,7,2] => [5,2,1]
[[],[[[]],[[],[[]]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,3,8,5,7,6,2] => [4,2,1,1]
[[],[[[]],[[[]],[]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,3,8,6,5,7,2] => [4,2,1,1]
[[],[[[]],[[[],[]]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,3,8,6,7,5,2] => [4,2,1,1]
[[],[[[]],[[[[]]]]]] => [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]
[[],[[[],[]],[],[],[]]] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,5,3,4,6,7,8,2] => [6,1,1]
[[],[[[[]]],[],[],[]]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,5,4,3,6,7,8,2] => [5,1,1,1]
[[],[[[[]]],[],[[]]]] => [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,5,4,3,6,8,7,2] => [4,2,1,1]
[[],[[[[]]],[[[]]]]] => [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]
[[],[[[],[],[]],[[]]]] => [1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,6,3,4,5,8,7,2] => [5,2,1]
[[],[[[],[[]]],[[]]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,6,3,5,4,8,7,2] => [4,2,1,1]
[[],[[[[]],[]],[[]]]] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,6,4,3,5,8,7,2] => [4,2,1,1]
[[],[[[[],[]]],[[]]]] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,6,4,5,3,8,7,2] => [4,2,1,1]
[[],[[[[[]]]],[[]]]] => [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]
[[],[[[],[],[],[]],[]]] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,7,3,4,5,6,8,2] => [6,1,1]
[[],[[[],[[[]]]],[]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,7,3,6,5,4,8,2] => [4,1,1,1,1]
[[],[[[[]],[[]]],[]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,7,4,3,6,5,8,2] => [4,2,1,1]
[[],[[[[],[]],[]],[]]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,7,4,5,3,6,8,2] => [5,1,1,1]
[[],[[[[],[],[]]],[]]] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,7,4,5,6,3,8,2] => [5,1,1,1]
[[],[[[[[[]]]]],[]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,7,6,5,4,3,8,2] => [3,1,1,1,1,1]
[[],[[[],[],[],[],[]]]] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,8,3,4,5,6,7,2] => [6,1,1]
[[],[[[],[],[[],[]]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,8,3,4,6,7,5,2] => [5,1,1,1]
[[],[[[],[[]],[[]]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,8,3,5,4,7,6,2] => [4,2,1,1]
[[],[[[],[[],[]],[]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,8,3,5,6,4,7,2] => [5,1,1,1]
[[],[[[],[[[]]],[]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,8,3,6,5,4,7,2] => [4,1,1,1,1]
[[],[[[],[[],[],[]]]]] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,8,3,5,6,7,4,2] => [5,1,1,1]
[[],[[[],[[],[[]]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,8,3,5,7,6,4,2] => [4,1,1,1,1]
[[],[[[],[[[],[]]]]]] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,8,3,7,5,6,4,2] => [4,1,1,1,1]
[[],[[[],[[[[]]]]]]] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,8,3,7,6,5,4,2] => [3,1,1,1,1,1]
[[],[[[[]],[],[],[]]]] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,8,4,3,5,6,7,2] => [5,1,1,1]
[[],[[[[]],[],[[]]]]] => [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,8,4,3,5,7,6,2] => [4,2,1,1]
[[],[[[[]],[[]],[]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,8,4,3,6,5,7,2] => [4,2,1,1]
[[],[[[[]],[[],[]]]]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,8,4,3,6,7,5,2] => [4,2,1,1]
[[],[[[[],[]],[],[]]]] => [1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,8,4,5,3,6,7,2] => [5,1,1,1]
[[],[[[[[]]],[],[]]]] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,8,5,4,3,6,7,2] => [4,1,1,1,1]
[[],[[[[[]]],[[]]]]] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,8,5,4,3,7,6,2] => [3,2,1,1,1]
[[],[[[[],[[]]],[]]]] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,8,4,6,5,3,7,2] => [4,1,1,1,1]
[[],[[[[[]],[]],[]]]] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,8,5,4,6,3,7,2] => [4,1,1,1,1]
[[],[[[[[[]]]],[]]]] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,8,6,5,4,3,7,2] => [3,1,1,1,1,1]
[[],[[[[],[],[],[]]]]] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,8,4,5,6,7,3,2] => [5,1,1,1]
[[],[[[[],[[]],[]]]]] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,8,4,6,5,7,3,2] => [4,1,1,1,1]
[[],[[[[],[[[]]]]]]] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,8,4,7,6,5,3,2] => [3,1,1,1,1,1]
[[],[[[[[]],[],[]]]]] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,8,5,4,6,7,3,2] => [4,1,1,1,1]
[[],[[[[[]],[[]]]]]] => [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]
[[],[[[[[],[]],[]]]]] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,8,6,4,5,7,3,2] => [4,1,1,1,1]
[[],[[[[[[]]],[]]]]] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,8,6,5,4,7,3,2] => [3,1,1,1,1,1]
[[],[[[[[],[],[]]]]]] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,8,7,4,5,6,3,2] => [4,1,1,1,1]
[[],[[[[[],[[]]]]]]] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,8,7,4,6,5,3,2] => [3,1,1,1,1,1]
[[],[[[[[[]],[]]]]]] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,8,7,5,4,6,3,2] => [3,1,1,1,1,1]
[[],[[[[[[],[]]]]]]] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,8,7,5,6,4,3,2] => [3,1,1,1,1,1]
[[],[[[[[[[]]]]]]]] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,7,6,5,4,3,2] => [2,1,1,1,1,1,1]
[[[]],[],[],[],[],[],[]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8] => [7,1]
[[[]],[],[],[],[],[[]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,8,7] => [6,2]
[[[]],[],[],[],[[]],[]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,7,6,8] => [6,2]
[[[]],[],[],[],[[],[]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,7,8,6] => [6,2]
[[[]],[],[],[],[[[]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,5,8,7,6] => [5,2,1]
[[[]],[],[],[[]],[],[]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,4,6,5,7,8] => [6,2]
[[[]],[],[],[[]],[[]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,4,6,5,8,7] => [5,3]
[[[]],[],[],[[],[],[]]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,4,6,7,8,5] => [6,2]
[[[]],[],[],[[[]],[]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,4,7,6,8,5] => [5,2,1]
[[[]],[],[],[[[],[]]]] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,4,8,6,7,5] => [5,2,1]
[[[]],[],[],[[[[]]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,8,7,6,5] => [4,2,1,1]
[[[]],[],[[]],[[],[]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,3,5,4,7,8,6] => [5,3]
[[[]],[],[[]],[[[]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,3,5,4,8,7,6] => [4,3,1]
[[[]],[],[[],[]],[[]]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,1,3,5,6,4,8,7] => [5,3]
[[[]],[],[[],[],[],[]]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,3,5,6,7,8,4] => [6,2]
[[[]],[],[[],[[],[]]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,1,3,5,8,6,7,4] => [5,2,1]
[[[]],[],[[[]],[[]]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,3,6,5,8,7,4] => [4,3,1]
[[[]],[],[[[],[],[]]]] => [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,1,3,8,5,6,7,4] => [5,2,1]
[[[]],[],[[[],[[]]]]] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,1,3,8,5,7,6,4] => [4,2,1,1]
[[[]],[],[[[[]],[]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,1,3,8,6,5,7,4] => [4,2,1,1]
[[[]],[],[[[[],[]]]]] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,3,8,6,7,5,4] => [4,2,1,1]
[[[]],[],[[[[[]]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,8,7,6,5,4] => [3,2,1,1,1]
[[[]],[[]],[],[],[],[]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8] => [6,2]
[[[]],[[]],[],[[],[]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,4,3,5,7,8,6] => [5,3]
[[[]],[[]],[],[[[]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,4,3,5,8,7,6] => [4,3,1]
[[[]],[[]],[[]],[],[]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,5,7,8] => [5,3]
[[[]],[[]],[[]],[[]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => [4,4]
[[[]],[[]],[[],[],[]]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,5] => [5,3]
[[[]],[[]],[[],[[]]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,8,7,5] => [4,3,1]
[[[]],[[]],[[[]],[]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,6,8,5] => [4,3,1]
[[[]],[[]],[[[],[]]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,3,8,6,7,5] => [4,3,1]
[[[]],[[]],[[[[]]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => [3,3,1,1]
[[[]],[[],[]],[],[],[]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,4,5,3,6,7,8] => [6,2]
[[[]],[[[]]],[],[],[]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,5,4,3,6,7,8] => [5,2,1]
[[[]],[[],[]],[],[[]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,1,4,5,3,6,8,7] => [5,3]
[[[]],[[[]]],[[]],[]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,1,5,4,3,7,6,8] => [4,3,1]
[[[]],[[],[]],[[[]]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,1,4,5,3,8,7,6] => [4,3,1]
[[[]],[[],[[]]],[],[]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,1,4,6,5,3,7,8] => [5,2,1]
[[[]],[[],[],[]],[[]]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,1,4,5,6,3,8,7] => [5,3]
[[[]],[[],[[]]],[[]]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,6,5,3,8,7] => [4,3,1]
[[[]],[[[]],[]],[[]]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,4,6,3,8,7] => [4,3,1]
[[[]],[[[],[]]],[[]]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,1,6,4,5,3,8,7] => [4,3,1]
[[[]],[[[[]]]],[[]]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => [3,3,1,1]
[[[]],[[],[],[],[]],[]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,7,3,8] => [6,2]
[[[]],[[[[[]]]]],[]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,7,6,5,4,3,8] => [3,2,1,1,1]
[[[]],[[],[],[],[],[]]] => [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]
[[[]],[[],[],[],[[]]]] => [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]
[[[]],[[],[],[[],[]]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,1,4,5,8,6,7,3] => [5,2,1]
[[[]],[[],[],[[[]]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,1,4,5,8,7,6,3] => [4,2,1,1]
[[[]],[[],[[]],[[]]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,1,4,6,5,8,7,3] => [4,3,1]
[[[]],[[],[[[]]],[]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,1,4,7,6,5,8,3] => [4,2,1,1]
[[[]],[[],[[],[],[]]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,1,4,8,5,6,7,3] => [5,2,1]
[[[]],[[],[[],[[]]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,1,4,8,5,7,6,3] => [4,2,1,1]
[[[]],[[],[[[]],[]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,1,4,8,6,5,7,3] => [4,2,1,1]
[[[]],[[],[[[],[]]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,4,8,6,7,5,3] => [4,2,1,1]
[[[]],[[],[[[[]]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,1,4,8,7,6,5,3] => [3,2,1,1,1]
[[[]],[[[]],[],[],[]]] => [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]
[[[]],[[[]],[],[[]]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,1,5,4,6,8,7,3] => [4,3,1]
[[[]],[[[]],[[]],[]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,4,7,6,8,3] => [4,3,1]
[[[]],[[[]],[[],[]]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,1,5,4,8,6,7,3] => [4,3,1]
[[[]],[[[]],[[[]]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,1,5,4,8,7,6,3] => [3,3,1,1]
[[[]],[[[],[]],[],[]]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,1,6,4,5,7,8,3] => [5,2,1]
[[[]],[[[],[]],[[]]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,1,6,4,5,8,7,3] => [4,3,1]
[[[]],[[[[]]],[[]]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,1,6,5,4,8,7,3] => [3,3,1,1]
[[[]],[[[],[[]]],[]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,1,7,4,6,5,8,3] => [4,2,1,1]
[[[]],[[[[],[]]],[]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,1,7,5,6,4,8,3] => [4,2,1,1]
[[[]],[[[[[]]]],[]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,1,7,6,5,4,8,3] => [3,2,1,1,1]
[[[]],[[[],[],[],[]]]] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,1,8,4,5,6,7,3] => [5,2,1]
[[[]],[[[],[],[[]]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,1,8,4,5,7,6,3] => [4,2,1,1]
[[[]],[[[],[[]],[]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,1,8,4,6,5,7,3] => [4,2,1,1]
[[[]],[[[],[[],[]]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,8,4,6,7,5,3] => [4,2,1,1]
[[[]],[[[],[[[]]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,1,8,4,7,6,5,3] => [3,2,1,1,1]
[[[]],[[[[]],[[]]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,1,8,5,4,7,6,3] => [3,3,1,1]
[[[]],[[[[],[]],[]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,1,8,5,6,4,7,3] => [4,2,1,1]
[[[]],[[[[[]]],[]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,1,8,6,5,4,7,3] => [3,2,1,1,1]
[[[]],[[[[],[],[]]]]] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,1,8,5,6,7,4,3] => [4,2,1,1]
[[[]],[[[[],[[]]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,1,8,5,7,6,4,3] => [3,2,1,1,1]
[[[]],[[[[[]],[]]]]] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,1,8,6,5,7,4,3] => [3,2,1,1,1]
[[[]],[[[[[],[]]]]]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,8,7,5,6,4,3] => [3,2,1,1,1]
[[[]],[[[[[[]]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => [2,2,1,1,1,1]
[[[],[]],[],[],[],[],[]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8] => [7,1]
[[[[]]],[],[],[],[],[]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8] => [6,1,1]
[[[],[]],[],[],[],[[]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,8,7] => [6,2]
[[[[]]],[],[],[],[[]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,6,8,7] => [5,2,1]
[[[],[]],[],[],[[]],[]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,3,1,4,5,7,6,8] => [6,2]
[[[],[]],[],[],[[],[]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,3,1,4,5,7,8,6] => [6,2]
[[[[]]],[],[],[[],[]]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [3,2,1,4,5,7,8,6] => [5,2,1]
[[[[]]],[],[],[[[]]]] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,2,1,4,5,8,7,6] => [4,2,2]
[[[],[]],[],[[]],[[]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,3,1,4,6,5,8,7] => [5,3]
[[[],[]],[],[[],[]],[]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,3,1,4,6,7,5,8] => [6,2]
[[[[]]],[],[[[]]],[]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [3,2,1,4,7,6,5,8] => [4,2,2]
[[[],[]],[],[[],[],[]]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,3,1,4,6,7,8,5] => [6,2]
[[[],[]],[],[[[]],[]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,3,1,4,7,6,8,5] => [5,2,1]
[[[],[]],[],[[[[]]]]] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,8,7,6,5] => [4,2,1,1]
[[[[]]],[],[[],[],[]]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [3,2,1,4,6,7,8,5] => [5,2,1]
[[[[]]],[],[[],[[]]]] => [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [3,2,1,4,6,8,7,5] => [4,2,2]
[[[[]]],[],[[[]],[]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [3,2,1,4,7,6,8,5] => [4,2,2]
[[[[]]],[],[[[],[]]]] => [1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [3,2,1,4,8,6,7,5] => [4,2,2]
[[[[]]],[],[[[[]]]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [3,2,1,4,8,7,6,5] => [3,2,2,1]
[[[],[]],[[]],[],[],[]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,3,1,5,4,6,7,8] => [6,2]
[[[],[]],[[]],[[]],[]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,8] => [5,3]
[[[[]]],[[]],[[]],[]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,1,5,4,7,6,8] => [4,3,1]
[[[],[]],[[],[]],[],[]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,3,1,5,6,4,7,8] => [6,2]
[[[],[]],[[[]]],[],[]] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,6,5,4,7,8] => [5,2,1]
[[[[]]],[[],[]],[],[]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [3,2,1,5,6,4,7,8] => [5,2,1]
[[[],[]],[[[]]],[[]]] => [1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,3,1,6,5,4,8,7] => [4,3,1]
[[[],[]],[[],[],[]],[]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,3,1,5,6,7,4,8] => [6,2]
[[[],[]],[[[],[]]],[]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,3,1,7,5,6,4,8] => [5,2,1]
[[[[]]],[[],[[]]],[]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [3,2,1,5,7,6,4,8] => [4,2,2]
[[[[]]],[[[[]]]],[]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,2,1,7,6,5,4,8] => [3,2,2,1]
[[[],[]],[[],[],[],[]]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,3,1,5,6,7,8,4] => [6,2]
[[[],[]],[[],[[]],[]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,3,1,5,7,6,8,4] => [5,2,1]
[[[],[]],[[[]],[[]]]] => [1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,3,1,6,5,8,7,4] => [4,3,1]
[[[],[]],[[[[]]],[]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,3,1,7,6,5,8,4] => [4,2,1,1]
[[[],[]],[[[],[],[]]]] => [1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,3,1,8,5,6,7,4] => [5,2,1]
[[[],[]],[[[[],[]]]]] => [1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,3,1,8,6,7,5,4] => [4,2,1,1]
[[[],[]],[[[[[]]]]]] => [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,1,8,7,6,5,4] => [3,2,1,1,1]
[[[[]]],[[],[],[],[]]] => [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]
[[[[]]],[[],[],[[]]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [3,2,1,5,6,8,7,4] => [4,2,2]
[[[[]]],[[],[[]],[]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [3,2,1,5,7,6,8,4] => [4,2,2]
[[[[]]],[[],[[],[]]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [3,2,1,5,8,6,7,4] => [4,2,2]
[[[[]]],[[],[[[]]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [3,2,1,5,8,7,6,4] => [3,2,2,1]
[[[[]]],[[[]],[],[]]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [3,2,1,6,5,7,8,4] => [4,2,2]
[[[[]]],[[[]],[[]]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [3,2,1,6,5,8,7,4] => [3,3,2]
[[[[]]],[[[],[]],[]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [3,2,1,7,5,6,8,4] => [4,2,2]
[[[[]]],[[[[]]],[]]] => [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]
[[[[]]],[[[],[],[]]]] => [1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,8,5,6,7,4] => [4,2,2]
[[[[]]],[[[],[[]]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [3,2,1,8,5,7,6,4] => [3,2,2,1]
[[[[]]],[[[[]],[]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [3,2,1,8,6,5,7,4] => [3,2,2,1]
[[[[]]],[[[[],[]]]]] => [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]
[[[[]]],[[[[[]]]]]] => [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]
[[[],[],[]],[],[],[],[]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8] => [7,1]
[[[],[[]]],[],[],[],[]] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7,8] => [6,1,1]
[[[[]],[]],[],[],[],[]] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8] => [6,1,1]
[[[[],[]]],[],[],[],[]] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [4,2,3,1,5,6,7,8] => [6,1,1]
[[[[[]]]],[],[],[],[]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8] => [5,1,1,1]
[[[],[],[]],[],[],[[]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5,6,8,7] => [6,2]
[[[[]],[]],[],[],[[]]] => [1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [3,2,4,1,5,6,8,7] => [5,2,1]
[[[],[],[]],[],[[]],[]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,4,1,5,7,6,8] => [6,2]
[[[[]],[]],[],[[]],[]] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [3,2,4,1,5,7,6,8] => [5,2,1]
[[[],[],[]],[],[[],[]]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,4,1,5,7,8,6] => [6,2]
[[[],[],[]],[],[[[]]]] => [1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,4,1,5,8,7,6] => [5,2,1]
[[[],[[]]],[],[[[]]]] => [1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [2,4,3,1,5,8,7,6] => [4,2,2]
[[[[]],[]],[],[[],[]]] => [1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [3,2,4,1,5,7,8,6] => [5,2,1]
[[[[]],[]],[],[[[]]]] => [1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [3,2,4,1,5,8,7,6] => [4,2,2]
[[[[],[]]],[],[[],[]]] => [1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [4,2,3,1,5,7,8,6] => [5,2,1]
[[[[[]]]],[],[[],[]]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [4,3,2,1,5,7,8,6] => [4,2,1,1]
[[[],[],[]],[[]],[],[]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,4,1,6,5,7,8] => [6,2]
[[[],[[]]],[[]],[],[]] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,4,3,1,6,5,7,8] => [5,2,1]
[[[[]],[]],[[]],[],[]] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [3,2,4,1,6,5,7,8] => [5,2,1]
[[[],[],[]],[[]],[[]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,8,7] => [5,3]
[[[],[[]]],[[]],[[]]] => [1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,4,3,1,6,5,8,7] => [4,3,1]
[[[[]],[]],[[]],[[]]] => [1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,2,4,1,6,5,8,7] => [4,3,1]
[[[[],[]]],[[]],[[]]] => [1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [4,2,3,1,6,5,8,7] => [4,3,1]
[[[[[]]]],[[]],[[]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7] => [3,3,1,1]
[[[],[],[]],[[],[]],[]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,4,1,6,7,5,8] => [6,2]
[[[],[],[]],[[[]]],[]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,4,1,7,6,5,8] => [5,2,1]
[[[[]],[]],[[],[]],[]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [3,2,4,1,6,7,5,8] => [5,2,1]
[[[[]],[]],[[[]]],[]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [3,2,4,1,7,6,5,8] => [4,2,2]
[[[],[],[]],[[],[],[]]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,5] => [6,2]
[[[],[],[]],[[],[[]]]] => [1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,4,1,6,8,7,5] => [5,2,1]
[[[],[],[]],[[[]],[]]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,4,1,7,6,8,5] => [5,2,1]
[[[],[],[]],[[[],[]]]] => [1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,4,1,8,6,7,5] => [5,2,1]
[[[],[],[]],[[[[]]]]] => [1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,4,1,8,7,6,5] => [4,2,1,1]
[[[],[[]]],[[],[],[]]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [2,4,3,1,6,7,8,5] => [5,2,1]
[[[],[[]]],[[],[[]]]] => [1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,4,3,1,6,8,7,5] => [4,2,2]
[[[],[[]]],[[[]],[]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,4,3,1,7,6,8,5] => [4,2,2]
[[[],[[]]],[[[[]]]]] => [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]
[[[[]],[]],[[],[],[]]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [3,2,4,1,6,7,8,5] => [5,2,1]
[[[[]],[]],[[],[[]]]] => [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [3,2,4,1,6,8,7,5] => [4,2,2]
[[[[]],[]],[[[]],[]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,2,4,1,7,6,8,5] => [4,2,2]
[[[[]],[]],[[[],[]]]] => [1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [3,2,4,1,8,6,7,5] => [4,2,2]
[[[[]],[]],[[[[]]]]] => [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]
[[[[],[]]],[[],[],[]]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [4,2,3,1,6,7,8,5] => [5,2,1]
[[[[],[]]],[[],[[]]]] => [1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [4,2,3,1,6,8,7,5] => [4,2,2]
[[[[],[]]],[[[]],[]]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [4,2,3,1,7,6,8,5] => [4,2,2]
[[[[],[]]],[[[],[]]]] => [1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [4,2,3,1,8,6,7,5] => [4,2,2]
[[[[],[]]],[[[[]]]]] => [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,2,3,1,8,7,6,5] => [3,2,2,1]
[[[[[]]]],[[],[],[]]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [4,3,2,1,6,7,8,5] => [4,2,1,1]
[[[[[]]]],[[],[[]]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [4,3,2,1,6,8,7,5] => [3,2,2,1]
[[[[[]]]],[[[]],[]]] => [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]
[[[[[]]]],[[[],[]]]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [4,3,2,1,8,6,7,5] => [3,2,2,1]
[[[[[]]]],[[[[]]]]] => [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]
[[[],[],[],[]],[],[],[]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8] => [7,1]
[[[],[],[[]]],[],[],[]] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,3,5,4,1,6,7,8] => [6,1,1]
[[[],[[]],[]],[],[],[]] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,4,3,5,1,6,7,8] => [6,1,1]
[[[],[[],[]]],[],[],[]] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [2,5,3,4,1,6,7,8] => [6,1,1]
[[[],[[[]]]],[],[],[]] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,5,4,3,1,6,7,8] => [5,1,1,1]
[[[[]],[],[]],[],[],[]] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [3,2,4,5,1,6,7,8] => [6,1,1]
[[[[]],[[]]],[],[],[]] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [3,2,5,4,1,6,7,8] => [5,2,1]
[[[[],[]],[]],[],[],[]] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [4,2,3,5,1,6,7,8] => [6,1,1]
[[[[[]]],[]],[],[],[]] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [4,3,2,5,1,6,7,8] => [5,1,1,1]
[[[[],[],[]]],[],[],[]] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [5,2,3,4,1,6,7,8] => [6,1,1]
[[[[],[[]]]],[],[],[]] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [5,2,4,3,1,6,7,8] => [5,1,1,1]
[[[[[]],[]]],[],[],[]] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [5,3,2,4,1,6,7,8] => [5,1,1,1]
[[[[[],[]]]],[],[],[]] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [5,3,4,2,1,6,7,8] => [5,1,1,1]
[[[[[[]]]]],[],[],[]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8] => [4,1,1,1,1]
[[[],[],[],[]],[],[[]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,5,1,6,8,7] => [6,2]
[[[],[],[[]]],[],[[]]] => [1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,3,5,4,1,6,8,7] => [5,2,1]
[[[],[[[]]]],[],[[]]] => [1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [2,5,4,3,1,6,8,7] => [4,2,1,1]
[[[[]],[[]]],[],[[]]] => [1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [3,2,5,4,1,6,8,7] => [4,3,1]
[[[[],[],[]]],[],[[]]] => [1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [5,2,3,4,1,6,8,7] => [5,2,1]
[[[[],[[]]]],[],[[]]] => [1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [5,2,4,3,1,6,8,7] => [4,2,1,1]
[[[[[]],[]]],[],[[]]] => [1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [5,3,2,4,1,6,8,7] => [4,2,1,1]
[[[[[],[]]]],[],[[]]] => [1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [5,3,4,2,1,6,8,7] => [4,2,1,1]
[[[[[[]]]]],[],[[]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [5,4,3,2,1,6,8,7] => [3,2,1,1,1]
[[[],[],[],[]],[[]],[]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,5,1,7,6,8] => [6,2]
[[[[]],[[]]],[[]],[]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [3,2,5,4,1,7,6,8] => [4,3,1]
[[[[],[[]]]],[[]],[]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [5,2,4,3,1,7,6,8] => [4,2,1,1]
[[[[[]],[]]],[[]],[]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [5,3,2,4,1,7,6,8] => [4,2,1,1]
[[[[[[]]]]],[[]],[]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [5,4,3,2,1,7,6,8] => [3,2,1,1,1]
[[[],[],[],[]],[[],[]]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,1,7,8,6] => [6,2]
[[[],[],[],[]],[[[]]]] => [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]
[[[],[],[[]]],[[[]]]] => [1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,4,1,8,7,6] => [4,2,2]
[[[],[[]],[]],[[],[]]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,4,3,5,1,7,8,6] => [5,2,1]
[[[],[[]],[]],[[[]]]] => [1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [2,4,3,5,1,8,7,6] => [4,2,2]
[[[],[[],[]]],[[[]]]] => [1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [2,5,3,4,1,8,7,6] => [4,2,2]
[[[],[[[]]]],[[[]]]] => [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]
[[[[]],[],[]],[[[]]]] => [1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [3,2,4,5,1,8,7,6] => [4,2,2]
[[[[]],[[]]],[[],[]]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [3,2,5,4,1,7,8,6] => [4,3,1]
[[[[]],[[]]],[[[]]]] => [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [3,2,5,4,1,8,7,6] => [3,3,2]
[[[[],[]],[]],[[[]]]] => [1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [4,2,3,5,1,8,7,6] => [4,2,2]
[[[[[]]],[]],[[],[]]] => [1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [4,3,2,5,1,7,8,6] => [4,2,1,1]
[[[[[]]],[]],[[[]]]] => [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]
[[[[],[],[]]],[[],[]]] => [1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [5,2,3,4,1,7,8,6] => [5,2,1]
[[[[],[],[]]],[[[]]]] => [1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [5,2,3,4,1,8,7,6] => [4,2,2]
[[[[],[[]]]],[[[]]]] => [1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [5,2,4,3,1,8,7,6] => [3,2,2,1]
[[[[[]],[]]],[[[]]]] => [1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [5,3,2,4,1,8,7,6] => [3,2,2,1]
[[[[[],[]]]],[[],[]]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [5,3,4,2,1,7,8,6] => [4,2,1,1]
[[[[[],[]]]],[[[]]]] => [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]
[[[[[[]]]]],[[],[]]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [5,4,3,2,1,7,8,6] => [3,2,1,1,1]
[[[[[[]]]]],[[[]]]] => [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]
[[[],[],[],[],[]],[],[]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,1,7,8] => [7,1]
[[[],[],[[],[]]],[],[]] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,3,6,4,5,1,7,8] => [6,1,1]
[[[],[[]],[[]]],[],[]] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [2,4,3,6,5,1,7,8] => [5,2,1]
[[[],[[],[],[]]],[],[]] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [2,6,3,4,5,1,7,8] => [6,1,1]
[[[[]],[],[],[]],[],[]] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,6,1,7,8] => [6,1,1]
[[[[],[]],[],[]],[],[]] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [4,2,3,5,6,1,7,8] => [6,1,1]
[[[[[]]],[],[]],[],[]] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [4,3,2,5,6,1,7,8] => [5,1,1,1]
[[[[[]]],[[]]],[],[]] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [4,3,2,6,5,1,7,8] => [4,2,1,1]
[[[[],[],[]],[]],[],[]] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [5,2,3,4,6,1,7,8] => [6,1,1]
[[[[[[]]]],[]],[],[]] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [5,4,3,2,6,1,7,8] => [4,1,1,1,1]
[[[[],[],[],[]]],[],[]] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [6,2,3,4,5,1,7,8] => [6,1,1]
[[[[[[]]],[]]],[],[]] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [6,4,3,2,5,1,7,8] => [4,1,1,1,1]
[[[[[[[]]]]]],[],[]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,5,4,3,2,1,7,8] => [3,1,1,1,1,1]
[[[],[],[],[],[]],[[]]] => [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]
[[[],[],[[],[]]],[[]]] => [1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,3,6,4,5,1,8,7] => [5,2,1]
[[[],[],[[[]]]],[[]]] => [1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,3,6,5,4,1,8,7] => [4,2,1,1]
[[[],[[]],[],[]],[[]]] => [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]
[[[],[[]],[[]]],[[]]] => [1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,4,3,6,5,1,8,7] => [4,3,1]
[[[],[[[]]],[]],[[]]] => [1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [2,5,4,3,6,1,8,7] => [4,2,1,1]
[[[],[[],[[]]]],[[]]] => [1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,6,3,5,4,1,8,7] => [4,2,1,1]
[[[],[[[]],[]]],[[]]] => [1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [2,6,4,3,5,1,8,7] => [4,2,1,1]
[[[],[[[[]]]]],[[]]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,6,5,4,3,1,8,7] => [3,2,1,1,1]
[[[[]],[[]],[]],[[]]] => [1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,2,5,4,6,1,8,7] => [4,3,1]
[[[[]],[[],[]]],[[]]] => [1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [3,2,6,4,5,1,8,7] => [4,3,1]
[[[[]],[[[]]]],[[]]] => [1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [3,2,6,5,4,1,8,7] => [3,3,1,1]
[[[[],[]],[],[]],[[]]] => [1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [4,2,3,5,6,1,8,7] => [5,2,1]
[[[[[]]],[],[]],[[]]] => [1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [4,3,2,5,6,1,8,7] => [4,2,1,1]
[[[[[]]],[[]]],[[]]] => [1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [4,3,2,6,5,1,8,7] => [3,3,1,1]
[[[[],[],[]],[]],[[]]] => [1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [5,2,3,4,6,1,8,7] => [5,2,1]
[[[[],[[]]],[]],[[]]] => [1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [5,2,4,3,6,1,8,7] => [4,2,1,1]
[[[[[],[]]],[]],[[]]] => [1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [5,3,4,2,6,1,8,7] => [4,2,1,1]
[[[[[[]]]],[]],[[]]] => [1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [5,4,3,2,6,1,8,7] => [3,2,1,1,1]
[[[[],[],[],[]]],[[]]] => [1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [6,2,3,4,5,1,8,7] => [5,2,1]
[[[[],[],[[]]]],[[]]] => [1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [6,2,3,5,4,1,8,7] => [4,2,1,1]
[[[[],[[]],[]]],[[]]] => [1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [6,2,4,3,5,1,8,7] => [4,2,1,1]
[[[[],[[[]]]]],[[]]] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [6,2,5,4,3,1,8,7] => [3,2,1,1,1]
[[[[[]],[[]]]],[[]]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [6,3,2,5,4,1,8,7] => [3,3,1,1]
[[[[[],[]],[]]],[[]]] => [1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [6,3,4,2,5,1,8,7] => [4,2,1,1]
[[[[[[]]],[]]],[[]]] => [1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [6,4,3,2,5,1,8,7] => [3,2,1,1,1]
[[[[[],[],[]]]],[[]]] => [1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [6,3,4,5,2,1,8,7] => [4,2,1,1]
[[[[[],[[]]]]],[[]]] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [6,3,5,4,2,1,8,7] => [3,2,1,1,1]
[[[[[[]],[]]]],[[]]] => [1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [6,4,3,5,2,1,8,7] => [3,2,1,1,1]
[[[[[[],[]]]]],[[]]] => [1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [6,5,3,4,2,1,8,7] => [3,2,1,1,1]
[[[[[[[]]]]]],[[]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,5,4,3,2,1,8,7] => [2,2,1,1,1,1]
[[[],[],[],[],[],[]],[]] => [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]
[[[],[],[],[],[[]]],[]] => [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]
[[[],[],[],[[]],[]],[]] => [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]
[[[],[],[],[[],[]]],[]] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,4,7,5,6,1,8] => [6,1,1]
[[[],[],[],[[[]]]],[]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,4,7,6,5,1,8] => [5,1,1,1]
[[[],[],[[]],[],[]],[]] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,3,5,4,6,7,1,8] => [6,1,1]
[[[],[],[[[]],[]]],[]] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,3,7,5,4,6,1,8] => [5,1,1,1]
[[[],[],[[[],[]]]],[]] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,3,7,5,6,4,1,8] => [5,1,1,1]
[[[],[],[[[[]]]]],[]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,3,7,6,5,4,1,8] => [4,1,1,1,1]
[[[],[[]],[[]],[]],[]] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,4,3,6,5,7,1,8] => [5,2,1]
[[[],[[],[],[],[]]],[]] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [2,7,3,4,5,6,1,8] => [6,1,1]
[[[],[[],[[[]]]]],[]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [2,7,3,6,5,4,1,8] => [4,1,1,1,1]
[[[],[[[],[],[]]]],[]] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [2,7,4,5,6,3,1,8] => [5,1,1,1]
[[[],[[[],[[]]]]],[]] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [2,7,4,6,5,3,1,8] => [4,1,1,1,1]
[[[],[[[[[]]]]]],[]] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,7,6,5,4,3,1,8] => [3,1,1,1,1,1]
[[[[]],[],[],[],[]],[]] => [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]
[[[[]],[[]],[[]]],[]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,7,6,1,8] => [4,3,1]
[[[[]],[[[]]],[]],[]] => [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]
[[[[]],[[],[],[]]],[]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [3,2,7,4,5,6,1,8] => [5,2,1]
[[[[]],[[],[[]]]],[]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [3,2,7,4,6,5,1,8] => [4,2,1,1]
[[[[]],[[[]],[]]],[]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [3,2,7,5,4,6,1,8] => [4,2,1,1]
[[[[]],[[[],[]]]],[]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [3,2,7,5,6,4,1,8] => [4,2,1,1]
[[[[]],[[[[]]]]],[]] => [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]
[[[[],[]],[],[],[]],[]] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [4,2,3,5,6,7,1,8] => [6,1,1]
[[[[[]]],[],[],[]],[]] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [4,3,2,5,6,7,1,8] => [5,1,1,1]
[[[[[]]],[],[[]]],[]] => [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]
[[[[],[],[]],[],[]],[]] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [5,2,3,4,6,7,1,8] => [6,1,1]
[[[[[[]]]],[],[]],[]] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [5,4,3,2,6,7,1,8] => [4,1,1,1,1]
[[[[],[],[]],[[]]],[]] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [5,2,3,4,7,6,1,8] => [5,2,1]
[[[[],[[]]],[[]]],[]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [5,2,4,3,7,6,1,8] => [4,2,1,1]
[[[[[]],[]],[[]]],[]] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [5,3,2,4,7,6,1,8] => [4,2,1,1]
[[[[[],[]]],[[]]],[]] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [5,3,4,2,7,6,1,8] => [4,2,1,1]
[[[[[[]]]],[[]]],[]] => [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]
[[[[],[[[]]]],[]],[]] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [6,2,5,4,3,7,1,8] => [4,1,1,1,1]
[[[[[]],[[]]],[]],[]] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [6,3,2,5,4,7,1,8] => [4,2,1,1]
[[[[[],[],[]]],[]],[]] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [6,3,4,5,2,7,1,8] => [5,1,1,1]
[[[[[],[[]]]],[]],[]] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [6,3,5,4,2,7,1,8] => [4,1,1,1,1]
[[[[[[[]]]]],[]],[]] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [6,5,4,3,2,7,1,8] => [3,1,1,1,1,1]
[[[[],[],[],[],[]]],[]] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [7,2,3,4,5,6,1,8] => [6,1,1]
[[[[],[],[[],[]]]],[]] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [7,2,3,5,6,4,1,8] => [5,1,1,1]
[[[[],[[]],[[]]]],[]] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [7,2,4,3,6,5,1,8] => [4,2,1,1]
[[[[],[[],[]],[]]],[]] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [7,2,4,5,3,6,1,8] => [5,1,1,1]
[[[[],[[[]]],[]]],[]] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [7,2,5,4,3,6,1,8] => [4,1,1,1,1]
[[[[],[[],[[]]]]],[]] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,4,6,5,3,1,8] => [4,1,1,1,1]
[[[[],[[[[]]]]]],[]] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [7,2,6,5,4,3,1,8] => [3,1,1,1,1,1]
[[[[[]],[[]],[]]],[]] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [7,3,2,5,4,6,1,8] => [4,2,1,1]
[[[[[[]]],[[]]]],[]] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [7,4,3,2,6,5,1,8] => [3,2,1,1,1]
[[[[[],[[]]],[]]],[]] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [7,3,5,4,2,6,1,8] => [4,1,1,1,1]
[[[[[[]],[]],[]]],[]] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [7,4,3,5,2,6,1,8] => [4,1,1,1,1]
[[[[[[[]]]],[]]],[]] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [7,5,4,3,2,6,1,8] => [3,1,1,1,1,1]
[[[[[],[[]],[]]]],[]] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [7,3,5,4,6,2,1,8] => [4,1,1,1,1]
[[[[[],[[],[]]]]],[]] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [7,3,6,4,5,2,1,8] => [4,1,1,1,1]
[[[[[],[[[]]]]]],[]] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [7,3,6,5,4,2,1,8] => [3,1,1,1,1,1]
[[[[[[]],[[]]]]],[]] => [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]
[[[[[[[]]],[]]]],[]] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,5,4,3,6,2,1,8] => [3,1,1,1,1,1]
[[[[[[],[],[]]]]],[]] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [7,6,3,4,5,2,1,8] => [4,1,1,1,1]
[[[[[[],[[]]]]]],[]] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [7,6,3,5,4,2,1,8] => [3,1,1,1,1,1]
[[[[[[[]],[]]]]],[]] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,6,4,3,5,2,1,8] => [3,1,1,1,1,1]
[[[[[[[],[]]]]]],[]] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,6,4,5,3,2,1,8] => [3,1,1,1,1,1]
[[[[[[[[]]]]]]],[]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,6,5,4,3,2,1,8] => [2,1,1,1,1,1,1]
[[[],[],[],[],[],[],[]]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,1] => [7,1]
[[[],[],[],[],[],[[]]]] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,8,7,1] => [6,1,1]
[[[],[],[],[],[[]],[]]] => [1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,7,6,8,1] => [6,1,1]
[[[],[],[],[],[[],[]]]] => [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]
[[[],[],[],[],[[[]]]]] => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,8,7,6,1] => [5,1,1,1]
[[[],[],[],[[]],[],[]]] => [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,4,6,5,7,8,1] => [6,1,1]
[[[],[],[],[[]],[[]]]] => [1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,4,6,5,8,7,1] => [5,2,1]
[[[],[],[],[[],[]],[]]] => [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]
[[[],[],[],[[[]]],[]]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,4,7,6,5,8,1] => [5,1,1,1]
[[[],[],[],[[],[],[]]]] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,8,5,6,7,1] => [6,1,1]
[[[],[],[],[[],[[]]]]] => [1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,4,8,5,7,6,1] => [5,1,1,1]
[[[],[],[],[[[]],[]]]] => [1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,4,8,6,5,7,1] => [5,1,1,1]
[[[],[],[],[[[],[]]]]] => [1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,4,8,6,7,5,1] => [5,1,1,1]
[[[],[],[],[[[[]]]]]] => [1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,8,7,6,5,1] => [4,1,1,1,1]
[[[],[],[[]],[],[],[]]] => [1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,3,5,4,6,7,8,1] => [6,1,1]
[[[],[],[[]],[[]],[]]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,3,5,4,7,6,8,1] => [5,2,1]
[[[],[],[[]],[[],[]]]] => [1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,3,5,4,8,6,7,1] => [5,2,1]
[[[],[],[[[]]],[],[]]] => [1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,3,6,5,4,7,8,1] => [5,1,1,1]
[[[],[],[[],[]],[[]]]] => [1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,3,6,4,5,8,7,1] => [5,2,1]
[[[],[],[[],[],[]],[]]] => [1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,3,7,4,5,6,8,1] => [6,1,1]
[[[],[],[[],[[]]],[]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,3,7,4,6,5,8,1] => [5,1,1,1]
[[[],[],[[[]],[]],[]]] => [1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,3,7,5,4,6,8,1] => [5,1,1,1]
[[[],[],[[[],[]]],[]]] => [1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,3,7,5,6,4,8,1] => [5,1,1,1]
[[[],[],[[[[]]]],[]]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,3,7,6,5,4,8,1] => [4,1,1,1,1]
[[[],[],[[],[],[],[]]]] => [1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,8,4,5,6,7,1] => [6,1,1]
[[[],[],[[],[[],[]]]]] => [1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,3,8,4,6,7,5,1] => [5,1,1,1]
[[[],[],[[[]],[],[]]]] => [1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,3,8,5,4,6,7,1] => [5,1,1,1]
[[[],[],[[[],[]],[]]]] => [1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,3,8,5,6,4,7,1] => [5,1,1,1]
[[[],[],[[[[]]],[]]]] => [1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,3,8,6,5,4,7,1] => [4,1,1,1,1]
[[[],[],[[[],[],[]]]]] => [1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,3,8,5,6,7,4,1] => [5,1,1,1]
[[[],[],[[[],[[]]]]]] => [1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,3,8,5,7,6,4,1] => [4,1,1,1,1]
[[[],[],[[[[[]]]]]]] => [1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,8,7,6,5,4,1] => [3,1,1,1,1,1]
[[[],[[]],[],[],[],[]]] => [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,8,1] => [6,1,1]
[[[],[[]],[],[],[[]]]] => [1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,4,3,5,6,8,7,1] => [5,2,1]
[[[],[[]],[],[[],[]]]] => [1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [2,4,3,5,8,6,7,1] => [5,2,1]
[[[],[[]],[[]],[],[]]] => [1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,4,3,6,5,7,8,1] => [5,2,1]
[[[],[[]],[[]],[[]]]] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,8,7,1] => [4,3,1]
[[[],[[]],[[],[]],[]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,4,3,7,5,6,8,1] => [5,2,1]
[[[],[[]],[[],[],[]]]] => [1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,4,3,8,5,6,7,1] => [5,2,1]
[[[],[[]],[[],[[]]]]] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,4,3,8,5,7,6,1] => [4,2,1,1]
[[[],[[]],[[[]],[]]]] => [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]
[[[],[[]],[[[[]]]]]] => [1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,4,3,8,7,6,5,1] => [3,2,1,1,1]
[[[],[[],[]],[],[],[]]] => [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]
[[[],[[],[]],[],[[]]]] => [1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [2,5,3,4,6,8,7,1] => [5,2,1]
[[[],[[],[]],[[]],[]]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [2,5,3,4,7,6,8,1] => [5,2,1]
[[[],[[],[]],[[],[]]]] => [1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [2,5,3,4,8,6,7,1] => [5,2,1]
[[[],[[[]]],[[],[]]]] => [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]
[[[],[[[]]],[[[]]]]] => [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,5,4,3,8,7,6,1] => [3,2,2,1]
[[[],[[[[]]]],[],[]]] => [1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,6,5,4,3,7,8,1] => [4,1,1,1,1]
[[[],[[],[],[]],[[]]]] => [1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [2,6,3,4,5,8,7,1] => [5,2,1]
[[[],[[],[[]]],[[]]]] => [1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,6,3,5,4,8,7,1] => [4,2,1,1]
[[[],[[[]],[]],[[]]]] => [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]
[[[],[[[[]]]],[[]]]] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,6,5,4,3,8,7,1] => [3,2,1,1,1]
[[[],[[],[[]],[]],[]]] => [1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [2,7,3,5,4,6,8,1] => [5,1,1,1]
[[[],[[],[[],[]]],[]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [2,7,3,5,6,4,8,1] => [5,1,1,1]
[[[],[[[]],[],[]],[]]] => [1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [2,7,4,3,5,6,8,1] => [5,1,1,1]
[[[],[[[]],[[]]],[]]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,7,4,3,6,5,8,1] => [4,2,1,1]
[[[],[[[[]]],[]],[]]] => [1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [2,7,5,4,3,6,8,1] => [4,1,1,1,1]
[[[],[[[],[],[]]],[]]] => [1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [2,7,4,5,6,3,8,1] => [5,1,1,1]
[[[],[[[],[[]]]],[]]] => [1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [2,7,4,6,5,3,8,1] => [4,1,1,1,1]
[[[],[[[[]],[]]],[]]] => [1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,7,5,4,6,3,8,1] => [4,1,1,1,1]
[[[],[[[[],[]]]],[]]] => [1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [2,7,6,4,5,3,8,1] => [4,1,1,1,1]
[[[],[[[[[]]]]],[]]] => [1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,7,6,5,4,3,8,1] => [3,1,1,1,1,1]
[[[],[[],[],[],[],[]]]] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,8,3,4,5,6,7,1] => [6,1,1]
[[[],[[],[],[],[[]]]]] => [1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [2,8,3,4,5,7,6,1] => [5,1,1,1]
[[[],[[],[[]],[[]]]]] => [1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,8,3,5,4,7,6,1] => [4,2,1,1]
[[[],[[],[[],[],[]]]]] => [1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,8,3,5,6,7,4,1] => [5,1,1,1]
[[[],[[],[[],[[]]]]]] => [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,8,3,5,7,6,4,1] => [4,1,1,1,1]
[[[],[[],[[[],[]]]]]] => [1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,8,3,7,5,6,4,1] => [4,1,1,1,1]
[[[],[[],[[[[]]]]]]] => [1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,8,3,7,6,5,4,1] => [3,1,1,1,1,1]
[[[],[[[]],[],[],[]]]] => [1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,8,4,3,5,6,7,1] => [5,1,1,1]
[[[],[[[]],[],[[]]]]] => [1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [2,8,4,3,5,7,6,1] => [4,2,1,1]
[[[],[[[]],[[]],[]]]] => [1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,8,4,3,6,5,7,1] => [4,2,1,1]
[[[],[[[]],[[],[]]]]] => [1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,8,4,3,6,7,5,1] => [4,2,1,1]
[[[],[[[]],[[[]]]]]] => [1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,8,4,3,7,6,5,1] => [3,2,1,1,1]
[[[],[[[],[]],[],[]]]] => [1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [2,8,4,5,3,6,7,1] => [5,1,1,1]
[[[],[[[[]]],[],[]]]] => [1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,8,5,4,3,6,7,1] => [4,1,1,1,1]
[[[],[[[[]]],[[]]]]] => [1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [2,8,5,4,3,7,6,1] => [3,2,1,1,1]
[[[],[[[],[],[]],[]]]] => [1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [2,8,4,5,6,3,7,1] => [5,1,1,1]
[[[],[[[],[[]]],[]]]] => [1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [2,8,4,6,5,3,7,1] => [4,1,1,1,1]
[[[],[[[],[],[],[]]]]] => [1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,8,4,5,6,7,3,1] => [5,1,1,1]
[[[],[[[],[[[]]]]]]] => [1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,8,4,7,6,5,3,1] => [3,1,1,1,1,1]
[[[],[[[[]],[],[]]]]] => [1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,8,5,4,6,7,3,1] => [4,1,1,1,1]
[[[],[[[[]],[[]]]]]] => [1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,8,5,4,7,6,3,1] => [3,2,1,1,1]
[[[],[[[[],[],[]]]]]] => [1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,8,7,4,5,6,3,1] => [4,1,1,1,1]
[[[],[[[[],[[]]]]]]] => [1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,8,7,4,6,5,3,1] => [3,1,1,1,1,1]
[[[],[[[[[]],[]]]]]] => [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,8,7,5,4,6,3,1] => [3,1,1,1,1,1]
[[[],[[[[[],[]]]]]]] => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,8,7,5,6,4,3,1] => [3,1,1,1,1,1]
[[[],[[[[[[]]]]]]]] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,8,7,6,5,4,3,1] => [2,1,1,1,1,1,1]
[[[[]],[],[],[],[],[]]] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,1] => [6,1,1]
[[[[]],[],[],[],[[]]]] => [1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,6,8,7,1] => [5,2,1]
[[[[]],[],[],[[]],[]]] => [1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [3,2,4,5,7,6,8,1] => [5,2,1]
[[[[]],[],[],[[],[]]]] => [1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [3,2,4,5,8,6,7,1] => [5,2,1]
[[[[]],[],[[]],[[]]]] => [1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [3,2,4,6,5,8,7,1] => [4,3,1]
[[[[]],[],[[],[]],[]]] => [1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [3,2,4,7,5,6,8,1] => [5,2,1]
[[[[]],[],[[],[],[]]]] => [1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [3,2,4,8,5,6,7,1] => [5,2,1]
[[[[]],[],[[[],[]]]]] => [1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,8,6,7,5,1] => [4,2,1,1]
[[[[]],[],[[[[]]]]]] => [1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,2,4,8,7,6,5,1] => [3,2,1,1,1]
[[[[]],[[]],[],[],[]]] => [1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [3,2,5,4,6,7,8,1] => [5,2,1]
[[[[]],[[]],[],[[]]]] => [1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [3,2,5,4,6,8,7,1] => [4,3,1]
[[[[]],[[]],[[]],[]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,7,6,8,1] => [4,3,1]
[[[[]],[[]],[[],[]]]] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [3,2,5,4,8,6,7,1] => [4,3,1]
[[[[]],[[[]]],[[]]]] => [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [3,2,6,5,4,8,7,1] => [3,3,1,1]
[[[[]],[[],[[]]],[]]] => [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]
[[[[]],[[[],[]]],[]]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [3,2,7,5,6,4,8,1] => [4,2,1,1]
[[[[]],[[[[]]]],[]]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [3,2,7,6,5,4,8,1] => [3,2,1,1,1]
[[[[]],[[],[],[],[]]]] => [1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [3,2,8,4,5,6,7,1] => [5,2,1]
[[[[]],[[],[[]],[]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [3,2,8,4,6,5,7,1] => [4,2,1,1]
[[[[]],[[[]],[],[]]]] => [1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [3,2,8,5,4,6,7,1] => [4,2,1,1]
[[[[]],[[[]],[[]]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [3,2,8,5,4,7,6,1] => [3,3,1,1]
[[[[]],[[[],[]],[]]]] => [1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [3,2,8,5,6,4,7,1] => [4,2,1,1]
[[[[]],[[[],[[]]]]]] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,2,8,5,7,6,4,1] => [3,2,1,1,1]
[[[[]],[[[[]],[]]]]] => [1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [3,2,8,6,5,7,4,1] => [3,2,1,1,1]
[[[[]],[[[[],[]]]]]] => [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]
[[[[]],[[[[[]]]]]]] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,2,8,7,6,5,4,1] => [2,2,1,1,1,1]
[[[[],[]],[],[],[],[]]] => [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]
[[[[[]]],[],[],[],[]]] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,1] => [5,1,1,1]
[[[[],[]],[],[],[[]]]] => [1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [4,2,3,5,6,8,7,1] => [5,2,1]
[[[[[]]],[],[],[[]]]] => [1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [4,3,2,5,6,8,7,1] => [4,2,1,1]
[[[[[]]],[],[[]],[]]] => [1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [4,3,2,5,7,6,8,1] => [4,2,1,1]
[[[[],[]],[],[[[]]]]] => [1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [4,2,3,5,8,7,6,1] => [4,2,1,1]
[[[[[]]],[],[[[]]]]] => [1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,3,2,5,8,7,6,1] => [3,2,2,1]
[[[[],[]],[[]],[[]]]] => [1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [4,2,3,6,5,8,7,1] => [4,3,1]
[[[[[]]],[[]],[[]]]] => [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [4,3,2,6,5,8,7,1] => [3,3,1,1]
[[[[],[]],[[],[]],[]]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [4,2,3,7,5,6,8,1] => [5,2,1]
[[[[],[]],[[[]]],[]]] => [1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [4,2,3,7,6,5,8,1] => [4,2,1,1]
[[[[[]]],[[],[]],[]]] => [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]
[[[[[]]],[[[]]],[]]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [4,3,2,7,6,5,8,1] => [3,2,2,1]
[[[[],[]],[[],[],[]]]] => [1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [4,2,3,8,5,6,7,1] => [5,2,1]
[[[[],[]],[[],[[]]]]] => [1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [4,2,3,8,5,7,6,1] => [4,2,1,1]
[[[[],[]],[[[[]]]]]] => [1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [4,2,3,8,7,6,5,1] => [3,2,1,1,1]
[[[[[]]],[[],[],[]]]] => [1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [4,3,2,8,5,6,7,1] => [4,2,1,1]
[[[[[]]],[[],[[]]]]] => [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]
[[[[[]]],[[[],[]]]]] => [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,2,8,6,7,5,1] => [3,2,2,1]
[[[[[]]],[[[[]]]]]] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,3,2,8,7,6,5,1] => [2,2,2,1,1]
[[[[],[],[]],[],[],[]]] => [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [5,2,3,4,6,7,8,1] => [6,1,1]
[[[[[[]]]],[],[],[]]] => [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [5,4,3,2,6,7,8,1] => [4,1,1,1,1]
[[[[[[]]]],[],[[]]]] => [1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,4,3,2,6,8,7,1] => [3,2,1,1,1]
[[[[],[[]]],[[]],[]]] => [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]
[[[[[],[]]],[[]],[]]] => [1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [5,3,4,2,7,6,8,1] => [4,2,1,1]
[[[[[[]]]],[[]],[]]] => [1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [5,4,3,2,7,6,8,1] => [3,2,1,1,1]
[[[[],[],[]],[[],[]]]] => [1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [5,2,3,4,8,6,7,1] => [5,2,1]
[[[[],[[]]],[[[]]]]] => [1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [5,2,4,3,8,7,6,1] => [3,2,2,1]
[[[[[],[]]],[[],[]]]] => [1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [5,3,4,2,8,6,7,1] => [4,2,1,1]
[[[[[[]]]],[[],[]]]] => [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]
[[[[[[]]]],[[[]]]]] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,4,3,2,8,7,6,1] => [2,2,2,1,1]
[[[[],[],[],[]],[],[]]] => [1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [6,2,3,4,5,7,8,1] => [6,1,1]
[[[[],[],[[]]],[],[]]] => [1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [6,2,3,5,4,7,8,1] => [5,1,1,1]
[[[[],[[[]]]],[],[]]] => [1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [6,2,5,4,3,7,8,1] => [4,1,1,1,1]
[[[[[]],[[]]],[],[]]] => [1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [6,3,2,5,4,7,8,1] => [4,2,1,1]
[[[[[],[[]]]],[],[]]] => [1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [6,3,5,4,2,7,8,1] => [4,1,1,1,1]
[[[[[[],[]]]],[],[]]] => [1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [6,5,3,4,2,7,8,1] => [4,1,1,1,1]
[[[[[[[]]]]],[],[]]] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5,4,3,2,7,8,1] => [3,1,1,1,1,1]
[[[[],[],[],[]],[[]]]] => [1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [6,2,3,4,5,8,7,1] => [5,2,1]
[[[[[]],[[]]],[[]]]] => [1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [6,3,2,5,4,8,7,1] => [3,3,1,1]
[[[[[[]]],[]],[[]]]] => [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]
[[[[[],[],[]]],[[]]]] => [1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [6,3,4,5,2,8,7,1] => [4,2,1,1]
[[[[[],[[]]]],[[]]]] => [1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [6,3,5,4,2,8,7,1] => [3,2,1,1,1]
[[[[[[[]]]]],[[]]]] => [1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,5,4,3,2,8,7,1] => [2,2,1,1,1,1]
[[[[],[],[],[],[]],[]]] => [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [7,2,3,4,5,6,8,1] => [6,1,1]
[[[[],[[]],[[]]],[]]] => [1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [7,2,4,3,6,5,8,1] => [4,2,1,1]
[[[[],[[],[]],[]],[]]] => [1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [7,2,4,5,3,6,8,1] => [5,1,1,1]
[[[[],[[],[[]]]],[]]] => [1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [7,2,4,6,5,3,8,1] => [4,1,1,1,1]
[[[[],[[[]],[]]],[]]] => [1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [7,2,5,4,6,3,8,1] => [4,1,1,1,1]
[[[[],[[[],[]]]],[]]] => [1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [7,2,6,4,5,3,8,1] => [4,1,1,1,1]
[[[[],[[[[]]]]],[]]] => [1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,6,5,4,3,8,1] => [3,1,1,1,1,1]
[[[[[]],[],[],[]],[]]] => [1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [7,3,2,4,5,6,8,1] => [5,1,1,1]
[[[[[]],[[],[]]],[]]] => [1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [7,3,2,5,6,4,8,1] => [4,2,1,1]
[[[[[],[]],[[]]],[]]] => [1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [7,3,4,2,6,5,8,1] => [4,2,1,1]
[[[[[[]]],[[]]],[]]] => [1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [7,4,3,2,6,5,8,1] => [3,2,1,1,1]
[[[[[[]],[]],[]],[]]] => [1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [7,4,3,5,2,6,8,1] => [4,1,1,1,1]
[[[[[],[[]],[]]],[]]] => [1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [7,3,5,4,6,2,8,1] => [4,1,1,1,1]
[[[[[],[[],[]]]],[]]] => [1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [7,3,6,4,5,2,8,1] => [4,1,1,1,1]
[[[[[],[[[]]]]],[]]] => [1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [7,3,6,5,4,2,8,1] => [3,1,1,1,1,1]
[[[[[[]],[[]]]],[]]] => [1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [7,4,3,6,5,2,8,1] => [3,2,1,1,1]
[[[[[[],[]],[]]],[]]] => [1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [7,5,3,4,6,2,8,1] => [4,1,1,1,1]
[[[[[[[]]],[]]],[]]] => [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [7,5,4,3,6,2,8,1] => [3,1,1,1,1,1]
[[[[[[],[],[]]]],[]]] => [1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [7,6,3,4,5,2,8,1] => [4,1,1,1,1]
[[[[[[],[[]]]]],[]]] => [1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [7,6,3,5,4,2,8,1] => [3,1,1,1,1,1]
[[[[[[[]],[]]]],[]]] => [1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [7,6,4,3,5,2,8,1] => [3,1,1,1,1,1]
[[[[[[[],[]]]]],[]]] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,6,4,5,3,2,8,1] => [3,1,1,1,1,1]
[[[[[[[[]]]]]],[]]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,6,5,4,3,2,8,1] => [2,1,1,1,1,1,1]
[[[[],[],[],[],[],[]]]] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8,2,3,4,5,6,7,1] => [6,1,1]
[[[[],[],[],[],[[]]]]] => [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [8,2,3,4,5,7,6,1] => [5,1,1,1]
[[[[],[],[],[[[]]]]]] => [1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [8,2,3,4,7,6,5,1] => [4,1,1,1,1]
[[[[],[],[[]],[],[]]]] => [1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [8,2,3,5,4,6,7,1] => [5,1,1,1]
[[[[],[],[[]],[[]]]]] => [1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [8,2,3,5,4,7,6,1] => [4,2,1,1]
[[[[],[],[[],[],[]]]]] => [1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [8,2,3,5,6,7,4,1] => [5,1,1,1]
[[[[],[],[[],[[]]]]]] => [1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [8,2,3,5,7,6,4,1] => [4,1,1,1,1]
[[[[],[],[[[],[]]]]]] => [1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [8,2,3,7,5,6,4,1] => [4,1,1,1,1]
[[[[],[],[[[[]]]]]]] => [1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [8,2,3,7,6,5,4,1] => [3,1,1,1,1,1]
[[[[],[[]],[[]],[]]]] => [1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [8,2,4,3,6,5,7,1] => [4,2,1,1]
[[[[],[[]],[[],[]]]]] => [1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [8,2,4,3,6,7,5,1] => [4,2,1,1]
[[[[],[[]],[[[]]]]]] => [1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [8,2,4,3,7,6,5,1] => [3,2,1,1,1]
[[[[],[[[]]],[],[]]]] => [1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [8,2,5,4,3,6,7,1] => [4,1,1,1,1]
[[[[],[[],[]],[[]]]]] => [1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [8,2,4,5,3,7,6,1] => [4,2,1,1]
[[[[],[[[]]],[[]]]]] => [1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [8,2,5,4,3,7,6,1] => [3,2,1,1,1]
[[[[],[[[],[]]],[]]]] => [1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [8,2,6,4,5,3,7,1] => [4,1,1,1,1]
[[[[],[[[[]]]],[]]]] => [1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [8,2,6,5,4,3,7,1] => [3,1,1,1,1,1]
[[[[],[[],[],[],[]]]]] => [1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [8,2,4,5,6,7,3,1] => [5,1,1,1]
[[[[],[[],[],[[]]]]]] => [1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [8,2,4,5,7,6,3,1] => [4,1,1,1,1]
[[[[],[[],[[],[]]]]]] => [1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [8,2,4,7,5,6,3,1] => [4,1,1,1,1]
[[[[],[[],[[[]]]]]]] => [1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [8,2,4,7,6,5,3,1] => [3,1,1,1,1,1]
[[[[],[[[],[]],[]]]]] => [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [8,2,6,4,5,7,3,1] => [4,1,1,1,1]
[[[[],[[[[]]],[]]]]] => [1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [8,2,6,5,4,7,3,1] => [3,1,1,1,1,1]
[[[[],[[[],[],[]]]]]] => [1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [8,2,7,4,5,6,3,1] => [4,1,1,1,1]
[[[[],[[[],[[]]]]]]] => [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [8,2,7,4,6,5,3,1] => [3,1,1,1,1,1]
[[[[],[[[[]],[]]]]]] => [1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [8,2,7,5,4,6,3,1] => [3,1,1,1,1,1]
[[[[],[[[[],[]]]]]]] => [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [8,2,7,5,6,4,3,1] => [3,1,1,1,1,1]
[[[[],[[[[[]]]]]]]] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [8,2,7,6,5,4,3,1] => [2,1,1,1,1,1,1]
[[[[[]],[],[],[],[]]]] => [1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [8,3,2,4,5,6,7,1] => [5,1,1,1]
[[[[[]],[],[[]],[]]]] => [1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [8,3,2,4,6,5,7,1] => [4,2,1,1]
[[[[[]],[],[[],[]]]]] => [1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [8,3,2,4,6,7,5,1] => [4,2,1,1]
[[[[[]],[],[[[]]]]]] => [1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [8,3,2,4,7,6,5,1] => [3,2,1,1,1]
[[[[[]],[[]],[[]]]]] => [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [8,3,2,5,4,7,6,1] => [3,3,1,1]
[[[[[]],[[],[],[]]]]] => [1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [8,3,2,5,6,7,4,1] => [4,2,1,1]
[[[[[]],[[],[[]]]]]] => [1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [8,3,2,5,7,6,4,1] => [3,2,1,1,1]
[[[[[]],[[[]],[]]]]] => [1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [8,3,2,6,5,7,4,1] => [3,2,1,1,1]
[[[[[]],[[[],[]]]]]] => [1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [8,3,2,7,5,6,4,1] => [3,2,1,1,1]
[[[[[]],[[[[]]]]]]] => [1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [8,3,2,7,6,5,4,1] => [2,2,1,1,1,1]
[[[[[],[]],[],[],[]]]] => [1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [8,3,4,2,5,6,7,1] => [5,1,1,1]
[[[[[[]]],[],[],[]]]] => [1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [8,4,3,2,5,6,7,1] => [4,1,1,1,1]
[[[[[[]]],[],[[]]]]] => [1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [8,4,3,2,5,7,6,1] => [3,2,1,1,1]
[[[[[[]]],[[]],[]]]] => [1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [8,4,3,2,6,5,7,1] => [3,2,1,1,1]
[[[[[[]]],[[[]]]]]] => [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]
[[[[[],[],[]],[],[]]]] => [1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [8,3,4,5,2,6,7,1] => [5,1,1,1]
[[[[[],[[]]],[],[]]]] => [1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [8,3,5,4,2,6,7,1] => [4,1,1,1,1]
[[[[[[],[]]],[],[]]]] => [1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [8,5,3,4,2,6,7,1] => [4,1,1,1,1]
[[[[[[[]]]],[],[]]]] => [1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [8,5,4,3,2,6,7,1] => [3,1,1,1,1,1]
[[[[[],[],[]],[[]]]]] => [1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [8,3,4,5,2,7,6,1] => [4,2,1,1]
[[[[[],[[]]],[[]]]]] => [1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [8,3,5,4,2,7,6,1] => [3,2,1,1,1]
[[[[[[]],[]],[[]]]]] => [1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [8,4,3,5,2,7,6,1] => [3,2,1,1,1]
[[[[[[],[]]],[[]]]]] => [1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [8,5,3,4,2,7,6,1] => [3,2,1,1,1]
[[[[[[[]]]],[[]]]]] => [1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [8,5,4,3,2,7,6,1] => [2,2,1,1,1,1]
[[[[[],[[],[]]],[]]]] => [1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [8,3,6,4,5,2,7,1] => [4,1,1,1,1]
[[[[[[]],[],[]],[]]]] => [1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [8,4,3,5,6,2,7,1] => [4,1,1,1,1]
[[[[[[],[[]]]],[]]]] => [1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [8,6,3,5,4,2,7,1] => [3,1,1,1,1,1]
[[[[[[[]],[]]],[]]]] => [1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [8,6,4,3,5,2,7,1] => [3,1,1,1,1,1]
[[[[[[[[]]]]],[]]]] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [8,6,5,4,3,2,7,1] => [2,1,1,1,1,1,1]
[[[[[],[],[],[],[]]]]] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [8,3,4,5,6,7,2,1] => [5,1,1,1]
[[[[[],[],[],[[]]]]]] => [1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [8,3,4,5,7,6,2,1] => [4,1,1,1,1]
[[[[[],[],[[[]]]]]]] => [1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [8,3,4,7,6,5,2,1] => [3,1,1,1,1,1]
[[[[[],[[]],[],[]]]]] => [1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [8,3,5,4,6,7,2,1] => [4,1,1,1,1]
[[[[[],[[]],[[]]]]]] => [1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [8,3,5,4,7,6,2,1] => [3,2,1,1,1]
[[[[[],[[[]]],[]]]]] => [1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [8,3,6,5,4,7,2,1] => [3,1,1,1,1,1]
[[[[[],[[],[],[]]]]]] => [1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [8,3,7,4,5,6,2,1] => [4,1,1,1,1]
[[[[[],[[],[[]]]]]]] => [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [8,3,7,4,6,5,2,1] => [3,1,1,1,1,1]
[[[[[],[[[]],[]]]]]] => [1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [8,3,7,5,4,6,2,1] => [3,1,1,1,1,1]
[[[[[],[[[],[]]]]]]] => [1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [8,3,7,5,6,4,2,1] => [3,1,1,1,1,1]
[[[[[],[[[[]]]]]]]] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [8,3,7,6,5,4,2,1] => [2,1,1,1,1,1,1]
[[[[[[]],[],[],[]]]]] => [1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [8,4,3,5,6,7,2,1] => [4,1,1,1,1]
[[[[[[]],[],[[]]]]]] => [1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [8,4,3,5,7,6,2,1] => [3,2,1,1,1]
[[[[[[]],[[],[]]]]]] => [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]
[[[[[[]],[[[]]]]]]] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [8,4,3,7,6,5,2,1] => [2,2,1,1,1,1]
[[[[[[],[]],[],[]]]]] => [1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [8,5,3,4,6,7,2,1] => [4,1,1,1,1]
[[[[[[],[]],[[]]]]]] => [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]
[[[[[[[]]],[[]]]]]] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [8,5,4,3,7,6,2,1] => [2,2,1,1,1,1]
[[[[[[],[[]]],[]]]]] => [1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [8,6,3,5,4,7,2,1] => [3,1,1,1,1,1]
[[[[[[[]],[]],[]]]]] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [8,6,4,3,5,7,2,1] => [3,1,1,1,1,1]
[[[[[[[[]]]],[]]]]] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [8,6,5,4,3,7,2,1] => [2,1,1,1,1,1,1]
[[[[[[],[],[],[]]]]]] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [8,7,3,4,5,6,2,1] => [4,1,1,1,1]
[[[[[[],[],[[]]]]]]] => [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [8,7,3,4,6,5,2,1] => [3,1,1,1,1,1]
[[[[[[],[[]],[]]]]]] => [1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [8,7,3,5,4,6,2,1] => [3,1,1,1,1,1]
[[[[[[],[[],[]]]]]]] => [1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [8,7,3,5,6,4,2,1] => [3,1,1,1,1,1]
[[[[[[],[[[]]]]]]]] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [8,7,3,6,5,4,2,1] => [2,1,1,1,1,1,1]
[[[[[[[]],[],[]]]]]] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [8,7,4,3,5,6,2,1] => [3,1,1,1,1,1]
[[[[[[[]],[[]]]]]]] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [8,7,4,3,6,5,2,1] => [2,2,1,1,1,1]
[[[[[[[[]]],[]]]]]] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [8,7,5,4,3,6,2,1] => [2,1,1,1,1,1,1]
[[[[[[[],[],[]]]]]]] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [8,7,4,5,6,3,2,1] => [3,1,1,1,1,1]
[[[[[[[],[[]]]]]]]] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [8,7,4,6,5,3,2,1] => [2,1,1,1,1,1,1]
[[[[[[[[]],[]]]]]]] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [8,7,5,4,6,3,2,1] => [2,1,1,1,1,1,1]
[[[[[[[[],[]]]]]]]] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [8,7,6,4,5,3,2,1] => [2,1,1,1,1,1,1]
[[[[[[[[[]]]]]]]]] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8,7,6,5,4,3,2,1] => [1,1,1,1,1,1,1,1]
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
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
Robinson-Schensted tableau shape
Description
Sends a permutation to its Robinson-Schensted tableau shape.
The Robinson-Schensted corrspondence is a bijection between permutations of length n and pairs of standard Young tableaux of the same shape and of size n, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to the shape of its corresponding insertion and recording tableau.
The Robinson-Schensted corrspondence is a bijection between permutations of length n and pairs of standard Young tableaux of the same shape and of size n, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to the shape of its corresponding insertion and recording tableau.
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