Identifier
Values
[] => [] => [] => 1
[[]] => [1,0] => [] => 1
[[],[]] => [1,0,1,0] => [1] => 2
[[[]]] => [1,1,0,0] => [] => 1
[[],[],[]] => [1,0,1,0,1,0] => [2,1] => 3
[[],[[]]] => [1,0,1,1,0,0] => [1,1] => 2
[[[]],[]] => [1,1,0,0,1,0] => [2] => 2
[[[],[]]] => [1,1,0,1,0,0] => [1] => 2
[[[[]]]] => [1,1,1,0,0,0] => [] => 1
[[],[],[],[]] => [1,0,1,0,1,0,1,0] => [3,2,1] => 4
[[],[],[[]]] => [1,0,1,0,1,1,0,0] => [2,2,1] => 3
[[],[[]],[]] => [1,0,1,1,0,0,1,0] => [3,1,1] => 3
[[],[[],[]]] => [1,0,1,1,0,1,0,0] => [2,1,1] => 3
[[],[[[]]]] => [1,0,1,1,1,0,0,0] => [1,1,1] => 2
[[[]],[],[]] => [1,1,0,0,1,0,1,0] => [3,2] => 3
[[[]],[[]]] => [1,1,0,0,1,1,0,0] => [2,2] => 2
[[[],[]],[]] => [1,1,0,1,0,0,1,0] => [3,1] => 3
[[[[]]],[]] => [1,1,1,0,0,0,1,0] => [3] => 2
[[[],[],[]]] => [1,1,0,1,0,1,0,0] => [2,1] => 3
[[[],[[]]]] => [1,1,0,1,1,0,0,0] => [1,1] => 2
[[[[]],[]]] => [1,1,1,0,0,1,0,0] => [2] => 2
[[[[],[]]]] => [1,1,1,0,1,0,0,0] => [1] => 2
[[[[[]]]]] => [1,1,1,1,0,0,0,0] => [] => 1
[[],[],[],[],[]] => [1,0,1,0,1,0,1,0,1,0] => [4,3,2,1] => 5
[[],[],[],[[]]] => [1,0,1,0,1,0,1,1,0,0] => [3,3,2,1] => 4
[[],[],[[]],[]] => [1,0,1,0,1,1,0,0,1,0] => [4,2,2,1] => 4
[[],[],[[],[]]] => [1,0,1,0,1,1,0,1,0,0] => [3,2,2,1] => 4
[[],[],[[[]]]] => [1,0,1,0,1,1,1,0,0,0] => [2,2,2,1] => 3
[[],[[]],[],[]] => [1,0,1,1,0,0,1,0,1,0] => [4,3,1,1] => 4
[[],[[]],[[]]] => [1,0,1,1,0,0,1,1,0,0] => [3,3,1,1] => 3
[[],[[],[]],[]] => [1,0,1,1,0,1,0,0,1,0] => [4,2,1,1] => 4
[[],[[[]]],[]] => [1,0,1,1,1,0,0,0,1,0] => [4,1,1,1] => 3
[[],[[],[],[]]] => [1,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => 4
[[],[[],[[]]]] => [1,0,1,1,0,1,1,0,0,0] => [2,2,1,1] => 3
[[],[[[]],[]]] => [1,0,1,1,1,0,0,1,0,0] => [3,1,1,1] => 3
[[],[[[],[]]]] => [1,0,1,1,1,0,1,0,0,0] => [2,1,1,1] => 3
[[],[[[[]]]]] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => 2
[[[]],[],[],[]] => [1,1,0,0,1,0,1,0,1,0] => [4,3,2] => 4
[[[]],[],[[]]] => [1,1,0,0,1,0,1,1,0,0] => [3,3,2] => 3
[[[]],[[]],[]] => [1,1,0,0,1,1,0,0,1,0] => [4,2,2] => 3
[[[]],[[],[]]] => [1,1,0,0,1,1,0,1,0,0] => [3,2,2] => 3
[[[]],[[[]]]] => [1,1,0,0,1,1,1,0,0,0] => [2,2,2] => 2
[[[],[]],[],[]] => [1,1,0,1,0,0,1,0,1,0] => [4,3,1] => 4
[[[[]]],[],[]] => [1,1,1,0,0,0,1,0,1,0] => [4,3] => 3
[[[],[]],[[]]] => [1,1,0,1,0,0,1,1,0,0] => [3,3,1] => 3
[[[[]]],[[]]] => [1,1,1,0,0,0,1,1,0,0] => [3,3] => 2
[[[],[],[]],[]] => [1,1,0,1,0,1,0,0,1,0] => [4,2,1] => 4
[[[],[[]]],[]] => [1,1,0,1,1,0,0,0,1,0] => [4,1,1] => 3
[[[[]],[]],[]] => [1,1,1,0,0,1,0,0,1,0] => [4,2] => 3
[[[[],[]]],[]] => [1,1,1,0,1,0,0,0,1,0] => [4,1] => 3
[[[[[]]]],[]] => [1,1,1,1,0,0,0,0,1,0] => [4] => 2
[[[],[],[],[]]] => [1,1,0,1,0,1,0,1,0,0] => [3,2,1] => 4
[[[],[],[[]]]] => [1,1,0,1,0,1,1,0,0,0] => [2,2,1] => 3
[[[],[[]],[]]] => [1,1,0,1,1,0,0,1,0,0] => [3,1,1] => 3
[[[],[[],[]]]] => [1,1,0,1,1,0,1,0,0,0] => [2,1,1] => 3
[[[],[[[]]]]] => [1,1,0,1,1,1,0,0,0,0] => [1,1,1] => 2
[[[[]],[],[]]] => [1,1,1,0,0,1,0,1,0,0] => [3,2] => 3
[[[[]],[[]]]] => [1,1,1,0,0,1,1,0,0,0] => [2,2] => 2
[[[[],[]],[]]] => [1,1,1,0,1,0,0,1,0,0] => [3,1] => 3
[[[[[]]],[]]] => [1,1,1,1,0,0,0,1,0,0] => [3] => 2
[[[[],[],[]]]] => [1,1,1,0,1,0,1,0,0,0] => [2,1] => 3
[[[[],[[]]]]] => [1,1,1,0,1,1,0,0,0,0] => [1,1] => 2
[[[[[]],[]]]] => [1,1,1,1,0,0,1,0,0,0] => [2] => 2
[[[[[],[]]]]] => [1,1,1,1,0,1,0,0,0,0] => [1] => 2
[[[[[[]]]]]] => [1,1,1,1,1,0,0,0,0,0] => [] => 1
[[],[],[],[],[],[]] => [1,0,1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => 6
[[],[],[],[],[[]]] => [1,0,1,0,1,0,1,0,1,1,0,0] => [4,4,3,2,1] => 5
[[],[],[],[[]],[]] => [1,0,1,0,1,0,1,1,0,0,1,0] => [5,3,3,2,1] => 5
[[],[],[],[[],[]]] => [1,0,1,0,1,0,1,1,0,1,0,0] => [4,3,3,2,1] => 5
[[],[],[],[[[]]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => [3,3,3,2,1] => 4
[[],[],[[]],[],[]] => [1,0,1,0,1,1,0,0,1,0,1,0] => [5,4,2,2,1] => 5
[[],[],[[]],[[]]] => [1,0,1,0,1,1,0,0,1,1,0,0] => [4,4,2,2,1] => 4
[[],[],[[],[]],[]] => [1,0,1,0,1,1,0,1,0,0,1,0] => [5,3,2,2,1] => 5
[[],[],[[[]]],[]] => [1,0,1,0,1,1,1,0,0,0,1,0] => [5,2,2,2,1] => 4
[[],[],[[],[],[]]] => [1,0,1,0,1,1,0,1,0,1,0,0] => [4,3,2,2,1] => 5
[[],[],[[],[[]]]] => [1,0,1,0,1,1,0,1,1,0,0,0] => [3,3,2,2,1] => 4
[[],[],[[[]],[]]] => [1,0,1,0,1,1,1,0,0,1,0,0] => [4,2,2,2,1] => 4
[[],[],[[[],[]]]] => [1,0,1,0,1,1,1,0,1,0,0,0] => [3,2,2,2,1] => 4
[[],[],[[[[]]]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => [2,2,2,2,1] => 3
[[],[[]],[],[],[]] => [1,0,1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,1] => 5
[[],[[]],[],[[]]] => [1,0,1,1,0,0,1,0,1,1,0,0] => [4,4,3,1,1] => 4
[[],[[]],[[]],[]] => [1,0,1,1,0,0,1,1,0,0,1,0] => [5,3,3,1,1] => 4
[[],[[]],[[],[]]] => [1,0,1,1,0,0,1,1,0,1,0,0] => [4,3,3,1,1] => 4
[[],[[]],[[[]]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => [3,3,3,1,1] => 3
[[],[[],[]],[],[]] => [1,0,1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,1] => 5
[[],[[[]]],[],[]] => [1,0,1,1,1,0,0,0,1,0,1,0] => [5,4,1,1,1] => 4
[[],[[],[]],[[]]] => [1,0,1,1,0,1,0,0,1,1,0,0] => [4,4,2,1,1] => 4
[[],[[[]]],[[]]] => [1,0,1,1,1,0,0,0,1,1,0,0] => [4,4,1,1,1] => 3
[[],[[],[],[]],[]] => [1,0,1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,1] => 5
[[],[[],[[]]],[]] => [1,0,1,1,0,1,1,0,0,0,1,0] => [5,2,2,1,1] => 4
[[],[[[]],[]],[]] => [1,0,1,1,1,0,0,1,0,0,1,0] => [5,3,1,1,1] => 4
[[],[[[],[]]],[]] => [1,0,1,1,1,0,1,0,0,0,1,0] => [5,2,1,1,1] => 4
[[],[[[[]]]],[]] => [1,0,1,1,1,1,0,0,0,0,1,0] => [5,1,1,1,1] => 3
[[],[[],[],[],[]]] => [1,0,1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,1] => 5
[[],[[],[],[[]]]] => [1,0,1,1,0,1,0,1,1,0,0,0] => [3,3,2,1,1] => 4
[[],[[],[[]],[]]] => [1,0,1,1,0,1,1,0,0,1,0,0] => [4,2,2,1,1] => 4
[[],[[],[[],[]]]] => [1,0,1,1,0,1,1,0,1,0,0,0] => [3,2,2,1,1] => 4
[[],[[],[[[]]]]] => [1,0,1,1,0,1,1,1,0,0,0,0] => [2,2,2,1,1] => 3
[[],[[[]],[],[]]] => [1,0,1,1,1,0,0,1,0,1,0,0] => [4,3,1,1,1] => 4
[[],[[[]],[[]]]] => [1,0,1,1,1,0,0,1,1,0,0,0] => [3,3,1,1,1] => 3
[[],[[[],[]],[]]] => [1,0,1,1,1,0,1,0,0,1,0,0] => [4,2,1,1,1] => 4
>>> Load all 531 entries. <<<
[[],[[[[]]],[]]] => [1,0,1,1,1,1,0,0,0,1,0,0] => [4,1,1,1,1] => 3
[[],[[[],[],[]]]] => [1,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,1,1] => 4
[[],[[[],[[]]]]] => [1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => 3
[[],[[[[]],[]]]] => [1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,1,1,1] => 3
[[],[[[[],[]]]]] => [1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => 3
[[],[[[[[]]]]]] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 2
[[[]],[],[],[],[]] => [1,1,0,0,1,0,1,0,1,0,1,0] => [5,4,3,2] => 5
[[[]],[],[],[[]]] => [1,1,0,0,1,0,1,0,1,1,0,0] => [4,4,3,2] => 4
[[[]],[],[[]],[]] => [1,1,0,0,1,0,1,1,0,0,1,0] => [5,3,3,2] => 4
[[[]],[],[[],[]]] => [1,1,0,0,1,0,1,1,0,1,0,0] => [4,3,3,2] => 4
[[[]],[],[[[]]]] => [1,1,0,0,1,0,1,1,1,0,0,0] => [3,3,3,2] => 3
[[[]],[[]],[],[]] => [1,1,0,0,1,1,0,0,1,0,1,0] => [5,4,2,2] => 4
[[[]],[[]],[[]]] => [1,1,0,0,1,1,0,0,1,1,0,0] => [4,4,2,2] => 3
[[[]],[[],[]],[]] => [1,1,0,0,1,1,0,1,0,0,1,0] => [5,3,2,2] => 4
[[[]],[[[]]],[]] => [1,1,0,0,1,1,1,0,0,0,1,0] => [5,2,2,2] => 3
[[[]],[[],[],[]]] => [1,1,0,0,1,1,0,1,0,1,0,0] => [4,3,2,2] => 4
[[[]],[[],[[]]]] => [1,1,0,0,1,1,0,1,1,0,0,0] => [3,3,2,2] => 3
[[[]],[[[]],[]]] => [1,1,0,0,1,1,1,0,0,1,0,0] => [4,2,2,2] => 3
[[[]],[[[],[]]]] => [1,1,0,0,1,1,1,0,1,0,0,0] => [3,2,2,2] => 3
[[[]],[[[[]]]]] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,2,2,2] => 2
[[[],[]],[],[],[]] => [1,1,0,1,0,0,1,0,1,0,1,0] => [5,4,3,1] => 5
[[[[]]],[],[],[]] => [1,1,1,0,0,0,1,0,1,0,1,0] => [5,4,3] => 4
[[[],[]],[],[[]]] => [1,1,0,1,0,0,1,0,1,1,0,0] => [4,4,3,1] => 4
[[[[]]],[],[[]]] => [1,1,1,0,0,0,1,0,1,1,0,0] => [4,4,3] => 3
[[[],[]],[[]],[]] => [1,1,0,1,0,0,1,1,0,0,1,0] => [5,3,3,1] => 4
[[[[]]],[[]],[]] => [1,1,1,0,0,0,1,1,0,0,1,0] => [5,3,3] => 3
[[[],[]],[[],[]]] => [1,1,0,1,0,0,1,1,0,1,0,0] => [4,3,3,1] => 4
[[[],[]],[[[]]]] => [1,1,0,1,0,0,1,1,1,0,0,0] => [3,3,3,1] => 3
[[[[]]],[[],[]]] => [1,1,1,0,0,0,1,1,0,1,0,0] => [4,3,3] => 3
[[[[]]],[[[]]]] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,3,3] => 2
[[[],[],[]],[],[]] => [1,1,0,1,0,1,0,0,1,0,1,0] => [5,4,2,1] => 5
[[[],[[]]],[],[]] => [1,1,0,1,1,0,0,0,1,0,1,0] => [5,4,1,1] => 4
[[[[]],[]],[],[]] => [1,1,1,0,0,1,0,0,1,0,1,0] => [5,4,2] => 4
[[[[],[]]],[],[]] => [1,1,1,0,1,0,0,0,1,0,1,0] => [5,4,1] => 4
[[[[[]]]],[],[]] => [1,1,1,1,0,0,0,0,1,0,1,0] => [5,4] => 3
[[[],[],[]],[[]]] => [1,1,0,1,0,1,0,0,1,1,0,0] => [4,4,2,1] => 4
[[[],[[]]],[[]]] => [1,1,0,1,1,0,0,0,1,1,0,0] => [4,4,1,1] => 3
[[[[]],[]],[[]]] => [1,1,1,0,0,1,0,0,1,1,0,0] => [4,4,2] => 3
[[[[],[]]],[[]]] => [1,1,1,0,1,0,0,0,1,1,0,0] => [4,4,1] => 3
[[[[[]]]],[[]]] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,4] => 2
[[[],[],[],[]],[]] => [1,1,0,1,0,1,0,1,0,0,1,0] => [5,3,2,1] => 5
[[[],[],[[]]],[]] => [1,1,0,1,0,1,1,0,0,0,1,0] => [5,2,2,1] => 4
[[[],[[]],[]],[]] => [1,1,0,1,1,0,0,1,0,0,1,0] => [5,3,1,1] => 4
[[[],[[],[]]],[]] => [1,1,0,1,1,0,1,0,0,0,1,0] => [5,2,1,1] => 4
[[[],[[[]]]],[]] => [1,1,0,1,1,1,0,0,0,0,1,0] => [5,1,1,1] => 3
[[[[]],[],[]],[]] => [1,1,1,0,0,1,0,1,0,0,1,0] => [5,3,2] => 4
[[[[]],[[]]],[]] => [1,1,1,0,0,1,1,0,0,0,1,0] => [5,2,2] => 3
[[[[],[]],[]],[]] => [1,1,1,0,1,0,0,1,0,0,1,0] => [5,3,1] => 4
[[[[[]]],[]],[]] => [1,1,1,1,0,0,0,1,0,0,1,0] => [5,3] => 3
[[[[],[],[]]],[]] => [1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,1] => 4
[[[[],[[]]]],[]] => [1,1,1,0,1,1,0,0,0,0,1,0] => [5,1,1] => 3
[[[[[]],[]]],[]] => [1,1,1,1,0,0,1,0,0,0,1,0] => [5,2] => 3
[[[[[],[]]]],[]] => [1,1,1,1,0,1,0,0,0,0,1,0] => [5,1] => 3
[[[[[[]]]]],[]] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5] => 2
[[[],[],[],[],[]]] => [1,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,1] => 5
[[[],[],[],[[]]]] => [1,1,0,1,0,1,0,1,1,0,0,0] => [3,3,2,1] => 4
[[[],[],[[]],[]]] => [1,1,0,1,0,1,1,0,0,1,0,0] => [4,2,2,1] => 4
[[[],[],[[],[]]]] => [1,1,0,1,0,1,1,0,1,0,0,0] => [3,2,2,1] => 4
[[[],[],[[[]]]]] => [1,1,0,1,0,1,1,1,0,0,0,0] => [2,2,2,1] => 3
[[[],[[]],[],[]]] => [1,1,0,1,1,0,0,1,0,1,0,0] => [4,3,1,1] => 4
[[[],[[]],[[]]]] => [1,1,0,1,1,0,0,1,1,0,0,0] => [3,3,1,1] => 3
[[[],[[],[]],[]]] => [1,1,0,1,1,0,1,0,0,1,0,0] => [4,2,1,1] => 4
[[[],[[[]]],[]]] => [1,1,0,1,1,1,0,0,0,1,0,0] => [4,1,1,1] => 3
[[[],[[],[],[]]]] => [1,1,0,1,1,0,1,0,1,0,0,0] => [3,2,1,1] => 4
[[[],[[],[[]]]]] => [1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,1,1] => 3
[[[],[[[]],[]]]] => [1,1,0,1,1,1,0,0,1,0,0,0] => [3,1,1,1] => 3
[[[],[[[],[]]]]] => [1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,1,1] => 3
[[[],[[[[]]]]]] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1] => 2
[[[[]],[],[],[]]] => [1,1,1,0,0,1,0,1,0,1,0,0] => [4,3,2] => 4
[[[[]],[],[[]]]] => [1,1,1,0,0,1,0,1,1,0,0,0] => [3,3,2] => 3
[[[[]],[[]],[]]] => [1,1,1,0,0,1,1,0,0,1,0,0] => [4,2,2] => 3
[[[[]],[[],[]]]] => [1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,2] => 3
[[[[]],[[[]]]]] => [1,1,1,0,0,1,1,1,0,0,0,0] => [2,2,2] => 2
[[[[],[]],[],[]]] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,3,1] => 4
[[[[[]]],[],[]]] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3] => 3
[[[[],[]],[[]]]] => [1,1,1,0,1,0,0,1,1,0,0,0] => [3,3,1] => 3
[[[[[]]],[[]]]] => [1,1,1,1,0,0,0,1,1,0,0,0] => [3,3] => 2
[[[[],[],[]],[]]] => [1,1,1,0,1,0,1,0,0,1,0,0] => [4,2,1] => 4
[[[[],[[]]],[]]] => [1,1,1,0,1,1,0,0,0,1,0,0] => [4,1,1] => 3
[[[[[]],[]],[]]] => [1,1,1,1,0,0,1,0,0,1,0,0] => [4,2] => 3
[[[[[],[]]],[]]] => [1,1,1,1,0,1,0,0,0,1,0,0] => [4,1] => 3
[[[[[[]]]],[]]] => [1,1,1,1,1,0,0,0,0,1,0,0] => [4] => 2
[[[[],[],[],[]]]] => [1,1,1,0,1,0,1,0,1,0,0,0] => [3,2,1] => 4
[[[[],[],[[]]]]] => [1,1,1,0,1,0,1,1,0,0,0,0] => [2,2,1] => 3
[[[[],[[]],[]]]] => [1,1,1,0,1,1,0,0,1,0,0,0] => [3,1,1] => 3
[[[[],[[],[]]]]] => [1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,1] => 3
[[[[],[[[]]]]]] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1] => 2
[[[[[]],[],[]]]] => [1,1,1,1,0,0,1,0,1,0,0,0] => [3,2] => 3
[[[[[]],[[]]]]] => [1,1,1,1,0,0,1,1,0,0,0,0] => [2,2] => 2
[[[[[],[]],[]]]] => [1,1,1,1,0,1,0,0,1,0,0,0] => [3,1] => 3
[[[[[[]]],[]]]] => [1,1,1,1,1,0,0,0,1,0,0,0] => [3] => 2
[[[[[],[],[]]]]] => [1,1,1,1,0,1,0,1,0,0,0,0] => [2,1] => 3
[[[[[],[[]]]]]] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1] => 2
[[[[[[]],[]]]]] => [1,1,1,1,1,0,0,1,0,0,0,0] => [2] => 2
[[[[[[],[]]]]]] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1] => 2
[[[[[[[]]]]]]] => [1,1,1,1,1,1,0,0,0,0,0,0] => [] => 1
[[],[[],[[],[[]]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => 4
[[],[[],[[[[]]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1,1] => 3
[[],[[[[[]]]],[]]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1,1] => 3
[[],[[[],[[],[]]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1,1] => 4
[[],[[[],[[[]]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1,1] => 3
[[],[[[[]],[[]]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1,1] => 3
[[],[[[[],[]],[]]]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1,1] => 4
[[],[[[[[]]],[]]]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1,1] => 3
[[],[[[[],[],[]]]]] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1,1] => 4
[[],[[[[],[[]]]]]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1,1] => 3
[[],[[[[[]],[]]]]] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1,1] => 3
[[],[[[[[],[]]]]]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 3
[[],[[[[[[]]]]]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 2
[[[]],[[[[[]]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2] => 2
[[[[[[]]]]],[[]]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => 2
[[[],[[[[]]]]],[]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1,1] => 3
[[[[[]],[]],[]],[]] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [6,4,2] => 4
[[[[[[]]]],[]],[]] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [6,4] => 3
[[[[],[[],[]]]],[]] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1] => 4
[[[[],[[[]]]]],[]] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1] => 3
[[[[[]],[[]]]],[]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,2,2] => 3
[[[[[],[]],[]]],[]] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,1] => 4
[[[[[[]]],[]]],[]] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,3] => 3
[[[[[],[],[]]]],[]] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,2,1] => 4
[[[[[],[[]]]]],[]] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,1,1] => 3
[[[[[[]],[]]]],[]] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,2] => 3
[[[[[[],[]]]]],[]] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1] => 3
[[[[[[[]]]]]],[]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 2
[[[],[],[],[],[],[]]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1] => 6
[[[],[],[],[],[[]]]] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2,1] => 5
[[[],[],[],[[]],[]]] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2,1] => 5
[[[],[],[],[[],[]]]] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1] => 5
[[[],[],[],[[[]]]]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1] => 4
[[[],[],[[]],[],[]]] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2,1] => 5
[[[],[],[[]],[[]]]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1] => 4
[[[],[],[[],[]],[]]] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2,1] => 5
[[[],[],[[[]]],[]]] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2,1] => 4
[[[],[],[[],[],[]]]] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1] => 5
[[[],[],[[],[[]]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1] => 4
[[[],[],[[[]],[]]]] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1] => 4
[[[],[],[[[],[]]]]] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1] => 4
[[[],[],[[[[]]]]]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1] => 3
[[[],[[]],[],[],[]]] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,1] => 5
[[[],[[]],[],[[]]]] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1,1] => 4
[[[],[[]],[[]],[]]] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1,1] => 4
[[[],[[]],[[],[]]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1] => 4
[[[],[[]],[[[]]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1] => 3
[[[],[[],[]],[],[]]] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,1] => 5
[[[],[[[]]],[],[]]] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1,1] => 4
[[[],[[],[]],[[]]]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1] => 4
[[[],[[[]]],[[]]]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1] => 3
[[[],[[],[],[]],[]]] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,1] => 5
[[[],[[],[[]]],[]]] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1] => 4
[[[],[[[]],[]],[]]] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1,1] => 4
[[[],[[[],[]]],[]]] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1,1] => 4
[[[],[[[[]]]],[]]] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1] => 3
[[[],[[],[],[],[]]]] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,1] => 5
[[[],[[],[],[[]]]]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1] => 4
[[[],[[],[[]],[]]]] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1] => 4
[[[],[[],[[],[]]]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1] => 4
[[[],[[],[[[]]]]]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1] => 3
[[[],[[[]],[],[]]]] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1,1] => 4
[[[],[[[]],[[]]]]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1] => 3
[[[],[[[],[]],[]]]] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1] => 4
[[[],[[[[]]],[]]]] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1] => 3
[[[],[[[],[],[]]]]] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1] => 4
[[[],[[[],[[]]]]]] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1] => 3
[[[],[[[[]],[]]]]] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1] => 3
[[[],[[[[],[]]]]]] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1] => 3
[[[],[[[[[]]]]]]] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1] => 2
[[[[]],[],[],[],[]]] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2] => 5
[[[[]],[],[],[[]]]] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2] => 4
[[[[]],[],[[]],[]]] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2] => 4
[[[[]],[],[[],[]]]] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2] => 4
[[[[]],[],[[[]]]]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2] => 3
[[[[]],[[]],[],[]]] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2] => 4
[[[[]],[[]],[[]]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2] => 3
[[[[]],[[],[]],[]]] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2] => 4
[[[[]],[[[]]],[]]] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2] => 3
[[[[]],[[],[],[]]]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2] => 4
[[[[]],[[],[[]]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2] => 3
[[[[]],[[[]],[]]]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2] => 3
[[[[]],[[[],[]]]]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2] => 3
[[[[]],[[[[]]]]]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2] => 2
[[[[],[]],[],[],[]]] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1] => 5
[[[[[]]],[],[],[]]] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [5,4,3] => 4
[[[[],[]],[],[[]]]] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1] => 4
[[[[[]]],[],[[]]]] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,4,3] => 3
[[[[],[]],[[]],[]]] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1] => 4
[[[[[]]],[[]],[]]] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [5,3,3] => 3
[[[[],[]],[[],[]]]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1] => 4
[[[[],[]],[[[]]]]] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1] => 3
[[[[[]]],[[],[]]]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,3] => 3
[[[[[]]],[[[]]]]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [3,3,3] => 2
[[[[],[],[]],[],[]]] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1] => 5
[[[[],[[]]],[],[]]] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1] => 4
[[[[[]],[]],[],[]]] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [5,4,2] => 4
[[[[[],[]]],[],[]]] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,4,1] => 4
[[[[[[]]]],[],[]]] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4] => 3
[[[[],[],[]],[[]]]] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1] => 4
[[[[],[[]]],[[]]]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1] => 3
[[[[[]],[]],[[]]]] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,4,2] => 3
[[[[[],[]]],[[]]]] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,4,1] => 3
[[[[[[]]]],[[]]]] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [4,4] => 2
[[[[],[],[],[]],[]]] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1] => 5
[[[[],[],[[]]],[]]] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1] => 4
[[[[],[[]],[]],[]]] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1] => 4
[[[[],[[],[]]],[]]] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1] => 4
[[[[],[[[]]]],[]]] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1] => 3
[[[[[]],[],[]],[]]] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [5,3,2] => 4
[[[[[]],[[]]],[]]] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [5,2,2] => 3
[[[[[],[]],[]],[]]] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [5,3,1] => 4
[[[[[[]]],[]],[]]] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,3] => 3
[[[[[],[],[]]],[]]] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [5,2,1] => 4
[[[[[],[[]]]],[]]] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [5,1,1] => 3
[[[[[[]],[]]],[]]] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,2] => 3
[[[[[[],[]]]],[]]] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,1] => 3
[[[[[[[]]]]],[]]] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => 2
[[[[],[],[],[],[]]]] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1] => 5
[[[[],[],[],[[]]]]] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1] => 4
[[[[],[],[[]],[]]]] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1] => 4
[[[[],[],[[],[]]]]] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => 4
[[[[],[],[[[]]]]]] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1] => 3
[[[[],[[]],[],[]]]] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1] => 4
[[[[],[[]],[[]]]]] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1] => 3
[[[[],[[],[]],[]]]] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1] => 4
[[[[],[[[]]],[]]]] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1] => 3
[[[[],[[],[],[]]]]] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1] => 4
[[[[],[[],[[]]]]]] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1] => 3
[[[[],[[[]],[]]]]] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1] => 3
[[[[],[[[],[]]]]]] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1] => 3
[[[[],[[[[]]]]]]] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1] => 2
[[[[[]],[],[],[]]]] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,3,2] => 4
[[[[[]],[],[[]]]]] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [3,3,2] => 3
[[[[[]],[[]],[]]]] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,2,2] => 3
[[[[[]],[[],[]]]]] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [3,2,2] => 3
[[[[[]],[[[]]]]]] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,2,2] => 2
[[[[[],[]],[],[]]]] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,3,1] => 4
[[[[[[]]],[],[]]]] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [4,3] => 3
[[[[[],[]],[[]]]]] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [3,3,1] => 3
[[[[[[]]],[[]]]]] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [3,3] => 2
[[[[[],[],[]],[]]]] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,2,1] => 4
[[[[[],[[]]],[]]]] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,1,1] => 3
[[[[[[]],[]],[]]]] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [4,2] => 3
[[[[[[],[]]],[]]]] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [4,1] => 3
[[[[[[[]]]],[]]]] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [4] => 2
[[[[[],[],[],[]]]]] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1] => 4
[[[[[],[],[[]]]]]] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,2,1] => 3
[[[[[],[[]],[]]]]] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [3,1,1] => 3
[[[[[],[[],[]]]]]] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,1,1] => 3
[[[[[],[[[]]]]]]] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1] => 2
[[[[[[]],[],[]]]]] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [3,2] => 3
[[[[[[]],[[]]]]]] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,2] => 2
[[[[[[],[]],[]]]]] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [3,1] => 3
[[[[[[[]]],[]]]]] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3] => 2
[[[[[[],[],[]]]]]] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,1] => 3
[[[[[[],[[]]]]]]] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1] => 2
[[[[[[[]],[]]]]]] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2] => 2
[[[[[[[],[]]]]]]] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1] => 2
[[[[[[[[]]]]]]]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [] => 1
[[],[[[[],[[[]]]]]]] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1,1] => 3
[[],[[[[[[]]],[]]]]] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1,1] => 3
[[],[[[[[],[],[]]]]]] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1,1] => 4
[[],[[[[[],[[]]]]]]] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1,1] => 3
[[],[[[[[[]],[]]]]]] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1,1] => 3
[[],[[[[[[],[]]]]]]] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => 3
[[],[[[[[[[]]]]]]]] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 2
[[[[[],[[[]]]]]],[]] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1] => 3
[[[[[[[]]],[]]]],[]] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,3] => 3
[[[[[[],[],[]]]]],[]] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [7,2,1] => 4
[[[[[[],[[]]]]]],[]] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [7,1,1] => 3
[[[[[[[]],[]]]]],[]] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,2] => 3
[[[[[[[],[]]]]]],[]] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1] => 3
[[[[[[[[]]]]]]],[]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 2
[[[],[[],[[],[[]]]]]] => [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1] => 4
[[[],[[],[[[[]]]]]]] => [1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1] => 3
[[[],[[[[[]]]],[]]]] => [1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1,1] => 3
[[[],[[[],[[],[]]]]]] => [1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1] => 4
[[[],[[[],[[[]]]]]]] => [1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1] => 3
[[[],[[[[]],[[]]]]]] => [1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1] => 3
[[[],[[[[],[]],[]]]]] => [1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1,1] => 4
[[[],[[[[[]]],[]]]]] => [1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1] => 3
[[[],[[[[],[],[]]]]]] => [1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1] => 4
[[[],[[[[],[[]]]]]]] => [1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1] => 3
[[[],[[[[[]],[]]]]]] => [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1] => 3
[[[],[[[[[],[]]]]]]] => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1] => 3
[[[],[[[[[[]]]]]]]] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 2
[[[[]],[[[[[]]]]]]] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2] => 2
[[[[[[[]]]]],[[]]]] => [1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [5,5] => 2
[[[[],[[[[]]]]],[]]] => [1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1] => 3
[[[[[[]],[]],[]],[]]] => [1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [6,4,2] => 4
[[[[[[[]]]],[]],[]]] => [1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [6,4] => 3
[[[[[],[[],[]]]],[]]] => [1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1] => 4
[[[[[],[[[]]]]],[]]] => [1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1] => 3
[[[[[[]],[[]]]],[]]] => [1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [6,2,2] => 3
[[[[[[],[]],[]]],[]]] => [1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [6,3,1] => 4
[[[[[[[]]],[]]],[]]] => [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,3] => 3
[[[[[[],[],[]]]],[]]] => [1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [6,2,1] => 4
[[[[[[],[[]]]]],[]]] => [1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [6,1,1] => 3
[[[[[[[]],[]]]],[]]] => [1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,2] => 3
[[[[[[[],[]]]]],[]]] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,1] => 3
[[[[[[[[]]]]]],[]]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 2
[[[[],[],[],[],[],[]]]] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1] => 6
[[[[],[],[],[],[[]]]]] => [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1] => 5
[[[[],[],[],[[]],[]]]] => [1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1] => 5
[[[[],[],[],[[],[]]]]] => [1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1] => 5
[[[[],[],[],[[[]]]]]] => [1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1] => 4
[[[[],[],[[]],[],[]]]] => [1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,1] => 5
[[[[],[],[[]],[[]]]]] => [1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1] => 4
[[[[],[],[[],[]],[]]]] => [1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1] => 5
[[[[],[],[[[]]],[]]]] => [1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1] => 4
[[[[],[],[[],[],[]]]]] => [1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1] => 5
[[[[],[],[[],[[]]]]]] => [1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1] => 4
[[[[],[],[[[]],[]]]]] => [1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1] => 4
[[[[],[],[[[],[]]]]]] => [1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1] => 4
[[[[],[],[[[[]]]]]]] => [1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1] => 3
[[[[],[[]],[],[],[]]]] => [1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,1] => 5
[[[[],[[]],[],[[]]]]] => [1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1] => 4
[[[[],[[]],[[]],[]]]] => [1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1] => 4
[[[[],[[]],[[],[]]]]] => [1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1] => 4
[[[[],[[]],[[[]]]]]] => [1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1] => 3
[[[[],[[],[]],[],[]]]] => [1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,1] => 5
[[[[],[[[]]],[],[]]]] => [1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1,1] => 4
[[[[],[[],[]],[[]]]]] => [1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1] => 4
[[[[],[[[]]],[[]]]]] => [1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1] => 3
[[[[],[[],[],[]],[]]]] => [1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,1] => 5
[[[[],[[],[[]]],[]]]] => [1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1] => 4
[[[[],[[[]],[]],[]]]] => [1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1,1] => 4
[[[[],[[[],[]]],[]]]] => [1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1] => 4
[[[[],[[[[]]]],[]]]] => [1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1] => 3
[[[[],[[],[],[],[]]]]] => [1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1] => 5
[[[[],[[],[],[[]]]]]] => [1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1] => 4
[[[[],[[],[[]],[]]]]] => [1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1] => 4
[[[[],[[],[[],[]]]]]] => [1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1] => 4
[[[[],[[],[[[]]]]]]] => [1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1] => 3
[[[[],[[[]],[],[]]]]] => [1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1] => 4
[[[[],[[[]],[[]]]]]] => [1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1] => 3
[[[[],[[[],[]],[]]]]] => [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1] => 4
[[[[],[[[[]]],[]]]]] => [1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1] => 3
[[[[],[[[],[],[]]]]]] => [1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1] => 4
[[[[],[[[],[[]]]]]]] => [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1] => 3
[[[[],[[[[]],[]]]]]] => [1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1] => 3
[[[[],[[[[],[]]]]]]] => [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1] => 3
[[[[],[[[[[]]]]]]]] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1] => 2
[[[[[]],[],[],[],[]]]] => [1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2] => 5
[[[[[]],[],[],[[]]]]] => [1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2] => 4
[[[[[]],[],[[]],[]]]] => [1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2] => 4
[[[[[]],[],[[],[]]]]] => [1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2] => 4
[[[[[]],[],[[[]]]]]] => [1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2] => 3
[[[[[]],[[]],[],[]]]] => [1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2] => 4
[[[[[]],[[]],[[]]]]] => [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2] => 3
[[[[[]],[[],[]],[]]]] => [1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2] => 4
[[[[[]],[[[]]],[]]]] => [1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2] => 3
[[[[[]],[[],[],[]]]]] => [1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2] => 4
[[[[[]],[[],[[]]]]]] => [1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2] => 3
[[[[[]],[[[]],[]]]]] => [1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2] => 3
[[[[[]],[[[],[]]]]]] => [1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2] => 3
[[[[[]],[[[[]]]]]]] => [1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2] => 2
[[[[[],[]],[],[],[]]]] => [1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1] => 5
[[[[[[]]],[],[],[]]]] => [1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [5,4,3] => 4
[[[[[],[]],[],[[]]]]] => [1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1] => 4
[[[[[[]]],[],[[]]]]] => [1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [4,4,3] => 3
[[[[[],[]],[[]],[]]]] => [1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1] => 4
[[[[[[]]],[[]],[]]]] => [1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [5,3,3] => 3
[[[[[],[]],[[],[]]]]] => [1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1] => 4
[[[[[],[]],[[[]]]]]] => [1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1] => 3
[[[[[[]]],[[],[]]]]] => [1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [4,3,3] => 3
[[[[[[]]],[[[]]]]]] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [3,3,3] => 2
[[[[[],[],[]],[],[]]]] => [1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1] => 5
[[[[[],[[]]],[],[]]]] => [1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1] => 4
[[[[[[]],[]],[],[]]]] => [1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [5,4,2] => 4
[[[[[[],[]]],[],[]]]] => [1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [5,4,1] => 4
[[[[[[[]]]],[],[]]]] => [1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [5,4] => 3
[[[[[],[],[]],[[]]]]] => [1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1] => 4
[[[[[],[[]]],[[]]]]] => [1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1] => 3
[[[[[[]],[]],[[]]]]] => [1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [4,4,2] => 3
[[[[[[],[]]],[[]]]]] => [1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [4,4,1] => 3
[[[[[[[]]]],[[]]]]] => [1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [4,4] => 2
[[[[[],[],[],[]],[]]]] => [1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1] => 5
[[[[[],[],[[]]],[]]]] => [1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1] => 4
[[[[[],[[]],[]],[]]]] => [1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1] => 4
[[[[[],[[],[]]],[]]]] => [1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1] => 4
[[[[[],[[[]]]],[]]]] => [1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1] => 3
[[[[[[]],[],[]],[]]]] => [1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,3,2] => 4
[[[[[[]],[[]]],[]]]] => [1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [5,2,2] => 3
[[[[[[],[]],[]],[]]]] => [1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [5,3,1] => 4
[[[[[[[]]],[]],[]]]] => [1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [5,3] => 3
[[[[[[],[],[]]],[]]]] => [1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,2,1] => 4
[[[[[[],[[]]]],[]]]] => [1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [5,1,1] => 3
[[[[[[[]],[]]],[]]]] => [1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [5,2] => 3
[[[[[[[],[]]]],[]]]] => [1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [5,1] => 3
[[[[[[[[]]]]],[]]]] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [5] => 2
[[[[[],[],[],[],[]]]]] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1] => 5
[[[[[],[],[],[[]]]]]] => [1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1] => 4
[[[[[],[],[[]],[]]]]] => [1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1] => 4
[[[[[],[],[[],[]]]]]] => [1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1] => 4
[[[[[],[],[[[]]]]]]] => [1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1] => 3
[[[[[],[[]],[],[]]]]] => [1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1] => 4
[[[[[],[[]],[[]]]]]] => [1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1] => 3
[[[[[],[[],[]],[]]]]] => [1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1] => 4
[[[[[],[[[]]],[]]]]] => [1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1] => 3
[[[[[],[[],[],[]]]]]] => [1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1] => 4
[[[[[],[[],[[]]]]]]] => [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1] => 3
[[[[[],[[[]],[]]]]]] => [1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1] => 3
[[[[[],[[[],[]]]]]]] => [1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1] => 3
[[[[[],[[[[]]]]]]]] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1] => 2
[[[[[[]],[],[],[]]]]] => [1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [4,3,2] => 4
[[[[[[]],[],[[]]]]]] => [1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [3,3,2] => 3
[[[[[[]],[[]],[]]]]] => [1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [4,2,2] => 3
[[[[[[]],[[],[]]]]]] => [1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [3,2,2] => 3
[[[[[[]],[[[]]]]]]] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [2,2,2] => 2
[[[[[[],[]],[],[]]]]] => [1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [4,3,1] => 4
[[[[[[[]]],[],[]]]]] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [4,3] => 3
[[[[[[],[]],[[]]]]]] => [1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [3,3,1] => 3
[[[[[[[]]],[[]]]]]] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [3,3] => 2
[[[[[[],[],[]],[]]]]] => [1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [4,2,1] => 4
[[[[[[],[[]]],[]]]]] => [1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [4,1,1] => 3
[[[[[[[]],[]],[]]]]] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [4,2] => 3
[[[[[[[],[]]],[]]]]] => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [4,1] => 3
[[[[[[[[]]]],[]]]]] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4] => 2
[[[[[[],[],[],[]]]]]] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,2,1] => 4
[[[[[[],[],[[]]]]]]] => [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [2,2,1] => 3
[[[[[[],[[]],[]]]]]] => [1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [3,1,1] => 3
[[[[[[],[[],[]]]]]]] => [1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [2,1,1] => 3
[[[[[[],[[[]]]]]]]] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,1] => 2
[[[[[[[]],[],[]]]]]] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [3,2] => 3
[[[[[[[]],[[]]]]]]] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [2,2] => 2
[[[[[[[],[]],[]]]]]] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [3,1] => 3
[[[[[[[[]]],[]]]]]] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => 2
[[[[[[[],[],[]]]]]]] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => 3
[[[[[[[],[[]]]]]]]] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1] => 2
[[[[[[[[]],[]]]]]]] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => 2
[[[[[[[[],[]]]]]]]] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1] => 2
[[[[[[[[[]]]]]]]]] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [] => 1
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
click to show known generating functions       
Description
The number of addable cells of the Ferrers diagram of an integer partition.
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.
Map
to partition
Description
The cut-out partition of a Dyck path.
The partition $\lambda$ associated to a Dyck path is defined to be the complementary partition inside the staircase partition $(n-1,\ldots,2,1)$ when cutting out $D$ considered as a path from $(0,0)$ to $(n,n)$.
In other words, $\lambda_{i}$ is the number of down-steps before the $(n+1-i)$-th up-step of $D$.
This map is a bijection between Dyck paths of size $n$ and partitions inside the staircase partition $(n-1,\ldots,2,1)$.