Identifier
Values
[] => [] => [] => [] => 0
[[]] => [1,0] => [] => [] => 0
[[],[]] => [1,0,1,0] => [1] => [1] => 0
[[[]]] => [1,1,0,0] => [] => [] => 0
[[],[],[]] => [1,0,1,0,1,0] => [2,1] => [3] => 1
[[],[[]]] => [1,0,1,1,0,0] => [1,1] => [2] => 1
[[[]],[]] => [1,1,0,0,1,0] => [2] => [1,1] => 0
[[[],[]]] => [1,1,0,1,0,0] => [1] => [1] => 0
[[[[]]]] => [1,1,1,0,0,0] => [] => [] => 0
[[],[],[],[]] => [1,0,1,0,1,0,1,0] => [3,2,1] => [5,1] => 1
[[],[],[[]]] => [1,0,1,0,1,1,0,0] => [2,2,1] => [2,2,1] => 1
[[],[[]],[]] => [1,0,1,1,0,0,1,0] => [3,1,1] => [4,1] => 1
[[],[[],[]]] => [1,0,1,1,0,1,0,0] => [2,1,1] => [2,2] => 1
[[],[[[]]]] => [1,0,1,1,1,0,0,0] => [1,1,1] => [2,1] => 1
[[[]],[],[]] => [1,1,0,0,1,0,1,0] => [3,2] => [5] => 1
[[[]],[[]]] => [1,1,0,0,1,1,0,0] => [2,2] => [4] => 1
[[[],[]],[]] => [1,1,0,1,0,0,1,0] => [3,1] => [2,1,1] => 1
[[[[]]],[]] => [1,1,1,0,0,0,1,0] => [3] => [1,1,1] => 0
[[[],[],[]]] => [1,1,0,1,0,1,0,0] => [2,1] => [3] => 1
[[[],[[]]]] => [1,1,0,1,1,0,0,0] => [1,1] => [2] => 1
[[[[]],[]]] => [1,1,1,0,0,1,0,0] => [2] => [1,1] => 0
[[[[],[]]]] => [1,1,1,0,1,0,0,0] => [1] => [1] => 0
[[[[[]]]]] => [1,1,1,1,0,0,0,0] => [] => [] => 0
[[],[],[],[],[]] => [1,0,1,0,1,0,1,0,1,0] => [4,3,2,1] => [7,3] => 2
[[],[],[],[[]]] => [1,0,1,0,1,0,1,1,0,0] => [3,3,2,1] => [3,2,2,2] => 1
[[],[],[[]],[]] => [1,0,1,0,1,1,0,0,1,0] => [4,2,2,1] => [6,3] => 2
[[],[],[[],[]]] => [1,0,1,0,1,1,0,1,0,0] => [3,2,2,1] => [3,2,2,1] => 2
[[],[],[[[]]]] => [1,0,1,0,1,1,1,0,0,0] => [2,2,2,1] => [4,1,1,1] => 1
[[],[[]],[],[]] => [1,0,1,1,0,0,1,0,1,0] => [4,3,1,1] => [7,2] => 2
[[],[[]],[[]]] => [1,0,1,1,0,0,1,1,0,0] => [3,3,1,1] => [6,2] => 2
[[],[[],[]],[]] => [1,0,1,1,0,1,0,0,1,0] => [4,2,1,1] => [4,4] => 1
[[],[[[]]],[]] => [1,0,1,1,1,0,0,0,1,0] => [4,1,1,1] => [3,2,1,1] => 2
[[],[[],[],[]]] => [1,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => [5,2] => 2
[[],[[],[[]]]] => [1,0,1,1,0,1,1,0,0,0] => [2,2,1,1] => [4,1,1] => 1
[[],[[[]],[]]] => [1,0,1,1,1,0,0,1,0,0] => [3,1,1,1] => [3,3] => 1
[[],[[[],[]]]] => [1,0,1,1,1,0,1,0,0,0] => [2,1,1,1] => [3,1,1] => 1
[[],[[[[]]]]] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => [3,1] => 1
[[[]],[],[],[]] => [1,1,0,0,1,0,1,0,1,0] => [4,3,2] => [7,1,1] => 1
[[[]],[],[[]]] => [1,1,0,0,1,0,1,1,0,0] => [3,3,2] => [2,2,2,2] => 1
[[[]],[[]],[]] => [1,1,0,0,1,1,0,0,1,0] => [4,2,2] => [6,1,1] => 1
[[[]],[[],[]]] => [1,1,0,0,1,1,0,1,0,0] => [3,2,2] => [2,2,2,1] => 1
[[[]],[[[]]]] => [1,1,0,0,1,1,1,0,0,0] => [2,2,2] => [2,2,2] => 1
[[[],[]],[],[]] => [1,1,0,1,0,0,1,0,1,0] => [4,3,1] => [7,1] => 1
[[[[]]],[],[]] => [1,1,1,0,0,0,1,0,1,0] => [4,3] => [7] => 1
[[[],[]],[[]]] => [1,1,0,1,0,0,1,1,0,0] => [3,3,1] => [6,1] => 1
[[[[]]],[[]]] => [1,1,1,0,0,0,1,1,0,0] => [3,3] => [6] => 1
[[[],[],[]],[]] => [1,1,0,1,0,1,0,0,1,0] => [4,2,1] => [5,1,1] => 1
[[[],[[]]],[]] => [1,1,0,1,1,0,0,0,1,0] => [4,1,1] => [3,1,1,1] => 1
[[[[]],[]],[]] => [1,1,1,0,0,1,0,0,1,0] => [4,2] => [2,2,1,1] => 1
[[[[],[]]],[]] => [1,1,1,0,1,0,0,0,1,0] => [4,1] => [2,1,1,1] => 1
[[[[[]]]],[]] => [1,1,1,1,0,0,0,0,1,0] => [4] => [1,1,1,1] => 0
[[[],[],[],[]]] => [1,1,0,1,0,1,0,1,0,0] => [3,2,1] => [5,1] => 1
[[[],[],[[]]]] => [1,1,0,1,0,1,1,0,0,0] => [2,2,1] => [2,2,1] => 1
[[[],[[]],[]]] => [1,1,0,1,1,0,0,1,0,0] => [3,1,1] => [4,1] => 1
[[[],[[],[]]]] => [1,1,0,1,1,0,1,0,0,0] => [2,1,1] => [2,2] => 1
[[[],[[[]]]]] => [1,1,0,1,1,1,0,0,0,0] => [1,1,1] => [2,1] => 1
[[[[]],[],[]]] => [1,1,1,0,0,1,0,1,0,0] => [3,2] => [5] => 1
[[[[]],[[]]]] => [1,1,1,0,0,1,1,0,0,0] => [2,2] => [4] => 1
[[[[],[]],[]]] => [1,1,1,0,1,0,0,1,0,0] => [3,1] => [2,1,1] => 1
[[[[[]]],[]]] => [1,1,1,1,0,0,0,1,0,0] => [3] => [1,1,1] => 0
[[[[],[],[]]]] => [1,1,1,0,1,0,1,0,0,0] => [2,1] => [3] => 1
[[[[],[[]]]]] => [1,1,1,0,1,1,0,0,0,0] => [1,1] => [2] => 1
[[[[[]],[]]]] => [1,1,1,1,0,0,1,0,0,0] => [2] => [1,1] => 0
[[[[[],[]]]]] => [1,1,1,1,0,1,0,0,0,0] => [1] => [1] => 0
[[[[[[]]]]]] => [1,1,1,1,1,0,0,0,0,0] => [] => [] => 0
[[],[],[],[[[]]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => [3,3,3,2,1] => [6,2,1,1,1,1] => 2
[[],[],[[[]]],[]] => [1,0,1,0,1,1,1,0,0,0,1,0] => [5,2,2,2,1] => [7,2,2,1] => 2
[[],[],[[],[],[]]] => [1,0,1,0,1,1,0,1,0,1,0,0] => [4,3,2,2,1] => [6,2,2,1,1] => 2
[[],[],[[],[[]]]] => [1,0,1,0,1,1,0,1,1,0,0,0] => [3,3,2,2,1] => [6,2,1,1,1] => 2
[[],[],[[[]],[]]] => [1,0,1,0,1,1,1,0,0,1,0,0] => [4,2,2,2,1] => [3,3,3,1,1] => 1
[[],[],[[[],[]]]] => [1,0,1,0,1,1,1,0,1,0,0,0] => [3,2,2,2,1] => [5,2,1,1,1] => 2
[[],[],[[[[]]]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => [2,2,2,2,1] => [5,4] => 1
[[],[[]],[[],[]]] => [1,0,1,1,0,0,1,1,0,1,0,0] => [4,3,3,1,1] => [4,2,2,2,2] => 2
[[],[[]],[[[]]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => [3,3,3,1,1] => [4,2,2,2,1] => 2
[[],[[[]]],[],[]] => [1,0,1,1,1,0,0,0,1,0,1,0] => [5,4,1,1,1] => [9,2,1] => 2
[[],[[],[]],[[]]] => [1,0,1,1,0,1,0,0,1,1,0,0] => [4,4,2,1,1] => [8,2,2] => 2
[[],[[[]]],[[]]] => [1,0,1,1,1,0,0,0,1,1,0,0] => [4,4,1,1,1] => [8,2,1] => 2
[[],[[],[],[]],[]] => [1,0,1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,1] => [7,4,1] => 2
[[],[[],[[]]],[]] => [1,0,1,1,0,1,1,0,0,0,1,0] => [5,2,2,1,1] => [6,2,2,1] => 2
[[],[[[]],[]],[]] => [1,0,1,1,1,0,0,1,0,0,1,0] => [5,3,1,1,1] => [5,5,1] => 1
[[],[[[],[]]],[]] => [1,0,1,1,1,0,1,0,0,0,1,0] => [5,2,1,1,1] => [4,2,2,1,1] => 2
[[],[[[[]]]],[]] => [1,0,1,1,1,1,0,0,0,0,1,0] => [5,1,1,1,1] => [4,2,1,1,1] => 2
[[],[[],[],[],[]]] => [1,0,1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,1] => [7,2,2] => 2
[[],[[],[],[[]]]] => [1,0,1,1,0,1,0,1,1,0,0,0] => [3,3,2,1,1] => [6,2,2] => 2
[[],[[],[[]],[]]] => [1,0,1,1,0,1,1,0,0,1,0,0] => [4,2,2,1,1] => [3,3,2,2] => 1
[[],[[],[[],[]]]] => [1,0,1,1,0,1,1,0,1,0,0,0] => [3,2,2,1,1] => [3,3,3] => 1
[[],[[],[[[]]]]] => [1,0,1,1,0,1,1,1,0,0,0,0] => [2,2,2,1,1] => [5,3] => 2
[[],[[[]],[],[]]] => [1,0,1,1,1,0,0,1,0,1,0,0] => [4,3,1,1,1] => [7,2,1] => 2
[[],[[[]],[[]]]] => [1,0,1,1,1,0,0,1,1,0,0,0] => [3,3,1,1,1] => [5,2,1,1] => 2
[[],[[[],[]],[]]] => [1,0,1,1,1,0,1,0,0,1,0,0] => [4,2,1,1,1] => [6,2,1] => 2
[[],[[[[]]],[]]] => [1,0,1,1,1,1,0,0,0,1,0,0] => [4,1,1,1,1] => [5,2,1] => 2
[[],[[[],[],[]]]] => [1,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,1,1] => [3,3,1,1] => 1
[[],[[[],[[]]]]] => [1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => [4,3] => 1
[[],[[[[]],[]]]] => [1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,1,1,1] => [3,2,2] => 1
[[],[[[[],[]]]]] => [1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => [4,2] => 2
[[],[[[[[]]]]]] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => [3,2] => 1
[[[]],[],[[],[]]] => [1,1,0,0,1,0,1,1,0,1,0,0] => [4,3,3,2] => [3,3,2,2,2] => 1
[[[]],[],[[[]]]] => [1,1,0,0,1,0,1,1,1,0,0,0] => [3,3,3,2] => [6,1,1,1,1,1] => 1
[[[]],[[]],[[]]] => [1,1,0,0,1,1,0,0,1,1,0,0] => [4,4,2,2] => [8,4] => 2
[[[]],[[],[]],[]] => [1,1,0,0,1,1,0,1,0,0,1,0] => [5,3,2,2] => [6,6] => 1
[[[]],[[[]]],[]] => [1,1,0,0,1,1,1,0,0,0,1,0] => [5,2,2,2] => [7,4] => 2
>>> Load all 581 entries. <<<
[[[]],[[],[],[]]] => [1,1,0,0,1,1,0,1,0,1,0,0] => [4,3,2,2] => [3,3,2,2,1] => 2
[[[]],[[],[[]]]] => [1,1,0,0,1,1,0,1,1,0,0,0] => [3,3,2,2] => [6,1,1,1,1] => 1
[[[]],[[[]],[]]] => [1,1,0,0,1,1,1,0,0,1,0,0] => [4,2,2,2] => [5,5] => 1
[[[]],[[[],[]]]] => [1,1,0,0,1,1,1,0,1,0,0,0] => [3,2,2,2] => [5,1,1,1,1] => 1
[[[]],[[[[]]]]] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,2,2,2] => [5,1,1,1] => 1
[[[[]]],[],[],[]] => [1,1,1,0,0,0,1,0,1,0,1,0] => [5,4,3] => [9,1,1,1] => 1
[[[],[]],[],[[]]] => [1,1,0,1,0,0,1,0,1,1,0,0] => [4,4,3,1] => [3,2,2,2,2,1] => 2
[[[[]]],[],[[]]] => [1,1,1,0,0,0,1,0,1,1,0,0] => [4,4,3] => [2,2,2,2,2,1] => 1
[[[],[]],[[]],[]] => [1,1,0,1,0,0,1,1,0,0,1,0] => [5,3,3,1] => [8,2,1,1] => 2
[[[[]]],[[]],[]] => [1,1,1,0,0,0,1,1,0,0,1,0] => [5,3,3] => [8,1,1,1] => 1
[[[],[]],[[],[]]] => [1,1,0,1,0,0,1,1,0,1,0,0] => [4,3,3,1] => [3,2,2,2,2] => 1
[[[],[]],[[[]]]] => [1,1,0,1,0,0,1,1,1,0,0,0] => [3,3,3,1] => [3,2,2,2,1] => 2
[[[[]]],[[],[]]] => [1,1,1,0,0,0,1,1,0,1,0,0] => [4,3,3] => [2,2,2,2,2] => 1
[[[[]]],[[[]]]] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,3,3] => [2,2,2,2,1] => 1
[[[],[],[]],[],[]] => [1,1,0,1,0,1,0,0,1,0,1,0] => [5,4,2,1] => [9,3] => 2
[[[],[[]]],[],[]] => [1,1,0,1,1,0,0,0,1,0,1,0] => [5,4,1,1] => [9,2] => 2
[[[[]],[]],[],[]] => [1,1,1,0,0,1,0,0,1,0,1,0] => [5,4,2] => [9,1,1] => 1
[[[[],[]]],[],[]] => [1,1,1,0,1,0,0,0,1,0,1,0] => [5,4,1] => [9,1] => 1
[[[[[]]]],[],[]] => [1,1,1,1,0,0,0,0,1,0,1,0] => [5,4] => [9] => 1
[[[],[],[]],[[]]] => [1,1,0,1,0,1,0,0,1,1,0,0] => [4,4,2,1] => [8,3] => 2
[[[],[[]]],[[]]] => [1,1,0,1,1,0,0,0,1,1,0,0] => [4,4,1,1] => [8,2] => 2
[[[[]],[]],[[]]] => [1,1,1,0,0,1,0,0,1,1,0,0] => [4,4,2] => [8,1,1] => 1
[[[[],[]]],[[]]] => [1,1,1,0,1,0,0,0,1,1,0,0] => [4,4,1] => [8,1] => 1
[[[[[]]]],[[]]] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,4] => [8] => 1
[[[],[],[],[]],[]] => [1,1,0,1,0,1,0,1,0,0,1,0] => [5,3,2,1] => [7,2,1,1] => 2
[[[],[],[[]]],[]] => [1,1,0,1,0,1,1,0,0,0,1,0] => [5,2,2,1] => [3,3,2,1,1] => 2
[[[],[[]],[]],[]] => [1,1,0,1,1,0,0,1,0,0,1,0] => [5,3,1,1] => [6,2,1,1] => 2
[[[],[[],[]]],[]] => [1,1,0,1,1,0,1,0,0,0,1,0] => [5,2,1,1] => [3,3,1,1,1] => 1
[[[],[[[]]]],[]] => [1,1,0,1,1,1,0,0,0,0,1,0] => [5,1,1,1] => [3,2,1,1,1] => 2
[[[[]],[],[]],[]] => [1,1,1,0,0,1,0,1,0,0,1,0] => [5,3,2] => [7,1,1,1] => 1
[[[[]],[[]]],[]] => [1,1,1,0,0,1,1,0,0,0,1,0] => [5,2,2] => [6,1,1,1] => 1
[[[[],[]],[]],[]] => [1,1,1,0,1,0,0,1,0,0,1,0] => [5,3,1] => [3,2,2,1,1] => 2
[[[[[]]],[]],[]] => [1,1,1,1,0,0,0,1,0,0,1,0] => [5,3] => [2,2,2,1,1] => 1
[[[[],[],[]]],[]] => [1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,1] => [4,1,1,1,1] => 1
[[[[],[[]]]],[]] => [1,1,1,0,1,1,0,0,0,0,1,0] => [5,1,1] => [3,1,1,1,1] => 1
[[[[[]],[]]],[]] => [1,1,1,1,0,0,1,0,0,0,1,0] => [5,2] => [2,2,1,1,1] => 1
[[[[[],[]]]],[]] => [1,1,1,1,0,1,0,0,0,0,1,0] => [5,1] => [2,1,1,1,1] => 1
[[[[[[]]]]],[]] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5] => [1,1,1,1,1] => 0
[[[],[],[],[],[]]] => [1,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,1] => [7,3] => 2
[[[],[],[],[[]]]] => [1,1,0,1,0,1,0,1,1,0,0,0] => [3,3,2,1] => [3,2,2,2] => 1
[[[],[],[[]],[]]] => [1,1,0,1,0,1,1,0,0,1,0,0] => [4,2,2,1] => [6,3] => 2
[[[],[],[[],[]]]] => [1,1,0,1,0,1,1,0,1,0,0,0] => [3,2,2,1] => [3,2,2,1] => 2
[[[],[],[[[]]]]] => [1,1,0,1,0,1,1,1,0,0,0,0] => [2,2,2,1] => [4,1,1,1] => 1
[[[],[[]],[],[]]] => [1,1,0,1,1,0,0,1,0,1,0,0] => [4,3,1,1] => [7,2] => 2
[[[],[[]],[[]]]] => [1,1,0,1,1,0,0,1,1,0,0,0] => [3,3,1,1] => [6,2] => 2
[[[],[[],[]],[]]] => [1,1,0,1,1,0,1,0,0,1,0,0] => [4,2,1,1] => [4,4] => 1
[[[],[[[]]],[]]] => [1,1,0,1,1,1,0,0,0,1,0,0] => [4,1,1,1] => [3,2,1,1] => 2
[[[],[[],[],[]]]] => [1,1,0,1,1,0,1,0,1,0,0,0] => [3,2,1,1] => [5,2] => 2
[[[],[[],[[]]]]] => [1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,1,1] => [4,1,1] => 1
[[[],[[[]],[]]]] => [1,1,0,1,1,1,0,0,1,0,0,0] => [3,1,1,1] => [3,3] => 1
[[[],[[[],[]]]]] => [1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,1,1] => [3,1,1] => 1
[[[],[[[[]]]]]] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1] => [3,1] => 1
[[[[]],[],[],[]]] => [1,1,1,0,0,1,0,1,0,1,0,0] => [4,3,2] => [7,1,1] => 1
[[[[]],[],[[]]]] => [1,1,1,0,0,1,0,1,1,0,0,0] => [3,3,2] => [2,2,2,2] => 1
[[[[]],[[]],[]]] => [1,1,1,0,0,1,1,0,0,1,0,0] => [4,2,2] => [6,1,1] => 1
[[[[]],[[],[]]]] => [1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,2] => [2,2,2,1] => 1
[[[[]],[[[]]]]] => [1,1,1,0,0,1,1,1,0,0,0,0] => [2,2,2] => [2,2,2] => 1
[[[[],[]],[],[]]] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,3,1] => [7,1] => 1
[[[[[]]],[],[]]] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3] => [7] => 1
[[[[],[]],[[]]]] => [1,1,1,0,1,0,0,1,1,0,0,0] => [3,3,1] => [6,1] => 1
[[[[[]]],[[]]]] => [1,1,1,1,0,0,0,1,1,0,0,0] => [3,3] => [6] => 1
[[[[],[],[]],[]]] => [1,1,1,0,1,0,1,0,0,1,0,0] => [4,2,1] => [5,1,1] => 1
[[[[],[[]]],[]]] => [1,1,1,0,1,1,0,0,0,1,0,0] => [4,1,1] => [3,1,1,1] => 1
[[[[[]],[]],[]]] => [1,1,1,1,0,0,1,0,0,1,0,0] => [4,2] => [2,2,1,1] => 1
[[[[[],[]]],[]]] => [1,1,1,1,0,1,0,0,0,1,0,0] => [4,1] => [2,1,1,1] => 1
[[[[[[]]]],[]]] => [1,1,1,1,1,0,0,0,0,1,0,0] => [4] => [1,1,1,1] => 0
[[[[],[],[],[]]]] => [1,1,1,0,1,0,1,0,1,0,0,0] => [3,2,1] => [5,1] => 1
[[[[],[],[[]]]]] => [1,1,1,0,1,0,1,1,0,0,0,0] => [2,2,1] => [2,2,1] => 1
[[[[],[[]],[]]]] => [1,1,1,0,1,1,0,0,1,0,0,0] => [3,1,1] => [4,1] => 1
[[[[],[[],[]]]]] => [1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,1] => [2,2] => 1
[[[[],[[[]]]]]] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1] => [2,1] => 1
[[[[[]],[],[]]]] => [1,1,1,1,0,0,1,0,1,0,0,0] => [3,2] => [5] => 1
[[[[[]],[[]]]]] => [1,1,1,1,0,0,1,1,0,0,0,0] => [2,2] => [4] => 1
[[[[[],[]],[]]]] => [1,1,1,1,0,1,0,0,1,0,0,0] => [3,1] => [2,1,1] => 1
[[[[[[]]],[]]]] => [1,1,1,1,1,0,0,0,1,0,0,0] => [3] => [1,1,1] => 0
[[[[[],[],[]]]]] => [1,1,1,1,0,1,0,1,0,0,0,0] => [2,1] => [3] => 1
[[[[[],[[]]]]]] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1] => [2] => 1
[[[[[[]],[]]]]] => [1,1,1,1,1,0,0,1,0,0,0,0] => [2] => [1,1] => 0
[[[[[[],[]]]]]] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1] => [1] => 0
[[[[[[[]]]]]]] => [1,1,1,1,1,1,0,0,0,0,0,0] => [] => [] => 0
[[],[],[[[[],[]]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2,1] => [6,5,1] => 1
[[],[],[[[[[]]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2,1] => [3,3,3,2] => 1
[[],[[[[],[]]]],[]] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1,1,1] => [5,3,1,1,1,1] => 2
[[],[[[[[]]]]],[]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1,1,1] => [4,3,1,1,1,1] => 1
[[],[[],[[],[[]]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => [7,3,1,1] => 2
[[],[[],[[[]],[]]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1,1] => [6,2,2,2] => 2
[[],[[],[[[],[]]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1,1] => [6,4,1] => 2
[[],[[],[[[[]]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1,1] => [3,3,3,1] => 1
[[],[[[]],[[[]]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1,1] => [4,3,2,2,1] => 3
[[],[[[[]]],[[]]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1,1] => [8,3,1] => 2
[[],[[[],[[]]],[]]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1,1] => [5,5,1,1] => 1
[[],[[[[]],[]],[]]] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1,1,1] => [4,4,4] => 1
[[],[[[[],[]]],[]]] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1,1,1] => [6,3,1,1] => 2
[[],[[[[[]]]],[]]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1,1] => [4,3,1,1,1] => 1
[[],[[[],[],[],[]]]] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,1,1] => [6,3,1,1,1] => 2
[[],[[[],[],[[]]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1,1] => [4,4,1,1,1] => 1
[[],[[[],[[]],[]]]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1,1] => [5,2,2,1,1] => 2
[[],[[[],[[],[]]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1,1] => [4,2,2,2] => 2
[[],[[[],[[[]]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1,1] => [3,3,2,1] => 2
[[],[[[[]],[],[]]]] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1,1,1] => [7,3,1] => 2
[[],[[[[]],[[]]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1,1] => [5,4,1] => 1
[[],[[[[],[]],[]]]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1,1] => [6,3,1] => 2
[[],[[[[[]]],[]]]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1,1] => [4,4,1] => 1
[[],[[[[],[],[]]]]] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1,1] => [5,2,2] => 2
[[],[[[[],[[]]]]]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1,1] => [3,3,2] => 1
[[],[[[[[]],[]]]]] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1,1] => [4,2,1,1] => 2
[[],[[[[[],[]]]]]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => [3,3,1] => 1
[[],[[[[[[]]]]]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => [3,2,1] => 2
[[[]],[[[],[[]]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2] => [7,5] => 2
[[[]],[[[[]],[]]]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [4,2,2,2,2] => [3,3,3,3] => 1
[[[]],[[[[],[]]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2] => [6,5] => 1
[[[]],[[[[[]]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2] => [6,4] => 2
[[[[]]],[[[[]]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3] => [7,1,1,1,1,1] => 1
[[[[[]]]],[[[]]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,4,4] => [2,2,2,2,2,2] => 1
[[[[[],[]]]],[],[]] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [6,5,1] => [11,1] => 1
[[[[[[]]]]],[],[]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,5] => [11] => 1
[[[[],[[]]]],[[]]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1] => [10,2] => 2
[[[[[]],[]]],[[]]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,5,2] => [10,1,1] => 1
[[[[[],[]]]],[[]]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,5,1] => [10,1] => 1
[[[[[[]]]]],[[]]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => [10] => 1
[[[],[[],[[]]]],[]] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1,1] => [5,2,2,1,1,1] => 2
[[[],[[[]],[]]],[]] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1,1] => [4,4,1,1,1,1] => 1
[[[],[[[],[]]]],[]] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1,1] => [4,2,2,1,1,1] => 2
[[[],[[[[]]]]],[]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1,1] => [4,2,1,1,1,1] => 2
[[[[]],[[[]]]],[]] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2] => [3,3,3,1,1,1] => 1
[[[[[]]],[[]]],[]] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [6,3,3] => [8,1,1,1,1] => 1
[[[[],[[]]],[]],[]] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [6,4,1,1] => [4,2,2,2,1,1] => 2
[[[[[]],[]],[]],[]] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [6,4,2] => [3,3,2,2,1,1] => 2
[[[[[],[]]],[]],[]] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [6,4,1] => [3,2,2,2,1,1] => 2
[[[[[[]]]],[]],[]] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [6,4] => [2,2,2,2,1,1] => 1
[[[[],[],[],[]]],[]] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1] => [7,2,1,1,1] => 2
[[[[],[],[[]]]],[]] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1] => [3,3,2,1,1,1] => 2
[[[[],[[]],[]]],[]] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1] => [5,2,1,1,1,1] => 2
[[[[],[[],[]]]],[]] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1] => [3,3,1,1,1,1] => 1
[[[[],[[[]]]]],[]] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1] => [3,2,1,1,1,1] => 2
[[[[[]],[],[]]],[]] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [6,3,2] => [7,1,1,1,1] => 1
[[[[[]],[[]]]],[]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,2,2] => [5,1,1,1,1,1] => 1
[[[[[],[]],[]]],[]] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,1] => [3,2,2,1,1,1] => 2
[[[[[[]]],[]]],[]] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,3] => [2,2,2,1,1,1] => 1
[[[[[],[],[]]]],[]] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,2,1] => [4,1,1,1,1,1] => 1
[[[[[],[[]]]]],[]] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,1,1] => [3,1,1,1,1,1] => 1
[[[[[[]],[]]]],[]] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,2] => [2,2,1,1,1,1] => 1
[[[[[[],[]]]]],[]] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1] => [2,1,1,1,1,1] => 1
[[[[[[[]]]]]],[]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => [1,1,1,1,1,1] => 0
[[[],[],[],[[[]]]]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1] => [6,2,1,1,1,1] => 2
[[[],[],[[[]]],[]]] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2,1] => [7,2,2,1] => 2
[[[],[],[[],[],[]]]] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1] => [6,2,2,1,1] => 2
[[[],[],[[],[[]]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1] => [6,2,1,1,1] => 2
[[[],[],[[[]],[]]]] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1] => [3,3,3,1,1] => 1
[[[],[],[[[],[]]]]] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1] => [5,2,1,1,1] => 2
[[[],[],[[[[]]]]]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1] => [5,4] => 1
[[[],[[]],[[],[]]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1] => [4,2,2,2,2] => 2
[[[],[[]],[[[]]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1] => [4,2,2,2,1] => 2
[[[],[[[]]],[],[]]] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1,1] => [9,2,1] => 2
[[[],[[],[]],[[]]]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1] => [8,2,2] => 2
[[[],[[[]]],[[]]]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1] => [8,2,1] => 2
[[[],[[],[],[]],[]]] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,1] => [7,4,1] => 2
[[[],[[],[[]]],[]]] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1] => [6,2,2,1] => 2
[[[],[[[]],[]],[]]] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1,1] => [5,5,1] => 1
[[[],[[[],[]]],[]]] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1,1] => [4,2,2,1,1] => 2
[[[],[[[[]]]],[]]] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1] => [4,2,1,1,1] => 2
[[[],[[],[],[],[]]]] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,1] => [7,2,2] => 2
[[[],[[],[],[[]]]]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1] => [6,2,2] => 2
[[[],[[],[[]],[]]]] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1] => [3,3,2,2] => 1
[[[],[[],[[],[]]]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1] => [3,3,3] => 1
[[[],[[],[[[]]]]]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1] => [5,3] => 2
[[[],[[[]],[],[]]]] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1,1] => [7,2,1] => 2
[[[],[[[]],[[]]]]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1] => [5,2,1,1] => 2
[[[],[[[],[]],[]]]] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1] => [6,2,1] => 2
[[[],[[[[]]],[]]]] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1] => [5,2,1] => 2
[[[],[[[],[],[]]]]] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1] => [3,3,1,1] => 1
[[[],[[[],[[]]]]]] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1] => [4,3] => 1
[[[],[[[[]],[]]]]] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1] => [3,2,2] => 1
[[[],[[[[],[]]]]]] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1] => [4,2] => 2
[[[],[[[[[]]]]]]] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1] => [3,2] => 1
[[[[]],[],[[],[]]]] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2] => [3,3,2,2,2] => 1
[[[[]],[],[[[]]]]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2] => [6,1,1,1,1,1] => 1
[[[[]],[[]],[[]]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2] => [8,4] => 2
[[[[]],[[],[]],[]]] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2] => [6,6] => 1
[[[[]],[[[]]],[]]] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2] => [7,4] => 2
[[[[]],[[],[],[]]]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2] => [3,3,2,2,1] => 2
[[[[]],[[],[[]]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2] => [6,1,1,1,1] => 1
[[[[]],[[[]],[]]]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2] => [5,5] => 1
[[[[]],[[[],[]]]]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2] => [5,1,1,1,1] => 1
[[[[]],[[[[]]]]]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2] => [5,1,1,1] => 1
[[[[[]]],[],[],[]]] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [5,4,3] => [9,1,1,1] => 1
[[[[],[]],[],[[]]]] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1] => [3,2,2,2,2,1] => 2
[[[[[]]],[],[[]]]] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,4,3] => [2,2,2,2,2,1] => 1
[[[[],[]],[[]],[]]] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1] => [8,2,1,1] => 2
[[[[[]]],[[]],[]]] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [5,3,3] => [8,1,1,1] => 1
[[[[],[]],[[],[]]]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1] => [3,2,2,2,2] => 1
[[[[],[]],[[[]]]]] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1] => [3,2,2,2,1] => 2
[[[[[]]],[[],[]]]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,3] => [2,2,2,2,2] => 1
[[[[[]]],[[[]]]]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [3,3,3] => [2,2,2,2,1] => 1
[[[[],[],[]],[],[]]] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1] => [9,3] => 2
[[[[],[[]]],[],[]]] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1] => [9,2] => 2
[[[[[]],[]],[],[]]] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [5,4,2] => [9,1,1] => 1
[[[[[],[]]],[],[]]] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,4,1] => [9,1] => 1
[[[[[[]]]],[],[]]] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4] => [9] => 1
[[[[],[],[]],[[]]]] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1] => [8,3] => 2
[[[[],[[]]],[[]]]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1] => [8,2] => 2
[[[[[]],[]],[[]]]] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,4,2] => [8,1,1] => 1
[[[[[],[]]],[[]]]] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,4,1] => [8,1] => 1
[[[[[[]]]],[[]]]] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [4,4] => [8] => 1
[[[[],[],[],[]],[]]] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1] => [7,2,1,1] => 2
[[[[],[],[[]]],[]]] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1] => [3,3,2,1,1] => 2
[[[[],[[]],[]],[]]] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1] => [6,2,1,1] => 2
[[[[],[[],[]]],[]]] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1] => [3,3,1,1,1] => 1
[[[[],[[[]]]],[]]] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1] => [3,2,1,1,1] => 2
[[[[[]],[],[]],[]]] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [5,3,2] => [7,1,1,1] => 1
[[[[[]],[[]]],[]]] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [5,2,2] => [6,1,1,1] => 1
[[[[[],[]],[]],[]]] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [5,3,1] => [3,2,2,1,1] => 2
[[[[[[]]],[]],[]]] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,3] => [2,2,2,1,1] => 1
[[[[[],[],[]]],[]]] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [5,2,1] => [4,1,1,1,1] => 1
[[[[[],[[]]]],[]]] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [5,1,1] => [3,1,1,1,1] => 1
[[[[[[]],[]]],[]]] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,2] => [2,2,1,1,1] => 1
[[[[[[],[]]]],[]]] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,1] => [2,1,1,1,1] => 1
[[[[[[[]]]]],[]]] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => [1,1,1,1,1] => 0
[[[[],[],[],[],[]]]] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1] => [7,3] => 2
[[[[],[],[],[[]]]]] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1] => [3,2,2,2] => 1
[[[[],[],[[]],[]]]] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1] => [6,3] => 2
[[[[],[],[[],[]]]]] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => [3,2,2,1] => 2
[[[[],[],[[[]]]]]] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1] => [4,1,1,1] => 1
[[[[],[[]],[],[]]]] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1] => [7,2] => 2
[[[[],[[]],[[]]]]] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1] => [6,2] => 2
[[[[],[[],[]],[]]]] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1] => [4,4] => 1
[[[[],[[[]]],[]]]] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1] => [3,2,1,1] => 2
[[[[],[[],[],[]]]]] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1] => [5,2] => 2
[[[[],[[],[[]]]]]] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1] => [4,1,1] => 1
[[[[],[[[]],[]]]]] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1] => [3,3] => 1
[[[[],[[[],[]]]]]] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1] => [3,1,1] => 1
[[[[],[[[[]]]]]]] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1] => [3,1] => 1
[[[[[]],[],[],[]]]] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,3,2] => [7,1,1] => 1
[[[[[]],[],[[]]]]] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [3,3,2] => [2,2,2,2] => 1
[[[[[]],[[]],[]]]] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,2,2] => [6,1,1] => 1
[[[[[]],[[],[]]]]] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [3,2,2] => [2,2,2,1] => 1
[[[[[]],[[[]]]]]] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,2,2] => [2,2,2] => 1
[[[[[],[]],[],[]]]] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,3,1] => [7,1] => 1
[[[[[[]]],[],[]]]] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [4,3] => [7] => 1
[[[[[],[]],[[]]]]] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [3,3,1] => [6,1] => 1
[[[[[[]]],[[]]]]] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [3,3] => [6] => 1
[[[[[],[],[]],[]]]] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,2,1] => [5,1,1] => 1
[[[[[],[[]]],[]]]] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,1,1] => [3,1,1,1] => 1
[[[[[[]],[]],[]]]] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [4,2] => [2,2,1,1] => 1
[[[[[[],[]]],[]]]] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [4,1] => [2,1,1,1] => 1
[[[[[[[]]]],[]]]] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [4] => [1,1,1,1] => 0
[[[[[],[],[],[]]]]] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1] => [5,1] => 1
[[[[[],[],[[]]]]]] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,2,1] => [2,2,1] => 1
[[[[[],[[]],[]]]]] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [3,1,1] => [4,1] => 1
[[[[[],[[],[]]]]]] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,1,1] => [2,2] => 1
[[[[[],[[[]]]]]]] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1] => [2,1] => 1
[[[[[[]],[],[]]]]] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [3,2] => [5] => 1
[[[[[[]],[[]]]]]] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,2] => [4] => 1
[[[[[[],[]],[]]]]] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [3,1] => [2,1,1] => 1
[[[[[[[]]],[]]]]] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3] => [1,1,1] => 0
[[[[[[],[],[]]]]]] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,1] => [3] => 1
[[[[[[],[[]]]]]]] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1] => [2] => 1
[[[[[[[]],[]]]]]] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2] => [1,1] => 0
[[[[[[[],[]]]]]]] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1] => [1] => 0
[[[[[[[[]]]]]]]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [] => [] => 0
[[],[[],[[[[[]]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1,1] => [5,2,2,2,1] => 2
[[],[[[[[[]]]]],[]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1,1,1] => [4,3,2,1,1,1] => 3
[[],[[[],[[[],[]]]]]] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1,1,1] => [6,4,1,1] => 2
[[],[[[],[[[[]]]]]]] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1,1] => [5,2,2,2] => 2
[[],[[[[[],[]]],[]]]] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1,1,1] => [5,5,2] => 2
[[],[[[[[[]]]],[]]]] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1,1,1] => [4,3,2,1,1] => 3
[[],[[[[],[],[[]]]]]] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1,1,1] => [6,3,3] => 2
[[],[[[[],[[]],[]]]]] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1,1,1] => [4,3,3,1,1] => 1
[[],[[[[],[[],[]]]]]] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1,1] => [5,3,1,1,1] => 2
[[],[[[[],[[[]]]]]]] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1,1] => [5,2,2,1] => 2
[[],[[[[[]],[],[]]]]] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1,1,1] => [7,3,2] => 2
[[],[[[[[]],[[]]]]]] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1,1] => [4,4,3] => 1
[[],[[[[[],[]],[]]]]] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1,1,1] => [6,3,2] => 2
[[],[[[[[[]]],[]]]]] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1,1] => [4,3,3] => 1
[[],[[[[[],[],[]]]]]] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1,1] => [4,4,1,1] => 1
[[],[[[[[],[[]]]]]]] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1,1] => [4,2,2,1] => 2
[[],[[[[[[]],[]]]]]] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1,1] => [5,3,1] => 2
[[],[[[[[[],[]]]]]]] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => [4,2,2] => 2
[[],[[[[[[[]]]]]]]] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => [4,2,1] => 2
[[[]],[[[[[[]]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2] => [3,3,3,2,1] => 2
[[[[[[[]]]]]],[[]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,6] => [12] => 1
[[[],[[[[[]]]]]],[]] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1,1,1] => [4,3,1,1,1,1,1] => 1
[[[[[[[]]]]],[]],[]] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [7,5] => [2,2,2,2,2,1,1] => 1
[[[[],[[[],[]]]]],[]] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,1,1] => [4,2,2,1,1,1,1] => 2
[[[[],[[[[]]]]]],[]] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1,1] => [4,2,1,1,1,1,1] => 2
[[[[[[],[]]],[]]],[]] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [7,4,1] => [3,2,2,2,1,1,1] => 2
[[[[[[[]]]],[]]],[]] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [7,4] => [2,2,2,2,1,1,1] => 1
[[[[[],[],[[]]]]],[]] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1] => [3,3,2,1,1,1,1] => 2
[[[[[],[[]],[]]]],[]] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,1] => [5,2,1,1,1,1,1] => 2
[[[[[],[[],[]]]]],[]] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,1] => [3,3,1,1,1,1,1] => 1
[[[[[],[[[]]]]]],[]] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1] => [3,2,1,1,1,1,1] => 2
[[[[[[]],[],[]]]],[]] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [7,3,2] => [6,1,1,1,1,1,1] => 1
[[[[[[]],[[]]]]],[]] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [7,2,2] => [5,1,1,1,1,1,1] => 1
[[[[[[],[]],[]]]],[]] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [7,3,1] => [3,2,2,1,1,1,1] => 2
[[[[[[[]]],[]]]],[]] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,3] => [2,2,2,1,1,1,1] => 1
[[[[[[],[],[]]]]],[]] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [7,2,1] => [4,1,1,1,1,1,1] => 1
[[[[[[],[[]]]]]],[]] => [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] => 1
[[[[[[[]],[]]]]],[]] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,2] => [2,2,1,1,1,1,1] => 1
[[[[[[[],[]]]]]],[]] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => 1
[[[[[[[[]]]]]]],[]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => [1,1,1,1,1,1,1] => 0
[[[],[],[[[[],[]]]]]] => [1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,1] => [6,5,1] => 1
[[[],[],[[[[[]]]]]]] => [1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1] => [3,3,3,2] => 1
[[[],[[[[],[]]]],[]]] => [1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1,1,1] => [5,3,1,1,1,1] => 2
[[[],[[[[[]]]]],[]]] => [1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1,1] => [4,3,1,1,1,1] => 1
[[[],[[],[[],[[]]]]]] => [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1] => [7,3,1,1] => 2
[[[],[[],[[[]],[]]]]] => [1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1,1] => [6,2,2,2] => 2
[[[],[[],[[[],[]]]]]] => [1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1,1] => [6,4,1] => 2
[[[],[[],[[[[]]]]]]] => [1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1] => [3,3,3,1] => 1
[[[],[[[]],[[[]]]]]] => [1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1] => [4,3,2,2,1] => 3
[[[],[[[[]]],[[]]]]] => [1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1,1] => [8,3,1] => 2
[[[],[[[],[[]]],[]]]] => [1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1,1] => [5,5,1,1] => 1
[[[],[[[[]],[]],[]]]] => [1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1,1,1] => [4,4,4] => 1
[[[],[[[[],[]]],[]]]] => [1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1,1] => [6,3,1,1] => 2
[[[],[[[[[]]]],[]]]] => [1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1,1] => [4,3,1,1,1] => 1
[[[],[[[],[],[],[]]]]] => [1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1,1] => [6,3,1,1,1] => 2
[[[],[[[],[],[[]]]]]] => [1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1,1] => [4,4,1,1,1] => 1
[[[],[[[],[[]],[]]]]] => [1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1,1] => [5,2,2,1,1] => 2
[[[],[[[],[[],[]]]]]] => [1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1] => [4,2,2,2] => 2
[[[],[[[],[[[]]]]]]] => [1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1] => [3,3,2,1] => 2
[[[],[[[[]],[],[]]]]] => [1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1,1] => [7,3,1] => 2
[[[],[[[[]],[[]]]]]] => [1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1] => [5,4,1] => 1
[[[],[[[[],[]],[]]]]] => [1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1,1] => [6,3,1] => 2
[[[],[[[[[]]],[]]]]] => [1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1] => [4,4,1] => 1
[[[],[[[[],[],[]]]]]] => [1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1] => [5,2,2] => 2
[[[],[[[[],[[]]]]]]] => [1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1] => [3,3,2] => 1
[[[],[[[[[]],[]]]]]] => [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1] => [4,2,1,1] => 2
[[[],[[[[[],[]]]]]]] => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1] => [3,3,1] => 1
[[[],[[[[[[]]]]]]]] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => [3,2,1] => 2
[[[[]],[[[],[[]]]]]] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2] => [7,5] => 2
[[[[]],[[[[]],[]]]]] => [1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2] => [3,3,3,3] => 1
[[[[]],[[[[],[]]]]]] => [1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2] => [6,5] => 1
[[[[]],[[[[[]]]]]]] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2] => [6,4] => 2
[[[[[]]],[[[[]]]]]] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3] => [7,1,1,1,1,1] => 1
[[[[[[]]]],[[[]]]]] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [4,4,4] => [2,2,2,2,2,2] => 1
[[[[[[],[]]]],[],[]]] => [1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [6,5,1] => [11,1] => 1
[[[[[[[]]]]],[],[]]] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5] => [11] => 1
[[[[[],[[]]]],[[]]]] => [1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1] => [10,2] => 2
[[[[[[]],[]]],[[]]]] => [1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [5,5,2] => [10,1,1] => 1
[[[[[[],[]]]],[[]]]] => [1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [5,5,1] => [10,1] => 1
[[[[[[[]]]]],[[]]]] => [1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [5,5] => [10] => 1
[[[[],[[],[[]]]],[]]] => [1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1,1] => [5,2,2,1,1,1] => 2
[[[[],[[[]],[]]],[]]] => [1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1,1] => [4,4,1,1,1,1] => 1
[[[[],[[[],[]]]],[]]] => [1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1,1] => [4,2,2,1,1,1] => 2
[[[[],[[[[]]]]],[]]] => [1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1] => [4,2,1,1,1,1] => 2
[[[[[]],[[[]]]],[]]] => [1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2] => [3,3,3,1,1,1] => 1
[[[[[[]]],[[]]],[]]] => [1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [6,3,3] => [8,1,1,1,1] => 1
[[[[[],[[]]],[]],[]]] => [1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,1] => [4,2,2,2,1,1] => 2
[[[[[[]],[]],[]],[]]] => [1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [6,4,2] => [3,3,2,2,1,1] => 2
[[[[[[],[]]],[]],[]]] => [1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [6,4,1] => [3,2,2,2,1,1] => 2
[[[[[[[]]]],[]],[]]] => [1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [6,4] => [2,2,2,2,1,1] => 1
[[[[[],[],[],[]]],[]]] => [1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1] => [7,2,1,1,1] => 2
[[[[[],[],[[]]]],[]]] => [1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1] => [3,3,2,1,1,1] => 2
[[[[[],[[]],[]]],[]]] => [1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1] => [5,2,1,1,1,1] => 2
[[[[[],[[],[]]]],[]]] => [1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1] => [3,3,1,1,1,1] => 1
[[[[[],[[[]]]]],[]]] => [1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1] => [3,2,1,1,1,1] => 2
[[[[[[]],[],[]]],[]]] => [1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [6,3,2] => [7,1,1,1,1] => 1
[[[[[[]],[[]]]],[]]] => [1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [6,2,2] => [5,1,1,1,1,1] => 1
[[[[[[],[]],[]]],[]]] => [1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [6,3,1] => [3,2,2,1,1,1] => 2
[[[[[[[]]],[]]],[]]] => [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,3] => [2,2,2,1,1,1] => 1
[[[[[[],[],[]]]],[]]] => [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] => 1
[[[[[[],[[]]]]],[]]] => [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
[[[[[[[]],[]]]],[]]] => [1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,2] => [2,2,1,1,1,1] => 1
[[[[[[[],[]]]]],[]]] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,1] => [2,1,1,1,1,1] => 1
[[[[[[[[]]]]]],[]]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => [1,1,1,1,1,1] => 0
[[[[],[],[],[[[]]]]]] => [1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1] => [6,2,1,1,1,1] => 2
[[[[],[],[[[]]],[]]]] => [1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1] => [7,2,2,1] => 2
[[[[],[],[[],[],[]]]]] => [1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1] => [6,2,2,1,1] => 2
[[[[],[],[[],[[]]]]]] => [1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1] => [6,2,1,1,1] => 2
[[[[],[],[[[]],[]]]]] => [1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1] => [3,3,3,1,1] => 1
[[[[],[],[[[],[]]]]]] => [1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1] => [5,2,1,1,1] => 2
[[[[],[],[[[[]]]]]]] => [1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1] => [5,4] => 1
[[[[],[[]],[[],[]]]]] => [1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1] => [4,2,2,2,2] => 2
[[[[],[[]],[[[]]]]]] => [1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1] => [4,2,2,2,1] => 2
[[[[],[[[]]],[],[]]]] => [1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1,1] => [9,2,1] => 2
[[[[],[[],[]],[[]]]]] => [1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1] => [8,2,2] => 2
[[[[],[[[]]],[[]]]]] => [1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1] => [8,2,1] => 2
[[[[],[[],[],[]],[]]]] => [1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,1] => [7,4,1] => 2
[[[[],[[],[[]]],[]]]] => [1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1] => [6,2,2,1] => 2
[[[[],[[[]],[]],[]]]] => [1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1,1] => [5,5,1] => 1
[[[[],[[[],[]]],[]]]] => [1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1] => [4,2,2,1,1] => 2
[[[[],[[[[]]]],[]]]] => [1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1] => [4,2,1,1,1] => 2
[[[[],[[],[],[],[]]]]] => [1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1] => [7,2,2] => 2
[[[[],[[],[],[[]]]]]] => [1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1] => [6,2,2] => 2
[[[[],[[],[[]],[]]]]] => [1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1] => [3,3,2,2] => 1
[[[[],[[],[[],[]]]]]] => [1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1] => [3,3,3] => 1
[[[[],[[],[[[]]]]]]] => [1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1] => [5,3] => 2
[[[[],[[[]],[],[]]]]] => [1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1] => [7,2,1] => 2
[[[[],[[[]],[[]]]]]] => [1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1] => [5,2,1,1] => 2
[[[[],[[[],[]],[]]]]] => [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1] => [6,2,1] => 2
[[[[],[[[[]]],[]]]]] => [1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1] => [5,2,1] => 2
[[[[],[[[],[],[]]]]]] => [1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1] => [3,3,1,1] => 1
[[[[],[[[],[[]]]]]]] => [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1] => [4,3] => 1
[[[[],[[[[]],[]]]]]] => [1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1] => [3,2,2] => 1
[[[[],[[[[],[]]]]]]] => [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1] => [4,2] => 2
[[[[],[[[[[]]]]]]]] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1] => [3,2] => 1
[[[[[]],[],[[],[]]]]] => [1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2] => [3,3,2,2,2] => 1
[[[[[]],[],[[[]]]]]] => [1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2] => [6,1,1,1,1,1] => 1
[[[[[]],[[]],[[]]]]] => [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2] => [8,4] => 2
[[[[[]],[[],[]],[]]]] => [1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2] => [6,6] => 1
[[[[[]],[[[]]],[]]]] => [1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2] => [7,4] => 2
[[[[[]],[[],[],[]]]]] => [1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2] => [3,3,2,2,1] => 2
[[[[[]],[[],[[]]]]]] => [1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2] => [6,1,1,1,1] => 1
[[[[[]],[[[]],[]]]]] => [1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2] => [5,5] => 1
[[[[[]],[[[],[]]]]]] => [1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2] => [5,1,1,1,1] => 1
[[[[[]],[[[[]]]]]]] => [1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2] => [5,1,1,1] => 1
[[[[[[]]],[],[],[]]]] => [1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [5,4,3] => [9,1,1,1] => 1
[[[[[],[]],[],[[]]]]] => [1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1] => [3,2,2,2,2,1] => 2
[[[[[[]]],[],[[]]]]] => [1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [4,4,3] => [2,2,2,2,2,1] => 1
[[[[[],[]],[[]],[]]]] => [1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1] => [8,2,1,1] => 2
[[[[[[]]],[[]],[]]]] => [1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [5,3,3] => [8,1,1,1] => 1
[[[[[],[]],[[],[]]]]] => [1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1] => [3,2,2,2,2] => 1
[[[[[],[]],[[[]]]]]] => [1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1] => [3,2,2,2,1] => 2
[[[[[[]]],[[],[]]]]] => [1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [4,3,3] => [2,2,2,2,2] => 1
[[[[[[]]],[[[]]]]]] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [3,3,3] => [2,2,2,2,1] => 1
[[[[[],[],[]],[],[]]]] => [1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1] => [9,3] => 2
[[[[[],[[]]],[],[]]]] => [1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1] => [9,2] => 2
[[[[[[]],[]],[],[]]]] => [1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [5,4,2] => [9,1,1] => 1
[[[[[[],[]]],[],[]]]] => [1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [5,4,1] => [9,1] => 1
[[[[[[[]]]],[],[]]]] => [1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [5,4] => [9] => 1
[[[[[],[],[]],[[]]]]] => [1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1] => [8,3] => 2
[[[[[],[[]]],[[]]]]] => [1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1] => [8,2] => 2
[[[[[[]],[]],[[]]]]] => [1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [4,4,2] => [8,1,1] => 1
[[[[[[],[]]],[[]]]]] => [1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [4,4,1] => [8,1] => 1
[[[[[[[]]]],[[]]]]] => [1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [4,4] => [8] => 1
[[[[[],[],[],[]],[]]]] => [1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1] => [7,2,1,1] => 2
[[[[[],[],[[]]],[]]]] => [1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1] => [3,3,2,1,1] => 2
[[[[[],[[]],[]],[]]]] => [1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1] => [6,2,1,1] => 2
[[[[[],[[],[]]],[]]]] => [1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1] => [3,3,1,1,1] => 1
[[[[[],[[[]]]],[]]]] => [1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1] => [3,2,1,1,1] => 2
[[[[[[]],[],[]],[]]]] => [1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,3,2] => [7,1,1,1] => 1
[[[[[[]],[[]]],[]]]] => [1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [5,2,2] => [6,1,1,1] => 1
[[[[[[],[]],[]],[]]]] => [1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [5,3,1] => [3,2,2,1,1] => 2
[[[[[[[]]],[]],[]]]] => [1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [5,3] => [2,2,2,1,1] => 1
[[[[[[],[],[]]],[]]]] => [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
[[[[[[],[[]]]],[]]]] => [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
[[[[[[[]],[]]],[]]]] => [1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [5,2] => [2,2,1,1,1] => 1
[[[[[[[],[]]]],[]]]] => [1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [5,1] => [2,1,1,1,1] => 1
[[[[[[[[]]]]],[]]]] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [5] => [1,1,1,1,1] => 0
[[[[[],[],[],[],[]]]]] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1] => [7,3] => 2
[[[[[],[],[],[[]]]]]] => [1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1] => [3,2,2,2] => 1
[[[[[],[],[[]],[]]]]] => [1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1] => [6,3] => 2
[[[[[],[],[[],[]]]]]] => [1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1] => [3,2,2,1] => 2
[[[[[],[],[[[]]]]]]] => [1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1] => [4,1,1,1] => 1
[[[[[],[[]],[],[]]]]] => [1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1] => [7,2] => 2
[[[[[],[[]],[[]]]]]] => [1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1] => [6,2] => 2
[[[[[],[[],[]],[]]]]] => [1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1] => [4,4] => 1
[[[[[],[[[]]],[]]]]] => [1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1] => [3,2,1,1] => 2
[[[[[],[[],[],[]]]]]] => [1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1] => [5,2] => 2
[[[[[],[[],[[]]]]]]] => [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1] => [4,1,1] => 1
[[[[[],[[[]],[]]]]]] => [1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1] => [3,3] => 1
[[[[[],[[[],[]]]]]]] => [1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1] => [3,1,1] => 1
[[[[[],[[[[]]]]]]]] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1] => [3,1] => 1
[[[[[[]],[],[],[]]]]] => [1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [4,3,2] => [7,1,1] => 1
[[[[[[]],[],[[]]]]]] => [1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [3,3,2] => [2,2,2,2] => 1
[[[[[[]],[[]],[]]]]] => [1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [4,2,2] => [6,1,1] => 1
[[[[[[]],[[],[]]]]]] => [1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [3,2,2] => [2,2,2,1] => 1
[[[[[[]],[[[]]]]]]] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [2,2,2] => [2,2,2] => 1
[[[[[[],[]],[],[]]]]] => [1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [4,3,1] => [7,1] => 1
[[[[[[[]]],[],[]]]]] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [4,3] => [7] => 1
[[[[[[],[]],[[]]]]]] => [1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [3,3,1] => [6,1] => 1
[[[[[[[]]],[[]]]]]] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [3,3] => [6] => 1
[[[[[[],[],[]],[]]]]] => [1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [4,2,1] => [5,1,1] => 1
[[[[[[],[[]]],[]]]]] => [1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [4,1,1] => [3,1,1,1] => 1
[[[[[[[]],[]],[]]]]] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [4,2] => [2,2,1,1] => 1
[[[[[[[],[]]],[]]]]] => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [4,1] => [2,1,1,1] => 1
[[[[[[[[]]]],[]]]]] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4] => [1,1,1,1] => 0
[[[[[[],[],[],[]]]]]] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,2,1] => [5,1] => 1
[[[[[[],[],[[]]]]]]] => [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [2,2,1] => [2,2,1] => 1
[[[[[[],[[]],[]]]]]] => [1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [3,1,1] => [4,1] => 1
[[[[[[],[[],[]]]]]]] => [1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [2,1,1] => [2,2] => 1
[[[[[[],[[[]]]]]]]] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,1] => [2,1] => 1
[[[[[[[]],[],[]]]]]] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [3,2] => [5] => 1
[[[[[[[]],[[]]]]]]] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [2,2] => [4] => 1
[[[[[[[],[]],[]]]]]] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [3,1] => [2,1,1] => 1
[[[[[[[[]]],[]]]]]] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => [1,1,1] => 0
[[[[[[[],[],[]]]]]]] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => [3] => 1
[[[[[[[],[[]]]]]]]] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1] => [2] => 1
[[[[[[[[]],[]]]]]]] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => [1,1] => 0
[[[[[[[[],[]]]]]]]] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1] => [1] => 0
[[[[[[[[[]]]]]]]]] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [] => [] => 0
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Description
The number of lower covers of a partition in dominance order.
According to [1], Corollary 2.4, the maximum number of elements one element (apparently for $n\neq 2$) can cover is
$$ \frac{1}{2}(\sqrt{1+8n}-3) $$
and an element which covers this number of elements is given by $(c+i,c,c-1,\dots,3,2,1)$, where $1\leq i\leq c+2$.
Map
Loehr-Warrington
Description
Return a partition whose diagonal inversion number is the length of the preimage.
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 $(n-1,\ldots,2,1)$.
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.